Linear and fractal diffusion coefficients in a family of one dimensional chaotic maps

We analyse deterministic diffusion in a simple, one-dimensional setting consisting of a family of four parameter dependent, chaotic maps defined over the real line. When iterated under these maps, a probability density function spreads out and one can define a diffusion coefficient. We look at how the diffusion coefficient varies across the family of maps and under parameter variation. Using a technique by which Taylor-Green-Kubo formulae are evaluated in terms of generalised Takagi functions, we derive exact, fully analytical expressions for the diffusion coefficients. Typically, for simple maps these quantities are fractal functions of control parameters. However, our family of four maps exhibits both fractal and linear behavior. We explain these different structures by looking at the topology of the Markov partitions and the ergodic properties of the maps.Comment: 21 pages, 19 figure

Thermostating by deterministic scattering: the periodic Lorentz gas

We present a novel mechanism for thermalizing a system of particles in equilibrium and nonequilibrium situations, based on specifically modeling energy transfer at the boundaries via a microscopic collision process. We apply our method to the periodic Lorentz gas, where a point particle moves diffusively through an ensemble of hard disks arranged on a triangular lattice. First, collision rules are defined for this system in thermal equilibrium. They determine the velocity of the moving particle such that the system is deterministic, time reversible, and microcanonical. These collision rules can systematically be adapted to the case where one associates arbitrarily many degrees of freedom to the disk, which here acts as a boundary. Subsequently, the system is investigated in nonequilibrium situations by applying an external field. We show that in the limit where the disk is endowed by infinitely many degrees of freedom it acts as a thermal reservoir yielding a well-defined nonequilibrium steady state. The characteristic properties of this state, as obtained from computer simulations, are finally compared to the ones of the so-called Gaussian thermostated driven Lorentz gas.Comment: 13 pages (revtex) with 10 figures (encapsulated postscript

Thermostatting by deterministic scattering

We present a mechanism for thermalizing a moving particle by microscopic deterministic scattering. As an example, we consider the periodic Lorentz gas. We modify the collision rules by including energy transfer between particle and scatterer such that the scatterer mimics a thermal reservoir with arbitrarily many degrees of freedom. The complete system is deterministic, time-reversible, and provides a microcanonical density in equilibrium. In the limit of the disk representing infinitely many degrees of freedom and by applying an electric field the system goes into a nonequilibrium steady state.Comment: 4 pages (revtex) with 4 figures (postscript

The Nose-hoover thermostated Lorentz gas

We apply the Nose-Hoover thermostat and three variations of it, which control different combinations of velocity moments, to the periodic Lorentz gas. Switching on an external electric field leads to nonequilibrium steady states for the four models with a constant average kinetic energy of the moving particle. We study the probability density, the conductivity and the attractor in nonequilibrium and compare the results to the Gaussian thermostated Lorentz gas and to the Lorentz gas as thermostated by deterministic scattering.Comment: 7 pages (revtex) with 10 figures (postscript), most of the figures are bitmapped with low-resolution. The originals are many MB, they can be obtained upon reques

Investigations on nucleophilic layers made with a novel plasma jet technique

In this work a novel plasma jet technique is used for the deposition of nucleophilic films based on (3-aminopropyl)trimethoxysilane at atmospheric pressure. Film deposition was varied with regard to duty cycles and working distance. Spectral ellipsometry and chemical derivatization with 4-(trifluoromethyl)benzaldehyde using ATR- FTIR spectroscopy measurements were used to characterize the films. It was found that the layer thickness and the film composition are mainly influenced by the duty cycle

Метод экспертных оценок в лингводидактике

Рассматривается использование метода экспертных оценок как в общей системе научно-педагогической экспертной деятельности, так и в рамках ее лингводидактического аспекта. Дается характеристика процедуры проведения экспертизы, а также оценивается перспективность обращения к интеллектуальным компьютерным системам как инструментам экспертного анализа

Deuterium retention in carbon, beryllium, and carbon layers on titanium and beryllium

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Is subdiffusional transport slower than normal?

We consider anomalous non-Markovian transport of Brownian particles in viscoelastic fluid-like media with very large but finite macroscopic viscosity under the influence of a constant force field F. The viscoelastic properties of the medium are characterized by a power-law viscoelastic memory kernel which ultra slow decays in time on the time scale \tau of strong viscoelastic correlations. The subdiffusive transport regime emerges transiently for t<\tau. However, the transport becomes asymptotically normal for t>>\tau. It is shown that even though transiently the mean displacement and the variance both scale sublinearly, i.e. anomalously slow, in time, ~ F t^\alpha, ~ t^\alpha, 0<\alpha<1, the mean displacement at each instant of time is nevertheless always larger than one obtained for normal transport in a purely viscous medium with the same macroscopic viscosity obtained in the Markovian approximation. This can have profound implications for the subdiffusive transport in biological cells as the notion of "ultra-slowness" can be misleading in the context of anomalous diffusion-limited transport and reaction processes occurring on nano- and mesoscales

Modeling of Atmospheric-Pressure Dielectric Barrier Discharges in Argon with Small Admixtures of Tetramethylsilane

A time-dependent, spatially one-dimensional fluid-Poisson model is applied to analyze the impact of small amounts of tetramethylsilane (TMS) as precursor on the discharge characteristics of an atmospheric-pressure dielectric barrier discharge (DBD) in argon. Based on an established reaction kinetics for argon, it includes a plasma chemistry for TMS, which is validated by measurements of the ignition voltage at the frequency f=86.2kHz for TMS amounts of up to 200 ppm. Details of both a reduced Ar-TMS reaction kinetics scheme and an extended plasma-chemistry model involving about 60 species and 580 reactions related to TMS are given. It is found that good agreement between measured and calculated data can be obtained, when assuming that 25% of the reactions of TMS with excited argon atoms with a rate coefficient of 3.0×10−16m3/s lead to the production of electrons due to Penning ionization. Modeling results for an applied voltage Ua,0=4kV show that TMS is depleted during the residence time of the plasma in the DBD, where the percentage consumption of TMS decreases with increasing TMS fraction because only a finite number of excited argon species is available to dissociate and/or ionize the precursor via energy transfer. Main species resulting from that TMS depletion are presented and discussed. In particular, the analysis clearly indicates that trimethylsilyl cations can be considered to be mainly responsible for the film formation