text:
• ### Spin dependence of {\eta} meson production in proton-proton collisions close to threshold(1709.04547)

Nov. 28, 2017 hep-ph, hep-ex, nucl-ex, nucl-th
Taking advantage of the high acceptance and axial symmetry of the WASA-at-COSY detector, and the high degree of the polarized proton beam of COSY, the reaction pp{\to} pp{\eta} has been measured close to threshold to explore the analyzing power Ay. The angular distribution of Ay is determined with the precision improved by more than one order of magnitude with respect to previous results allowing a first accurate comparison with theoretical predictions. The determined analyzing power is consistent with zero for an excess energy of Q = 15 MeV signaling s wave production with no evidence for higher partial waves. At Q = 72 MeV the data reveals strong interference of P s and P p partial waves and cancellation of (P p) and Ss*Sd contributions. These results rule out the presently available theoretical predictions for the production mechanism of the {\eta} meson.
• ### Measurement of the $pn \to pp\pi^0\pi^-$ Reaction in Search for the Recently Observed Resonance Structure in $d\pi^0\pi^0$ and $d\pi^+\pi^-$ systems(1306.5130)

Nov. 12, 2013 nucl-ex
Exclusive measurements of the quasi-free $pn \to pp\pi^0\pi^-$ reaction have been performed by means of $pd$ collisions at $T_p$ = 1.2 GeV using the WASA detector setup at COSY. Total and differential cross sections have been obtained covering the energy region $\sqrt s$ = (2.35 - 2.46) GeV, which includes the region of the ABC effect and its associated resonance structure. No ABC effect, {\it i.e.} low-mass enhancement is found in the $\pi^0\pi^-$-invariant mass spectrum -- in agreement with the constraint from Bose statistics that the isovector pion pair can not be in relative s-wave. At the upper end of the covered energy region $t$-channel processes for Roper, $\Delta(1600)$ and $\Delta\Delta$ excitations provide a reasonable description of the data, but at low energies the measured cross sections are much larger than predicted by such processes. Adding a resonance amplitude for the resonance at $m$=~2.37 GeV with $\Gamma$ =~70 MeV and $I(J^P)=~0(3^+)$ observed recently in $pn \to d\pi^0\pi^0$ and $pn \to d\pi^+\pi^-$ reactions leads to an agreement with the data also at low energies.
• ### Lineshape of the Lambda(1405) Hyperon Measured Through its Sigma0 pion0 Decay(0705.1039)

Jan. 15, 2008 nucl-ex
The pp -> p K+ Y0 reaction has been studied for hyperon masses m(Y0)<1540 MeV/c2 at COSY-Juelich by using a 3.65 GeV/c circulating proton beam incident on an internal hydrogen target. Final states comprising two protons, one positively charged kaon and one negatively charged pion have been identified with the ANKE spectrometer. Such configurations are sensitive to the production of the ground state Lambda and Sigma0 hyperons as well as the Sigma0(1385) and Lambda(1405) resonances. Applying invariant- and missing-mass techniques, the two overlapping excited states could be well separated, though with limited statistics. The shape and position of the Lambda(1405) distribution, reconstructed cleanly in the Sigma0 pion0 channel, are similar to those found from other decay modes and there is no obvious mass shift. This finding constitutes a challenging test for models that predict Lambda(1405) to be a two-state resonance.
• ### Study of omega-meson production in pp collisions at ANKE(nucl-ex/0609010)

Sept. 8, 2006 nucl-ex
The production of omega-mesons in the pp->pp omega reaction has been investigated with the COSY-ANKE spectrometer for excess energies of 60 and 92MeV by detecting the two final protons and reconstructing their missing mass. The large multipion background was subtracted using an event-by-event transformation of the proton momenta between the two energies. Differential distributions and total cross sections were obtained after careful studies of possible systematic uncertainties in the overall ANKE acceptance. The results are compared with the predictions of theoretical models. Combined with data on the phi-meson, a more refined estimate is made of the Okubo-Zweig-Iizuka rule violation in the phi/omega production ratio.
• ### Evidence for an Excited Hyperon State in pp -> p K^+ Y^{0*}(nucl-ex/0506014)

Nov. 17, 2005 nucl-ex
Indications for the production of a neutral excited hyperon in the reaction pp -> p K^+ Y^{0*} are observed in an experiment performed with the ANKE spectrometer at COSY-J\"ulich at a beam momentum of 3.65 GeV/c. Two final states were investigated simultaneously, viz. Y^{0*} -> pi^+X^- and pi^-X^+, and consistent results were obtained in spite of the quite different experimental conditions. The parameters of the hyperon state are M(Y^{0*})= (1480 +/- 15) MeV/c^2 and Gamma(Y^{0*})= (60 +/- 15) MeV/c^2. The production cross section is of the order of few hundred nanobarns. Since the isospin of the Y^{0*} has not been determined here, it could either be an observation of the Sigma(1480), a one-star resonance of the PDG tables, or alternatively a Lambda hyperon. Relativistic quark models for the baryon spectrum do not predict any excited hyperon in this mass range and so the Y^{0*} may be of exotic nature.
• ### Inclusive K^+ meson production in proton-nucleus interactions(nucl-ex/0401031)

June 2, 2004 nucl-ex
The production of K^+ mesons in pA (A = D, C, Cu, Ag, Au) collisions has been investigated at the COoler SYnchrotron COSY-J\"ulich for beam energies T_p = 1.0 - 2.3 GeV. Double differential inclusive pC cross sections at forward angles theta < 12 degrees as well as the target-mass dependence of the K^+ momentum spectra have been measured with the ANKE spectrometer. Far below the free NN threshold at T_{NN}=1.58 GeV the spectra reveal a high degree of collectivity in the target nucleus. From the target-mass dependence of the cross sections at higher energies, the repulsive in-medium potential of K^+ mesons can be deduced. Using pN cross-section parameterisations from literature and our measured pD data we derive a cross-section ratio of sigma(pn -> K^+ X) / sigma(pp -> K^+ X) ~ (3-4).


text:
# scipy.special.bdtr¶

scipy.special.bdtr(k, n, p) = <ufunc 'bdtr'>

Binomial distribution cumulative distribution function.

Sum of the terms 0 through floor(k) of the Binomial probability density.

$\mathrm{bdtr}(k, n, p) = \sum_{j=0}^{\lfloor k \rfloor} {{n}\choose{j}} p^j (1-p)^{n-j}$
Parameters
karray_like

Number of successes (double), rounded down to the nearest integer.

narray_like

Number of events (int).

parray_like

Probability of success in a single event (float).

Returns
yndarray

Probability of floor(k) or fewer successes in n independent events with success probabilities of p.

Notes

The terms are not summed directly; instead the regularized incomplete beta function is employed, according to the formula,

$\mathrm{bdtr}(k, n, p) = I_{1 - p}(n - \lfloor k \rfloor, \lfloor k \rfloor + 1).$

Wrapper for the Cephes [1] routine bdtr.

References

1

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/

#### Previous topic

scipy.special.itmodstruve0

#### Next topic

scipy.special.bdtrc

format: plain


text:
# Math Help - [SOLVED] am I thinking right??

1. ## [SOLVED] am I thinking right??

The integral 1/(sqrt((x^2)-9)

so far I have this....

x = 3sec(t)
dx = 3sec(t)tan(t)dt
this gives me --> integral (3sec(t)tan(t))dt/9(tan^2)(t)
1/3 integral sec(t)dt/tan(t) --> 1/3 integral csc(t)dt
1/3(-csc(t)cot(t)) + C = 1/3( -x/(sqrt(x^2 - 9)) * 3/(sqrt(x^2 - 9))

Please any help would be much appreciated!!! I don't know if I messed up or something. Any ideas?

2. Originally Posted by codex123
The integral 1/(sqrt((x^2)-9)

so far I have this....

x = 3sec(t)
dx = 3sec(t)tan(t)dt
this gives me --> integral (3sec(t)tan(t))dt/9(tan^2)(t)
1/3 integral sec(t)dt/tan(t) --> 1/3 integral csc(t)dt
1/3(-csc(t)cot(t)) + C = 1/3( -x/(sqrt(x^2 - 9)) * 3/(sqrt(x^2 - 9))

Please any help would be much appreciated!!! I don't know if I messed up or something. Any ideas?
Everything is fine up to the part in red. Your integral should be $\int\frac{3\sec t\tan t\,dt}{\sqrt{9\tan^2t}}=\int\frac{3\sec t\tan t\,dt}{3\tan t}=\int \sec t\,dt$

Now, to integrate $\int\sec t\,dt$, you will need to apply this trick:

$\int\sec t\,dt=\int\sec t\frac{\sec t+\tan t}{\sec t+\tan t}\,dt=\int\frac{\sec^2t+\sec t\tan t}{\sec t+\tan t}\,dt$. Applying the substitution $z=\sec t+\tan t$, we end up with $\int\frac{\,dz}{z}=\ln\!\left|z\right|+C\implies \int\sec t\,dt=\ln\!\left|\sec t+\tan t\right|+C$

So what do you think your final answer should be?

3. ## Thanks!

Yeah I skipped a step but that is where I messed up. Thanks for helping out! So the final answer would be
ln|(x/3 + sqrt(x^2 -9)/3 | + C


text:
# Showing that $2^{17} - 1$ is prime.

The question is:

Show that $131071=2^{17} - 1$ is prime.

So in this section we have the corollary to a theorem that clearly applies to this question.

Corollary. Any Divisor of $2^p -1$ is of the form $2kp + 1$.

How would you approach this problem?

WHAT I HAVE:

Let $q=2kp +1$ be an odd prime.

Then we have $2^{17} \equiv 1$ (mod q).

Using the a theorem that states that is the order of 2 (mod q) is $t$ then $2^n \equiv 1$ (mod q) iff $t|n$

this implies that $t=1$ or $t=17$

if $t=1$ we have that $2 \equiv 1$(mod q) so $q=1$ obviously impossible since we said $q$ was an odd prime.

So, $t=17$.

Using this I get that $q=131071$ is an odd prime.

• In your case, the corollary indicates that any possible prime divisor should be of the form $17\times 2k+1=34k+1$. Aug 8, 2012 at 0:42
• @anon The theorem states that if $p$ and $q$ are odd primes and $q|a^p -1$, then either $q|a-1$ or $q=2kp + 1$ for some integer $k$. Aug 8, 2012 at 0:54

As J.M. noted, any divisor must be of the form $34k+1$. We only have to check potential divisors up to $\sqrt{131071} \approx 362$, so only about 10 numbers. You can do this manually relatively quickly. Certain cases can be ruled out quickly like anything ending in a five (35, 205), etc.
• @tomasz: You don't have to verify the primality of the divisors; you just have to check to see if they divide $131071$. Aug 8, 2012 at 0:57
• Howard, there's no elegant reason why $2^{17}-1$ is prime (and, say, $2^{23}-1$ is not); there's no way to avoid doing a certain amount of trial division. Well, there is something called the Lucas-Lehmer test, but that's probably more trouble than it's worth for this particular problem. Aug 8, 2012 at 1:17
• Historical note: Euler proved that $2^{31}-1$ is prime by this restricted trial division (although, he also used that property that divisors of Mersenne numbers are of the form 8n+/-1). He also had access to a list of the primes less than 100,000. (see e.g. my talk slides.) Aug 8, 2012 at 4:13


text:
# Tianke Youke

A Base for Secreting and Running at Night

0%

# 齐次坐标系

## 齐次坐标系的现实意义

This is part of my journey of learning NeRF.

# 1. Introduction to NeRF

## What is NeRF

Reference: Original NeRF paper; an online ariticle

# Learning NeRF

This is part of my journey of learning NeRF.

### Classical

This is part of my journey of learning NeRF.

## 2.5. Manipulate Neural Fields

Neural fields is ready to be a prime representation, similar as point clouds or meshes, that is able to be manipulated.

This is part of my journey of learning NeRF.

## 2.3. Differentiable Forward Maps

### Differentiable rendering

This is part of my journey of learning NeRF.

## 2.2. Hybrid representations

### Tradeoffs of choosing a proper representation

This is part of my journey of learning NeRF.

## 2.1. Network Architecture

### 1. Input Encoding

Similar as NLP, they use position encodings. Like Sinusoid functions. I also remember an encoding method which takes into consider of the 光线的散射

I am currently burying myself into the sea of NeRF. I plan to archive my learning notes here. I am still a beginner, so the notes absolutely contain errors, and are not finished yet.

# Contents

Learning NeRF: Reading list, learning references, and plans

Notes of CVPR22' Tutorial:

This is part of my journey of learning NeRF.

## 2.4. Prior-based reconstruction of neural fields

Sounds like a one-shot task: instead of fitting and optimizing a neural field each for one scene; let's learn a prior distribution of neural field. Then, given a specific scene, it adjusts the neural field in just one forward.

I was so confused when doing a homework on implementing the Luong Attention, because it tells that the decoder is a RNN, which takes $$y_{t-1}$$ and $$s_{t-1}$$ as input, and outputs $$s_t$$, i.e., $$s_t = RNN(y_{t-1}, s_{t-1})$$.

But the pytorch implementation of RNN is: $$outputs, hidden\_last = RNN(inputs, hidden\_init)$$, which takes in a sequence of elements, computes in serials, and outputs a sequence also.

I was confused about what is the $$s_t$$. Is it the $$outputs$$, or the $$hidden\_states$$?


text:
news

# Transfection technologies market to value $1.5 billion by 2026 0 SHARES Share via Growth in the global transfection technologies market will be driven by emerging methods and the increasing prevalence of chronic diseases over the next five years. According to a market research report, the global transfection technologies market is expected to reach a value of$1.5 billion by 2026, owing to the increasing prevalence of cancer and various chronic lifestyle diseases and the widespread adoption of reagent-based transfection methods.

The report suggests that the market will achieve a compound annual growth rate of 8.44 percent between 2021 and 2026.

Transfection technologies such as CRISPR-Cas are used to artificially introduce nucleic acid, such as DNA, RNA or oligonucleotides, into cells, modifying their physical, chemical and/or biological properties. Various methods exist, including co-transfection, electroporation, cationic lipid transfection and in vivo transfection.

Transfection is commonly used for genomic studies that include gene expression, screening, RNA interference and in vivo research, along with the bioproduction of viruses and proteins.

According to the report, major factors promoting the growth of the global transfection technologies market include the increasing prevalence of cancer and various chronic lifestyle diseases, and the adoption of reagent-based methods for transfection. Reagent-based methods are typically less complicated and more cost effective than traditional transfection methods, wrote the study authors. Additionally, instrument-based methods are gaining traction, with examples including microinjection and laserfection.

The research also shows that technological advancements in cell research and therapeutic discovery are acting as another major growth-inducing factor. In addition, research in gene transfer is mainly performed under in vivo conditions for the development of novel therapeutic drugs and various other applications.

Other factors driving market growth include increasing investments by both government and private organisations to develop large scale transfection facilities, along with extensive R&D activities in the field of protein therapeutics.

Key players in the global transfection technologies market are Agilent Technologies Inc., Bio-RAD Laboratories Inc., Lonza Group AG, Maxcyte Inc., Mirus Bio LLC, Polyplus Transfection, Promega Corporation, Roche Holding AG, Sigma-Aldrich Corporation and Thermo Fisher Scientific Inc.

### Related organisations

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text:
# K|n!+k from k=2,3,4 .n

1. Jul 8, 2014

### jonroberts74

1. The problem statement, all variables and given/known data

prove by induction that K|n!+k for all integers $$n \ge 2$$ and k = 2,3,4,......,n

this one is different than other proofs I have had because Ive only dealt with n changing but now n and k change.

k goes up to n, does this mean k and n have the same values?

for instance,

P(2)

$$2|2! + 2 \Rightarrow 2|4$$

so p(k)

is $$k|n!+k; n=k$$

$$k|k!+k$$

??

Last edited: Jul 8, 2014
2. Jul 8, 2014

### Ray Vickson

You ask: "does this mean k and n have the same values?". No, that is not what it says and not what it means. Look at some small-n examples. If n = 3 it says that 2|3!+2 and 3|3!+3. So, k is not 3; it is any number in the set {2,3}. If n = 4 it says that all three of the statements 2|4!+2, 3|4!+3 and 4|4!+4 are true.

3. Jul 8, 2014

### jonroberts74

ah okay

whatever n is, then k takes on each value in the set {2,...,n}

4. Jul 8, 2014

### HallsofIvy

Staff Emeritus
The fact that if k< n the n k divides n! makes this pretty close to trivial.

5. Jul 8, 2014

### jonroberts74

$$2|n!+2$$
$$3|n!+3$$
$$4|n!+4$$
$$\downarrow$$
$$k|n!+k$$

where k takes on the values of 2,3,4...n and n is an integer greater than or equal to 2

and because for all k<n, k|n and when n=k, k|n

so my p(k) is

$$k|n!+k$$

and

p(k+1)

$$(k+1)|n!+(k+1)$$

Last edited: Jul 9, 2014
6. Jul 9, 2014

### jonroberts74

I have to make a correction. its not asking for induction. all the other problems on this problem set were induction but I confirmed with my prof this is not an induction proof question

7. Jul 9, 2014

### WWGD

Can you see a common factor in the numerator?

8. Jul 9, 2014

### jonroberts74

k is a factor of k, clearly and k is a also a factor of n! by the given information

$$2 \le k \le n$$ and by definition of a factorial k had to be used somewhere along the product

$$\prod_{k=2}^{n} k$$

case 1

k = 2, n > or equal 2

$$\frac{2*.....*n + 2}{2}$$

case 2

2 < k <n

$$\frac{2*...*k*....*n + k}{k}$$

case 3

n=k

$$\frac{2*......*k + k}{k}$$

Last edited: Jul 9, 2014
9. Jul 9, 2014

### HallsofIvy

Staff Emeritus
Those case are not necessary. WWDG's point is that if $k\le n$ then k is a factor of n!.

10. Jul 9, 2014

### jonroberts74

I understand that but I am expected to show a proof. Seems a tad bit too easy to say if

$$k \le n$$ then k is a factor of n!

11. Jul 9, 2014

### Ray Vickson

But that is absolutely correct, so IS a proof! Sometimes proofs are easy---after you "see" them.


text:
# Is there a way to define a newcommand that can evaluate mathematical expressions

Let's suppose that I have a very complicated function that depends on i and j. So I define a new command, say

\newcommand{\foo}[2]{X_{i+j+1}}. % This might be an complicated expression, but I want to keep it simple

Using this definition, I can invoke this command like \foo{\alpha}{\beta} or \foo{2}{3}. Now, what I want to get is if both of arguments are numerical values, I want to force them to evalue this expression, i.e., \foo{2}{3} should generate X_{6} instead of X_{2+3+1}. It is sometimes annoying that I should manually simplify it even though I know the full expression.

I actually feel this seems almost impossible but I anyway would like to ask in case there exists some workarounds.

• There are packages (tikz for one) which perform calculations. But it you want to do it yourself, you can use counters amd lengths (or counts and dims for plain TeX), but you will be limited to addition and multiplication. – John Kormylo Sep 4 '14 at 23:57
• The sagetex package gives you access to a computer algebra system and the Python language. You insert calculations with \sage{} similar to the \foo{} macro you mention. You'll need to install Sage on your computer or use Sagemath Cloud (free). – DJP Sep 5 '14 at 0:00

This seems to be a job for l3regex:

\documentclass{article}
\usepackage{xparse,l3regex}

\ExplSyntaxOn
\NewDocumentCommand{\evaluateorprint}{m}
{
\regex_match:nnTF { [^0-9+\-] } { #1 }
{ #1 }                 % symbolic expression
{ \int_eval:n { #1 } } % only numbers, + or -
}
\ExplSyntaxOff

\newcommand\foo[2]{%
X_{\evaluateorprint{#1+#2+1}}%
}

\begin{document}
$\foo{2}{3}+\foo{\alpha}{\beta}$
\end{document}

A version without l3regex that might be more likely accepted by publishers relying on older TeX distributions (courtesy of Bruno Le Floch):

\ExplSyntaxOn
\NewDocumentCommand{\evaluateorprint}{m}
{
\group_begin:
\cs_set_eq:NN \__sungmin_eval:n \int_eval:n
\tl_map_inline:nn { #1 }
{
\tl_if_in:nnF { 0123456789+-*() } { ##1 }
{
\cs_set_eq:NN \__sungmin_eval:n \use:n
}
}
\__sungmin_eval:n { #1 }
\group_end:
}
\ExplSyntaxOff

The function \__sungmin_eval:n is tentatively set equal to \int_eval:n; then the argument is scanned token by token; if something not legal in a numeric expression is found, \__sungmin_eval:n is changed into \use:n that simply outputs the argument without any processing.

• It is a brilliant idea to use regex in this context. I have two more questions regarding the status of those packages(Please forgive me if i the questions sound too ignorant.) As far as I understood, xparse and l3regex were made to become major building blocks of the future latex3. Is it still safe and stable to use it under latex2e environment? At some point, my work will be submitted to a scientific(physics) journal. Do ypu consider the usage of these packages are generally accepted? – Sungmin Sep 5 '14 at 8:22
• @Sungmin It might be rejected: several publishers rely on older TeX distributions, unfortunately. You should contact the publisher to know. – egreg Sep 5 '14 at 8:31
• @egreg: In this simple case it is not too hard to provide a solution which avoids l3regex and just uses expl3, which should work in journals (at least arXiv appears to have TeXLive 2011). Basically loop trough the input with \cs_set_eq:NN\my_eval:n\int_eval:n\tl_map_inline:nn{#1}{\tl_if_in:nnF{0123456789+-*()}{##1}{\cs_set_eq:NN\my_eval:n\use:n}}\my_eval:n{#1}. Do you want to add that to your answer, or should I provide a separate one? – Bruno Le Floch Sep 5 '14 at 8:42
• @BrunoLeFloch Thanks. It's a pain having to be compatible with such older distributions. How many packages have appeared since TeX Live 2011 has been frozen? – egreg Sep 5 '14 at 8:52
• I don't know how computationally expensive l3regex is, but as a rule I tend to avoid regular expressions unless they are absolutely necessary. And as @BrunoLeFloch says, it is not that hard to avoid them in this particular case. – You Sep 5 '14 at 9:08

I know that my solution don't look such elegant (as egregs) from first point of view, but it uses only TeX primitives so it is working for all. And it uses only 27 lines of code (on the other hand the \usepackage{xparse,l3regex} loads many tens of thousands lines of code).

% \replacestring + \addto from OPmac:
\newcount\tmpnum
\bgroup \catcode!=3 \catcode?=3
\gdef\replacestrings#1#2{%
\expandafter\def\expandafter\tmpb\expandafter{\expandafter}\expandafter\tmp\tmpb?#1!%
\def\tmp##1?{\def\tmpb{##1}}\expandafter\tmp\tmpb
}
\egroup

% \evalindex{text} evaluates text if it is sum of numbers; else the text is printed
\def\evalindex#1{\def\tmpa{#1}\evalindexA#1\evalindexB.\evalindexB\evalindexA}
\def\evalindexA#1#2\evalindexA{%
\ifx-#1\def\tmpb{#1#2}\else\def\tmpb{+#1#2}\fi
\replacestrings+{\evalindexB+}\replacestrings-{\evalindexB-}%
\tmpnum=0 \tmpb
}
\def\evalindexB#1#2\evalindexB{\ifx#1.\the\tmpnum
\else \setbox0=\hbox{$\tmpnum=0#2$}%
\ifdim\wd0=0pt \advance\tmpnum by#1#2 \else \evalindexC \fi
\expandafter\evalindexB \fi
}
\def\evalindexC#1.\evalindexB{\fi\fi \tmpa}

\def\foo#1#2{X_{\evalindex{#1+#2+1}}}

% tests:
$\evalindex{i+j+1} \quad \evalindex{1+2\alpha+3}\quad \evalindex{-1+20-3}$
%           i+j+1                   1+2\alpha+3                  16

$\foo ij \quad \foo\alpha\beta \quad \foo 23$
% X_{i+j+1}     X_{\alpha+\beta+1}    X_6

\end

This gives the same results as egregs solution. But I know, you will not vote this up. It is only my hobby to play with my toys -- primitive features.

• Why not vote up? We certainly do ;-) +1. – user11232 Sep 5 '14 at 9:37
• +1, of course. The problem is not loading thousands of lines of code (TeX now does it in much less time it needed for shipping out a page twenty years ago); besides one can always prepare a format with that code preloaded. The problem is ensuring the code is usable in older TeX distributions, for the reasons I explained in my answer and comments thereto. I firmly believe that a well-structured approach providing predefined functions for common tasks is preferable. – egreg Sep 5 '14 at 9:47

Such commands can be done easily with the calculator package, although a counter approach is also possible, as long only integer indices are used.

In this case, the two arguments of \foo should be added and increased by 1, this is possible by using

\ADD{#1}{#2}{\resulta}%

By using counters, there are for example two possibilities -- applying \setcounter and \addtocounter or \numexpr approach. \Foo and \FooAgain demonstrate this.

\documentclass{scrbook}

\usepackage{calculator}
\usepackage{forloop}

\newcounter{acounter}
\newcounter{bcounter}

\newcommand{\foo}[2]{%
\begingroup
\def\resultA{}%
\def\resultB{}%
X_{\resultB}
\endgroup%
}%

\newcounter{mydummycounter}
\newcommand{\Foo}[2]{%
\setcounter{mydummycounter}{#1}%
Y_{\arabic{mydummycounter}}%
}%

\newcommand{\FooAgain}[2]{%
\setcounter{mydummycounter}{\numexpr #1 + #2 +1}%
Z_{\arabic{mydummycounter}}%
}%

\begin{document}
Testing:
$\foo{2}{3}$

Some playing around:
\LARGE \bfseries
\forloop{acounter}{1}{\value{acounter} < 11}{%
\forloop{bcounter}{1}{\value{bcounter} < \value{acounter}}{%
$$\foo{\number\value{acounter}}{\number\value{bcounter}}$$
}

}
\end{document}


text:
Article Contents
Article Contents

Right accessibility of semicontinuous initial data for Hamilton-Jacobi equations

• We study Hamilton-Jacobi equations with upper semicontinuous initial data without convexity assumptions on the Hamiltonian. We analyse the behavior of generalized u.s.c solutions at the initial time $t=0$, and find necessary and sufficient conditions on the Hamiltonian such that the solution attains the initial data along a sequence (right accessibility).
Mathematics Subject Classification: 35F25(primary), 49L25.

 Citation:


text:
# Accuracy between ill-conditioned matrix-free vs. matrix-based operators

As far as I know, precision errors become larger as the condition number of a matrix increases.

Consider a matrix-based operator:

$$A = \nabla \bullet k \nabla$$

And a matrix-free operator:

$$\tilde{A} = B_{1} + B_{2} + B_{3}, \qquad B_{i} = \partial_{x_i} k \partial_{x_i}$$

One difference between the matrix-free operator and matrix-based operator is that the diagonal of $A$ combines derivatives along all 3 directions, whereas the matrix-free operator must add the diagonal for all 3 directions each time.

I tried comparing these two approaches numerically, and I see a difference between them on the order of machine accuracy. It seems that the difference between the operators also increases where $k$ is large.

Here are my questions:

1) Am I just visualizing the local condition number where $k$ is large?

2) Is one of these methods superior being that the difference becomes larger? Or is this just lack of precision becoming more apparent from the increasing condition number?

3) Am I just completely wrong? (this should not happen)

When solving a linear system $Ax=b$, you suffer from two sources of error:

• Round-off error
• The ill-conditionedness of the matrix.

The condition number of a computational representation of a matrix is, for all practical purposes equal to the condition number of the exact matrix (which you can't represent computationally), so it does not matter whether you represent it as a split, matrix-free form, or not.

Likewise, whether you add the three matrices together or not does not make any difference for the difference between your computational representation of the matrix and the "exact" matrix. That is, because for all practical purposes, the addition of 3 terms is as accurate as the computation of each of these terms -- 3 times round off is, in practice, equal to round off, namely very small.

In other words, there will be no practical difference between the two representations of your matrix, unless your condition number is on the order of one over the level of round-off. That is hopefully not the case.

Your "two approaches" are actually the same thing. You know already that they are mathematically the same. But they are also computationally the same thing, except for a possible change in the order of operations. A change in the order of operations will give an error of order of machine epsilon.

You're right of the condition number, in the following sense. As $k$ increases, the effect of roundoff error is amplified proportionately. So if $k$ is much larger than the quantity your operator is applied to, you'll notice more roundoff error.


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# zbMATH — the first resource for mathematics

Kronecker’s solution of Pell’s equation for CM fields. (La solution de Kronecker des équations Pell pour les corps CM.) (English. French summary) Zbl 1295.11044
Summary: We generalize Kronecker’s solution of Pell’s equation to CM fields $$K$$ whose Galois group over $$\mathbb Q$$ is an elementary abelian 2-group. This is an identity which relates CM values of a certain Hilbert modular function to products of logarithms of fundamental units. When $$K$$ is imaginary quadratic, these CM values are algebraic numbers related to elliptic units in the Hilbert class field of $$K$$. Assuming Schanuel’s conjecture, we show that when $$K$$ has degree greater than 2 over $$\mathbb Q$$ these CM values are transcendental.
##### MSC:
 11F41 Automorphic forms on $$\mbox{GL}(2)$$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11R42 Zeta functions and $$L$$-functions of number fields
##### Keywords:
CM point; Hilbert modular function; Pell’s equation
Full Text:
##### References:
 [1] Asai, Tetsuya, On a certain function analogous to $${\rm log}_{η }\,(z),$$ Nagoya Math. J., 40, 193-211, (1970) · Zbl 0213.05701 [2] Bruinier, Jan Hendrik; Yang, Tonghai, CM-values of Hilbert modular functions, Invent. Math., 163, 2, 229-288, (2006) · Zbl 1093.11041 [3] Buell, D. A.; Williams, H. C.; Williams, K. S., On the imaginary bicyclic biquadratic fields with class-number $$2,$$ Math. Comp., 31, 140, 1034-1042, (1977) · Zbl 0379.12002 [4] Howard, Benjamin; Yang, Tonghai, Intersections of Hirzebruch-Zagier divisors and CM cycles, 2041, viii+140 pp., (2012), Springer, Heidelberg · Zbl 1238.11069 [5] Konno, Shuji, On kronecker’s limit formula in a totally imaginary quadratic field over a totally real algebraic number field, J. Math. Soc. Japan, 17, 411-424, (1965) · Zbl 0147.03603 [6] Murty, M. Ram; Murty, V. Kumar, Transcendental values of class group $$L$$-functions, Math. Ann., 351, 4, 835-855, (2011) · Zbl 1281.11071 [7] Murty, M. Ram; Murty, V. Kumar, Transcendental values of class group $$L$$-functions, II, Proc. Amer. Math. Soc., 140, 9, 3041-3047, (2012) · Zbl 1282.11082 [8] Siegel, Carl Ludwig, Lectures on advanced analytic number theory, iii+331+iii pp., (1965), Tata Institute of Fundamental Research, Bombay · Zbl 0278.10001 [9] Waldschmidt, Michel, Diophantine approximation on linear algebraic groups, 326, xxiv+633 pp., (2000), Springer-Verlag, Berlin · Zbl 0944.11024 [10] Washington, Lawrence C., Introduction to cyclotomic fields, 83, xiv+487 pp., (1997), Springer-Verlag, New York · Zbl 0484.12001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


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Tectonophysics [T]

T31E MCC:3005 Wednesday 0800h

Intraplate Tectonics: North China and Other Regions III

Presiding:Y Zhang, University of Michigan; X Song, University of Illinois at Urbana-Champaign

T31E-01 INVITED 08:00h

Temporal And Spatial Variation In Geochemistry Of Cenozoic Basalts In North China: Implication For The Origin Of Intraplate Volcanism

* Xu, Y (yigangxu@gig.ac.cn) , Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Wushan, Guangzhou, 510640 China

In North China, Cenozoic basalts were erupted in association with formations of graben basins and their regional boundary faults. Radiometric dating shows that eruption age is between early Tertiary to Quaternary. While Sr-Nd isotopic ratios and relative abundances of incompatible elements are consistent with a dominant asthenospheric origin, Cenozoic basalts from both sides of the Daxin'anling-Taihang gravity lineament (DTGL) that separates the North China Craton (NCC) into two parts, namely the western and eastern NCC, show contrasting evolution trends. In the western NCC, magmas evolved from xenolith-bearing alkali basalts of late Eocene-Oligocene age to coexisting alkali and tholeiitic basalts of late Miocene-Quaternary age. This change in basalt type is accompanied by a decrease in La/Yb and increase in Yb content. This temporal variation in basalt geochemistry is interpreted as reflecting progressive lithospheric thinning in the western NCC during the Cenozoic. An opposite trend is observed for Cenozoic basalts from the eastern NCC, suggesting lithospheric thickening during this time period. This thickening was probably related to regional thermal decay following peak magmatism in the late Cretaceous-Early Tertiary. Such contrasting lithospheric processes may reflect diachronous extension in the NCC, with extension taking place earlier in the eastern NCC than in western NCC. Recent seismic tomography reveals a flat subducting slab at the transition zone. The west end of this stagnant slab virtually coincides with the location of the DTGL. It is thus possible that Cenozoic volcanism resulted from interaction between two different tectonic regimes. The generation of Cenozoic basalts from the eastern NCC could be related to the back-arc extension owing to late Mesozoic-Paleogene Pacific subduction underneath the Asian continent, whereas subsequent extension in the western NCC may have been induced by the early Tertiary Indian-Eurasian collision. This interpretation also implies that the formation of the DTGL was likely coeval with the late Mesozoic destruction of the Archean lithospheric root beneath the eastern NCC.

T31E-02 08:20h

Geochemistry of basalts from Northeast China

Chen, Y (yangcz@umich.edu) , The University of Michigan, Department of Geological Sciences, Ann Arbor, MI 48109-1063 United States
* Zhang, Y (youxue@umich.edu) , The University of Michigan, Department of Geological Sciences, Ann Arbor, MI 48109-1063 United States

One of the notable areas of intraplate volcanism is northeast China. In an area of about two million square kilometers, there are numerous volcanic fields (about 600 volcanos known, Liu, 1999) with ages from Late Cretaceous (80 Ma) to recent (the most recent eruption was 300 years ago). Individual volcanic centers are usually small and a volcanic field typically consists of several to tens of volcanic centers. In this report, we review petrological and geochemical data in literature, present our new data, examine compositional correlations for this vast volcanic province, and explore possible controls of geochemistry by other parameters such as lithosphere thickness, crustal thickness and heat flow. Preliminary results show that not all data are consistent, probably reflecting analytical uncertainties of various labs. Isotopically, the basalts range from depleted mantle to bulk silicate Earth. Some elemental concentrations are correlated, and the correlation is strong along one linear belt of volcanic fields. There are systematic geochemical differences between alkali basalts from northeast China and intraplate alkali basalts from east Australia or from Hawaii. Basalt chemistry seems to vary systematically along a linear volcanic belt. The variations can be roughly explained by varying the degree and depth of mantle partial melting (such as the presence or absence of garnet), and might be related to lithosphere thickness. More work is in progress to examine basalt chemistry and other parameters and to understand the significance of the correlations and variations.

T31E-03 08:35h

The Late Paleozoic- Early Mesozoic tectonomagmatic activities in the Yanshan belt: implications for the Mesozoic intraplate deformation

* Zhang, S (tozhangshuanhong@163.com) , Institute of Geomechanics, Chinese Academy of Geological Sciences, No.11 Minzudaxue Nan Road, Haidian District, Beijing, 100081 China
Zhao, Y , Institute of Geomechanics, Chinese Academy of Geological Sciences, No.11 Minzudaxue Nan Road, Haidian District, Beijing, 100081 China
Song, B , Beijing SHRIMP center and Institute of Geology, Chinese Academy of Geological Sciences, No.26 Baiwanzhuang Road, Xicheng District, Beijing, 100037 China
Hu, J , Institute of Geomechanics, Chinese Academy of Geological Sciences, No.11 Minzudaxue Nan Road, Haidian District, Beijing, 100081 China
Xu, G , Institute of Geomechanics, Chinese Academy of Geological Sciences, No.11 Minzudaxue Nan Road, Haidian District, Beijing, 100081 China
Wu, H , Geological Information Center, Ministry of Land and Resource, Yanjiao, Hebei Province, Sanhe, 065201 China
Liu, J , Institute of Geomechanics, Chinese Academy of Geological Sciences, No.11 Minzudaxue Nan Road, Haidian District, Beijing, 100081 China
Pei, J , Institute of Geomechanics, Chinese Academy of Geological Sciences, No.11 Minzudaxue Nan Road, Haidian District, Beijing, 100081 China

Reactivation of pre-existing structures or thermal weakening zones associated with magmatism is very important for the localization of intraplate deformations (e. g., Holdsworth et al, 1997; D'Lemos et al, 1997). The Yanshan tectonic belt, which is located at the northern margin of the North China block (NCB), is a typical intraplate fold-and-thrust belt in Mesozoic (Davis et al, 1998; 2001). Although much work has been done during last a few decades, the Late Paleozoic-Early Mesozoic magmatic and deformation history of the Yanshan tectonic belt is still poorly understood. Recently, several variably deformed Late Paleozoic-Early Mesozoic granitoid plutons such as Longhua quartz diorite (311 -A2 Ma), Daguangding quartz diorite (327 -A7 Ma), Boluonuo quartz diorite (303 -A4 Ma), Guanglingshan granite (253 -A4 Ma) etc. in the Yanshan belt were determined from the so-called Archean-Paleoproterozoic crystalline basement by our SHRIMP U-Pb zircon dating, which indicate that the strong magmatisms accompany with deformation occurred during Late Paleozoic to Early Mesozoic. Preliminary geochemical analysis results show that the formation of these plutons is a result of the southward subduction of the Paleo-Asian oceanic plate beneath the NCB and the collision between the Paleo-Mongolian composite terrane and the NCB. Structural analyses of the Late Paleozoic plutons and the country rocks revealed several E-W trending mylonite zones formed during Late Paleozoic-Early Mesozoic, and the inherences between the former mylonite zones and the Mesozoic regional fault zones such as the Damiao fault, the Shangyi-Chicheng fault, and the Fengning-Longhua fault, are very obvious. Because some of the mylonite zones and deformed plutons are unconformably overlain by Jurassic volcanic or sedimentary rocks, and the eldest strata overlain upon the unconformity are Lower Jurassic Nadaling Formation and Xiahuayuan Formation, they had been deformed and exhumed to surface before Early Jurassic. 40Ar-39Ar dating and deformation environment analysis results of the mylonites indicate a multistage process of deformation from Late Paleozoic to Early Mesozoic (Cui et al, 2000; Hu, et al, 2003; Zhang, 2004). These multistage deformation zones, with strong Late Paleozoic-Early Mesozoic magmatic activities, formed many pre-Mesozoic crustal heterogeneities and thermally weakened zones, which played a very important role on the initiation of the intraplate deformation in Yanshan area from Early Mesozoic (pre-180 Ma?, Davis et al, 2001). Therefore the Mesozoic Yanshan intraplate fold-and-thrust belt is developed from a Late Paleozoic plate boundary tectonic belt.

http://www.agu.org/yanshan

T31E-04 08:50h

Processes of Active Intraplate Deformation in the Mongolian Altai and Gobi Altai

* Cunningham, D (wdc2@le.ac.uk) , University of Leicester, Department of Geology, Leicester, LE17RH United Kingdom

The Mongolian Altai and Gobi Altai regions are natural laboratories for studying active processes of intracontinental, intraplate transpressional mountain building. This type of orogen has unique structural, geomorphological and topographic characteristics that are generally underappreciated by geologists and geophysicists. Both ranges are dominated by 25 $\pm$5 km-spaced regional strike-slip faults which are linked to oblique-slip thrust and dip-slip thrust faults. These discrete belts of deformation and uplift are separated by non-extending sedimentary basins or geomorphologically mature landscapes. Individual ranges can be characterised as terminal restraining bends, double restraining bends, partial restraining bends, thrust ridges linked to strike-slip faults, triangular block uplifts between conjugate strike-slip faults, and individual thrust ridges. Neither orogen contains a regional thrust wedge, nor bounding foredeep, and structural vergence is inconsistent. Basins between ranges can be classified as ramp basins, confined asymmetric thrust-bound basins, open-sided thrust basins, strike-slip basins, and tectonically inactive remnant lows. Although parts of the Altai and Gobi Altai were previously a Mesozoic rift province, very few examples of fault reactivation and rift inversion have been identified in either region. The geometrical relationship between basement structural grain, rigid Precambrian block boundaries, and SHmax dictates Late Cenozoic fault kinematics and overall mechanisms of uplift. Ongoing transpressional deformation is incompletely slip partitioned as indicated by historical oblique-slip earthquake focal mechanism solutions and oblique-slip fault displacements as revealed by outcrop slickenside data. The geometry of active faulting is best described as regional transpressional duplexing, intermediate between strike-slip and thrust duplexing. Late Cenozoic upper crustal transpressional deformation may be balanced in the lower crust by crustal thickening due to lower crustal inflation, and possibly lower crustal outflow towards the Russian Altai-Sayan region where late Cenozoic plateau uplift is recorded, but unexplained.

T31E-05 09:05h

Tertiary Deformation in the Kashgar Basin, Southern Margin of the Tian Shan, China

* Heermance, R V (richard@crustal.ucsb.edu) , University of California, Santa Barbara, Department of Geological Sciences, 1006 Webb Hall, Santa Barbara, CA 93106 United States
Chen, J (chenjie@eq-igl.ac.cn) , State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Seismological Bureau, P.O. Box 9803, Beijing, 100029 China
Scharer, K (kscharer@darkwing.uoregon.edu) , Department of Geological Sciences, 1272 University of Oregon, Eugene, OR 97403 United States
Burbank, D (burbank@crustal.ucsb.edu) , University of California, Santa Barbara, Department of Geological Sciences, 1006 Webb Hall, Santa Barbara, CA 93106 United States

The northwest corner of the Tarim Platform, near the town of Kashgar, China, is an actively deforming fold-and-thrust belt related to uplift of the Tian Shan. Mapping of 5000 km$^{2}$ in the area north of Kashgar city and west of the Kepintage thrust zone indicates at least 15 km of shortening has occurred since the Miocene. Shortening is accomodated along 5 major structures that extend $>$60 km ~east-west along strike. These structures, from north to south, are the basin-bounding Tuotergongbaizi fault(TF), the Kepintage-Yishilakekalawuer fault (KYTF), the Keketamu syncline-anticline pair (KEK), the Atushi-Talanghe (AT) anticline, and the Kashi (K) anticline. Smaller-displacement imbricate faults and small-wavelength folds occur throughout the region associated with these major structures. Scharer et al (in press) document 7 km of shortening in the AT and K anticlines. Our new values add at least 8 km of shortening accomodated in the TF, KYTF, and KEK structures for a total of $>$15 km in the region. Uplifted and deformed fluvial terraces are observed along the AT, K, and KYTF, indicating that deformation is active and occurring throughout the fold-and thrust belt, not only in the southern foreland. In the north the TF and KYTF are south-vergent faults that juxtapose Paleozoic basement with Tertiary sediments. The KEK anticline is a south vergent fault-propagation-fold, but the AT and K are detachment structures that display both north and south vergence. Detachment horizons are likely gypsum-rich Miocene layers near the base of the ($>$5 km thick) Tertiary section. The TF cuts poorly sorted, debris-flow facies conglomerate in its footwall. The conglomerate changes facies southward, toward the foreland, to well-sorted fluvial deposits. New magnetostratigraphy reveals the the basal age of the conglomerate becomes younger towards the south, from $\sim$5.2 Ma 10 km south of the fault, to $<$2 Ma 20 km south of the fault. These observations imply significant erosional topography along the TF prior to 5.2 Ma, and progradation of a conglomerate wedge into the basin. Our shortening estimates for this area since the latest Miocene imply minimum long-term shortening rates of $\sim$3mm/year, or less than half of the present-day shortening rates (7-10 mm/year) determined by GPS measurements across the region.

T31E-06 09:20h

Slip-distribution and Rupture Pattern of the 14 November 2001, Mw 7.8 Kokoxili Earthquake (China)

* Klinger, Y (klinger@ipgp.jussieu.fr) , Tectonique - IPGP, UMR7578 - BP89 4 place Jussieu, Paris, 75005 France
Michel, R (remi.michel@cea.fr) , LDG/CEA, BP12, Bruyeres le Chatel, 91680 France
Van der Woerd, J (jeromev@eost.u-strasbg.fr) , EOST, 5 rue Descartes, Strasbourg, 67000 France
Xu, X (xiweixu@vip.sina.com) , Institut of Geology, Chinese Earthquake Administration, Beijing, 100029 China
Tapponnier, P (tappon@ipgp.jussieu.fr) , Tectonique - IPGP, UMR7578 - BP89 4 place Jussieu, Paris, 75005 France

The Mw=7.8 Kokoxili earthquake ruptured about 430 km of the Kusai segment of the Kunlun fault (from 90.2E to 94.7E). This event, the largest continental event ever recorded in Asia, follows nearly four years later, the 8 November 1997, Mw=7.6 Manyi earthquake. The surface break follows the geomorphic trace of the fault, which bears evidence for cumulative displacements. Using Ikonos and Quickbird satellite images with nominal resolution of 1m and 60cm, respectively, we mapped in detail the central segment of the rupture and documented the slip-partitioning process that took place during the earthquake rupture. Some new details about the rupture in the epicentral area west of the Tayang Lake are also presented. From field explorations of the rupture we show evidences for normal fault breaks and left-lateral ruptures along the steep faceted southern flank of the BukaDaban Feng, a 40km-long range reaching 6800m asl. Hence this mountain range clearly results from continuous oblique left-lateral faulting along the extensional corridor connecting the epicenter area to the main rupture segment. Due to the remoteness and harsh climatic condition of the earthquake location, an exhaustive survey of the entire fault rupture is difficult. While several teams have been involved in measuring geomorphic offsets due to this earthquake. The amount of data collected, however, remains small compared to the length of the rupture. Also considering the complexity of the rupture, measuring the earthquake dislocation has proved to be difficult in many places and has raised arguments about the shape of the slip-curve and the maximum horizontal offset associated to the Kokoxili earthquake. Using sub-pixel intercorrelation of optical satellite images (satellite Spot, pixel 10m) we produced a slip-curve that encompasses the entire rupture with an independent measurement every kilometer on average. This technique allows us to detect displacement down to 1m. The slip-distribution we obtained shows clearly that the maximum slip is highly localized on few asperities whereas it remains moderate (<4m) along large parts of the rupture. The maximum slip we could measure is 12m, which is much lower than some values previously reported. The large variation of slip along the rupture for a single event bears important consequences and should be seriously considered when long-term rupture behavior of the fault is discussed based on cumulative offset measurements or paleoseismological investigation.

T31E-07 09:35h

Mesozoic and Cenozoic Intracontinental Deformation in Southeastern Mongolia

* Webb, L E (lewebb@syr.edu) , Dept of Earth Sciences, Syracuse University, Syracuse, NY 13244 United States
Johnson, C L , Dept of Geology and Geophysics, University of Utah, Salt Lake City, UT 84112 United States
Minjin, C , School of Geology, Mongolian University of Science and Technology, Ulaanbaatar, 210646 Mongolia
Sersmaa, G , School of Geology, Mongolian University of Science and Technology, Ulaanbaatar, 210646 Mongolia
Affolter, M D , School of Geology, Mongolian University of Science and Technology, Ulaanbaatar, 210646 Mongolia
Manchuk, N , School of Geology, Mongolian University of Science and Technology, Ulaanbaatar, 210646 Mongolia

Structural and basin analysis studies of the NE-trending East Gobi Fault Zone (EGFZ) reveal distinct deformation events postdating Late Paleozoic arc accretion and continental amalgamation. This presentation, a companion abstract to Johnson et al. (2004), focuses on the kinematic signatures of these deformation events and their relationship to the larger Asian tectonic framework and its evolution. Metamorphic tectonites of basement blocks in the EGFZ, previously mapped as Precambrian basement, belong to a Late Triassic sinistral shear zone that comprises a suite of synkinematic intrusions, amphibolite-facies gneisses and greenschist-facies mylonites. The shear zone is dominated by steeply dipping foliations and subhorizontal ENE or WSW-plunging stretching lineations. At higher structural levels, variably metamorphosed Paleozoic sedimentary sequences are caught up in discrete zones of mylonitic deformation. We have documented the shear zone at several localities over a distance of 250 km along strike in the EGFZ. High-angle fabrics associated with the Late Triassic sinistral shear zone were exploited by Early Cretaceous basin-bounding faults that formed in the brittle-ductile to brittle regime. A NW-SE horizontal extension direction indicated by this oldest generation of brittle faults is similar to that implied by stretching lineations at the Yagan-Onch Hayrhan metamorphic core complex located to the SW along the Chinese-Mongolia border. Early Cretaceous rift basins were inverted by mid Cretaceous dextral transpression along mainly WNW-trending faults. All Mesozoic rocks are cut by Cenozoic conjugate strike-slip and thrust faults that accommodate NNW-SSE compression. These youngest faults are associated with gouge zones, cut unconsolidated alluvium, and control the present day topographic expression of basement blocks within the EGFZ. Our data suggest that extrusion tectonics have been active in Asia since the Early Mesozoic, and bear on the viability of tectonic models that postulate linkages between the Altyn Tagh and EGFZ. Though a Cenozoic linkage between the two faults is permissible, major sinistral offset on the EGFZ likely occurred in the Late Triassic.

T31E-08 09:50h

Sedimentary Basin Evolution in the Context of Polyphase Intracontinental Deformation: New Insights From Southeastern Mongolia

* Johnson, C L (cjohnson@mines.utah.edu) , Dept of Geology and Geophysics, University of Utah, Salt Lake City, UT 84112 United States
Webb, L E (lewebb@syr.edu) , Dept of Earth Sciences, Syracuse University, Syracuse, NY 13244
Minjin, C (minjin@must.edu.mn) , School of Geology, Mongolian University of Science and Technology, Ulaanbaatar, 210646 Mongolia
Sersmaa, G (sers@must.edu.mn) , School of Geology, Mongolian University of Science and Technology, Ulaanbaatar, 210646 Mongolia
Affolter, M (qfl247@netscape.net) , Dept of Geology and Geophysics, University of Utah, Salt Lake City, UT 84112 United States
Manchuk, N (minjin@must.edu.mn) , School of Geology, Mongolian University of Science and Technology, Ulaanbaatar, 210646 Mongolia

At least four major intracontinental deformation events have punctuated the geologic evolution of SE Mongolia since Late Paleozoic time. Much of the structural deformation was concentrated along the northeast-trending East Gobi Fault Zone (EGFZ), which we have studied in multiple localities along its 250 km (minimum) length. Our structural and geochronologic studies, described in more detail in a companion abstract by Webb et al. (2004), define a general tectonic framework of Late Triassic sinistral shear, Late Jurassic-Early Cretaceous extension, mid-Cretaceous transpression and basin inversion, and Cenozoic compression and strike-slip faulting. Perhaps the best-known phase of basin development in this area is Late Jurassic-Early Cretaceous rifting which formed multiple NE-SW-trending grabens, as well as a metamorphic core complex. This rifting event, in which most structures of the EGFZ were active as a series of high angle normal faults, postdates motion on a Late Triassic sinistral shear zone. As a result of Early Mesozoic sinistral shear, Paleozoic basins may have been dismembered and offset by some 100s of km prior to late Mesozoic rifting. Similarly, we have new evidence for mid-Cretaceous and Cenozoic transpression along the EGFZ following the rifting event. Postrift reactivation of the EGFZ may have coincided with Cenozoic activity along the Altyn Tagh fault zone, and suggests that motion along these faults may have been linked for at least part of their histories. Multi-phase reactivation of the EGFZ has important implications for evolution of sedimentary basins that formed along it, as well as for other regions subject to intracontinental deformation. Such implications include the importance of inherited shear zones, particularly in areas where basement is extremely heterogeneous, as a controlling factor in the development of polyphase sedimentary basins. This work also emphasizes the need for careful analysis of offset piercing points in order to accommodate accurate paleogeographic reconstructions of the basin.


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MathSciNet bibliographic data MR1348707 (96e:11042) 11D41 Darmon, Henri; Granville, Andrew On the equations \$z\sp m=F(x,y)\$$z\sp m=F(x,y)$ and \$Ax\sp p+By\sp q=Cz\sp r\$$Ax\sp p+By\sp q=Cz\sp r$. Bull. London Math. Soc. 27 (1995), no. 6, 513–543. Article

For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.


text:
Max-Planck-Institut für Gravitationsphysik,   Albert-Einstein-Institut

## Critical phenomena and the Aretakis instability of extremal black hole perturbations

 Starts at: Wed 23 Jan 2019, 14:00 Speaker: Peter Zimmerman Institute: Max Planck Institute for Gravitational Physics Pot Abstract: Perturbations of extremal black holes are asymptotically self-similar under the near-horizon, late-time scaling symmetry of the background metric. In this talk, I will explain why this effect is universal and how it accounts for the Aretakis instability $$growth of transverse derivatives$$ as a critical phenomenon associated with the emergent symmetry. Taking Kerr as an example, I will show how the decay of each perturbing mode is characterized by a critical exponent after defining suitable notions of weak and strong self-similarity. I will end with a simple argument for why all generally covariant scalar quantities decay to zero despite the growth of transverse derivatives. Seminartype: Ordinary Room: Seminarraum 0.01 Contact: Alexander Prostimkin


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# March 2023¶

## Wednesday 1st March¶

Good day, taught Laura a lot! had a decent sleep in after all this chaos.

## Thursday 2nd March¶

Had a meeting with Katya and Laura about Laura’s project, and then taught in the afternnon. am exhausted

### From meeting re Laura:¶

• Start on lit review asap
• What goals need to be covered, then work backwards from there
• Focus on the broad issues, then explore the underlying issues
• Keep description and properties of fluorophores to a minimum
• Week 3: Aims
• Week 6: Skills and knowledge
• Week 8: Intro - draft after mid-sem (week 7)
• Week 11: Overall reflection
• Week 12: Report (in form of paper)
• Week 13: presentation

Ask Sophie to schedule practice presentation.

## Friday 3rd March¶

Finally a day where I’m not teaching!!! Hopefuly I can get some work done

• Redoing bsc jobs from an MP2 guess since they were behaving really weirdly with superci
• r800 is still going…

From meeting

• Case study of a single species with ESD in low polarity solvent
• Currently re-opt s1 and s2 with calchess and angulargrid 6
• Then Freqs of all states
• Then ESD
• +Deconvolution

I’ve written code additions for generation of an adiabatic hessian (hessian of other state at current state geom) and for ESD additions, and I’m waiting for some other jobs to finish before I can get these through.

## Saturday 4th March¶

I’ve been pushing through the ESD jobs and have been trying to get all the other stalled opts up and running again.

## Monday 6th March¶

For ESD stuff, I realised that I can use dirac deltas instead of gaussians as my output lineshape, which means I should be able to pick the most significant peaks. I could use a convolution and pass it over to find the most significant peak

I need to write a standalone deconvolution script for sophie:

Files to save out:

• CSV of the three specra
1. Processed/smoothed raw spectra
2. Deriv space spectra
3. Normalised spectra
• CSV with deriv space fitted gaussians (loc, amp, sigma)
• CSV with re-fitted gaussians (loc, amp, sigma)
• TOML settings file with ALL the input parameters
• Save image file

## Tuesday 7th March¶

Well, I felt very drained today, but I found a way to process my ESD spectr, by Gaussian smoothing the spectra and then ofsetting the smoothed spectra by a certin amount. Any point above that line can be considered important

## Wednesday 8th March¶

So I couldn’t sleep from like 4am, and ended up coding for the next three hours… The good thing is that the deconvolution notebook for Sophie is nearly done. I just need to write a function to export the data now.

That is done, and my module is ready for use! https://github.com/adreasnow/uv-vis-deconvolution

I spent the afternoon helping Laura and Sophie get their work out, and managed to queue up a huge bunch of jobs to churn through.

Laura is currently calculating casscf freqs to see how good our geoms are.

## Thursday 9th March¶

Didn’t manage to get a huge aount done today… Meeting with Katya and Laura, and I added another little feature to the deconvolution tool in order to allow for ftting of a small region, without clipping out the rest of the spectrum.

## Sunday 12th March¶

NWChem 7.2.0 has finally been released which makes me think that I should possibly start exploring VEM/SMSSP results, but I think I’m starting to realise that TD-DFT results are absolutely meaningless for comparing to a spectrum, without either 0-0 energies, or ESD calculations.

#### For Laura:¶

I think Laura is going to need to compare 0-0 energies for her work

FUCK!

So in my hormonal/withdrawal mess this afternoon, while trying to distract myself in code, I managed to rsync all my files into the aether. All gone.

I grabbed what I could from Laura’s folder and and trying to just focus on getting some robust gas phase computations done for now. I’ve started with CASSCF opts, and have queued up wB97X-D opts for the opts that are complete.

Yes, I did email mcc-help to ask for them to restore my data from a backup, but I’m not sure how old it will be. I’m also working from a different directory in case they overwrite my current jobs when they restore the backup (however old it may be).

## Monday-Tuesday 13-14th March¶

Teaching day today… then shit hit the fan in the evening interpersonally. I’m struggling a fair bit, but I’ll keep pushing through.

## Wednesday 15th March¶

Okay, I have an emergency appointment with the GP at monash health and will hopefully get something to help with this stress/sleep.

We still haven’t heard anyhting back from TCI about procuring the asp, so I’ve decided to cull it from the dataset. I can’t find any other commercially avaialble thiophene based fluorophores, so I don’t think I’ll replace iot with another species.

## Thursday 16th March¶

So I’m taking most of the day off today, but I did notice one thing in my spectra that needs addressing. In all the spectra Laura took yesterday, there were a lot of lower energy peaks that mirrored that of the primary transition, or existed as an individual gaussian. In reading, these can be attributed to three distinct scattering phenonmena:

1. Rayleigh scattering ($$\lambda=\lambda_{excitation}$$) - This is simply scattering that happens at the same wavelength as the excitation source, and can be easily accounted for by making sure there’s a 10nm gap between excitation and emission recording. This appears as a single gaussian.
2. Raman scattering (Stokes) ($$\lambda>\lambda_{excitation}$$) - This appears as a single gaussian and should be accounted for in the 10nm gap for Rayleigh scattering.
3. Raman scattering (Stokes) ($$\lambda<\lambda_{excitation}$$) - This also appears as a single gaussian but is much more difficult, since the scattered light may overlap with the fluorescence spectrum. One way to account for this is the obtain a spectrum of JUST the solvent and subtract this from the flurescence spectrum.
4. Second (and third) order diffractions - These appear as a copy of a part of the spectrum at a lower energy region, and include bot the fluorescence spectrum, and the three kinds of scattered light. This can mostly be accounted for by using emission filters to block out light that comes in from a greater angle to the diffraction grating. Setting the emiison filter on the Cary Elcipse from “Open” to “Auto” seems to do the trick.

## Saturday 18th March¶

#### Thought:¶

Running ESD for every job to identify transitions seems a tad extreme, but what if we use gs/es hessians to figure out a vibrational state-specific transition energy.

For this approach, we’d need:

• GS hessian
• nEq ES@R(GS) hessian

From these we should be able to figure out the excitation 0-0 transition (this will be different from the Eq/Eq 0-0 for Goerigk and Grimme) and the corresponding energies for each of the subsequent higher vibrational transitions.

We’re making heavy assumptions that the process will be adiabatic here though, and that the harmonic oscillator approach will hold.

To verify the harmonic oscillator, I’m running some anharmonic vibrational corrections using NWChem’s VSCF module. It’s slow, but we should be able to quantify some errors.

• I’m trying to reduce costs by only calculating correctiosn for the diagonal ter,s, and I’m halving the resolution form 16 displacement steps to 8 (any lowere and I got weird errors)

## Sunday 19th March¶

I realised that I made some errors in the above protocol that have since been ammended. Mostly that for this approach to work, both hessians need to be based on the starting geom (GS for excitation, ES for emission)

Also… HOLY CRAP is NWChem’s TDDFT module slow! Perhaps I ned to use a smaller grid and cheaper functional…

## Monday 20th March¶

Teaching day. Nothing to report.

## Tuesday 21st March¶

I’ve been feeling a bunch of burnout building, so I spent my day working on an API that runs on my home server and takes in job status updates to spit out a nicely formatted table of jobs, their cluster, status, and when their status last changed. I have it up and running and it looks good! (well, useful).

It was pretty easy to write the Flask and SQL app, but the hard part (that took many hours) was getting to run as a subdomain using Apache.

## Wednesday 22nd March¶

Another teaching day, so not much to report…

## Thursday 23rd March¶

Burnout recovery day, just worked on compiling NWchem better

## Friday-Sunday 24th-26th March¶

More burnout recovery today, but I realised a few important things while in the lab with Laura:

1. Our nda sample may not be pure
2. I’m going to need a solvent blank for EVERY fluorophore/solvent emission at every different excitation wavelength to account for raman scattering
3. This means I need more cuvettes so that I don’t constantly have to empy and blank between each reading (Toby is going to order more)
• This can’t really be mitigated with protocol work since I need to play with the excitation wavelength to get the correct peak and minimise scatter, so I need at least one more that I can get a solvent blank with.

## Monday, Wednesday 27th-29th March¶

Another big teaching week, don’t expect too much from me

#### NWChem Testing (all performed with 8 cores 16GB on hi01)¶

identifier Crashes on test CPU Time Wall Time ⬇ efficiency
-f90 no 1166.0 1169.5 99.7%
-knl no 1207.2 1211.3 99.7%
- no 1280.5 1286.4 99.5%
knl+f90
- no
-mpipr no
-openib unstable

## Questions I’m currently trying to answer¶

• Can we use frequency calulations dierectly to think about the individual transitions?
• How significant is anharmonicity in effecting transition energies?
• Even if it’s significant in overall thermodynamic properties, do the errors cancel out when considering both GS and ES PES anharmonically?
• In investigating 0-0 transition energies, what is the most correct formal approach?
• Adiabatic 0-0 - R(initial) Eq → R(initial) nEq !! This approach is fundamentally flawed, as you will ALWAYS get negative frequencies !!
• Using relaxed densities is probably important here though since the wfn will have time to relax
• QChem: CIS_RELAXED_DENSITY TRUE
• Equilibirated 0-0 - R(initial) Eq → R(final) Eq
• This doesn’t give the distinct difference in abs and fluor 0-0 peaks though

• az
• r800
• nda
• dapi
• daa

## Job Matrix¶

### CAS (M3)¶

State Active Spaces Opt Freq FIC-CASPT2K SC-NEVPT2 QD-NEVPT2
s0
s1+2

### DFT - Gas (MonARCH)¶

State Functional Opt Freq Pol Ex/Em ESD
s0 ωB97X-D
s1+2 ωB97X-D
s0 CAM-B3LYP N/A
s1+2 CAM-B3LYP N/A

### DFT - n-Hexane¶

State Functional Opt Freq Pol SS VEM ESD
s0 ωB97X-D
s1+2 ωB97X-D
s0 CAM-B3LYP
s1+2 CAM-B3LYP

## To Run an ESD job:¶

1. Calculate frequencies of GS and ES
2. Run ESD Calcs for both states - both with eq solvaion
• GS: ESD(ABS)
• ES: ESD(FLUOR)

## To do:¶

• Read Betaine 30 paper 10.1002/chem.201604619
• Jobs to wr
• Test QChem to figure out how to do VEM/cLR/LR/IBSF emission
• Code
• Write standalone deconvolution notebook
• Write energy extractors
• pullQChem_Freq
• $$\Delta E_{ZPVE}$$
• $$\Delta E_{elec}$$
• Number of -ve freqs
• Extend and test for CASSCF
• Q-chem ex/em extractors
• ss-ex
• ss-em
• lr-ex
• lr-em
• Documentation

• Transfers documentation
• Contact List
• ORCA and QChem examples
• Try lerping between states

## GANTT Chart¶

gantt
dateFormat D/M/YY
title Adrea's PhD Plan
%%excludes    weekends

section Preparation
Preliminary reading                     :active,                    5/4/22,     10/2/23
Method "Play"                               :done,                      5/4/22,     10/6/22
Software comparisons                    :done,                      10/6/22,    13/7/22
Preliminary benchmarking            :done,                      12/7/22,    27/10/22
Christmas break                             :crit,                      22/12/22,   3/1/23
Dataset design                              :active,                    12/7/22,    18/12/22
Experimental design                     :active,                    28/11/22,   27/1/23

section IPR/Confirmation
IPR writeup                   :ipr,                         19/12/22, 10/2/23
IPR                           :milestone, ipr,  23/2/23,    0d
Confirmation writeup                    :                                   29/3/23,    10/5/23
Confirmation                                    :crit, milestone, 24/5/23,  0d

section Dataset paper
Data collection                             :dc,                            6/3/23,     12w
Data processing                             :                                   6/3/23,     18w
Writeup                                             :w, after dc,                           8w
R&R break                                         :crit, after w,                         2w

section Computational dataset analysis paper
Computation                                       :                                   6/3/23,     30w
Analysis                                          :                                   1/6/23,     20w
Writeup                                               :                                   1/8/23,     20w
Christmas break                               :crit,                      22/12/23,   3w

section Solvent model extension/development
Computation                                       :                                   9/1/24,     5/7/24
Writeup                                               :                                   5/7/24,     6/9/24
R&R break                                         :crit,                      6/9/24,     2w

section Progress review
Progress review writeup               :                                   14/3/24,    9/5/24
Progress review                             :milestone,             23/5/24,    0d

section Fourth paper (possibly benchmarking or deconvolution)
Computation                                       :                                   27/9/24,    19/12/24
Christmas break                               :crit,                      20/12/24,   2w
Writeup                                               :                                   6/1/25,     3/3/25

section End of PhD
Final review writeup                    :                                   28/3/25,    9/5/25
Final review                                    :milestone,             23/5/25,    0d
Drop everyhting for thesis      :                                   25/4/25,    25/7/25
Thesis submission                           :crit, milestone,   22/8/25,    0d

## Code Object Structure¶

flowchart LR
subgraph Legend
1((Entity))
3[[module]]
4[(database)]
5[/Data Types/]
6[Hidden Code\n12000+ lines]:::backend
7[User Facing Code\n3000+ lines]:::ui
end

classDef backend fill:#bfbdbd;
classDef ui fill:#fa4ba0;
classDef db fill:#00f2ff;
flowchart TD
a -- Output Files --> g
g -- SLURM Scripts -->
a((HPC Clusters))
subgraph Backend Code
s[/Spectrum Object/]:::backend
m[/Fluorophores/]:::backend
n[/Solvents/]:::backend
o[/PCM Models/]:::backend
p[/Software/]:::backend
r[/Methods/]:::backend
q[/Basis Sets/]:::backend
s & m & n & o & p & r & q -.-> l[[Data Types]]:::backend -.- w
g[[HPC Manager]]:::backend -.- w
w[[Resources module]]:::backend
end

c <-- Job Status --> v
c -- QM Properties --> k

subgraph Databases
j[DB Manager]:::ui -.- b & e & k
e[(ΔE/λ/Φ/τ DB)]:::backend
b[(Spectra DB)]:::backend
k[(Computational Results DB)]:::backend
v[(Computational Progress DB)]:::backend
v <--> j
end

subgraph Experiment
h[Spectra Importer]:::ui
i[Spectra Analyser/Plotter]:::ui
t -- .txt files --> h
d -- .csv files --> h
t((TCSPC))
d((UV-Vis/Fl))
end

c[Job Manager]:::ui
b <-- Fitted spectra --> i

h -.- i -- Spectral Features --> e
b <-- Fitted spectra --> h

w -. Jobs -.- c
w -.- j

k & e --> u[Stats Scripts]:::ui

classDef backend fill:#bfbdbd;
classDef ui fill:#fa4ba0;
classDef db fill:#00f2ff;


text:
NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/
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lookang
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 « Embed this message on: November 12, 2010, 11:59:00 am »

Ejs Open Source 1 Dimension Doppler Effect Sound Wave Java Applet
Ejs Open Source Doppler Effect Sound Wave Java Applet
reference
this version is by Fu-Kwun Hwang http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=873.0
remixed by lookang

Original is Designed by Fu-Kwun Hwang http://www.phy.ntnu.edu.tw/ntnujava/ remixed by lookang
Reference taken from Juan M. Aguirregabiria's http://www.compadre.org/osp/items/detail.cfm?ID=7902
and Andrew Duffy's http://www.compadre.org/osp/items/detail.cfm?ID=9982
which made the remixing of this simulation a lot easier
lookang thanks all of them (Fu-Kwun Hwang, Juan M. Aguirregabiria and Andrew Duffy) these are great physics teachers.

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)
Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License
• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

other Doppler effect ejs applets
EJS version of Doppler effect (You can hear sound) by Fu-Kwun Hwang http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=873.0
Ejs Doppler Effect Model written by Juan Aguirregabiria edited by Wolfgang Christian http://www.compadre.org/osp/items/detail.cfm?ID=7902
Doppler Effect Model written by Andrew Duffy http://www.compadre.org/osp/items/detail.cfm?ID=9982

The Doppler effect
The Doppler effect describes the shift in frequency of a wave that is produced by the motion of either the wave source or the observer of the wave (or both).
A sound source is moving with velocity v along the horizontal axis. Every period T a wave front leaves the source and travels with velocity c with respect to a medium (say air), assuming no air motion. A detector is located at position (x, y) and may move with velocity (dx/dt, dy/dt). To promote ease of learning, only the x direction is enabled, thus, making exploration confined to 1 Dimension.
You may change via sliders and edit the values of the aforementioned quantities, as well as the time interval dt between animation frames.
The source and detector position may also be chosen by means of the sliders.
Press Initial to set t = 0 and the source at its initial position.
Press Continue to start or continue the animation.
Press Stop to pause the animation, and Reset to recover the default settings.
In the graphics window below the animation a vertical red (green) bar is displayed each time a wave front leaves the source (reaches the detector).

Activities
Note that the velocities are specified in terms of the wave velocity, where positive is directed right. Thus, a source speed of 1 means that the observer moves at the speed of the waves.

1 Start with the source at rest and the observer at rest, and observe the pattern produced when you press the Play button. Describe the pattern also in terms of the relationship of f and f'. Hint: f = f'
2 Now, keep the source at rest, and give the observer an initial velocity. Explore how the frequency of the waves reaching the observer changes as you vary the observer's velocity. Does this depend on whether the observer is moving toward the source or away from the source? Does the motion of the observer effectively change the speed of the waves or the wavelength?
3 Now, keep the observer at rest and explore the effect of the motion of the source. How does the frequency of the waves reaching the observer depend on the source velocity? Does the frequency shift depend on whether the motion of the source is toward or away from the observer? Does the motion of the source effectively change the speed of the waves or the wavelength?
4 Now that you are more familiar with the simulations terms, objects and quantities, design and experiment to deduce the relationship between f' and f. Hint: a table with your inquiry quantities will be useful in your self directed science discovery.
5 What happens when the source travels at the same speed of the waves? Hint: your explanation should include/ make reference to terms like Mach, Shockwave, Sound Barrier and Sonic Boom.
6 What happens when the source travels faster than the wave speed? Hint: your explanation should include terms/make reference to Mach, Shockwave and SuperSonic.

Advanced learners! pedagogy of constructionism
7 Use EJs and change the simulation to include 2 dimensions hint: Fu-Kwun Hwang http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=873.0
8. Use EJs and change the simulation to include the reference frame, hint:Andrew Duffy http://www.compadre.org/osp/items/detail.cfm?ID=9982
9 Use EJs and change the simulation to include the effect of wind hint: Juan Aguirregabiria edited by Wolfgang Christian http://www.compadre.org/osp/items/detail.cfm?ID=7902
 Ejs_Open_Source_1_Dimension_Doppler_Effect_Sound_Wave_Java_Applet.png (46.85 KB, 709x534 - viewed 896 times.) « Last Edit: September 24, 2011, 11:05:44 pm by lookang » Logged
lookang
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 « Embed this message Reply #1 on: November 12, 2010, 12:00:20 pm »

trying to find time to make an applet that has best features of all the above applets made by great physicists.
it is more difficult than it seems hmmmmm.

reference: http://www.physicsclassroom.com/class/waves/u10l3d.cfm
The Doppler effect is observed whenever the source of waves is moving with respect to an observer. The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for observers from whom the source is receding. It is important to note that the effect does not result because of an actual change in the frequency of the source. Using the simulation above, the source is still producing disturbances such as sound at a rate of f = 0.5 disturbances per second (select T period as 2 second); it just appears to the observer that the source of the wave is approaching say vsource = 170 m/s that the disturbances are being produced at a frequency greater than 0.5 disturbances/second. using the formula f' = f ( c+vobserver) / (c - vsource) = 0.5* ( 330+0)/(330-170) = 1.03 Hz.
when the source is traveling away from the observer, the formula is now formula f' = f ( c-vobserver) / (c + vsource) = 0.5* ( 330-0)/(330+170) = 0.33 Hz.

The Doppler effect can be observed for any type of wave - water wave, sound wave, light wave, etc. We are most familiar with the Doppler effect because of our experiences with sound waves. Perhaps you recall an instance in which a police car or emergency vehicle was traveling towards you on the highway. As the car approached with its siren blasting, the pitch of the siren sound (a measure of the siren's frequency) was high; and then suddenly after the car passed by, the pitch of the siren sound was low. That was the Doppler effect - an apparent shift in frequency for a sound wave produced by a moving source.

The Doppler effect is of intense interest to astronomers who use the information about the shift in frequency of electromagnetic waves produced by moving stars in our galaxy and beyond in order to derive information about those stars and galaxies. The belief that the universe is expanding is based in part upon observations of electromagnetic waves emitted by stars in distant galaxies. Furthermore, specific information about stars within galaxies can be determined by application of the Doppler effect. Galaxies are clusters of stars that typically rotate about some center of mass point. Electromagnetic radiation emitted by such stars in a distant galaxy would appear to be shifted downward in frequency (a red shift) if the star is rotating in its cluster in a direction that is away from the Earth. On the other hand, there is an upward shift in frequency (a blue shift) of such observed radiation if the star is rotating in a direction that is towards the Earth.
 « Last Edit: September 12, 2011, 01:28:52 pm by lookang » Logged
lookang
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 « Embed this message Reply #2 on: September 09, 2011, 03:44:14 pm » posted from:SINGAPORE,SINGAPORE,SINGAPORE

changes.

add new controls fit my usual design
redrawn for customization to sound Doppler effect v =330 m/s instead of the older 25 m/s
customized to 1 Dimension only
redo the applet on Fu-Kwun Hwang http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=873.0
added visualization of detected and emitted with reference to Ejs Doppler Effect Model written by Juan Aguirregabiria edited by Wolfgang Christian http://www.compadre.org/osp/items/detail.cfm?ID=7902
add sound from Toolkit.getDefaultToolkit().beep(); // taken from http://www.compadre.org/OSP/items/detail.cfm?ID=8385&Attached=1
//Ceiling Bounce Model written by Wolfgang Christian
made the initial v = 170 m/s
made T = 2 s
redrawn by the Plotting Panel for the numbers in x and y direction
11 September 2011
added The perceived frequency (f prime) is related to the actual frequency (f) and the relative speeds of the source (vsource), observer (vobserver), and the speed (c) of waves in the medium by http://www.kettering.edu/physics/drussell/Demos/doppler/doppler.html
f prime = f ( c + vobserver ) / ( c - vsource) for towards each other (approaching)
f prime = f ( c - vobserver ) / ( c + vsource) for moving away from each other (separating)
codes are:
frequencyemitted = 1/T;
if ((x-xe)*(v0-vobserver) >0){ // towards each other

frequencydetected = frequencyemitted*( v0+ vobserver)/( v0+ vs);
}
else {
frequencydetected = frequencyemitted*( v0- vobserver)/( v0- vs);
}
24 September 2011
added better text thanks to bbbeard http://weelookang.blogspot.com/2011/09/ejs-open-source-1-dimension-doppler.html
if (Math.abs(vs) >Math.abs(v0) ) // consider only 1 D in x
{
text = "Supersonic";
}
else if (Math.abs(vs) ==Math.abs(v0) ) // consider only 1 D in x
{
text = "Breaking the sound barrier";
}

else {
text = "Doppler Effect";
}

attached is a previously worked on version that i could not continue improving
 Ejs_Open_Source_Doppler_Effect_Sound_Wave_Java_Appletold.png (43.2 KB, 708x505 - viewed 2314 times.)  Ejs_Open_Source_1_Dimension_Doppler_Effect_Sound_Wave_Java_Applet.png (46.85 KB, 709x534 - viewed 1026 times.) *** There are 4 more attached files. You need to login to acces it! « Last Edit: October 20, 2011, 11:06:29 pm by lookang » Logged
lookang
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 « Embed this message Reply #3 on: September 12, 2011, 03:05:36 pm » posted from:SINGAPORE,SINGAPORE,SINGAPORE

completed some remixing

enjoy!

reference: http://www.physicsclassroom.com/class/waves/u10l3d.cfm
The Doppler effect is observed whenever the source of waves is moving with respect to an observer. The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for observers from whom the source is receding. It is important to note that the effect does not result because of an actual change in the frequency of the source. Using the simulation above, the source is still producing disturbances such as sound at a rate of f = 0.5 disturbances per second (select T period as 2 second); it just appears to the observer that the source of the wave is approaching say vsource = 170 m/s that the disturbances are being produced at a frequency greater than 0.5 disturbances/second. using the formula f' = f ( c+vobserver) / (c - vsource) = 0.5* ( 330+0)/(330-170) = 1.03 Hz.
when the source is traveling away from the observer, the formula is now formula f' = f ( c-vobserver) / (c + vsource) = 0.5* ( 330-0)/(330+170) = 0.33 Hz.

 http://www.physicsclassroom.com/class/waves/u10l3d3.gif

The Doppler effect can be observed for any type of wave - water wave, sound wave, light wave, etc. We are most familiar with the Doppler effect because of our experiences with sound waves. Perhaps you recall an instance in which a police car or emergency vehicle was traveling towards you on the highway. As the car approached with its siren blasting, the pitch of the siren sound (a measure of the siren's frequency) was high; and then suddenly after the car passed by, the pitch of the siren sound was low. That was the Doppler effect - an apparent shift in frequency for a sound wave produced by a moving source.

The Doppler effect is of intense interest to astronomers who use the information about the shift in frequency of electromagnetic waves produced by moving stars in our galaxy and beyond in order to derive information about those stars and galaxies. The belief that the universe is expanding is based in part upon observations of electromagnetic waves emitted by stars in distant galaxies. Furthermore, specific information about stars within galaxies can be determined by application of the Doppler effect. Galaxies are clusters of stars that typically rotate about some center of mass point. Electromagnetic radiation emitted by such stars in a distant galaxy would appear to be shifted downward in frequency (a red shift) if the star is rotating in its cluster in a direction that is away from the Earth. On the other hand, there is an upward shift in frequency (a blue shift) of such observed radiation if the star is rotating in a direction that is towards the Earth.

reference http://www.kettering.edu/physics/drussell/Demos/doppler/doppler.html

f prime = f ( c + vobserver ) / ( c - vsource) for towards each other (approaching)
f prime = f ( c - vobserver ) / ( c + vsource) for moving away from each other (separating)
codes are:
frequencyemitted = 1/T;
if ((x-xe)*(v0-vobserver) >0){ // towards each other

frequencydetected = frequencyemitted*( v0+ vobserver)/( v0+ vs);
}
else {
frequencydetected = frequencyemitted*( v0- vobserver)/( v0- vs);
}
Or as in Wikipedia,
In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency f and emitted frequency f0 is given by:[3]

$f = \left( \frac{c \pm v_r}{c \mp v_{s}} \right) f_0 \,$

where
$c \;$ is the velocity of waves in the medium
$v_{r} \,$ is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source.
$v_{s} \,$ is the velocity of the source relative to the medium; positive if the source is moving away from the receiver.

Read the top signs to use when approaching and bottom signs when separating

Stationary Sound Source

 Stationary Sound Source

Stationary sound source produces sound waves at a constant frequency f, and the wave-fronts propagate symmetrically away from the source at a constant speed c (assuming speed of sound, c = 330 m/s), which is the speed of sound in the medium. The distance between wave-fronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source where f = f0.

Source moving with vsource = 0.7*vsound ( Mach 0.7 )

 Source moving with vsource = 0.7*vsound ( Mach 0.7 )

The same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving to the right with a speed vs = 0.7 c (Mach 0.7). The wave-fronts are produced with the same frequency as before. However, since the source is moving, the center of each new wavefront is now slightly displaced to the right. As a result, the wave-fronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source. An observer in front of the source will hear a higher frequency $f = \left( \frac{c + v_r}{c - v_{s}} \right) f_0 = 3.33f_0\,$, and an observer behind the source will hear a lower frequency $f = \left( \frac{c - v_r}{c + v_{s}} \right) f_0 = 0.59f_0\,$

Source moving with vsource = vsound ( Mach 1 , breaking the sound barrier )

 Source moving with vsource = vsound ( Mach 1 , breaking the sound barrier )

Now the source is moving at the speed of sound in the medium (vs = c, or Mach 1). assuming the speed of sound in air at sea level is about 330 m/s . The wave fronts in front of the source are now all bunched up at the same point. As a result, an observer in front of the source will detect nothing until the source arrives where $f = \left( \frac{c + v_r}{c - v_{s}} \right) f_0 = infinity Hz\,$. An observer behind of the source $f = \left( \frac{c - v_r}{c + v_{s}} \right) f_0 = 0.5f_0\,$. The pressure front will be quite intense (a shock wave), due to all the wavefronts adding together, and will not be percieved as a pitch but as a "thump" of sound as the pressure wall passes by. The figure at right shows a bullet travelling at Mach 1.01. You can see the shock wave front just ahead of the bullet.

 US Navy Photo F/A-18 Hornet passing through the sound barrier. Navy Ensign John Gay made this phenomenal photograph on July 7, 1999 while aboard the carrier USS Constallation as Navy Lt. Ron Candiloro flew by. An MPEG movie of the flyby is also available. http://www.kettering.edu/physics/drussell/Demos/doppler/mach1.html

Jet pilots flying at Mach 1 report that there is a noticeable "wall" or "barrier" which must be penetrated before achieving supersonic speeds. This "wall" is due to the intense pressure front, and flying within this pressure front produces a very turbulent and bouncy ride. Chuck Yeager was the first person to break the sound barrier when he flew faster than the speed of sound in the X-1 rocket-powered aircraft on October 14, 1947. Check out the movie The Right Stuff for more about this significant milestone, and the beginnings of the US space project. The figure at right shows a n F-18 at the exact instant it goes supersonic. Click on the figure to see more information and a MPEG movie of this event.

Source moving with vsource = 1.4*vsound (Mach 1.4 , supersonic)

 Source moving with vsource = 1.4*vsound (Mach 1.4 , supersonic)

The sound source has now broken through the sound speed barrier, and is traveling at 1.4 times the speed of sound, c (Mach 1.4). Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer actually hears the sound it creates. As a result, an observer in front of the source will detect $f = \left( \frac{c + v_r}{c - v_{s}} \right) f_0 = infinity Hz\,$ and an observer behind the source $f = \left( \frac{c - v_r}{c + v_{s}} \right) f_0 = 0.42f_0\,$.

As you watch the animation, notice the clear formation of the Mach cone, the angle of which depends on the ratio of source speed to sound speed. It is this intense pressure front on the Mach cone that causes the shock wave known as a sonic boom as a supersonic aircraft passes overhead. The shock wave advances at the speed of sound v, and since it is built up from all of the combined wave fronts, the sound heard by an observer will be quite intense. A supersonic aircraft usually produces two sonic booms, one from the aircraft's nose and the other from its tail, resulting in a double thump.

 bullet traveling at Mach 2.45. http://www.kettering.edu/physics/drussell/Demos/doppler/bullet-3.gif

The figure at right shows a bullet traveling at Mach 2.45. The mach cone and shock wave-fronts are very noticeable.

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