Related papers: A product integration rule on equispaced nodes for…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
This work deals with the numerical approximation of plasmas which are confined by the effect of a fast oscillating magnetic field (see \cite{Bostan2012}) in the Vlasov model. The presence of this magnetic field induces oscillations (in…
Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important…
Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…
We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.
In this paper, we consider a product of a symmetric stable process in $\mathbb{R}^d$ and a one-dimensional Brownian motion in $\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process. We show that…
We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials. This paper extends the investigation started in [J.-M. Lion,…
Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated…
In this paper a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented. The main goal of the present…
In this paper, we present a novel estimation and control strategy to balance a formation of discrete-time oscillators on a circle. We consider the case in which each oscillator only gathers noisy proximity measurements, whose range is lower…
We show that for odd-valued piecewise-constant skew products over a certain two parameter family of interval exchanges, the skew product is ergodic for a full-measure choice of parameters.
In this work we propose composition products in the class of complex harmonic functions so that the composition of two such functions is again a complex harmonic function. From here we begin the study of the iterations of the functions of…
In this paper we present a new criterion on characterization of real inner product spaces. We conclude that a real normed space $(X, \|...\|)$ is an inner product space if $$\sum_{\epsilon_i \in \{-1,1\}} \|x_1 +…
Elastic constants are central material properties, frequently reported in experimental and theoretical studies. While their computation is straightforward in the absence of thermal fluctuations, finite--temperature methods often suffer from…
In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level…
In engineering, it is a common desire to couple existing simulation tools together into one big system by passing information from subsystems as parameters into the subsystems under influence. As executed at fixed time points, this data…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate…
A method to isolate the poles of dimensionally regulated multi-loop integrals and to calculate the pole coefficients numerically is extended to be applicable to phase space integrals as well.
We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…