Related papers: Dynamics of driven flow with exclusion in graphene…
We consider the motion by mean curvature of an $n$-dimensional graph over a time-dependent domain in $\mathbb{R}^n$, intersecting $\mathbb{R}^n$ at a constant angle. In the general case, we prove local existence for the corresponding…
In this work, we provide a theoretical understanding of the framelet-based graph neural networks through the perspective of energy gradient flow. By viewing the framelet-based models as discretized gradient flows of some energy, we show it…
We study transport properties of graphene nanostructures consisted of alternating slabs of gapless and gapped graphene in the presence of piecewise constant external potential equal to zero in the gapless regions. The transmission through…
The dual-fermion approach offers a way to perform diagrammatic expansion around the dynamical mean-field theory. Using this formalism, the influence of antiferromagnetic fluctuations on the self-energy is taken into account through…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton-Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption…
Several one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary…
We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
The carriers in graphene tuned close to the Dirac point envisage signatures of the strongly interacting fluid and are subject to hydrodynamic description. The important question is whether strong disorder induces the metal-insulator…
We investigate the effects of nuclear mean-field as well as the formation and decay of nuclear clusters on the directed flow $v_1$ in high energy nucleus-nucleus collisions from $\sqrt{s_{NN}}=7.7$ GeV to 27 GeV incident energies within a…
We construct a dynamical field theory for noninteracting Brownian particles in the presence of a quenched Gaussian random potential. The main variable for the field theory is the density fluctuation which measures the difference between the…
A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas…
A mechanistic theory is developed to describe segregation in confined multicomponent suspensions such as blood. It incorporates the two key phenomena arising in these systems at low Reynolds number: hydrodynamic pair collisions and…
The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
The aim of this paper is to discuss the appropriate modelling of in- and outflow boundary conditions for nonlinear drift-diffusion models for the transport of particles including size exclusion and their effect on the behaviour of…
We study the dynamics of an asymmetric simple exclusion process with open boundaries and local interactions using a pair approximation which generalizes the 2-node cluster mean field theory and the Markov chain approach to kinetics and…
We present a graphon mean-field logit dynamic, a stationary mean-field game based on logit interactions. This dynamic emerges from a stochastic control problem involving a continuum of nonexchangeable and interacting agents and reduces to…