Related papers: A Laplace Transform Method for Molecular Mass Dist…
A tutorial discussion of the propagation of waves in random media is presented. In first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are present. These corrections are…
Reparameterizable densities are an important way to learn probability distributions in a deep learning setting. For many distributions it is possible to create low-variance gradient estimators by utilizing a `reparameterization trick'. Due…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
A method of modelling the three-dimensional microstructure of random isotropic two-phase materials is proposed. The information required to implement the technique can be obtained from two-dimensional images of the microstructure. The…
To calculate linear oscillations and waves in dynamics of gas and plasma one uses as a rule the old classical method of dispersion equation for complex frequencies $\omega$ and wave numbers $k$: $\epsilon(\omega,k)=0$. This method appears…
A simple one-dimensional model is constructed for polymer motion. It exhibits the crossover from reptation to Rouse dynamics through gradually allowing hernia creation and annihilation. The model is treated by the density matrix technique…
A mathematical model is developed for the process of mass transfer from a fluid flowing through a packed column. Mass loss, whether by absorption or adsorption, may be significant. This is appropriate for example when removing contaminants…
The long time dynamics of polymeric materials has been extensively studied in the past through various experimental techniques and computer simulations. While computer simulations typically treat generic, simplified models, experiments deal…
The transport of deformable particles through porous media underlies a wealth of applications ranging from filtration to oil recovery to the transport and spreading of biological agents. Using direct numerical simulations, we analyze the…
Polydispersity is inevitable in industrially produced polymers. Established theories of polymer dynamics and rheology, however, were mostly built on monodisperse linear polymers. Dynamics of polydisperse polymers is yet to be fully explored…
The transport coefficients of dense polymeric fluids are approximately calculated from the microscopic intermolecular forces. The following finite molecular weight effects are discussed within the Polymer-Mode-Coupling theory (PMC) and…
The miscible displacement of a shear-thinning fluid by another of same rheological properties is studied experimentally in a transparent fracture by an optical technique imaging relative concentration distributions. The fracture walls have…
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…
We consider generalizations of the classical inverse problem to Bayesien type estimators, where the result is not one optimal parameter but an optimal probability distribution in parameter space. The practical computational tool to compute…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
An ongoing problem in the study of a classical many-body system is the characterization of its equilibrium behaviour by theory or numerical simulation. For purely repulsive particles, locating the melting line in the pressure-temperature…
We calculate exactly the Laplace transform of the Fr\'{e}chet distribution in the form $\gamma x^{-(1+\gamma)} \exp(-x^{-\gamma})$, $\gamma > 0$, $0 \leq x < \infty$, for arbitrary rational values of the shape parameter $\gamma$, i.e. for…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…
Powdered materials of sizes ranging from nanometers to microns are widely used in materials science and are carefully selected to enhance the performance of a matrix. Fillers have been used in order to improve, among the others, mechanical,…
We study a mesoscopic model for the flow of amorphous solids. The model is based on the key features identified at the microscopic level, namely peri- ods of elastic deformation interspersed with localised rearrangements of parti- cles that…