Related papers: A path integral approach to the dynamics of random…
The behavior of active matter under confinement poses significant challenges due to the intricate coupling between dynamics near boundaries and those in the bulk. A defining feature of active matter systems is that a substantial portion of…
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose path integral formalism for a single variable stochastic dynamics, we…
Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
We describe a simple meanfield variational approach to study a number of properties of intrinsically stiff chains which are appropriate models for a large class of biopolymers. We present the calculation of the distribution of end-to-end…
Asymptotic properties of discrete, stochastic approximations to hybrid systems, modeled as hybrid inclusions, are studied. First, the internal chain transitivity of omega-limits of solutions is concluded, along with other properties related…
Using a path integral approach, we derive an analytical solution of a nonlinear and singular Langevin equation, which has been introduced previously by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion of a solid…
We study the Hamiltonian dynamics of a one-dimensional chain of linearly coupled particles in a spatially periodic potential which is subjected to a time-periodic mono-frequency external field. The average over time and space of the related…
Robots are still poor at traversing cluttered large obstacles required for important applications like search and rescue. By contrast, animals are excellent at doing so, often using direct physical interaction with obstacles rather than…
We propose a simple friction model for isolated polymer chains on a solid substrate. The chains are pulled at constant velocity by one end, the other end can be trapped on the solid substrate on localised sites. We focus on the energy…
A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental three-dimensional…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
Most networks encountered in nature, society, and technology have weighted edges, representing the strength of the interaction/association between their vertices. Randomizing the structure of a network is a classic procedure used to…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by…
In this work we give specific examples of competition models, with six and eight species, whose three-dimensional dynamics naturally leads to the formation of string networks with junctions, associated with regions that have a high…
The reptation concept in polymer dynamics is studied for model chains with added stiffness. The main idea of a chain diffusing inside a tube can be transferred from fully flexible chains. However, the picture, which renormalizes the chain…