We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to esta...

We give a convergence estimate for a Petrov-Galerkin Algebraic Multigrid method. In this method, the prolongations are defined using the concept of smoothed aggregation while the restrictions are simple aggregation operators. The analysis is carried out by showing that these methods can be interpreted as variational Ritz-Galerkin ones using modified transfer and smoothing operators. The estimat...

Distance sampling is a technique for estimating the abundance of animals or other objects in a region, allowing for imperfect detection. This paper evaluates the statistical efficiency of the method when its assumptions are met, both theoretically and by simulation. The theoretical component of the paper is a derivation of the asymptotic variance penalty for the distance sampling estimator aris...

Three different high-order finite element methods are used to solve the advection problem—two implementations of a discontinuous Galerkin and a spectral element (high-order continuous Galerkin) method. The three methods are tested using a 2D Gaussian hill as a test function, and the relative L2 errors are compared. Using an explicit Runge–Kutta time stepping scheme, all three methods can be par...

In this paper, we present a distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method. The dynamic model comprises system of three coupled reaction-diffusion models, involving the tumor cells, the normal tissues and the drug concentration. An optimal control problem is formulated with the goal of minimizing the tumor cell density and reducing ...

In this paper, a novel adaptive asymmetrical barrier function-based vibration control law is proposed for the nonlinear flexible cantilever beam system with obstacle restriction, model uncertainties, and distributed disturbances. Firstly, by employing Hamilton’s principle Galerkin projection method, dynamic of piezoelectric actuator constructed in partial differential equations simplified to or...

For the solution of convection-diffusion problems we present a multilevel self-adaptive mesh-refinement algorithm to resolve locally strong varying behavior, like boundary and interior layers. The method is based on discontinuous Galerkin (Baumann-Oden DG) discretization. The recursive mesh-adaptation is interwoven with the multigrid solver. The solver is based on multigrid V-cycles with damped...

Wen-Jei Yang Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, Michigan 1 A n experimental study is performed to investigate the pressure drop distribution and turbulence intensity for airflow through a stack of parallel plates with periodic interruptions. The interrupted surfaces are constructed in an offset-strip f6rm and a perforated form. Hot...