Search results for "Mathematica"

Levy flights in confining environments: Random paths and their statistics

2013

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental inhomogeneities), the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Since there is no Langevin representation of the dynamics in question, our main goal here is to establish the appropriate path-wise description of the underlying jump-type process and next infer the $\rho (x,t)$ dynamics directly from the random paths statistics. A pr…

Adversarial reverse mapping of equilibrated condensed-phase molecular structures

2020

A tight and consistent link between resolutions is crucial to further expand the impact of multiscale modeling for complex materials. We herein tackle the generation of condensed molecular structures as a refinement -- backmapping -- of a coarse-grained structure. Traditional schemes start from a rough coarse-to-fine mapping and perform further energy minimization and molecular dynamics simulations to equilibrate the system. In this study we introduce DeepBackmap: A deep neural network based approach to directly predict equilibrated molecular structures for condensed-phase systems. We use generative adversarial networks to learn the Boltzmann distribution from training data and realize reve…

The strictly-correlated electron functional for spherically symmetric systems revisited

2017

The strong-interaction limit of the Hohenberg-Kohn functional defines a multimarginal optimal transport problem with Coulomb cost. From physical arguments, the solution of this limit is expected to yield strictly-correlated particle positions, related to each other by co-motion functions (or optimal maps), but the existence of such a deterministic solution in the general three-dimensional case is still an open question. A conjecture for the co-motion functions for radially symmetric densities was presented in Phys.~Rev.~A {\bf 75}, 042511 (2007), and later used to build approximate exchange-correlation functionals for electrons confined in low-density quantum dots. Colombo and Stra [Math.~M…

On interactive multiobjective optimization with NIMBUS® in chemical process design

2005

We study multiobjective optimization problems arising from chemical process simulation. The interactive multiobjective optimization method NIMBUS®, developed at the University of Jyvaskyla, is combined with the BALAS® process simulator, developed at the VTT Technical Research Center of Finland, in order to provide a new interactive tool for designing chemical processes. Continuous interaction between the method and the designer provides a new efficient approach to explore Pareto optimal solutions and helps the designer to learn about the behaviour of the process. As an example of how the new tool can be used, we report the results of applying it in a heat recovery system design problem rela…

Tieftemperatur-Remissionsspektren oktaedrisch koordinierter Cu2+ -Ionen im Ligandenfeldbereich / Low temperature reflectance spectra of octahedrally …

1973

Abstract The ligand field reflectance spectra of octahedrally coordinated Cu2+-ions in different host lattices and at different temperature (300 °K - 4 °K) are critically compared. Especially the band shifts with decreasing temperature are analysed with respect to transitions from a dynamical to a static Jahn-Teller effect (macroscopic Jahn -Teller distortion of the lattice). In addition the square planar coordination of Cu2+ is discussed and alternative descriptions in the crystal field formalism and the angular overlap model are given.

Spatially limited diffusion coupled with ohmic potential drop and/or slow interfacial exchange: a new method to determine the diffusion time constant…

2004

Abstract We have analyzed chronoamperometric curves, I ( t ), after small-amplitude potential steps Δ E (PITT technique) for the model of linear diffusion of a species inside an electroactive film, taking into account ohmic effects in the external media (solution and electrode) as well as a finite rate of the interfacial exchange. For its short-time interval, t ≪ τ d ( τ d is the diffusion time constant, corresponding to unlimited diffusion from the interface), three approximate analytical expressions have been proposed. One of these represents an interpolation formula between the value of the current at the start of the diffusion process, I (0)=Δ E / R ext (after the end of the EDL chargin…

Theorie der Verbrennungsgeschwindigkeit in brennbaren Gemischen

1948

Abstract Aus den Erhaltungssätzen für Masse und Impuls folgt, daß stationäre Flammenwanderung nur in zwei deutlich voneinander getrennten Geschwindigkeitsbereichen der Wandergeschwindigkeit möglich ist: Die Geschwindigkeit muß entweder kleiner sein als die obere Grenze, die in der Ungleichung (1) angegeben ist, oder größer als die untere Grenze der Ungleichung (2). Für die dazwischen liegenden Geschwindigkeiten gibt es nur instationäre Flammenwanderung. Die Arbeit behandelt stationäre Flammen mit Geschwindigkeiten im ersten Geschwindigkeitsgebiet, die sog. „Verbrennungen“. Für solche gibt der Energiesatz eine einfache Beziehung (5), mit der man z. B. beurteilen kann, ob ein Kraftstoffgemisc…

1973

In the present paper the connection between an arbitrary polydisperse property and the molecular weight distribution is investigated using exact mathematical methods. On the basis of the superposition principle a general equation is derived which can be applied e.g. to the polydispersity problems connected with the Gel Permeation Chromatography, to the light scattering from dilute solutions of high polymers, or the ultracentrifuge. From this point of view, each of these phenomena is described by help of a linear operator with a special kernel, the analytical or numerical inversion of the operator yielding the molecular weight distribution of the system by help of an uniform algorithm. In de…

Improved embedded molecular cluster model

2002

We demonstrate that boundary effects (i.e., displacements of the cluster boundary atoms from their lattice sites and the difference between effective charges of the perfect crystal atoms and those of the cluster atoms in the case of a cluster with no point defect in it) in an embedded molecular cluster (EMC) model can be radically reduced. A new embedding scheme is proposed. It includes search for the structural elements (SE) of which perfect crystal is composed, use of corresponding to these SE expression for the total energy, and application of the degree of localization of equations consistent with the wave functions of the cluster. To get equations for the cluster wave functions, the pr…

Experimental evidence for fractional time evolution in glass forming materials

2002

The infinitesimal generator of time evolution in the standard equation for exponential (Debye) relaxation is replaced with the infinitesimal generator of composite fractional translations. Composite fractional translations are defined as a combination of translation and the fractional time evolution introduced in [Physica A, 221 (1995) 89]. The fractional differential equation for composite fractional relaxation is solved. The resulting dynamical susceptibility is used to fit broad band dielectric spectroscopy data of glycerol. The composite fractional susceptibility function can exhibit an asymmetric relaxation peak and an excess wing at high frequencies in the imaginary part. Nevertheless…