We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step of the process one edge is selected from a small set of potential edges sharing common vertices and added to the graph. We show that the evolution can be acc...

In this paper, we investigate the almost periodic dynamical behaviors for a class of general Cohen–Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and nonsmooth analysis theory with generalized Lyapunov approach, we obtain the existence, uniqueness and global stability of almost periodic solu...

Estimation of coeecients of partial diierential equations is ill-posed. Output-least-squares method is often used in practice. Convergence of the commonly used minimization algorithms for the inverse problem is often very slow. By using the augmented Lagrangian method, the inverse problem is reduced to a coupled linear algebraic system, which can be solved eeciently. Total variation techniques ...

This article introduces a generalization of problems in the domain of the optimal control of quantum systems viz. costs imposed on impulsive and bounded controls for quantum spin systems with drift. The dynamic programming approach from optimal control is used to analyze the former, and the discontinuous nature of the optimal cost function is used to motivate the need for an interpretation in t...

We present preliminary results of a discontinuous Galerkin scheme applied to deterministic computations of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The collisional term models optical-phonon interactions which become dominant under strong energetic conditions corresponding to nanoscale active regions under applied bias. The proposed...

In this paper, numerical methods are proposed for some interface problems in polar or Cartesian coordinates. The new methods are based on a formulation that transforms the interface problem with a non-smooth or discontinuous solution to a problem with a smooth solution. The new formulation leads to a simple second order finite difference scheme for the partial differential equation and a new in...

We present a compact discontinuous Galerkin (CDG) method for an elliptic model problem. The problem is first cast as a system of first order equations by introducing the gradient of the primal unknown, or flux, as an additional variable. A standard discontinuous Galerkin (DG) method is then applied to the resulting system of equations. The numerical inter-element fluxes are such that the equati...

X iv :1 40 1. 46 80 v3 [ ph ys ic s. so cph ] 2 2 Ja n 20 14 Bootstrap Percolation on Complex Networks with Community Structure Chong Wu1, Shenggong Ji1, Rui Zhang1,2,3, Liujun Chen4,∗ Jiawei Chen4, Xiaobin Li1, and Yanqing Hu1† 1School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China 2Levich Institute and Physics Department, City College of the City University of New York, ...

It is well-known that a system with linear structure subjected to bounded control inputs for optimal closed-loop control yields nonlinear feedback of discontinuous bang-bang type. This paper investigates new types of nonlinear feedback in the case of optimal impulsive closedloop control which may naturally generate discontinuous trajectories. The realization of such feedback under impulsive inp...

Abstract. A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock [1]...