Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This work is motivated by the recent experiments of two reacting fluids in a Hele-Shaw cell (Podgorski etźal., 2007) and associated linear stability analysis of a curvature akening model (He etźal., 2012). Unlike the classical Hele-Shaw problem posed for moving interfaces with surface tension, the curvature akening model is concerned with a newly-produced gel-like phase that stiffens the interface, thus the interface is modeled as an elastic membrane with curvature dependent rigidity that reflects geometrically induced breaking of intermolecular bonds. Here  are interested in exploring the long-time interface dynamics in the nonlinear regime.  perform simulations using a spectrally accurate boundary integral method, together with a rescaling scheme to dramatically speed up the intrinsically slow evolution of the interface.  find curvature akening inhibits tip-splitting and promotes side-branching morphology. At long times, numerical results reveal that there exist nonlinear, stable, self-similarly evolving morphologies.
['Meng Zhao', 'Andrew Belmonte', 'Shuwang Li', 'Xiaofan Li', 'John S. Lowengrub']
I am writing a research paper on a idea Nonlinear simulations of elastic fingering in a Hele-Shaw cell
[{"from": "human", "value": "I am writing a research paper on a idea Nonlinear simulations of elastic fingering in a Hele-Shaw cell"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: This work is motivated by the recent experiments of two reacting fluids in a Hele-Shaw cell (Podgorski et\u017aal., 2007) and associated linear stability analysis of a curvature akening model (He et\u017aal., 2012). Unlike the classical Hele-Shaw problem posed for moving interfaces with surface tension, the curvature akening model is concerned with a newly-produced gel-like phase that stiffens the interface, thus the interface is modeled as an elastic membrane with curvature dependent rigidity that reflects geometrically induced breaking of intermolecular bonds. Here  are interested in exploring the long-time interface dynamics in the nonlinear regime.  perform simulations using a spectrally accurate boundary integral method, together with a rescaling scheme to dramatically speed up the intrinsically slow evolution of the interface.  find curvature akening inhibits tip-splitting and promotes side-branching morphology. At long times, numerical results reveal that there exist nonlinear, stable, self-similarly evolving morphologies."}]