Related papers: Computational Complexity of Determining the Barrie…
We consider two (2D) and three (3D) dimensional granular systems exposed to compression, and ask what is the influence of the number of physical dimensions on the properties of the interaction networks that spontaneously form as these…
We have previously studied properties of a one-dimensional potential with $N$ equally spaced identical barriers in a (fixed) finite interval for both finite and infinite $N$. It was observed that scattering and spectral properties depend…
Quantifying stochastic processes is essential to understand many natural phenomena, particularly in biology, including cell-fate decision in developmental processes as well as genesis and progression of cancers. While various attempts have…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
The dynamics of complex systems often involve thermally activated barrier crossing events that allow these systems to move from one basin of attraction on the high dimensional energy surface to another. Such events are ubiquitous, but…
We describe a robust and efficient chain-of-states method for computing Minimum Energy Paths~(MEPs) associated to barrier-crossing events in poly-atomic systems. The path is parametrized in terms of a continuous variable $t \in [0,1]$ that…
Computing reactive trajectories and free energy (FE) landscapes associated to rare event kinetics is key to understanding the dynamics of complex systems. The analysis of the FE surface on which the underlying dynamics takes place has…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtained by constructing a barrier function that satisfies certain…
We consider a two-dimensional model of a porous medium where circular grains are uniformly distributed in a squared container. We assume that such medium is partially filled with water and that the stationary interface separating the water…
The paper is devoted to the thermodynamics of normal surface electromagnetic fields within a nonuniform dispersive and absorptive system. This system is formed by vacuum and lossy medium separated by a plane interface. As a medium, we used…
When studying high-dimensional dynamical systems such as macromolecules, quantum systems and polymers, a prime concern is the identification of the most probable states and their stationary probabilities or free energies. Often, these…
Recent observations demonstrate that densely packed tissues exhibit features of glassy dynamics, such as caging behavior and dynamical heterogeneities, although it has remained unclear how single-cell properties control this behavior. Here…
We consider a nearly-elastic model system with one degree of freedom. In each collision with the "wall", the system can either lose or gain a small amount of energy due to stochastic perturbation. The weak limit of the corresponding slow…
Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the…
How useful it is to think about the potential energy landscape of a complex many-body system depends in large measure on how direct the connection is to the system's dynamics. In this paper we show that, within what we call the potential…
The energies of a pair of strongly-interacting subsystems with arbitrary noninteger charges are examined from closed and open system perspectives. An ensemble representation of the charge dependence is derived, valid at all interaction…
Making decisions freely presupposes that there is some indeterminacy in the environment and in the decision making engine. The former is reflected on the behavioral changes due to communicating: few changes indicate rigid environments;…
Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the…