Evolution Equations on Co-evolving Graphs: Long-Time Behaviour and the Graph-Continuity Equation [0.03%]
共演化图上的进化方程：长时间行为和图连续性方程
José Antonio Carrillo,Antonio Esposito,László Mikolás
José Antonio Carrillo
We focus on evolution equations on co-evolving infinite graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the so-calle...
Sofia B S D Castro,Alastair M Rucklidge
Sofia B S D Castro
Heteroclinic cycles are sequences of equilibria along with trajectories that connect them in a cyclic manner. We investigate a class of robust heteroclinic cycles that do not satisfy the usual condition that all connections between equilibr...
Murad Banaji,Balázs Boros,Josef Hofbauer
Murad Banaji
We consider local bifurcations of equilibria in dynamical systems arising from chemical reaction networks with mass action kinetics. In particular, given any mass action network admitting a local bifurcation of equilibria, assuming only a g...
Maxime Herda,Ansgar Jüngel,Stefan Portisch
Maxime Herda
An instationary drift-diffusion system for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The e...
Ramy Rashad,Stefano Stramigioli
Ramy Rashad
In this paper, we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems. L...
Effects of Neuromodulation on Excitatory-Inhibitory Neural Network Dynamics Depend on Network Connectivity Structure [0.03%]
神经调制对兴奋-抑制神经网络动力学的影响取决于网络连接结构
Scott Rich,Michal Zochowski,Victoria Booth
Scott Rich
Acetylcholine (ACh), one of the brain's most potent neuromodulators, can affect intrinsic neuron properties through blockade of an M-type potassium current. The effect of ACh on excitatory and inhibitory cells with this potassium channel mo...
François Gay-Balmaz,Cesare Tronci
François Gay-Balmaz
Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential ...
Dispersive Hydrodynamics of Soliton Condensates for the Korteweg-de Vries Equation [0.03%]
Korteweg-de Vries方程孤子凝聚的色散流体动力学
T Congy,G A El,G Roberti et al.
T Congy et al.
We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg-de Vries (KdV) equation in the special "condensate" limit. We prove that in this limit the integro-differential kinetic equation for the spectral density...
Theoretical and Computational Analysis of the Thermal Quasi-Geostrophic Model [0.03%]
热准地转模型的理论和计算分析
D Crisan,D D Holm,E Luesink et al.
D Crisan et al.
This work involves theoretical and numerical analysis of the thermal quasi-geostrophic (TQG) model of submesoscale geophysical fluid dynamics (GFD). Physically, the TQG model involves thermal geostrophic balance, in which the Rossby number,...
A New Decomposition of the Graph Laplacian and the Binomial Structure of Mass-Action Systems [0.03%]
图拉普拉斯的新分解及质量作用系统的二项式结构
Stefan Müller
Stefan Müller
We provide a new decomposition of the Laplacian matrix (for labeled directed graphs with strongly connected components), involving an invertible core matrix, the vector of tree constants, and the incidence matrix of an auxiliary graph, repr...