相关论文: Hack's law in a drainage network model: A Brownian…

We investigate the wave-packet dynamics of the power-law bond disordered one-dimensional Anderson model with hopping amplitudes decreasing as $H_{nm}\propto |n-m|^{-\alpha}$. We consider the critical case ($\alpha=1$). Using an exact…

Using coarse grained models we investigate the behavior of water adjacent to an extended hydrophobic surface peppered with various fractions of hydrophilic patches of different sizes. We study the spatial dependence of the mean interface…

By dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are…

We consider a variant of the radial spanning tree introduced by Baccelli and Bordenave. Like the original model, our model is a tree rooted at the origin, built on the realization of a planar Poisson point process. Unlike it, the paths of…

Internet is known to display a highly heterogeneous structure and complex fluctuations in its traffic dynamics. Congestion seems to be an inevitable result of user's behavior coupled to the network dynamics and it effects should be…

The goal of this note is to provide a theoretical explanation for the saturation of the drag coefficient in strong wind conditions. The hydrodynamic model under consideration takes into account the important effects of airborne droplets of…

In the rough phase, the width of interfaces separating different phases of statistical systems increases logarithmically with the system size. This phenomenon is commonly described in terms of the capillary wave model, which deals with…

We study the Asymmetric Brownian Energy, a model of heat conduction defined on the one-dimensional finite lattice with open boundaries. The system is shown to be dual to the Symmetric inclusion process with absorbing boundaries. The proof…

We use computer simulations to test a simple idea for mapping between long-time self diffusivities obtained from molecular and Brownian dynamics. The strategy we explore is motivated by the behavior of fluids comprising particles that…

We investigate the behavior of active Brownian particles (ABP) within a temporal complex network framework approach. We focused on the node degree distribution, average path length, and average clustering coefficient across the P\'eclet…

This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two…

We demonstrate experimentally that the long-range hydrodynamic interactions in an incompressible quasi 2D isotropic fluid result in an anisotropic viscous drag acting on elongated particles. The anisotropy of the drag is increasing with…

The efficiency of flow-based networking mechanisms strongly depends on traffic characteristics and should thus be assessed using accurate flow models. For example, in the case of algorithms based on the distinction between elephant and mice…

We consider a stochastic model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows in a network where bandwidth is…

We derive an effective equation of motion for binary Bose mixtures, which generalizes the Cahn-Hilliard description of classical binary fluids to superfluid systems. Within this approach, based on a microscopic Hamiltonian formulation, we…

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface…

Transport networks are crucial for the functioning of natural and technological systems. We study a mathematical model of vascular network adaptation, where the network structure dynamically adjusts to changes in blood flow and pressure.…

We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…

Large language models are remarkably capable, yet how computation propagates through their layers remains poorly understood. A growing line of work treats depth as discrete time and the residual stream as a dynamical system, where each…

The online increasing subsequence problem is a stochastic optimisation task with the objective to maximise the expected length of subsequence chosen from a random series by means of a nonanticipating decision strategy. We study the…