Path Selection of Growing Networks in a Poisson Field
We study the evolution of network in a Poisson field and the dynamics of a growing channel. We develop a theory that defines the direction of the growth of a stream based on the flux field in the vicinity of the channel head. By reconstructing the past of the seepage network in Florida, we provide a growth law that ties the water flux into a channel to an erosion process and to the propagation velocity of a channel.
Y. Cohen and D. H. Rothman, Path Selection in a Poisson Field, Journal of Statistical Physics, 2016.
Y. Cohen, O. Devauchelle, H. F. Seybold, R. S. Yi, P. Szymczak and D. H. Rothman, Path selection in the growth of rivers, PNAS 112 (46), 14132 (2015).
CO2 sequestration is important for mitigating climate change and reducing atmospheric CO2 concentration. However, a complete physical picture able to predict both the pattern formation and the structure developing within the porous medium is lacking. We propose a theoretical model that couples transport, reaction, and the intricate geometry of the rock, in order to study the long time evolution of carbon in the brine-rock environment.
Y. Cohen and D. H. Rothman, Mechanisms for mechanical trapping of geologically sequestered CO2, Proceedings of the Royal Society A 471, (2175).
We investigate the crack formation in thin elastic layers attached to a substrate. We show that small variations in the volume contraction and substrate restraint can produce widely different crack patterns ranging from spirals to complex hierarchical networks.
Y. Cohen, J. Mathiesen and I. Procaccia, Drying patterns: Sensitivity to residual stresses, Physical Review E 79, 046109 (2009).
Tearing of a thin sheet might be one of the simplest act that is done on a daily basis. Nevertheless, the shape of the torn sheet remains elusive and is not well understood.
Here, we study how a crack is developed when a thin sheet is subjected to out-of-plane load. We show that the stress in the vicinity of the crack tip reveals higher singularity than in the standard mode III crack. We provide a criterion for a path selection that defines the shape and the trajectory of the crack.
Y. Cohen and I. Procaccia, Dynamics of cracks in torn thin sheets, Physical Review E 81, 066103 (2010).
Y. Cohen and I. Procaccia, Stress Intensity Factor of mode III cracks in thin sheets, Physical Review E 83, 026106 (2011).
Relaxation Processes in an Amorphous Solid
The properties of an amorphous solid, i.e. glasses materials, are highly dependent on their atomic structure and their chemical bonding. Thus, these properties can not be explained in the framework of continuum mechanics. Modern statistical mechanics approaches provide good theories for the advanced liquid state and amorphous solids. These theories aim to explain the poorly understood problems of glasses materials and its underlying physics.
By means of computer simulations we investigate the current assumptions and the basic physical properties of amorphous systems. In particular, we study relaxation mechanisms and explain the cooperative nature of the secondary peak in the loss modulus, also known as β relaxation.
Y. Cohen, S. Karmakar, I. Procaccia and K. Samwer, The Nature of the β-peak in the Loss Modulus of Amorphous Solids, Europhysics Letters 100, 36003 (2012).
Y. Cohen and I. Procaccia, Elastic Moduli in Nano-Size Samples of Amorphous Solids: System Size Dependence, Europhysics Letter 99, 46002 (2012).