相关论文: Vlasov Equations on Directed Hypergraph Measures

Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…

We explore the conditions on a pair interaction for the validity of the Vlasov equation to describe the dynamics of an interacting $N$ particle system in the large $N$ limit. Using a coarse-graining in phase space of the exact Klimontovich…

Ideal density-functional approximations (DFAs) should account for dynamic, static, and nondynamic correlation. While common DFAs struggle with the latter two, the Ziegler-Rauk-Baerends-Daul multiplet sum method (MSM) provides a pragmatic…

In this paper we study Markov processes and related first passage problems on a class of weighted, modular graphs which generalize the Dyson hierarchical model. In these networks, the coupling strength between two nodes depends on their…

Hypergraph networks are closer to real life because they can reflect higher-order interactions, so researchers have begun using them to build models for real-world networks. The mean-field approach is the current tool for studying the…

We consider systems of $N$ particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, we formally expect convergence towards the…

We present a new approach for quantifying the abundance of galaxy clusters and constraining cosmological parameters using dynamical measurements. In the standard method, galaxy line-of-sight (LOS) velocities, $v$, or velocity dispersions…

We introduce diagrammatic technique for Hubbard nonequilibrium Green functions (NEGF). The formulation is an extension of equilibrium considerations for strongly correlated lattice models to description of current carrying molecular…

Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…

The use of effective local Coulomb interactions that are dynamical, that is, frequency-dependent, is an efficient tool to describe the effect of long-range Coulomb interactions and screening thereof in solids. The dynamical character of the…

We develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field limits and particle approximations, and we establish a…

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…

Dynamical mean-field theory (DMFT) is a non-perturbative technique for the investigation of correlated electron systems. Its combination with the local density approximation (LDA) has recently led to a material-specific computational scheme…

Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…

The decomposition of the energy of a compressible fluid parcel into slow (deterministic) and fast (stochastic) components is interpreted as a stochastic Hamiltonian interacting particle system (HIPS). It is shown that the McKean-Vlasov…

In its Euclidean form, the Dense Neighborhood Lemma (DNL) asserts that if $V$ is a finite set of points of $\mathbb{R}^N$ such that for each $v \in V$ the ball $B(v,1)$ intersects $V$ on at least $\delta |V|$ points, then for every…

This paper aims at addressing distributed averaging problems for signed networks in the presence of general directed topologies that are represented by signed digraphs. A new class of improved Laplacian potential functions is proposed by…

We consider the model of Directed Polymers in an i.i.d. gaussian or bounded Environment in the $L^2$ region. We prove the convergence of the law of the environment seen by the particle. As a main technical step, we establish a lower tail…

Relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas-Kroll-Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods including spin-orbit coupling in the Molcas/OpenMolcas…

Diagonal linear networks (DLNs) are a tractable model that captures several nontrivial behaviors in neural network training, such as initialization-dependent solutions and incremental learning. These phenomena are typically studied in…