Search results for " Applied"

Adaptive rational interpolation for point values

2019

Abstract G. Ramponi et al. introduced in Carrato et al. (1997,1998), Castagno and Ramponi (1996) and Ramponi (1995) a non linear rational interpolator of order two. In this paper we extend this result to get order four. We observe the Gibbs phenomenon that is obtained near discontinuities with its weights. With the weights we propose we obtain approximations of order four in smooth regions and three near discontinuities. We also introduce a rational nonlinear extrapolation which is also of order four in the smooth region of the given function. In the experiments we calculate numerically approximation orders for the different methods described in this paper and see that they coincide with th…

A generalized Newton iteration for computing the solution of the inverse Henderson problem

2020

We develop a generalized Newton scheme IHNC for the construction of effective pair potentials for systems of interacting point-like particles.The construction is made in such a way that the distribution of the particles matches a given radial distribution function. The IHNC iteration uses the hypernetted-chain integral equation for an approximate evaluation of the inverse of the Jacobian of the forward operator. In contrast to the full Newton method realized in the Inverse Monte Carlo (IMC) scheme, the IHNC algorithm requires only a single molecular dynamics computation of the radial distribution function per iteration step, and no further expensive cross-correlations. Numerical experiments…

Normalized solutions to the mixed dispersion nonlinear Schr��dinger equation in the mass critical and supercritical regime

2019

In this paper, we study the existence of solutions to the mixed dispersion nonlinear Schrödinger equation γΔ2u − Δu + αu =

The Liouville theorem and linear operators satisfying the maximum principle

2020

A result by Courr\`ege says that linear translation invariant operators satisfy the maximum principle if and only if they are of the form $\mathcal{L}=\mathcal{L}^{\sigma,b}+\mathcal{L}^\mu$ where $$ \mathcal{L}^{\sigma,b}[u](x)=\text{tr}(\sigma \sigma^{\texttt{T}} D^2u(x))+b\cdot Du(x) $$ and $$ \mathcal{L}^\mu[u](x)=\int \big(u(x+z)-u-z\cdot Du(x) \mathbf{1}_{|z| \leq 1}\big) \,\mathrm{d} \mu(z). $$ This class of operators coincides with the infinitesimal generators of L\'evy processes in probability theory. In this paper we give a complete characterization of the translation invariant operators of this form that satisfy the Liouville theorem: Bounded solutions $u$ of $\mathcal{L}[u]=0$ i…

Perturbations of the derivative along periodic orbits

2006

International audience; We show that a periodic orbit of large period of a diffeomorphism or flow, either admits a dominated splitting of a prescribed strength, or can be turned into a sink or a source by a C1-small perturbation along the orbit. As a consequence we show that the linear Poincaré flow of a C1-vector field admits a dominated splitting over any robustly transitive set.

Monotonicity-based inversion of the fractional Schr\"odinger equation II. General potentials and stability

2019

In this work, we use monotonicity-based methods for the fractional Schr\"odinger equation with general potentials $q\in L^\infty(\Omega)$ in a Lipschitz bounded open set $\Omega\subset \mathbb R^n$ in any dimension $n\in \mathbb N$. We demonstrate that if-and-only-if monotonicity relations between potentials and the Dirichlet-to-Neumann map hold up to a finite dimensional subspace. Based on these if-and-only-if monotonicity relations, we derive a constructive global uniqueness results for the fractional Calder\'on problem and its linearized version. We also derive a reconstruction method for unknown obstacles in a given domain that only requires the background solution of the fractional Sch…

Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid

2015

The Calderón Problem for a Space-Time Fractional Parabolic Equation

2020

In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with $0<s<1$ in any space dimension. We uniquely determine the unknown bounded...

Development of La3+ Doped CeOthick film humidity sensors

2014

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/297632 Open Access The humidity sensitive characteristics of the sensor fabricated from 10 mol% Ladoped CeOnanopowders with particle size 17.26 nm synthesized via hydrothermal method were investigated at different frequencies. It was found that the sensor shows high humidity sensitivity, rapid response-recovery characteristics, and narrow hysteresis loop at 100 Hz in the relative humidity range from 11% to 95%. The impedance of the sensor decreases by about five orders of magnitude as relative humidity increases. The maximum humidity hysteresis …

Our Friend and Mathematician Karl Strambach

2020

This paper is dedicated to Karl Strambach on the occasion of his 80th birthday. Here we want to describe our work with Prof. Karl Strambach.