Small Mean Free Path Research Articles

On the sampling of step length in Monte Carlo simulation of trajectories with very small mean free path

In detailed (event-by-event) simulation of trajectories of particles (electrons, ions) in liquids and solids the step length sampling method is often based on a total mean free path λ=(n·σ)−1, where n is the number of scatterers per unit volume and σ the total cross section. Typically, the step length s between scattering events is then generated by means of a sampling formula s=−λln(1−R), where R a random number in the interval 0<R<1; the probability for the particle to travel a distanced s without interaction is then exp(−s/λ). It is here argued that this “conventional” sampling method, which implies that the average distance between successive events is equal to λ, is erroneous unless λ is much larger than the distance dnn=n−1/3 between nearest neighbour scatterers. An alternative sampling method, M (monolayer) sampling, is proposed, with a fixed step length D=dnn and a finite probability I=1−exp(−D/λ) of interaction at the end of each step. According to M sampling, conventional sampling exaggerates the number of events per unit path length unless λ⪢dnn. Consequently, quantities like stopping power are overestimated, while transport mean free path is underestimated. The true (corrected) mean free path λc between events is found to be λc=D/(1−exp(−D/λ). The correction is substantial when λ is comparable to or smaller than the distance between the scatterers, in practice for very low energy particles in liquids and solids. In the opposite limit λ⪢D, conventional and M sampling produce the same result. Present results further indicate that conventional sampling using the corrected total mean free path λc is a good approximation to M sampling.

Neutron electric dipole moment measurement with a buffer gas comagnetometer

A neutron EDM measurement with a comagnetometer is discussed. For magnetometry, polarized xenon atoms are injected into a cylindrical cell where a cylindrically symmetric magnetic field and an electric field are applied for the EDM measurement. The geometric phase effect (GPE), which originates from particle motion in a magnetic field gradient, is analyzed in terms of the Dyson series. The motion of the xenon atom is largely suppressed because of a small mean free path. The field gradient is controlled by means of NMR measurements, where the false effect of Earthʼs rotation is removed. As a result, the GPE is reduced below 10−28e cm.

Diffusion Limit of Small Mean Free Path of Transfer Equation in

This article is devoted to establish the well-posedness of solutions and diffusion limit of the small mean free path of the nonlinear transfer equations, which describes the spatial transport of radiation in a material medium. By using the comparison principle, we obtain the lower bound and upper bound of the solution, and then we prove the existence and uniqueness of the global solution. We show that the nonlinear transfer equation has a diffusion limit as the mean free path tends to zero. Our proof is based on asymptotic expansions. We show that the validity of these asymptotic expansions relies only on the smoothness of initial data, while two hypotheses, Fredholm alternative and centering condition, are removed.

Attosecond spectroscopy of solids: Streaking phase shift due to lattice scattering

Theory of laser-assisted photoemission from solids is developed for a numerically exactly solvable model with full inclusion of band structure effects. The strong lattice scattering in the vicinity of band gaps leads to a distortion and a temporal shift of the streaking spectrogram of the order of 100 as. The effect is explained in terms of Bloch electron dynamics and is shown to remain large for an arbitrarily small photoelectron mean free path. The implications for the streaking experiment on W(110) [A. L. Cavalieri et al., Nature (London) {\bf 449}, 1029 (2007)]

The parameters optimization and abrasion wear mechanism of liquid fuel HVOF sprayed bimodal WC–12Co coating

In this work, the spray parameters of the bimodal WC–12Co powder are optimized by Taguchi experiment program by using liquid fuel JP-8000 HVOF spray system with mass flow meter controlling the flux of the medium. The phase composition, microstructure, hardness, porosities, fracture toughness, per-pass deposited thickness and the abrasive wear mechanism of the coatings have been studied in detail. The results indicate that the varying of the spraying parameters shows little effect on the phase composition of the WC–12Co coatings but great influence on their other performance such as hardness, porosity, fracture toughness and the per-pass thickness of coatings. High hardness of the coatings usually means low porosity, low fracture toughness, low per-pass thickness and high wear resistance for the HVOF WC–12Co coatings. The bimodal coating deposited under the optimal spray parameter exhibits excellent performance, which can be attributed to its small mean free path of the cobalt binder resulting from the bimodal distribution of WC particles. As last, three groups of spray parameters, named as economic, moderate and high level spray parameters, are suggested according to the results of Taguchi experiment program and the applied situation of the coated parts as well as their preparation cost.

Numerical approximation of Knudsen layer for the Euler-Poisson system

In this work, we consider the computation of the boundary conditions for the linearized Euler-Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute numerically the boundary conditions in the hydrodynamic limit relying on an analysis of the boundary layers. In this paper, we will extend these techniques in the case of the coupled Euler-Poisson system.

Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes

AbstractWe propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime. The typical example we discuss is the derivation of the Euler system from the BGK equation. The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.

Effect of temperature and load on three-body abrasion of cermets and steel

The effect of temperature and load on three-body abrasion resistance has been examined for stainless steel, Cr 3C 2–Ni cermet, plain WC–Co hardmetal and yttria stabilized zirconia doped WC-based composites. Series of tests at various tribo-conditions were performed on a recently developed device. Coefficient of friction and materials response to abrasive actions have been analyzed and positive effect of zirconia addition on materials wear resistance has been shown. The low wear rates of ZrO 2 containing cermets are due to lower susceptibility of zirconia to transgranular crack propagation, smaller mean free path between ceramic grains and formation of lubricating glazed silica-rich layer.

High Thermoelectric Figure-of-Merit in Kondo Insulator Nanowires at Low Temperatures

We predict a large thermoelectric figure-of-merit in Kondo insulator nanowires at low temperatures. The high ZT values are due to the Kondo effect for electrons and boundary scattering on phonons. We simulated the electron properties of the bulk Kondo insulators within the framework of dynamical mean field theory and found that electrons have short mean free path. In nanowire structures, electron transport is hardly affected by the boundary scattering due to their small intrinsic mean free paths while phonons are strongly scattered due to classical size effect. The results suggest that the nanostructures of Kondo insulators can be designed for high performance thermoelectric cooling devices at low temperatures.

Solar near-relativistic electron observations as a proof of a back-scatter region beyond 1 AU during the 2000 February 18 event

Aims. We study the near-relativistic (NR; > 30 keV) electron event observed on 2000 February 18 by near-Earth spacecraft. Previous works have explained this event by assuming that the propagation of NR electrons is essentially “scatter-free” at heliocentric radial distances r 1 AU, and that beyond 1 AU particles are “back-scattered” by magnetic field irregularities.Methods. Our aim is to re-visit this interplanetary propagation scenario and infer the injection profile at the Sun by fitting the electron directional intensities observed by the Advanced Composition Explorer .Results. We use a Monte Carlo transport model to explore this approach. We assume that the interplanetary magnetic field is an Archimedean spiral and that the interplanetary transport of NR electrons is characterized by a large radial mean free path ( > 0.5 AU) and anisotropic pitch-angle scattering for r AU, and a small radial mean free path ( 0.5 AU) and isotropic scattering in the back-scatter region.Conclusions. The event cannot be explained without assuming a back-scatter region beyond 1 AU. The best fit is obtained by assuming = 3.2 AU in the inner heliosphere and a back-scatter region characterized by a small mean free path = 0.2 AU located beyond 1.2 AU.

Fractional Diffusion Limit for Collisional Kinetic Equations

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation.

Convergence to rarefaction waves for the nonlinear Boltzmann equation and compressible Navier–Stokes equations

The main purpose of this paper is to study the asymptotic equivalence of the Boltzmann equation for the hard-sphere collision model to its corresponding Euler equations of compressible gas dynamics in the limit of small mean free path. When the fluid flow is a smooth rarefaction (or centered rarefaction) wave with finite strength, the corresponding Boltzmann solution exists globally in time, and the solution converges to the rarefaction wave uniformly for all time (or away from t = 0 ) as ϵ → 0 . A decomposition of a Boltzmann solution into its macroscopic (fluid) part and microscopic (kinetic) part is adopted to rewrite the Boltzmann equation in a form of compressible Navier–Stokes equations with source terms. In this setting, the same asymptotic equivalence of the full compressible Navier–Stokes equations to its corresponding Euler equations in the limit of small viscosity and heat conductivity (depending on the viscosity) is also obtained.

Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates.

A transport calculation with an embedded (3+1)d hydrodynamic evolution: Elliptic flow as a function of transverse momentum at SPS energies

The transverse momentum dependence of elliptic flow of pions calculated in a full (3+1)d Boltzmann approach with an intermediate hydrodynamic stage for heavy ion reactions for CERN-SPS energies is discussed in the context of the experimental data. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to larger elliptic flow. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data. Within this integrated dynamical approach different equations of state are applied without adjusting the initial state and the freeze-out conditions. We employ a hadron gas equation of state to investigate the differences in the dynamics and viscosity effects, a chiral equation of state with a moderate first order phase transition and a critical endpoint and a bag model equation of state with a large latent heat. The elliptic flow results are shown to be rather insensitive to changes in the equation of state.

Ideal hydrodynamics and elliptic flow at CERN Super Proton Synchrotron (SPS) energies: Importance of the initial conditions

The elliptic flow excitation function calculated in a full ($3+1$) dimensional hybrid Boltzmann approach with an intermediate hydrodynamic stage for heavy ion reactions from GSI Schwerionen Synchrotron to the highest CERN Super Proton Synchrotron (SPS) energies is discussed in the context of the experimental data. In this study, we employ a hadron gas equation of state to investigate the differences in the dynamics and viscosity effects. The specific event-by-event setup with initial conditions and freeze-out from a nonequilibrium transport model allows for a direct comparison between ideal fluid dynamics and transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. In contrast to previous studies within pure hydrodynamics, the more realistic initial conditions employed here and the inclusion of a sequential final state hadronic decoupling provides results that are in line with the experimental data almost over the whole energy range from ${E}_{\mathrm{lab}}=2\text{\ensuremath{-}}160A$ GeV. Thus, this new approach leads to a substantially different shape of the ${v}_{2}/\ensuremath{\epsilon}$ scaling curve as a function of $(1/S{\mathit{dN}}_{\mathrm{ch}}/\mathit{dy})$ in line with the experimental data compared to previous ideal hydrodynamic calculations. This hints at a strong influence of the initial conditions for the hydrodynamic evolution on the finally observed ${v}_{2}$ values, thus questioning the standard interpretation that the hydrodynamic limit is only reached at BNL Relativistic Heavy Ion Collider energies.

Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions

The elliptic flow excitation function calculated in a Boltzmann approach with an intermediate hydrodynamic stage for heavy-ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. The specific setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and hadronic transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. The lower mean free path leads to higher pressure gradients in the early stage and as a consequence to higher elliptic flow values even without a phase transition. Special emphasis is put on the influence of the initial conditions on the results of the hybrid model calculation. Event-by-event fluctuations are directly taken into account via event-wise non-equilibrium initial conditions generated by the primary collisions and string fragmentations in the microscopic UrQMD model. This leads to non-trivial velocity and energy density distributions for the hydrodynamical initial conditions. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data almost over the whole energy range from E lab=2–160A GeV.

Synthesis and electric, magnetic properties of single crystalline and twin-crystalline Co-doped ZnO thin films

c-oriented Co-doped ZnO （Zn0.96Co0.04O） thin films have been grown on the a-plane and c-plane sapphire substrates using molecular-beam epitaxy, respectively. In contrast to single crystalline Zn0.96Co0.04O film grown on a-plane sapphire, the film grown on c-plane sapphire were found to be twin-crystalline; some domains have a 30° rotation to reduce the large mismatch. The presence of these rotation domains in the twin-crystalline ZnO thin film causes much more carrier scattering at the boundaries, leading to much lower mobility and smaller mean free path of the mobile carriers, as compared with those of the single crystalline one. X-ray absorption fine structure studies revealed that most Co ions were in divalent state and actually substituted into ZnO lattice without formation of any detectable secondary phase. As compared with just a small saturation moment in the single crystalline Zn0.96Co0.04O thin film, the much stronger ferromagnetism in the twin-crystalline one indicates that the ferromagnetic origin should be highly correlated with structural defects in the twin-crystalline film. The possible magnetic mechanisms were discussed.

Transport coefficients of multi-particle collision algorithms with velocity-dependent collisionrules

Detailed calculations of the transport coefficients of a recently introduced particle-basedmodel for fluid dynamics with a non-ideal equation of state are presented. Excluded volumeinteractions are modeled by means of biased stochastic multi-particle collisions whichdepend on the local velocities and densities. Momentum and energy are exactly conservedlocally. A general scheme to derive transport coefficients for such biased, velocity-dependentcollision rules is developed. Analytic expressions for the self-diffusion coefficientand the shear viscosity are obtained, and very good agreement is found withnumerical results at small and large mean free paths. The viscosity turns out to beproportional to the square root of temperature, as in a real gas. In addition, thetheoretical framework is applied to a two-component version of the model, andexpressions for the viscosity and the difference in diffusion of the two speciesare given.

Uniformalization of AT cut quartz crystal wafer thickness using open‐air type plasma CVM process

AbstractImprovement of thickness variation of the AT cut quartz crystal wafer is very important to advance the performance of the quartz resonator and to improve the productivity. However, conventional machining cannot exceed its technical limit any more, because quartz crystal is brittle and the wafer having thickness less than several tens of micrometers is required. We have newly developed the chemical finishing process to correct the thickness variation of the quartz crystal wafer, which utilizes localized atmospheric pressure plasma without gas replacing process. In the case of the atmospheric pressure plasma, high‐density plasma region is localized in the vicinity of the electrode because of its small mean free path. Removal volume is proportional to the dwelling time of the plasma on the workpiece surface. Therefore, free figuring without mask pattern is realized by numerically controlled scanning of the localized reactive area. By applying our proposed correcting process, thickness variation of the commercially available AT cut quartz crystal wafer was improved from 270 to 40 nm. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Numerical Schemes of Diffusion Asymptotics and Moment Closures for Kinetic Equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.