相关论文: Microscopic, mesoscopic, and macroscopic descripti…

This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…

Statistical solutions of incompressible Euler describe turbulent dynamics as time-parameterized laws on $L^2$ whose multi-point correlations satisfy an infinite hierarchy of weak identities. Modern generative samplers for PDE forecasting…

This paper formalises the concepts of weakly and weakly regularly persistent input trajectory as well as their link to the Observability Grammian and the existence and uniqueness of solutions of Moving Horizon Estimation (MHE) problems.…

In this paper, we are concerned with the quantification of uncertainties that arise from intra-day oscillations in the demand for natural gas transported through large-scale networks. The short-term transient dynamics of the gas flow is…

A continuous-time average consensus system is a linear dynamical system defined over a graph, where each node has its own state value that evolves according to a simultaneous linear differential equation. A node is allowed to interact with…

We study the derivation of second order macroscopic traffic models from kinetic descriptions. In particular, we recover the celebrated Aw-Rascle model as the hydrodynamic limit of an Enskog-type kinetic equation out of a precise…

An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as…

We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler…

One aim of the equal load sharing fiber bundle model is to describe the critical behavior of failure events. One way of accomplishing this, is through a discrete recursive dynamics. We introduce a continuous mesoscopic equation catching the…

Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are…

Dynamic/kinematic model is of great significance in decision and control of intelligent vehicles. However, due to the singularity of dynamic models at low speed, kinematic models have been the only choice under many driving scenarios. This…

Microscopic traffic models describe how cars interact with their neighbors in an uninterrupted traffic flow and are frequently used for reference in advanced vehicle control design. In this paper, we propose a novel mechanical system…

In the present work, a hyperelastic constitutive model based on neural networks is proposed which fulfills all common constitutive conditions by construction, and in particular, is applicable to compressible material behavior. Using…

A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…

A multi-component lattice Boltzmann model recently introduced (R. Benzi et al. Phys. Rev. Lett 102, 026002 (2009)) to describe some dynamical behaviors of soft-flowing materials is theoretically analyzed. Equilibrium and transport…

We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual…

This work focuses on the numerical approximations of neutral stochastic delay differential equations with their drift and diffusion coefficients growing super-linearly with respect to both delay variables and state variables. Under…

Spatial coupling has recently emerged as a powerful paradigm to construct graphical models that work well under low-complexity message-passing algorithms. Although much progress has been made on the analysis of spatially coupled models…

The Euler-Poisson-Alignment (EPA) system appears in mathematical biology and is used to model, in a hydrodynamic limit, a set agents interacting through mutual attraction/repulsion as well as alignment forces. We consider one-dimensional…

The Euler characteristic transform (ECT) is a signature from topological data analysis (TDA) which summarises shapes embedded in Euclidean space. Compared with other TDA methods, the ECT is fast to compute and it is a sufficient statistic…