Conventional Boundary Conditions Research Articles

Effects of the confining interaction on mesoscopic superconducting cylinders

AbstractThe most important feature of a mesoscopic superconductor is that its shape and size have an important effect on the interplay of the magnetic field and superconducting condensate. Usually this effect is investigated via the Ginzburg‐Landau (GL) equations, solved together with the conventional boundary condition. This condition implies that the normal component of the superconducting current is equal to zero. However, the approach based on the GL functional for the free energy does not include the contribution acquired by the cooper pairs due to the confining interaction. In this work we use a generalized GL theory proposed by Shanenko and Ivanov, including the confining interaction, in order to study the way the terms arising from the confining potential affect the critical behavior in mesoscopic superconducting samples with cylindrical symmetry without an applied magnetic field. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

3D quantum transport solver based on the perfectly matched layer and spectral element methods for the simulation of semiconductor nanodevices

A 3D quantum transport solver based on the spectral element method (SEM) and perfectly matched layer (PML) is introduced to solve the 3D Schrödinger equation with a tensor effective mass. In this solver, the influence of the environment is replaced with the artificial PML open boundary extended beyond the contact regions of the device. These contact regions are treated as waveguides with known incident waves from waveguide mode solutions. As the transmitted wave function is treated as a total wave, there is no need to decompose it into waveguide modes, thus significantly simplifying the problem in comparison with conventional open boundary conditions. The spectral element method leads to an exponentially improving accuracy with the increase in the polynomial order and sampling points. The PML region can be designed such that less than −100 dB outgoing waves are reflected by this artificial material. The computational efficiency of the SEM solver is demonstrated by comparing the numerical and analytical results from waveguide and plane-wave examples and its utility is illustrated by multiple-terminal devices and semiconductor nanotube devices.

Cosmic inflation and the past hypothesis

The past hypothesis is that the entropy of the universe was very low in the distant past. It is put forward to explain the entropic arrow of time but it has been suggested (e.g. [Penrose, R. (1989a). The emperor’s new mind. London:Vintage Books; Penrose, R. (1989b). Annals of the New York Academy of Sciences, 571, 249–264; Price, H. (1995). In S. F. Savitt (Ed.), Times’s arrows today. Cambridge: Cambridge University Press; Price, H. (1996). Time’s arrow and Archimedes’ point. Oxford: Oxford University Press; Price, H. (2004). In C. Hitchcock (Ed.), Contemporary debates in philosophy of science. Oxford: Blackwell]) that it is itself in need of explanation. It has also been suggested that cosmic inflation could provide the explanation, but Price (2004) raises a serious objection to this suggestion, which has otherwise received very little attention in the philosophical literature. Price points out that the standard inflationary explanation involves a double standard: although the evolution of the universe described by the inflationary model seems natural from the standard temporal perspective it looks highly unnatural from the reversed temporal perspective. The main purpose of this paper is to propose a novel form of the inflationary explanation that avoids this objection. It is argued that the inflationary model would not involve a double standard (but would still explain the past hypothesis) if we construct the model with a global “boundary” condition instead of a conventional boundary condition: if we assume that the universe is as generic as possible overall, rather than as generic as possible at some given point (e.g. the Big Bang) as is assumed in the standard inflationary model. This novel form of the inflationary explanation is then compared with Price’s 1996 preferred explanation, a version of the so-called “Weyl hypothesis”.

On relativistic models of strange stars

The superdense stars with mass-to-size ratio exceeding 0.3 are expected to be made of strange matter. Assuming that the 3-space of the interior space-time of a strange star is that of a three-paraboloid immersed in a four-dimensional Euclidean space, we obtain a two-parameter family of their physically viable relativistic models. This ansatz determines density distribution of the interior self-gravitating matter up to one unknown parameter. The Einstein’s field equations determine the fluid pressure and the remaining geometrical variables. The information about mass-to-size ratio together with the conventional boundary conditions lead to the determination of total mass, radius and other parameters of the stellar configuration.

A new time-domain drag description and its influence on the dynamic behaviour of a cantilever pipe conveying fluid

Studying dynamic stability of a vertically suspended, fully submerged pipe conveying fluid upwards, researchers have found a contradiction between theoretical predictions and experiments. Experiments did not show any instability, while theory predicts instability at infinitesimally low fluid velocities for a pipe without dissipation mechanisms. To explain this contradiction, in 2005 Paidoussis and co-workers postulated a new description of the boundary condition at the free end of the pipe. Subject to this boundary condition the pipe is predicted to become unstable by divergence (stable node to saddle bifurcation) at a velocity higher than yet achieved in experiments. In this paper, it is shown that a realistic description of hydrodynamic drag in combination with conventional boundary conditions might result in even higher critical velocity, and hence, this could also be an explanation of the contradiction. The description of the hydrodynamic drag is based on experimental data available in literature. This data has been obtained by experimenting with submerged rigid cylinders. To make it applicable to flexible pipes, a key step is undertaken in this paper to translate the data from the frequency domain to the time domain. Using the time-domain description of the hydrodynamic drag in combination with the conventional boundary conditions at the free end, it is shown that the pipe becomes unstable by flutter (stable focus to unstable focus bifurcation) at a critical velocity, which is much higher than that attainable in small-scale experiments. For fluid velocities exceeding the critical one, the pipe motion reaches a steady oscillation of finite amplitude, i.e. a stable limit cycle.

General continuum boundary conditions for miscible binary fluids from molecular dynamics simulations

Molecular dynamics simulations are used to explore the flow behavior and diffusion of miscible fluids near solid surfaces. The solid produces deviations from bulk fluid behavior that decay over a distance of the order of the fluid correlation length. Atomistic results are mapped onto two types of continuum model: Mesoscopic models that follow this decay and conventional sharp interface boundary conditions for the stress and velocity. The atomistic results, and mesoscopic models derived from them, are consistent with the conventional Marangoni stress boundary condition. However, there are deviations from the conventional Navier boundary condition that states that the slip velocity between wall and fluid is proportional to the strain rate. A general slip boundary condition is derived from the mesoscopic model that contains additional terms associated with the Marangoni stress and diffusion, and is shown to describe the atomistic simulations. The additional terms lead to strong flows when there is a concentration gradient. The potential for using this effect to make a nanomotor or pump is evaluated.

A continuum of unusual self-adjoint linear partial differential operators

In an earlier publication a linear operator T Har was defined as an unusual self-adjoint extension generated by each linear elliptic partial differential expression, satisfying suitable conditions on a bounded region Ω of some Euclidean space. In this present work the authors define an extensive class of T Har -like self-adjoint operators on the Hilbert function space L 2 ( Ω ) ; but here for brevity we restrict the development to the classical Laplacian differential expression, with Ω now the planar unit disk. It is demonstrated that there exists a non-denumerable set of such T Har -like operators (each a self-adjoint extension generated by the Laplacian), each of which has a domain in L 2 ( Ω ) that does not lie within the usual Sobolev Hilbert function space W 2 ( Ω ) . These T Har -like operators cannot be specified by conventional differential boundary conditions on the boundary of ∂ Ω , and may have non-empty essential spectra.

Optical transitions in semiconductor nanostructures

Abstract Employing the Maxwell equations and conventional boundary conditions for the radiation field on the nanostructure interfaces, we compute the radiative spontaneous decay rate of optical transitions in spherical semiconductor nanocrystals, core–shell nanocrystals and nanostructures comprising more than one shell. We also show that the coupling between optical transitions localized in the shell of core–shell nanocrystals and radiation field is determined by both conventional electro-multipole momenta and electro-multipole “inverse” momenta. The latter are proportional to the core radius even for interband transitions that should result in very strong optical transitions.

Slipping Stokes flow around a slightly deformed sphere

When a fluid may slip at the surface of a particle, the conventional boundary condition must be modified to incorporate the tangential stress at the surface. Even for the simplest nontrivial shapes of the slip particle, the resulting Stokes problem could not be analytically solved. We present a first attempt to obtain analytical approximations for the resistance relations for a rigid, slightly deformed slip sphere in an unbounded Stokesian flow. To the first order in the small parameter characterizing the deformation, we derive expressions for the hydrodynamic force and torque exerted on the particle, which are found to be in very good agreement with the available numerical results, even in the case in which deformations are not small. The drag force on a spheroid is found to be an either decaying or growing function of the aspect ratio of the particle.

Elastic Bag Model for Molecular Dynamics Simulations of Solvated Systems: Application to Liquid Water and Solvated Peptides

The fluctuating elastic boundary (FEB) model for molecular dynamics has recently been developed and validated through simulations of liquid argon. In the FEB model, a flexible boundary which consists of particles connected by springs is used to confine the solvated system, thereby eliminating the need for periodic boundary conditions. In this study, we extend this model to the simulation of bulk water and solvated alanine dipeptide. Both the confining potential and boundary particle interaction functions are modified to preserve the structural integrity of the boundary and prevent the leakage of the solute-solvent system through the boundary. A broad spectrum of structural and dynamic properties of liquid water are computed and compared with those obtained from conventional periodic boundary condition simulations. The applicability of the model to biomolecular simulations is investigated through the analysis of conformational population distribution of solvated alanine dipeptide. In most cases we find remarkable agreement between the two simulation approaches.

Slip, Immiscibility, and Boundary Conditions at the Liquid-Liquid Interface

The conventional boundary conditions at the interface between two flowing liquids include continuity of the tangential velocity. We have tested this assumption with molecular dynamics simulations of Couette and Poiseuille flows of two-layered liquid systems, with various molecular structures and interactions. When the total liquid density near the interface drops significantly compared to the bulk values, the tangential velocity varies very rapidly there, and would appear discontinuous at continuum resolution. The value of this apparent slip is given by a Navier boundary condition.

NUMERICAL SIMULATION OF ISOTHERMAL MICRO FLOWS BY LATTICE BOLTZMANN METHOD AND THEORETICAL ANALYSIS OF THE DIFFUSE SCATTERING BOUNDARY CONDITION

A Lattice Boltzmann model for simulating micro flows has been proposed by us recently (Europhysics Letters, 67(4), 600–606 (2004)). In this paper, we will present a further theoretical and numerical validation of the model. In this regards, a theoretical analysis of the diffuse-scattering boundary condition for a simple flow is carried out and the result is consistent with the conventional slip velocity boundary condition. Numerical validation is highlighted by simulating the two-dimensional isothermal pressure-driven micro-channel flows and the thin-film gas bearing lubrication problems, and comparing the simulation results with available experimental data and analytical predictions.

An accurate and efficient self-consistent approach for calculating electron transport throughmolecular electronic devices: including the corrections of electrodes

A self-consistent ab initio approach for calculating electron transport through molecularelectronic devices is developed. It is based on density functional theory (DFT) calculationsand the Green’s function technique employing a finite basis of local orbitals. The device isrigorously separated into the extended molecule region and the electrode region. In theDFT part calculating the Hamiltonian matrix of the extended molecule fromits density matrix, the electrostatic correction induced by electrodes and theexchange–correlation correction due to the spatial diffuseness of localized basis functionsare included. Our approach is efficient and accurate, with a controllable error todeal with such open systems. A one-dimensional infinite gold monatomic chain,whose electronic structure can be known from conventional DFT calculations withperiodic boundary conditions (PBCs), is employed to validate the accuracy of ourapproach. With both corrections, our result for the gold chain at equilibrium is inexcellent agreement with the PBC DFT result. We find that, for the gold chain, theexchange–correlation correction is more significant than the electrostatic correction.

Experimental study of substrate roughness and surfactant effects on the Landau-Levich law

In this work we present an experimental study of deviations from the classical Landau-Levich law in the problem of dip coating. Among the examined causes leading to deviations are the nature of the liquid-gas and liquid-solid interfaces. The thickness of the coating film created by withdrawal of a plate from a bath was measured gravimetrically over a wide range of capillary numbers for both smooth and well-characterized rough substrates, and for clean and surfactant interface cases. In view of the dependence of the lifetime of a film on the type of liquid and substrate, and liquid-gas and liquid-solid interfaces, we characterized the range of measurability of the film thickness in the parameter space defined by the withdrawal capillary number, the surfactant concentration, and substrate roughness size. We then study experimentally the effect of a film thickening due to the presence of surfactants. Our recent theory based on a purely hydrodynamic role of the surface active substance suggests that there is a sorption-controlled coating regime in which Marangoni effects should lead to film thinning. However, our experiments conducted in this regime demonstrate film thickening, calling into question the conventional wisdom, which is that Marangoni stresses (as accounted by the conventional interfacial boundary conditions) lead to film thickening. Next we examine the effect of well-characterized substrate roughness on the coated film thickness, which also reveals its influence on wetting-related processes and an effective boundary condition at the wall. In particular, it is found that roughness results in a significant thickening of the film relative to that on a smooth substrate and a different power of capillary number than the classical Landau-Levich law.

Kinetic Boundary Condition at a Vapor-Liquid Interface

By molecular dynamics simulations, the boundary condition for the Boltzmann equation at a vapor-liquid interface is found to be the product of three one-dimensional Maxwellian distributions for the three velocity components of vapor molecules and a factor including a well-defined condensation coefficient. The Maxwellian distribution for the velocity component normal to the interface is characterized by the liquid temperature, as in a conventional model boundary condition, while those for the tangential components are prescribed by a different temperature, which is a linear function of energy flux across the interface. The condensation coefficient is found to be constant and equal to the evaporation coefficient determined by the liquid temperature only.

Oxygen exchange and diffusion measurements: The importance of extracting the correct initial and boundary conditions

18O / 16O exchange followed by Secondary Ion Mass Spectrometry (SIMS) analysis is often used to determine the oxygen tracer diffusion coefficient D* and the oxygen surface exchange coefficient k* of oxide materials. Conventionally, the experiment consists of annealing an equilibrated, semi-infinite medium, in which the initial isotope fraction is c bg, in a volume of gas of constant isotope fraction c g. In this paper we consider the errors that may be introduced into the transport parameters if the conventional initial and boundary conditions are assumed, when extracting D* and k* from experimental data, but the actual conditions, under which the anneal was carried out, are significantly different. Particular attention is given to the problem of isotope depletion from the gas phase when annealing materials that display high values of D* and k*.

Finite-Temperature Field Theory on the Light Front

The formulation of statistical physics using light-front quantization, instead of conventional equal-time boundary conditions, has important advantages for describing relativistic statistical systems, such as heavy ion collisions. We develop light-front field theory at finite temperature and density with special attention to quantum chromodynamics. First, we construct the most general form of the statistical operator allowed by the Poincare algebra. In light-front quantization, the Green's functions of a quark in a medium can be defined in terms of just 2-component spinors and does not lead to doublers in the transverse directions. Since the theory is non-local along the light cone, we use causality arguments to construct a solution to the related zero-mode problem. A seminal property of light-front Green's functions is that they are related to parton densities in coordinate space. Namely, the diagonal and off-diagonal parton distributions measured in hard scattering experiments can be interpreted as light-front density matrices.

Finite-Element Analysis of Scattering From a Complex BOR Using Spherical Infinite Elements

Recently, a new type of infinite elements (IFEs) was proposed as an accurate and efficient mesh truncation method for the finite element analysis of open–region acoustic scattering. These IFEs are based on the radial expansion of the scattered field and are used to model the scattered field outside a separable surface characterized by a constant radial coordinate (such as a spherical or a spheroidal surface in three dimensions). In this paper, spherical infinite elements are formulated and implemented for the finite element (FE) analysis of time–harmonic electromagnetic scattering from a complex body of revolution (BOR), and their performance is studied by comparison with the finite element solution using conventional absorbing boundary conditions (ABCs). Numerical results are presented to demonstrate that the new type of infinite elements is indeed more accurate than both the first– and second–order ABCs.

Boundary conditions for 3D dynamic models of ablation of ceramics by pulsed mid-infrared lasers

We present and discuss a set of boundary conditions (BCs) to use in three-dimensional, mesoscopic, finite element models of mid-infrared pulsed laser ablation of brittle materials. These models allow the study of the transient displacement and stress fields generated at micrometer scales during and after one laser pulse, where using conventional BCs may lead to some results without physical significance that can be considered an artefact of the calculations. The proposed BCs are tested and applied to a micrometer-scale continuous model of human dental enamel under CO 2 radiation (10.6 μm, 0.35 μs pulse, sub-ablative fluence), giving rise to the following results: the highest stress is obtained at the irradiated surface of the model, at the end of the laser pulse, but afterwards it decreases rapidly until it becomes significantly lower than the stress in a region 2.5 μm deep in the model; a thermally induced vibration in the material is predicted. This non-intuitive dynamics in stress and displacement distribution cannot be neglected and has to be considered in dynamic laser ablation models, since it may have serious implications in the mechanisms of ablation.

DSMC simulation of low-speed gas flow and heat transfer in 2D rectangular micro-channel

Effective boundary condition is one of the most critical problems in the computation of micro-channel flows with direct simulation Monte-Carlo (DSMC) method. In the present work, the implementation of DSMC with specified pressure boundary condition (PBC) was discussed in detail. The variations of gaseous local pressure, temperature and number density of the particles caused by the temperature difference between channel walls and gas were presented. It was found that with the increase of both gaseous compressibility and rarefaction, the pressure distribution along micro-channel became more nonlinear. Heat transfer occurred almost only at channel inlet and outlet, and the average wall heat flux increased almost linearly to the inlet-to-outlet pressure ratio. The computational results also showed that PBC was more suitable for the simulation of micro-channel flow problems than the conventional velocity boundary condition (VBC).