Search results for "Applied Mathematics"
showing 10 items of 4379 documents
An experimental methodology to study polymer crystallization under processing conditions. The influence of high cooling rates
2002
Abstract A new experimental route for investigating polymer crystallization under very high cooling rates (up to 2000°C/s) is described. A complete and exhaustive description of the apparatus employed for preparing thin quenched samples (100– 200 μm thick) is reported, the cooling mechanism and the temperature distribution across sample thickness is also analysed, showing that the final structure is determined only by the thermal history imposed by the fast quench apparatus. Details concerning the characterization techniques used to probe the final structure are reported, including density measurements and wide angle X-ray diffraction patterns. Experimental results concerning isotactic poly…
Fast and robust phase-shift estimation in two-dimensional structured illumination microscopy.
2019
A method of determining unknown phase-shifts between elementary images in two-dimensional Structured Illumination Microscopy (2D-SIM) is presented. The proposed method is based on the comparison of the peak intensity of spectral components. These components correspond to the inherent structured illumination spectral content and the residual compo- nent that appears from wrongly estimated phase-shifts. The estimation of the phase-shifts is carried out by finding the absolute maximum of a function defined as the normalized peak intensity difference in the Fourier domain. This task is performed by an optimization method providing a fast estimation of the phase-shift. The algorithm stability an…
Pattern formation in clouds via Turing instabilities
2020
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare. From many scientific disciplines the occurrence of patterns in non-equilibrium systems due to Turing instabilities is known, i.e. unstable modes grow and form spatial structures. In this study we investigate a generic cloud model for the possibility of Turing instabilities. For this purpose, the model is extended by diffusion terms. We can show that for some cloud models, i.e special cases of the generic model, no Turing instabilities are possible. However,…
Levy targeting and the principle of detailed balance
2011
We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) …
Functional A Posteriori Error Estimate for a Nonsymmetric Stationary Diffusion Problem
2015
In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm for the global minimization of the error estimate with respect to an auxiliary function over some finite dimensional subspace is presented. In numerical tests, global minimization is done over the subspace generated by Raviart-Thomas elements. The improvement of the error bound due to the p-refinement of these spaces is investigated.
Stochastic homogenization: Theory and numerics
2015
In this chapter, we pursue two related goals. First, we derive a theoretical stochastic homogenization result for the stochastic forward problem introduced in the first chapter. The key ingredient to obtain this result is the use of the Feynman-Kac formula for the complete electrode model. The proof is constructive in the sense that it yields a strategy to achieve our second goal, the numerical approximation of the effective conductivity. In contrast to periodic homogenization, which is well understood, numerical homogenization of random media still poses major practical challenges. In order to cope with these challenges, we propose a new numerical method inspired by a highly efficient stoc…
Well-posed nonlinear problems in integrated circuits modeling
1991
In this paper we study the problem (E) + (BC) + (IC) (see below) which represents a model for integrated circuits. We assume that the distributed parametersr(x) andc(x) are nonconstant, dielectric leakages depend on thex-coordinate as well as the voltage level, while the interconnecting multiport is nonlinear and possibly multivalued.
On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid
2016
We study the existence of weak solution for unsteady fluid-structure interaction problem for shear-thickening flow. The time dependent domain has at one part a flexible elastic wall. The evolution of fluid domain is governed by the generalized string equation with action of the fluid forces. The power-law viscosity model is applied to describe shear-dependent non-Newtonian fluids.
From “Mixed” to “Applied” Mathematics: Tracing an important dimension of mathematics and its history
2013
On Boundary Value Problems for ϕ-Laplacian on the Semi-Infinite Interval
2017
The Dirichlet problem and the problem with functional boundary condition for ϕ-Laplacian on the semi-infinite interval are studied as well as solutions between the lower and upper functions.