Related papers: Conservation laws for voter-like models on directe…
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant…
We study the evolution of opinions on a directed network with community structure. Individuals update their opinions synchronously based on a weighted average of their neighbors' opinions, their own previous opinions, and external media…
The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such…
This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total…
Strand displacement and tile assembly systems are designed to follow prescribed kinetic rules (i.e., exhibit a specific time-evolution). However, the expected behavior in the limit of infinite time--known as thermodynamic equilibrium--is…
A theory of thermohydrodynamics in two-dimensional electron systems in quantizing magnetic fields is developed including a nonlinear transport regime. Spatio-temporal variations of the electron temperature and the chemical potential in the…
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely…
One dimensional systems sometimes show pathologically slow decay of currents. This robustness can be traced to the fact that an integrable model is nearby in parameter space. In integrable models some part of the current can be conserved,…
Current fluctuations in boundary-driven diffusive systems are, in many cases, studied using hydrodynamic theories. Their predictions are then expected to be valid for currents which scale inversely with the system size. To study this…
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples.…
In this work we present a nonlocal conservation law with a velocity depending on an integral term over a part of the space. The model class covers already existing models in literature, but it is also able to describe new dynamics mainly…
We prove global existence of a solution to an initial and boundary value problem for a highly nonlinear PDE system. The problem arises from a thermomechanical dissipative model describing hydrogen storage by use of metal hydrides. In order…
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…
We consider continuous-time consensus seeking systems whose time-dependent interactions are cut-balanced, in the following sense: if a group of agents influences the remaining ones, the former group is also influenced by the remaining ones…
We study driven 1d lattice gas models with two types of particles and nearest neighbor hopping. We find the most general case when there is a shock solution with a product measure which has a density-profile of a step function for both…
Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch…
We study the behavior of a generalized consensus dynamics on a temporal network of interactions, the activity driven network with attractiveness. In this temporal network model, agents are endowed with an intrinsic activity $a$, ruling the…
A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…