langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. the brownian motion generated from molecular bombardment was taken as a wiener stochastic process and approximated by a gaussian white noise. euler-maruyama method was used to solve the langevin equation numerically. the accuracy of brownian simulation was checked by performing a series of simulati...

Pedal coordinates provide a natural framework for studying force problems of classical mechanics in the plane. The trajectory test particle under influence central and Lorentz-like forces can be translated into pedal at once without need solving any differential equation. We generalize this result to cover more general laws also show advantage certain variational problems. These enable us link ...

The application of Concurrency Theory to Systems Biology is in its earliest stage of progress. The metaphor of cells as computing systems by Regev and Shapiro [85] opened the employment of concurrent languages for the modelling of biological systems. Their peculiar characteristics led to the design of many bio-inspired formalisms which achieve higher faithfulness and specificity. In this thesis...

The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial density including preservation of mass. Consequently we derive a variational regularization model for the reconstruction, which besides the usual data fidelity a...

In this paper we propose a variant of a binary level set approach for solving elliptic problems with piecewise constant coefficients. The inverse problem is solved by a variational augmented Lagrangian approach with a total variation regularisation. In the binary formulation, the seeked interfaces between the domains with different values of the coefficient are represented by discontinuities of...

In hyperspectral images, once the pure spectra of the materials are known, hyperspectral unmixing seeks to find their relative abundances throughout the scene. We present a novel variational model for hyperspectral unmixing from incomplete noisy data, which combines a spatial regularity prior with the knowledge of the pure spectra. The material abundances are found by minimizing the resulting c...

The aim of this paper is to discuss and evaluate total variation based regularization methods for motion estimation, with particular focus on optical flow models. In addition to standard L2 and L1 data fidelities we give an overview of different variants of total variation regularization obtained from combination with higher order models and a unified computational optimization approach based o...

We propose several formulations for recovering discontinuous coefficients in elliptic problems by using total variation (TV) regularization. The motivation for using TV is its wellestablished ability to recover sharp discontinuities. We employ an augmented Lagrangian variational formulation for solving the output-least-squares inverse problem. In addition to the basic outputleast-squares formul...

Stein’s method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation, the functional equation is a first-order differential equation. Malliavin calculus is an infinite-dimensional differential calculus whose operators act on functionals of general Gaussian processes. Nourdin and Peccati (Probab. Theory Relat. Fields 145(1–2), 75...

Multiplicative noise removal is of momentous significance in coherent imaging systems and various image processing applications. This paper proposes a new nonconvex variational model for multiplicative noise removal under the Weberized total variation (TV) regularization framework. Then, we propose and investigate another surrogate strictly convex objective function for Weberized TV regularizat...