1,250 Works

Generalized necessary scaling condition and stability of chemical reactors with several educts

Messoud A. Efendiev, Georg Hebermehl & Rupert Lasser
We present, for a class of industrially relevant chemical reactions with two educts the dependence of stability on important chemical parameters, such as coolant, dilution and diffusion rates. The main analytical tools are generalized upscaling balance condition for the equilibria concentrations and spectral properties of corresponding operators. Although we illustrate the stability analysis for a model reactor (2 educts, E1 and E2), it should be emphasized that our approach is applicable to more complex reaction...

Quenched large deviations for simple random walks on percolation clusters including long-range correlations

Noam Berger, Chiranjib Mukherjee & Kazuki Okamura
We prove a quenched large deviation principle (LDP)for a simple random walk on a supercritical percolation cluster (SRWPC) on the lattice.The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and its vacant set and the level sets of the Gaussian free field. Inspired by the methods developed by Kosygina, Rezakhanlou and Varadhan ([KRV06]) for proving quenched...

Optimal change-point estimation in inverse problems

Michael H. Neumann
We develop a method of estimating change-points of a function in the case of indirect noisy observations. As two paradigmatic problems we consider deconvolution and errors-in-variables regression. We estimate the scalar products of our indirectly observed function with appropriate test functions, which are shifted over the interval of interest. An estimator of the change point is obtained by the extremal point of this quantity. We derive rates of convergence for this estimator. They depend on...

A threshold model for local volatility: Evidence of leverage and mean reversion effects on historical data

Antoine Lejay & Paolo Pigato
In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous...

A semidiscrete scheme for a Penrose-Fife system and some Stefan problems in R(3)

Olaf Klein
This paper is concerned with the Penrose-Fife phase-field model and some Stefan problems in which the heat flux is proportional to the gradient of the inverse absolute temperature. Recently, Colli and Sprekels proved that, as some parameters in the Penrose-Fife equations tend to zero, the corresponding solutions converge against the solutions to these Stefan problems. Following their approach, we derive a time-discrete scheme for the Penrose-Fife equations, such that analogous convergence properties hold. Furthermore, we...

On the effect of estimating the error density in nonparametric deconvolution

Michael H. Neumann
It is quite common in the statistical literature on nonparametric deconvolution to assume that the error density is perfectly known. Since this seems to be unrealistic in many practical applications, we study the effect of estimating the unknown error density. We derive minimax rates of convergence and propose a modification of the usual kernel-based estimation scheme, which takes the uncertainty about the error density into account. A simulation study quantifies the possible gains by this...

Metastates in the Hopfield model in the replica symmetric regime

Anton Bovier & Véronique Gayrard
We study the finite dimensional marginals of the Gibbs measure in the Hopfield model at low temperature when the number of patterns, M, is proportional to the volume with a sufficiently small proportionality constant ɑ > 0. It is shown that even when a single pattern is selected (by a magnetic field or by conditioning), the marginals do not converge almost surely, but only in law. The corresponding limiting law is constructed explicitly. We fit...

Error bounds and their application

Paul Bosch, Abderrahim Jourani & René Henrion
Our aim in this paper is to present sufficient conditions for error bounds in terms of Frechet and limiting Frechet subdifferentials outside of Asplund spaces. This allows us to develop sufficient conditions in terms of the approximate subdifferential for systems of the form (푥, 푦) ∈ 퐶 × 퐷, 푔(푥, 푦, 푢) = 0, where 푔 takes values in an infinite dimensional space and 푢 plays the role of a parameter. This symmetric structure offers...

Stochastic Eulerian model for the flow simulation in porous media

Dmitry R. Kolyukhin & Karl K. Sabelfeld
This work deals with the stochastic flow simulation in statistically isotropic and anisotropic saturated porous media in 3D case. The hydraulic conductivity is assumed to be a random field with lognormal distribution. Under the assumption of smallness of fluctuations in the hydraulic conductivity we construct a stochastic Eulerian model for the incompressible flow as a divergenceless Gaussian random field with a spectral tensor of a special structure derived from Darcy's law. A randomized spectral representation...

Convergence estimates for the numerical approximation of homoclinic solutions

Björn Sandstede
This article is concerned with the numerical computation of homoclinic solutions converging to a hyperbolic or semi-hyperbolic equilibrium of a system u̇ = ƒ (u, μ). The approximation is done by replacing the original problem by a boundary value problem on a finite interval and introducing an additional phase condition to make the solution unique. Numerical experiments have indicated that the parameter μ is much better approximated than the homoclinic solution. This was proved in...

Analysis and optimisation of a variational model for mixed Gaussian and Salt Pepper noise removal

Kostas Calatroni & Kostas Papafitsoros
We analyse a variational regularisation problem for mixed noise removal that was recently proposed in [14]. The data discrepancy term of the model combines L1 and L2 terms in an infimal convolution fashion and it is appropriate for the joint removal of Gaussian and Salt & Pepper noise. In this work we perform a finer analysis of the model which emphasises on the balancing effect of the two parameters appearing in the discrepancy term. Namely,...

Wavelet approximation of correlated wavefunctions. II. Hyperbolic wavelets and adaptive approximation schemes

Hongjun Luo, Dietmar Kolb, Heinz-Jürgen Flad, Wolfgang Hackbusch & Thomas Koprucki
We have studied various aspects concerning the use of hyperbolic wavelets and adaptive approximation schemes for wavelet expansions of correlated wavefunctions. In order to analyze the consequences of reduced regularity of the wavefunction at the electron-electron cusp, we first considered a realistic exactly solvable many-particle model in one dimension. Convergence rates of wavelet expansions, with respect to L2 and H1 norms and the energy, were established for this model. We compare the performance of hyperbolic...

Analysis of a hybrid model for the electrothermal behavior of semiconductor heterostructures

Annegret Glitzky, Matthias Liero & Grigot Nika
We prove existence of a weak solution for a hybrid model for the electro-thermal behavior of semiconductor heterostructures. This hybrid model combines an electro-thermal model based on drift-diffusion with thermistor type models in different subregions of the semiconductor heterostructure. The proof uses a regularization method and Schauder's fixed point theorem. For boundary data compatible with thermodynamic equilibrium we verify, additionally, uniqueness. Moreover, we derive bounds and higher integrability properties for the electrostatic potential and the...

A new kinetic equation for dense gases

Alejandro L. Garcia & Wolfgang Wagner
This paper establishes a theoretical foundation for the Consistent Boltzmann Algorithm by deriving the limiting kinetic equation. Besides its relation to the algorithm, this new equation serves as a useful alternative to the Enskog equation in the kinetic theory of dense gases. For a simplified model, the limiting equation is solved numerically, and very good agreement with the predictions of the theory is found.

A posteriori error estimates for a time discrete scheme for a phase-field system of Penrose-Fife type

Olaf Klein & Claudi Verdi
A time discrete scheme is used to approximate the solution to a phase field system of Penrose-Fife type with a non-conserved order parameter. An a posteriori error estimate is presented that allows to estimate the difference between continuous and semidiscrete solutions by quantities that can be calculated from the approximation and given data.

An approximation method for Navier-Stokes equations based on probabilistic approach

Yana Belopolskaya & Grigori N. Milstein
A new layer method solving the space-periodic problem for the Navier-Stokes equations is constructed by using probabilistic representations of their solutions. The method exploits the ideas of weak sense numerical integration of stochastic differential equations. Despite its probabilistic nature this method is nevertheless deterministic. A convergence theorem is proved.

On the approximation of kinetic equations by moment systems

Wolfgang Dreyer, Michael Junk & Matthias Kunik
The aim of this article is to show that moment approximations of kinetic equations based on a Maximum Entropy approach can suffer from severe drawbacks if the kinetic velocity space is unbounded. As example, we study the Fokker Planck equation where explicit expressions for the moments of solutions to Riemann problems can be derived. The quality of the closure relation obtained from the Maximum Entropy approach as well as the Hermite/Grad approach is studied in...

Instability of localised buckling modes in a one-dimensional strut model

Björn Sandstede
Stability of localised equilibria arising in a fourth-order partial differential equation modelling struts is investigated. It was shown in Buffoni, Champneys & Toland (1996) that the model exhibits many multi-modal buckling states bifurcating from a primary buckling mode. In this article, using analytical and numerical techniques, the primary mode is shown to be unstable under dead loading in a large range of parameter values, while is likely to be stable under rigid loading for small...

Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice

Vladimir Spokoiny
New method of adaptive estimation of a regression function is proposed. The resulting estimator achieves near optimal rate of estimation in the classical sense of mean integrated squared error. At the same time, the estimator is shown to be very sensitive to discontinuities or change-points of the underlying function ƒ or its derivatives. For instance, in the case of a jump of a regression function, beyond the interval of length (in order) n-1 log n...

Compact interface property for symbiotic branching

Alison M. Etheridge & Klaus Fleischmann
A process which we call symbiotic branching, is suggested covering three well-known interacting models: mutually catalytic branching, the stepping stone model, and the Anderson model. Basic tools such as self-duality, particle system moment duality, measure case moment duality, and moment equations are still available in this generalized context. As an application, we show that in the setting of the one-dimensional continuum the compact interface property holds: starting from complementary Heaviside states, the interface is finite...

Higher order approximate Markov chain filters.

Peter E. Kloeden, Eckhard Platen & Henri Schurz
The aim of this paper is to construct higher order approximate discrete time filters for continuous time finite-state Markov chains with observations that are perturbed by the noise of a Wiener process.

Instationary drift-diffusion problems with Gauss--Fermi statistics and field-dependent mobility for organic semiconductor devices

Annegret Glitzky & Matthias Liero
This paper deals with the analysis of an instationary drift-diffusion model for organic semiconductor devices including Gauss--Fermi statistics and application-specific mobility functions. The charge transport in organic materials is realized by hopping of carriers between adjacent energetic sites and is described by complicated mobility laws with a strong nonlinear dependence on temperature, carrier densities and the electric field strength. To prove the existence of global weak solutions, we consider a problem with (for small densities)...

Extremality of the disordered state for the Ising model on general trees

Dmitry Ioffe
We develop a method to study extremality of the disordered state ℙβ for the Ising model on a general countable tree T. It is shown that the tail σ-field is ℙβ-trivial as soon as β is less than the spin glass critical inverse temperature βS Gc , which is determined from the relation tanh(βS Gc) = 1/√br(T). The method is based on the FK representation of ferromagnetic systems and recursive estimates on conditional expectations of...

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