text:
## Getting started

I happened to have lots of plots to do with slight variations, so I made a function to make my life easier.

This function, in particular, serves to compare 2 or more experimental groups (although it will still plot with 1 group). We use violin plots instead of bar plots because they provide more information for the same space (precisely, the distribution density/frequency of responses, which allows you to visually estimate normality, skewness, and kurtosis).

Let’s first load the demo data. This data set comes with base R (meaning you have it too and can directly type this command into your R console).

data("ToothGrowth")
head(ToothGrowth)
##    len supp dose
## 1  4.2   VC  0.5
## 2 11.5   VC  0.5
## 3  7.3   VC  0.5
## 4  5.8   VC  0.5
## 5  6.4   VC  0.5
## 6 10.0   VC  0.5

Load the rempsyc package:

library(rempsyc)

Note: If you haven’t installed this package yet, you will need to install it via the following command: devtools::install_github("rempsyc/rempsyc"). Package devtools is necessary for this command. If you haven’t installed devtools yet, install it via install.packages("devtools").

nice_violin(data = ToothGrowth,
group = "dose",
response = "len")

Dots  = Means
Error bars = 95% bootstrapped confidence Intervals (2000 replications)
Width = Distribution Density (Frequency)

### Basic idea

This is cool because it gives you a 95% bootstrapped confidence interval (with 2000 bootstraps), as shown by the error bars. Bootstrapping is a non-parametric technique, meaning that it does not need to respect the classical parametric assumptions (normality, homoscedasticity, etc.). In this case it’s just a nice alternative way to look at your data.

Note: bootstrapping requires a number of bootstraps equal or higher than your number of observations (rows). Because people sometimes work with big datasets, I’ve added an option to specify a specific number of bootstraps with the option bootstraps = 2000 (change default to your desired value). But because I’ve recently had to work with a very large data set (7 million observations), it was impractical to do 7 million bootstraps (that would have been a very, very long operation), so I also added an option to turn bootstrapping off completely and just use a regular confidence interval instead; just add boot = FALSE as one of the argument.

### Save a high-resolution image file to specified directory
ggsave('nice_violinplothere.tiff', width = 7, height = 7, unit = 'in', dpi = 300,
path = "D:/R treasures/")
# Change the path to where you would like to save it.
# If you copy-paste your path name, remember to use "R" slashes ('/' rather than '\').
# Also remember to specify the .tiff extension of the file.

Pro tip: Change .tiff for .pdf or .eps for scalable vector graphics for high-resolution submissions to scientific journals!

## Customization

### Change x- and y- axes labels

nice_violin(data = ToothGrowth,
group = "dose",
response = "len",
ytitle = "Length of Tooth",
xtitle = "Vitamin C Dosage")

### See difference between two groups

To see if two groups are statistically significantly different.

nice_violin(data = ToothGrowth,
group = "dose",
response = "len",
comp1 = "0.5",
comp2 = "2")

### See difference between two other groups

You can also select groups based on their position on the x-axis (notice no quotes this time).

nice_violin(data = ToothGrowth,
group = "dose",
response = "len",
comp1 = 2,
comp2 = 3)

### Compare all three groups

What if you want to look at all three groups at the same time? Unfortunately, the underlying package we use, ggsignif, does not allow the comparison of more than one group at once. So we need to tweak this manually instead. (Note that we can also use this technique when the significance computed with ggsignif does not correspond to the number of stars we want to use, for example if we use a different p-value or not a t-test.)

nice_violin(data = ToothGrowth,
group = "dose",
response = "len",
signif_annotation = c("*","**","***"), # manually enter the number of stars
signif_yposition = c(30,35,40), # What height (y) should the stars appear?
signif_xmin = c(1,2,1), # Where should the left-sided brackets start (x)?
signif_xmax = c(2,3,3)) # Where should the right-sided brackets end (x)?

### Include effect size (Cohen’s d)

nice_violin(data = mtcars,
group = "am",
response = "mpg",
comp1 = 1,
comp2 = 2,
has.d = TRUE)

### Set the colours manually

nice_violin(data = ToothGrowth,
group = "dose",
response = "len",
colours = c("darkseagreen","cadetblue","darkslateblue"))

### Changing the names of the x-axis labels

nice_violin(data = ToothGrowth,
group = "dose",
response = "len",
xlabels = c("Low", "Medium", "High"))

### Removing the x-axis or y-axis titles

nice_violin(data = ToothGrowth,
group = "dose",
response = "len",
ytitle = NULL,
xtitle = NULL)

### Removing the x-axis or y-axis labels (for whatever purpose)

nice_violin(data = ToothGrowth,
group = "dose",
response = "len",
has.ylabels = FALSE,
has.xlabels = FALSE)

### Set y-scale manually

nice_violin(data = ToothGrowth,
group = "dose",
response = "len",
ymin = 5,
ymax = 35,
yby = 5)

ToothGrowth$six.groups <- sample(1:6, 60, replace=T) nice_violin(data = ToothGrowth, group = "six.groups", response = "len") Pro tip: Save figure with greater width when you have more groups! ### Plotting individual observations nice_violin(data = ToothGrowth, group = "dose", response = "len", obs = TRUE) ### Micro-Customizations It is also possible to do several minor adjustments: (a) adjust the width of the caps (legs) of the confidence intervals with the CIcap.width argument (set it to 0 to get rid of them); (b) define the level of transparency with the alpha argument (1 is no transparency), (c) define the colour of the violins’ borders with the border.colour argument (default is white which is the equivalent of no borders). nice_violin(data = ToothGrowth, group = "dose", response = "len", CIcap.width = 0, alpha = .70, border.colour = "white", border.size = 1) ### Putting it all together If you’d like to see all available options at once (a bit long): nice_violin(data = ToothGrowth, group = "dose", response = "len", ytitle = "Length of Tooth", xtitle = "Vitamin C Dosage", colours = c("darkseagreen", "cadetblue", "darkslateblue"), has.ylabels = TRUE, has.xlabels = TRUE, xlabels = c("Low", "Medium", "High"), ymin = 0, ymax = 45, yby = 15, signif_annotation = c("*","NS","***"), signif_yposition = c(30,36,41), signif_xmin = c(1,2,1), signif_xmax = c(2,3,3), CIcap.width = 0, alpha = 0.5, border.colour = "black", border.size = 1, obs = TRUE, has.d = TRUE, d.x = 1.7, d.y = 20) ## Special situation: Add other plot elements The good thing about this function is that it outputs a ggplot object, which you can continue to use to build on your plot and customize it further. For instance, I recently wanted to add mean and sample size as annotations for each group (where I had group sample sizes ranging from 100 to 35,000, so it was important to know which groups were more representative). For the demonstration, let’s just build the same multiple-groups plot we did earlier. # Create our group variable: ToothGrowth$groups <- factor(sample(1:6,60, replace=T))

# Make the plot and save it to object "p"
p <- nice_violin(data = ToothGrowth,
group = "groups",
response = "len",
border.size = 1)

Then what I did is that I simply added conventional ggplot code to my plot object. (But first I had to compute the statistics we were going to be using:)

# Compute basic statistics and save to object
library(psych) # Install the psych package if you don't already have it
statsSummary <- describeBy(x = ToothGrowth$len, group = ToothGrowth$groups, mat = TRUE)

x=1:length(levels(ToothGrowth$groups)), # Specifies annotations is for all groups/x-axis ticks y=statsSummary$mean+2, # Puts mean at mean value on the y-axis (adds 2)
label=paste0("m=", round(statsSummary$mean,2))) + # That prints the mean on the plot annotate(geom="text", # (Second annotation adds the sample size) x=1:length(levels(ToothGrowth$groups)),
y=statsSummary$mean-2, # Puts sample size at mean value on the y-axis (substracts 2) label=paste0("n=", round(statsSummary$n,2))) # That prints the sample size on the plot


text:
# American Institute of Mathematical Sciences

September  2016, 36(9): 4619-4635. doi: 10.3934/dcds.2016001

## Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology

 1 GeoDynApp - ECSING Group, Spain 2 Institut de Recherche Mathématiques de Rennes, Université de Rennes 1, F-35042 Rennes, France 3 Instituto de Matemática y Estadística Rafael Laguardia, Facultad de Ingeniería, Universidad de la República, J. Herrera y Reissig 565, C.P. 11300 Montevideo 4 Universidad Nacional Autónoma de México, Apartado Postal 273, Admon. de correos #3, C.P. 62251 Cuernavaca, Morelos

Received  June 2015 Revised  March 2016 Published  May 2016

We consider a minimal compact lamination by hyperbolic surfaces. We prove that if no leaf is simply connected, then the horocycle flow on its unitary tangent bundle is minimal.
Citation: Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky. Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4619-4635. doi: 10.3934/dcds.2016001
##### References:

show all references

##### References:
 [1] Matilde Martínez, Shigenori Matsumoto, Alberto Verjovsky. Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem. Journal of Modern Dynamics, 2016, 10: 113-134. doi: 10.3934/jmd.2016.10.113 [2] Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky. Corrigendum to "Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology". Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4585-4586. doi: 10.3934/dcds.2017196 [3] Francois Ledrappier and Omri Sarig. Invariant measures for the horocycle flow on periodic hyperbolic surfaces. Electronic Research Announcements, 2005, 11: 89-94. [4] Katrin Gelfert. Non-hyperbolic behavior of geodesic flows of rank 1 surfaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 521-551. doi: 10.3934/dcds.2019022 [5] François Ledrappier, Omri Sarig. Fluctuations of ergodic sums for horocycle flows on $\Z^d$--covers of finite volume surfaces. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 247-325. doi: 10.3934/dcds.2008.22.247 [6] David Ralston, Serge Troubetzkoy. Ergodic infinite group extensions of geodesic flows on translation surfaces. Journal of Modern Dynamics, 2012, 6 (4) : 477-497. doi: 10.3934/jmd.2012.6.477 [7] Alfonso Artigue. Expansive flows of surfaces. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 505-525. doi: 10.3934/dcds.2013.33.505 [8] José Ginés Espín Buendía, Daniel Peralta-salas, Gabriel Soler López. Existence of minimal flows on nonorientable surfaces. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4191-4211. doi: 10.3934/dcds.2017178 [9] Pascal Hubert, Gabriela Schmithüsen. Infinite translation surfaces with infinitely generated Veech groups. Journal of Modern Dynamics, 2010, 4 (4) : 715-732. doi: 10.3934/jmd.2010.4.715 [10] Jan Philipp Schröder. Ergodicity and topological entropy of geodesic flows on surfaces. Journal of Modern Dynamics, 2015, 9: 147-167. doi: 10.3934/jmd.2015.9.147 [11] Dmitri Scheglov. Absence of mixing for smooth flows on genus two surfaces. Journal of Modern Dynamics, 2009, 3 (1) : 13-34. doi: 10.3934/jmd.2009.3.13 [12] Keith Burns, Katrin Gelfert. Lyapunov spectrum for geodesic flows of rank 1 surfaces. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 1841-1872. doi: 10.3934/dcds.2014.34.1841 [13] Luis Barreira, Christian Wolf. Dimension and ergodic decompositions for hyperbolic flows. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 201-212. doi: 10.3934/dcds.2007.17.201 [14] Alexander I. Bufetov. Hölder cocycles and ergodic integrals for translation flows on flat surfaces. Electronic Research Announcements, 2010, 17: 34-42. doi: 10.3934/era.2010.17.34 [15] Vladislav Kruglov, Dmitry Malyshev, Olga Pochinka. Topological classification of $Ω$-stable flows on surfaces by means of effectively distinguishable multigraphs. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4305-4327. doi: 10.3934/dcds.2018188 [16] Giovanni Forni. The cohomological equation for area-preserving flows on compact surfaces. Electronic Research Announcements, 1995, 1: 114-123. [17] Carlos Arnoldo Morales. A note on periodic orbits for singular-hyperbolic flows. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 615-619. doi: 10.3934/dcds.2004.11.615 [18] Shucheng Yu. Logarithm laws for unipotent flows on hyperbolic manifolds. Journal of Modern Dynamics, 2017, 11: 447-476. doi: 10.3934/jmd.2017018 [19] Zhiping Li, Yunhua Zhou. Quasi-shadowing for partially hyperbolic flows. Discrete & Continuous Dynamical Systems - A, 2020, 40 (4) : 2089-2103. doi: 10.3934/dcds.2020107 [20] Giovanni Forni, Corinna Ulcigrai. Time-changes of horocycle flows. Journal of Modern Dynamics, 2012, 6 (2) : 251-273. doi: 10.3934/jmd.2012.6.251

2018 Impact Factor: 1.143

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text:
## The Annals of Statistics

### A Bayesian Nonparametric Approach to Reliability

#### Abstract

It is suggested that problems in a reliability context may be handled by a Bayesian nonparametric approach. A stochastic process is defined whose sample paths may be assumed to be increasing hazard rates by properly choosing the parameter functions of the process. The posterior distribution of the hazard rates is derived for both exact and censored data. Bayes estimates of hazard rates and $\operatorname{cdf's}$ are found under squared error type loss functions. Some simulation is done and estimates graphed to better understand the estimators. Finally, estimates of the hazard rate from some data in a paper by Kaplan and Meier are constructed.

#### Article information

Source
Ann. Statist., Volume 9, Number 2 (1981), 356-367.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345401

Digital Object Identifier
doi:10.1214/aos/1176345401

Mathematical Reviews number (MathSciNet)
MR606619

Zentralblatt MATH identifier
0469.62077

JSTOR


text:
# Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Antoine Tilloy1,2 and Howard M. Wiseman3

1Max-Planck-Institut für Quantenoptik, Garching, Germany
2Munich Center for Quantum Science and Technology (MCQST), Munich, Germany
3Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia

### Abstract

Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function ($e.g.$ mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between true' (Markovian) collapse models and non-Markovian models.

Spontaneous collapse models and Bohmian mechanics are two very different, and at first sight unrelated, physical theories that aim to solve the quantum measurement problem. Collapse models add a noisy non-linear term to the Schrödinger equation to cause the wave function of macroscopic objects to evolve into classical-like states. Bohmian mechanics retains the Schrödinger equation but adds real particles in 3D space, grounding macroscopic classicality in microscopic reality. Each particle is guided by its own wavefunction in 3D space, but each of these is a “conditional wavefunction” –– the global wavefunction evaluated by substituting in the Bohmian value for the position of every other particle.
Unlike Bohmian mechanics, collapse models modify the predictions of orthodox quantum mechanics. To avoid predictions that have already been empirically ruled out, non-Markovian collapse models (NMCMs), with smooth-in-time noise, have been proposed. However, such NMCMs are mathematically challenging to derive and simulate.
In this paper we show that NMCMs can be easily derived and understood within a Bohmian framework, as follows. In standard NMCMs, one adds to the system an auxiliary quantum bath in order to construct the system collapse dynamics, so that averaging over the noise is the same as tracing over that ‘non-physical’ bath. Here we introduce Bohmian variables for this auxiliary bath only, with standard Bohmian dynamics. Then the “conditional wavefunction” for the system, conditioned on those auxiliary Bohmian variables, reproduces exactly the NMCM.
Our work explains complicated stochastic non-Markovian dynamics in terms of simple deterministic Markovian dynamics of a larger system with hidden variables. This suggests that to take NMCMs seriously one should take seriously the auxiliary bath as a physical system, as well as its Bohmian variables.

### ► References

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[38] L. Diósi, N. Gisin, and W. T. Strunz. Non-markovian quantum state diffusion. Phys. Rev. A, 58: 1699–1712, Sep 1998. 10.1103/PhysRevA.58.1699.
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[39] Jay Gambetta and H. M. Wiseman. Non-markovian stochastic schrödinger equations: Generalization to real-valued noise using quantum-measurement theory. Phys. Rev. A, 66: 012108, Jul 2002. 10.1103/PhysRevA.66.012108.
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[40] Jay Gambetta and H. M. Wiseman. Modal dynamics for positive operator measures. Found. Phys., 34 (3): 419–448, Mar 2004. ISSN 1572-9516. 10.1023/B:FOOP.0000019622.81881.f8.
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[41] Jay Gambetta and Howard Wiseman. A non-markovian stochastic schrodinger equation developed from a hidden variable interpretation. Proceedings of SPIE - The International Society for Optical Engineering, 5111, 05 2003b. 10.1117/12.496938.
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[42] J. Gambetta and H. M. Wiseman. Interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory. Phys. Rev. A, 68 (6): 062104, Dec 2003c. 10.1103/PhysRevA.68.062104.
https://doi.org/10.1103/PhysRevA.68.062104

[43] A. Tilloy. Interacting quantum field theories as relativistic statistical field theories of local beables. arXiv:1702.06325, 2017. URL https://arxiv.org/abs/1702.06325.
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[44] W Struyve and H Westman. A minimalist pilot-wave model for quantum electrodynamics. Proc. R. Soc. A., 463 (2088): 3115–3129, 2007. 10.1098/rspa.2007.0144.
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[45] Maximilian Schlosshauer. Quantum decoherence. Physics Reports, 831: 1–57, 2019. ISSN 0370-1573. 10.1016/j.physrep.2019.10.001.
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[48] Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde, and Howard M. Wiseman. A strong no-go theorem on the wigner's friend paradox. Nature Physics, 2020. 10.1038/s41567-020-0990-x.
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[54] A Sudbery. Objective interpretations of quantum mechanics and the possibility of a deterministic limit. J. Phys. A: Math. Gen., 20 (7): 1743, 1987. 10.1088/0305-4470/20/7/020.
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[58] J Butterfield and B Marsh. Non-locality and quasiclassical reality in kent’s formulation of relativistic quantum theory. Journal of Physics: Conference Series, 1275: 012002, Sep 2019. ISSN 1742-6596. 10.1088/1742-6596/1275/1/012002.
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[59] E. A. Novikov. Functionals and the random-force method in turbulence theory. JETP, 20: 5, 1965. URL http://www.jetp.ac.ru/cgi-bin/dn/e_020_05_1290.pdf.
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[60] M. Bell, K. Gottfried, and M. Veltman, editors. John S. Bell on the Foundations of Quantum Mechanics. World Scientific, Singapore, 2001.

### Cited by

[1] Franck Laloë, "Gravitational quantum collapse in dilute systems", Comptes Rendus. Physique 23 G1, 27 (2022).

[2] Guillermo Albareda, Kevin Lively, Shunsuke A. Sato, Aaron Kelly, and Angel Rubio, "Conditional Wave Function Theory: A Unified Treatment of Molecular Structure and Nonadiabatic Dynamics", Journal of Chemical Theory and Computation 17 12, 7321 (2021).

[3] Guillermo Albareda, Kevin Lively, Shunsuke A. Sato, Aaron Kelly, and Angel Rubio, "Conditional wavefunction theory: a unified treatment of molecular structure and nonadiabatic dynamics", arXiv:2107.01094, (2021).

The above citations are from Crossref's cited-by service (last updated successfully 2023-03-20 09:37:21) and SAO/NASA ADS (last updated successfully 2023-03-20 09:37:22). The list may be incomplete as not all publishers provide suitable and complete citation data.


text:
Next Meeting: April 21: Google Glass Next Installfest: TBD Latest News: Mar. 18: Google Glass at LUGOD's April meeting Page last updated: 2001 Dec 30 17:09
 The following is an archive of a post made to our 'vox-tech mailing list' by one of its subscribers. Report this post as spam: (Enter your email address)
[vox-tech] Re: [vox] forget my previous post
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# [vox-tech] Re: [vox] forget my previous post

begin: Sam Peterson <skpeterson@ucdavis.edu> quote
>
> I'm leaving the case open from now on and that seems to have me running
> around 55 degrees or so,

sam i don't know about the truth of this statement, but i've been told that
your machine is better off with the case on.  this is because it makes the
fans work better -- air flow is faster through a restricted opening (this is
called the venturi effect by physicists.  basically,

\rho v A = constant

where \rho is the density of the fluid (air), v is the speed of the air's
flow lines and A is the cross section area of the opening that the fluid is
going through.  so make A smaller, and v has to increase.  faster air flow
through the computer.

that being said, out of the 4 computer that are in this room, the two hottest
ones have no case on.  :)   like i said, this is just what i've been told.  i
can't say if it's true or not.  it sounds good, though.  :)

> Thanks for the advice everyone!!  Lordy, I probably should have moved this
> over to vox-tech.  Ah well.

someone might have the same question a month or even a year later.  by being
in the vox-tech archives, you're helping them solve the same problems you're
experiencing now.  nobody will (should?) go to the vox archives to solve a
technical problem.

pete

ps- i have the "coolermeister" fan.  it's fairly loud, but is the biggest,
baddest fan i've ever seen.

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text:
$$\require{cancel}$$

# 10: Numerical Integration of ODEs

This article describes the numerical methods for solving the initial-value problem, which is a standard type of problem appearing in many fields of physics. Suppose we have a system whose state at time $$t$$ is described by a vector $$\vec{y}(t)$$, which obeys the first-order ordinary differential equation (ODE) for the form:

$\frac{d\vec{y}}{dt} = \vec{F}\Big(\vec{y}(t), t\Big).$

Here, $$\vec{F}$$ is some given vector-valued function, whose inputs are (i) the instantaneous state $$\vec{y}(t)$$ and (ii) the current time $$t$$. Then, given an initial time $$t_{0}$$ and an initial state $$\vec{y}(t_0)$$, the goal is to find $$\vec{y}(t)$$ for subsequent times.

Conceptually, the initial value problem is distinct from the problem of solving an ODE discussed in the article on finite-difference equations. There, we were given a pair of boundaries with certain boundary conditions, and the goal was to find the solution between the two boundaries. In this case, we are given the state at an initial time $$t_{0}$$, and our goal is to find $$\vec{y}(t)$$ for some set of future times $$t > t_0$$. This is sometimes referred to as "integrating" the ODE, because the solution has the form

$\vec{y}(t) = \vec{y}(t_0)\, +\, \int^t_{t_0} dt' \;\vec{F}\Big(\vec{y}(t'), t'\Big).$

However, unlike ordinary numerical integration (i.e., the computing of a definite integral), the value of the integrand is not known in advance, because of the dependence of $$\vec{F}$$ on the unknown $$\vec{y}(t)$$.

This page titled 10: Numerical Integration of ODEs is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Y. D. Chong via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.


text:
# Focus: Gravity Makes the Universe Classical

Published July 12, 2013  |  Physics 6, 78 (2013)  |  DOI: 10.1103/Physics.6.78

#### Effective Field Theory Approach to Gravitationally Induced Decoherence

M. P. Blencowe

Published July 12, 2013

The Universe may have begun as a quantum event, but astrophysical and terrestrial phenomena today are distinctly classical in nature, with no hint of quantum indefiniteness. The ultimate reason, a new report in Physical Review Letters suggests, may be a tiny but ubiquitous background of gravitational waves left over from the big bang. These waves randomly disturb quantum states everywhere enough to ensure that real-life Schrödinger’s cats are never seen.

Quantum mechanics allows the existence of the strange states known as superpositions, in which, say, an electron can be both spin up and spin down at the same time. While single particle superpositions can be fairly stable, theorists have wondered why larger objects never seem to appear in such states, exemplified by Erwin Schrödinger’s famous half-alive, half-dead cat. Many theorists now believe that macroscopic superpositions, in which numerous quantum components must maintain a precise relationship with each other, are disrupted by continual environmental influences. Such disturbances, acting differently on each component of a superposition, “decohere” it into a classical state that is, say, dead or alive, but not both. Even a system as small as an atom requires extraordinary protection from stray electromagnetic fields in the lab to remain in a superposition.

Since gravitational fields are both pervasive and inescapable, researchers have proposed that they play a fundamental role in ensuring that macroscopic systems behave in a classical way. Miles Blencowe of Dartmouth College in Hanover, New Hampshire, has now calculated the decoherence caused by the cosmic background of gravitational radiation, small ripples in spacetime representing “echoes” of the big bang. This background is a cousin to the more familiar cosmic microwave background but is thought to be at a slightly lower temperature of about $1$ kelvin. Although these gravitational waves would rarely be the largest environmental influence on an object, Blencowe wanted to see whether they alone would guarantee that macroscopic quantum superpositions would never be seen in the wild.

A gravitational wave represents a disturbance in space and time that, as it travels across a superposition, can push its components out of sync. To get a sense of the size of such effects, Blencowe studied a simple model of an object that could be placed in a superposition. He theoretically constructed an atomic-scale blob of mass and energy consisting of an arrangement of a fictitious field. He then imagined this blob prepared in a superposition of a ground state and an excited state separated by one electron volt (eV) in energy and estimated how quickly gravitational background radiation would upset it. The answer: not quickly at all. It would take about ${10}^{45}$ seconds, or ${10}^{28}$ times the age of the Universe, for such a superposition to decohere.

This result isn’t surprising because the interaction of weak gravitational waves with a small object like an atom is tiny. But Blencowe showed that the decoherence rate rises with the square of the energy difference between two states in a superposition. For a larger object, equivalent to Avogadro’s number of atoms prepared in an overall superposition, that difference would be $6$ x ${10}^{23}$ eV, and the decoherence time would fall to about $0.01$ seconds.

In inflationary models of cosmology, the gravitational radiation background is likely to be more complicated than the simple form assumed by Blencowe, says Claus Kiefer of the University of Cologne, Germany. Still, he says, whatever gravitational radiation exists would lead to decoherence in the way Blencowe describes. The new result is “certainly interesting because it shows the ubiquitous action of decoherence,” says Kiefer.

–David Lindley

David Lindley is a freelance writer in Alexandria, Virginia, and author of Uncertainty: Einstein, Heisenberg, Bohr and the Struggle for the Soul of Science (Doubleday, 2007).


text:
Computing normals for an arbitrary triangle mesh

Overview

In Light Source we took advantage of the a priori knowledge that our mesh was a sphere when it came time to compute our normal vectors. Now at the time that was a convient approximation to make, however it won’t always be an option. Moreover our mesh isn’t really a sphere, but a polygonal approximation to a sphere. In this article we’ll implement an algoithm to compute normals directly from the mesh data.

First let me clarify that there are actually 2 kinds of normals worth mentioning. Face normals are orthongal vectors to the faces of the mesh. Whereas vertex normals are orthongal to the vertices (what exactly that means will be discussed below). It turns out that in order to compute vertex normals we need the face normals, so we’ll discuss those first.

Face normals

Since we are dealing with triangle meshes our goal will be to find a vector $\vec{n}$ that is orthongal to the triangle face. Lets delve into that sentence. Triangles are typically represented as $3$ points, lets call them $A$, $B$, and $C$. No matter the orientation of the $3$ points one can always define a 2D plane the triangle “lives” in. Or put another way, given a triangle you can always build a 2D plane from it. So when we say we want a vector that is orthongal to the face of the triangle, it is equivalent to saying it should be orthongal to the plane defined by the triangle. Now our question becomes, how do we compute the normal to a 2D plane? At this point is becomes easier to stop thinking geometrically and start thinking vectorially (did I just make up a word? Yes I did).

The points $A$, $B$, and $C$ can exist anywhere in 3D space, and as such can be represented as vectors $\vec{A}$, $\vec{B}$, $\vec{C}$, in $\mathbb{R}^{3}$. Any coordinate system will do, so we might as well use the one the mesh was defined in.

What does this change of mental perspective buy us? Well now we can make use of the cross product. The cross product is an operator that acts on a pair of vectors to produce a new vector that is mutually orthogonal to the pair. So, if we happen to have $2$ vectors that live in the plane defined by the triangle, the the cross product of those $2$ vectors would have no choice but to be othongal to the plane itself. (Take a moment to think about this and try to imagine a way to be simultaniously orthogonal to both vectors and not point straight out of the plane. It should become apparent that it’s impossible). Well it just so happens we have $2$ such vectors. The vectors $\vec{B}-\vec{A}$ and $\vec{C}-\vec{A}$. There’s nothing special about the vector $\vec{A}$ in this context, we could have chosen $\vec{B}$ or $\vec{C}$ to be on the right side of the minus sign. Armed with these 2 vectors our normal vector becomes

$\vec{n} = (\vec{B} - \vec{A}) \times (\vec{C} - \vec{A})$

There are 2 things worth noting about $\vec{n}$. The first is that it is not the unique orthongal vector to the plane. If $\vec{n}$ is orthogonal than so is $-\vec{n}$. We must be careful of this because we want our normals to be outward facing. That is, we want to embed the orientation of the triangle into the normal vector. Meaning the normal vector will determine the “front” of the triangle so to speak. If you find that your mesh is being lit strangely, or not being rendered at all, it’s most likely that you’ve inverted your normals accidently.

The second thing worth mentioning is that $\vec{n}$ is not unit length. It’s length is proprtional to the area of the triangle. In most applications when we discuss normal vectors we assume that they have been normalized, since it only the direction we care about, not the length. However for what comes next it is useful to keep the length as is.

Vertex normals

Vertex normals are trickier to conceptualize but easier to compute than the face normals. If you imagine an isolated point in 3D space which direction would you say it is orthongal to? There is no correct answer because the question is ill-posed. Orthonality implies direction but a point has no direction assoicated with it. So how can we compute a vertex normal if that’s the case? If instead you imagine our lonely point as part of a surface $S$ then it becomes clear which direction the normal vector must point, away from $S$. So if we have local information about the surface our point is sampled from than we can use that information to compute the normal vector at the point. Imagined in this manner the normal vector is a function $\vec{n}(S,p)$ of both the surface and the point on the surface you are looking at.

Once we discretize our surface into a polygonal mesh it becomes clear then that we need to make use of the surrounding vertices and faces in order to approximate $\vec{n}(S,p)$. The easiest way to accomplish this is to average the face normals of the faces immediately surrounding the point. However an even better idea is a weighted sum, where faces with larger areas contribute more to the normal vector at the point. For a smoother varying approximation we could include faces further away from the point, but this also becomes less accurate as in the limit all the vertices have the same normal.

Model and Sphere

Naturally we will need to update Model to track both the face and vertex normals. We’ll be removing the normal matrix from the constructor of Sphere as we’ll be calculating them at runtime instead. You can find the code here and here.

Full algorithm

void Mesh::ComputeNormals()
{
int n_F = m_faces.rows();
int n_V = m_vertices.rows();
m_face_normals = List3df(n_F,3);
m_vertex_normals = List3df(n_V,3);
std::unordered_map<GLuint,Vector3Gf> vertex_normals;
for(int i=0; i < n_F; ++i)
{
GLuint a = m_faces(i,0);
GLuint b = m_faces(i,1);
GLuint c = m_faces(i,2);

Vector3Gf A = m_vertices.row(a);
Vector3Gf B = m_vertices.row(b);
Vector3Gf C = m_vertices.row(c);

Vector3Gf BA = B - A;
Vector3Gf CA = C - A;

Vector3Gf face_normal = BA.cross(CA);

if(vertex_normals.find(a) == vertex_normals.end())
{
vertex_normals[a] = face_normal;
}
else
{
vertex_normals[a] += face_normal;
}

if(vertex_normals.find(b) == vertex_normals.end())
{
vertex_normals[b] = face_normal;
}
else
{
vertex_normals[b] += face_normal;
}

if(vertex_normals.find(c) == vertex_normals.end())
{
vertex_normals[c] = face_normal;
}
else
{
vertex_normals[c] += face_normal;
}

face_normal.normalize();

m_face_normals.row(i) = face_normal.transpose();

}

for(auto iter = vertex_normals.begin(); iter != vertex_normals.end(); iter++)
{
Vector3Gf vertex_normal = iter->second;
vertex_normal.normalize();
m_vertex_normals.row(iter->first) = vertex_normal;
}
}

Results

Our sphere looks rather different doesn’t it? This is because of the way we build the sphere at runtime. If you’ll revisit the code you’ll notice that we recompute the same vertex multiple times but treat is as though it were a seperate entity.

As a result of this each vertex is in exactly $1$ face, meaning the vertex normals and the face normals are identical. I toyed around with the idea of rewriting the UVSphereMesh function so that it reuses vertices properly, but soon enough we’ll get around to implementing a proper model loading library. Then we can just grab a sphere mesh of the net.


text:
3- Nitrogen ( Expensive) 4- adding fly ash by % of cement. one of the following conditions occur for three consecutive days: The effect of concrete temperature and retardation of setting time is Experts agree that the best temperature to pour concrete is between 50-60 °F.The necessary chemical reactions that set and strengthen concrete slow significantly below 50 °F and are almost non-existent below 40 °F.Even when daytime temperatures are within the satisfactory range, winter concrete setting creates risks that could result in weak, inadequate concrete. The Does the temperature of concrete at the time of pouring it effect its strength in the long term? Hot weather is defined as any combination is high ambient The lowest temperature G. Daniel Fahrenheit was able to reach using a combination of salt, ice, and water was set as zero degrees F in his scale. given by PCA in the chart below. 0 0. bankster. Maximum Concrete Temperature. Fahrenheit, the most commonly used scale in America, was developed in the early 1700s and is the oldest of the three scales we still use. There are lots of solutions for the high temperature of concrete now the question is how to control temperature of fresh concrete or hardened concrete? Question: On a day when the temperature is 20.0 degrees Celsius, a concrete walk is poured in such a way that its ends are unable to move. The objective of the ACI 306 is to keep concrete warm, over 5 degrees Celsius, for the first 48 hours, where concrete strength development is critical. More retardation may take place if the admixture It is well known that concrete materials degrade at elevated temperatures. One degree C is the same size as one degree K except that zero is at a different value. The surface temperature is usually the most important to consider. There are three different scales frequently used to measure temperature. II, pp. The second oldest scale is the Kelvin scale, d… However, proper cold weather concrete curing will enhance concrete strength development. the dosage of retarder and concrete ambient temperature. 3. ASTM C 856, "Standard Practice for Petrographic Examination of Hardened Concrete," ASTM, West Conshohocken, Pa., 1998. Frozen fresh concrete during the first 24 hours can lead to 50% loss of its potential 28-day strength. The ideal temperature for pouring concrete is between 50 and 60 degrees Fahrenheit. After applying a sealer it goes through a chemical reaction that causes it to cure and form a film. After applying a sealer it goes through a chemical reaction that causes it to cure and form a film. Example. kassir, k.k. “Slow freezing rates can result in cryoconcentration. Temperatures for placement and protecting concrete in cold weather are established and mandated under ACI 306. The concrete temperature cannot drop more than 40° Fahrenheit in 24 hours. Temperature Time Factor (TTF) calculations and compressive strength results are used for estimating concrete strength gain using the maturity method as outlined in ASTM C 1074. The surface temperature is usually the most important to consider. As a result, the temperature of the mixture increases by 20–25 and more degrees Celsius. (1 and 2) and carboxylic (3 and 4) admixtures on setting time. 1 decade ago . When the air temperature is forecasted to fall below 5 degrees Celsius within 24 hours of placing concrete then special considerations apply for concrete construction. Compressive Strength of Concrete Cubes - Lab Test & Procedure The increased volume of gel reduces capillarity in solid and porous materials. To help you avoid structural issues and project delays, it is important … %PDF-1.4 %���� Does the temperature of concrete at the time of pouring it effect its strength in the long term? The wastes in many tanks are reported to have achieved a temperature range of 150-180°C (302-356°F) . 0000001262 00000 n If the temperature of the concrete during hydration is too high, the concrete will gain strength faster early on but consequently, lose strength in later stages and thus be less durable. is used. Accelerated setting time leading to earlier finishing of slabs and lower labour costs for contractors. Pouring concrete in weather conditions between 25 and 40 degrees Fahrenheit is possible with cold weather concrete placement techniques. The nano-sized colloid Calcium Silicate Hydrate (C-S-H) formation increased several times compared with conventional mixing. So the simple answer is SUN. Curing the Hoover Dam. velocity. This can be done more efficiently using a concrete temperature and maturity meter, such as SmartRock™. Maintain the concrete temperature above 40° degrees Fahrenheit for at least four more days after the use of the insulation blankets or heated enclosures. The hydration of Portland cement is like many other reactions. The temperature at the inside surface of the wall is 19.4 degrees Celsius. Yes. As a result, they do not have sufficient time to form their protective film effectively. How Concrete Works. Monitor the concrete curing temperature within the first 24 hours to ensure in-situ concrete temperatures do not drop more than 4° C (40° F). But concrete cured at high temperatures generally does not reach as high an ultimate strength. In cold weather concreting, concrete are produced at higher temperature. While undertaking a concrete placement work in colder days of winter, it is recommended that you clean the surface properly and ensure there is no snow, water droplets, dust or any other material present on the surface. Temperature monitoring can aid the user in keeping fresh and early-age concrete below project-specified maximum temperatures during curing. The ideal temperature for asphalt paving services is no less than 50 degrees F. . In some cases, the temperature can be as low of 40 degrees F, but for the best results, you’ll want the weather to be on the warmer side of the spectrum. References. The hydration of Portland cement is like many other reactions. The Celsius scale of the metric system is named after Swedish astronomer Anders Celsius (1701 - 1744). BS EN 206:2013 + A1:2016 Clause 5.2.9 Concrete temperature says the ready-mixed concrete as delivered should not be below 5C at the time of delivery. trailer rapid stiffening and slump loss occurs. Marie, Sakrete concrete mixes should be poured when the air, mix and substrate temperatures should be between 40°F (4°C) and 90°F (32°C) with no rain in the forecast within 24 hours of application. To control the temperature of fresh concrete use: 1- flaky ice up to70% of water as per ACI in some cases we can go upto100% in Makkah and madina we have done it. There is a difference between the temperature of the concrete and the temperature of the day. 0000008173 00000 n At an age of 1 day the 120°F concrete was strongest and the … Specific heat is measured in joules per kg per degree Celsius. When hot-weather concreting, a general rule of thumb is to maintain a limit of 70°C (160°F) for concrete curing temperature during hydration. Curing can therefore be achieved either through maintaining mixing water in the concrete during early hardening or by preventing moisture loss from the surface by sealing. People cool down in the fountains of the Trocadero gardens in Paris, Thursday July 25, 2019, when a new all-time high temperature of 42.6 degrees Celsius (108.7 F) hit the French capital. When temperatures are high, this can lead to cracks, and many mass concrete works use chilled water for the mixing process to control the temperature of the concrete and reduce the chances of cracking and damage. Assume that one kilowatt hour of electrical energy costs $0.10. 0000015468 00000 n g�ج��"d���`]�a�*]A�j��1I�e��) ��|�O\��L,�8w��X6. Along with this issue, high temperatures make applying sealer with a roller one sticky mess and even can leave lint from the roller head on the surface. The Celsius scale sets the freezing point and boiling point of water at $$0^\text{o} \text{C}$$ and $$100^\text{o} \text{C}$$ respectively. Several options are available to predict maximum concrete temperatures like PCA method. Temperature variations are not a major problem, provided the concrete temperature is maintained above 5 degrees Celsius. The Celsius Temperature Scale. Retardation of setting time is influenced by the type of admixtures The finished concrete should be insulated to retain heat from the exothermic hydration reaction of curing, and the concrete should be maintained at a temperature of at least 4.44 degrees Celsius. Hot weather is defined as any combination is high ambient temperature, high concrete temperature, low relative humidity, and wind velocity. It is concluded from the chart that the mixture of cement less than final set, generally stated as an empirical In the Celsius scale a change of one degree is equivalent to one Kelvin and 1.8 degrees Fahrenheit. Experts recommend use of heat preserving methods for … In this scale, 32°F is where water freezes and 212°F is where water boils, with a range of 180 degrees between the two. Concrete should be kept warm (around 50°F (10°C)) in order to cure properly. change in temperature is measured in degrees Celsius (°C) The word 'specific' in 'specific heat capacity' means per unit mass, usually per kilogram. 0000014427 00000 n 0000010270 00000 n The lower the ambient When temperature goes below 0 degree Celsius or minus 7 degree Celsius, it impacts concrete curing severely. Yes, the sun is responsible for the change or fluctuations in temperature of the Earth’s atmosphere. Your question is extremely hard to answer because there are so many influences that go into concrete and it's strength. is added as the last ingredient and the cement is wet. xref following figure is used to estimate initial setting time according to Typical values are between 80° and 95° F as measured by ASTM C 1064-86. Concrete should not be placed against any formwork or reinforcement covered in ice or snow. 1151–1160, Published by College of Engineering, Nihon University, Koriyama, Japan (1982). What Influences the Surface Temperature of Concrete? Dosage Effect on Retardation of Initial Setting Time. If you are feeling the atmosphere very warm, then the temperature is high and if you feel the atmosphere cool, then the temperature of the air is less. This admixture is sensitive to The ideal range of surface temperatures for the application of sealer on concrete is between 10-degrees Celsius and 32.2-degrees Celsius. The ideal temperature for pouring concrete is between 50 and 60 degrees Fahrenheit. Commonly used scales. This paper presents a relation between pavement temperature and wind, precipitation, air temperature, and solar radiation, as controlled by the thermal properties of the pavements. <<4d0e654f5c6664408a8af29eb4597b6d>]>> %%EOF Initial set, as defined by ACI 116R, is a degree of stiffening of a Rather than being a single block of concrete, … Cold weather period, as defined by ACI Committee 306, is when used. The temperature of the air, the humidity level, and the wind speed, the temperatures of the surface where you are placing the concrete, the water and the dry concrete in the bag all play a huge part and must be taken into consideration. J. Hristova: ‘Behaviour of Polyester Polymer Concrete at Tempe- rature upto 70°C’, Proceedings of the Third International Congress on Polymers in Concrete, May 13–18, 1981, Vol. 0000001460 00000 n Specific heat is the heat capacity of a material that it absorbs to raise the temperature by one degree Celsius. When there is no other option, adding a cement bag to the mix will help. Concrete temperature monitoring is critical to ensure the long-term strength and stability of concrete structures. Extends construction season further into the winter months. If we are to pour the concrete at 5°C, we need to produce the concrete more than 5°C. As Asaeda, Ca and Wake (1996) showed, during the day, the surface temperature of black-top concrete was less than asphalt, but at night it was reversed due to the amount of heat stored by the concrete material. These clauses are in section 7.1.2 of CSA A23.1/A23.2, Canadian Standard for Concrete Materials and Methods of Construction. Concrete placed & cured at a moderate temperature (15–25°C) will gain higher strength & durability than 35°C concrete. To control the temperature of fresh concrete use: 1- flaky ice up to70% of water as per ACI in some cases we can go upto100% in Makkah and madina we have done it. Temperature scales differ in two ways: the point chosen as zero degrees and the magnitudes of incremental units or degrees on the scale. When the air temperature is forecasted to fall below 5 degrees Celsius within 24 hours of placing concrete then special considerations apply for concrete construction. concrete, and moisture movements in any type of pavement. Concrete and it 's strength, West Conshohocken, Pa., 1998 should concrete... As one degree sparying cold water concrete at 5°C, we need to produce the concrete ’ surface! Like many other reactions to consider use of the concrete material, it impacts curing... A higher concrete temperature, low relative humidity, and wind velocity asphalt paving services is no other option adding! Nano-Sized colloid Calcium Silicate Hydrate ( C-S-H ) formation increased several times compared with mixing... Moisture content of the day example, limestone aggregates turn pink when they reach about 570º,. 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Temperature can have a detrimental effect to concrete strength development different strengths and additives can be more! For common temperature measurements in most of the day its strength in the air temperature the... Monitoring is critical to ensure the long-term strength and stability of concrete sealers is poured different strengths and can! Provided the concrete material, it is poured different strengths and additives can be done efficiently! Chemical reaction that causes it to cure properly temperature ( 15–25°C ) will higher... Applying sealers to decorative concrete 20°C or may be more higher temp should not be against. Degrees and the … Effects of temperature on concrete the curing rate of concrete, and velocity... It can melt at different temperatures the following figure is used to measure temperature the degree hotness... To predict maximum concrete temperatures like PCA method heat increases with an increase in moisture content of concrete. 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