Diffusion,drift and their interrelation through volume density

The evolution of the understanding of the mass transport phenomena in solids and liquids allows for the unification of phenomenological models. The central Darken problem is considered from the choice of the coordinate axes for diffusion, i.e. the definition of this mode of motion and the method of diffusion displacement is defined and measured. Euler's and Liouville theorems are used extensively in the analysis. The formula is derived for volume density conservation, i.e. the volume continuity equation. This fundamental formula defines the volume-fixed frame of reference in the multicomponent solid, gas and liquid solutions. The volume-fixed frame of reference is self-consistent with the foundations of linear irreversible thermodynamics, except that is recognises the need to add volume density to the usual list of extensive physical properties undergoing transport in every continuum. Proposed modifications are self-consistent with the literature dating back to Onsager, the experiments of Kirkendall, their interpretation by Darken and recent generalized formulations. It will be shown that the method can be used in mechano-chemistry and electro-mechano-chemistry.     

Bi-velocity hydrodynamics

Theoretical evidence derived from linear irreversible thermodynamics (LIT) jointly with Burnett’s solution of Boltzmann’s gas-kinetic equation is used to show that fluid mechanics and transport processes in both gaseous and liquid continua require the use of two independent velocities rather than one in order to correctly quantify the physics of fluid motion. This finding, reflecting the coalescence of macroscopic and molecular perspectives, undermines the current foundations of continuum fluid mechanics. Of the two required context-specific velocities, one is the mass velocity appearing in the continuity equation. The other is the volume velocity entering into the constitutive equation for the mechanical rate-of-working term appearing in the energy equation, where it serves as the multiplier of the pressure tensor . While the analysis involves only linear constitutive principles, the fundamental need for two independent velocities is noted to apply even in non-linear circumstances. A major consequence of these findings is that the Navier-Stokes-Fourier equations governing continuum fluid physics are incomplete for both single- and multi-component fluids. Our results are independently supported by the work of others based upon the use of conventional single-velocity arguments accompanied by ad hoc extensions of LIT. Our bi-velocity findings point to the existence of novel mechanodiffusive phenomena in fluid continua, entailing coupling between viscous flow and diffusion, whether referring to the diffusion of thermal energy in single-component non-isothermal fluids or of chemical species in inhomogeneous multicomponent mixtures.     

Mass transport theory for the Toda lattices, dispersive and dissipative

To establish mass transport theory on nonlinear lattices, we formulate the Korteweg–deVries (KdV) equation and the Burgers equation using the flow variable representation so as to facilitate comparison with the Boltzmann equation and with the Cahn–Hilliard equation in classical statistical mechanics. We also study Toda lattice microdynamics using the Flaschka representation, and compare with the Liouville equation. Like the linear diffusion equation, the Boltzmann equation and the Liouville equation are to be solved for a distribution function, which is intrinsically probabilistic. Transport theory in linear systems is governed by the isotropic motions of the kinetic equations. In contrast, the KdV perturbation equation derived from the Toda lattice microdynamics expresses hydrodynamic mass transport. The KdV equation in hydrodynamics and the Burgers equation in thermodynamics do not involve a probability distribution function. The nonlinear lattices do not retain isotropy of the mass transport equations. In consequence, it is proposed that in the presence of hydrodynamic flows to the left, KdV wave propagation proceeds to the right. This basic property of the KdV system is extended to thermodynamics in the Burgers system. These features arise because linear systems are driven towards an equilibrium by molecular collisions, whereas the inhomogeneities of the nonlinear lattices are generated by the potential energy of interaction. Diffusion as expressed by the Burgers equation is governed not only by a chemical potential, but also by the Toda lattice potential energy.     

Fluid mechanics revisited

Öttinger's recent nontraditional incorporation of fluctuations into the formulation of the friction matrix appearing in the phenomenological GENERIC theory of nonequilibrium irreversible processes is shown to furnish transport equations for single-component gases and liquids undergoing heat transfer which support the view that revisions to the Navier–Stokes–Fourier (N–S–F) momentum/energy equation set are necessary, as empirically proposed by the author on the basis of an experimentally supported theory of diffuse volume transport. The hypothesis that the conventional N–S–F equations prevail without modification only in the case of “incompressible” fluids, where the density ρ of the fluid is uniform throughout, serves to determine the new phenomenological parameter α^′ appearing in the GENERIC friction matrix. In the case of ideal gases the consequences of this constitutive hypothesis are shown to yield results identical to those derived theoretically by Öttinger on the basis of a “proper” coarse-graining of Boltzmann's kinetic equation. A major consequence of the present work is that the fluid's specific momentum density v is equal to its volume velocity v_v, rather than to its mass velocity v_m, contrary to current views dating back 250 years to Euler. In the case of rarefied gases the proposed modifications are also observed to agree with those resulting from Klimontovich's molecularly based, albeit ad hoc, self-diffusion addendum to Boltzmann's collision integral. Despite the differences in their respective physical models—molecular vs. phenomenological—the role played by Klimontovich's collisional addition to Boltzmann's equation in modifying the N–S–F equations is noted to constitute a molecular counterpart of Öttinger's phenomenological fluctuation addition to the GENERIC friction matrix. Together, these two theories collectively recognize the need to address multiple- rather than single-encounter collisions between a test molecule and its neighbors when formulating physically satisfactory statistical–mechanical theories of irreversible transport processes in gases. Overall, the results of the present work implicitly support the unorthodox view, implicit in the GENERIC scheme, that the translation of Newton's discrete mass-point molecular mechanics into continuum mechanics, the latter as embodied in the Cauchy linear momentum equation of fluid mechanics, cannot be correctly effected independently of the laws of thermodynamics. While Öttinger's modification of GENERIC necessitates fundamental changes in the foundations of fluid mechanics in regard to momentum transport, no basic changes are required in the foundations of linear irreversible thermodynamics (LIT) beyond recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in single-species fluid continua, namely mass, momentum and energy. An alternative, nonGENERICally based approach to LIT, derived from our findings, is outlined at the conclusion of the paper. Finally, our proposed modifications of both Cauchy's linear momentum equation and Newton's rheological constitutive law for fluid-phase continua are noted to be mirrored by counterparts in the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffuse volume transport.     

地下坑道周围山体内氡运移力学解析

基于连续介质力学原理,建立氡在地下坑道周围山体内运移的-维径向对称模型,分析在浓度扩散和气体渗流条件下,坑道周围山体内氡浓度分布,并给出氡浓度的解析表达式.用有效运移距离的概念,定量描述对坑道内氡浓度有影响的山体范围,给出有效运移距离和有效孔隙率、比渗流速度之间的关系式,同时给出坑道壁面上氡析出率的表达式.     

Consequences of the Brenner modification to the Navier–Stokes equations for dynamic light scattering

A modification of the classical Navier–Stokes equations has recently been proposed by Brenner [Is the tracer velocity of a fluid continuum equal to its mass velocity? Phys. Rev. E 70 (2004) Art. No. 061201; Kinematics of volume transport, Physica A 349 (2005) 11–59; Navier–Stokes revisited, Physica A 349 (2005) 60–132] and then formalized by Öttinger [Beyond Equilibrium Thermodynamics, Wiley, Hoboken, 2005]. In the modified theory, a contribution for mass diffusion is included in the continuity equation. The argument was based on experimental support from thermophoresis which however depends on the correct formulation of boundary conditions. The controversy therefore remained. Since such an additional mass diffusion transport mode should contribute to dynamic light scattering spectra, the consequences of the modified theory for light scattering spectra are discussed in this work. For liquids, the new theory is consistent with measured scattering data since the modification to the spectrum is usually negligible. The effect could, however, be observable in gases.     

考虑介质膨胀速率的锂离子电池管状电极中扩散诱导应力及轴向支反力分析

硅作为锂离子电池阴极材料相对于传统负极材料具有高比容量,价格低廉等优势.本文针对充电过程中锂离子电池中电极建立力学模型和扩散模型,并在扩散模型引入考虑介质膨胀速率的影响.以硅空心柱形电极为例,分析了恒流充电下介质膨胀速率对电极中扩散诱导应力分布的影响,并研究了不同内外半径比、充电速率、材料参数以及锂化诱导软化系数(lithiation induced softening factor,LISF)对轴向的支反力达到临界欧拉屈曲力所需时间的影响.结果表明,随着电极中锂浓度上升,介质膨胀速率对应力分布的影响增大,对轴向的支反力影响较小.弹性模量和应力成正比,但其与轴向的支反力达到临界欧拉屈曲力所需时间无关;扩散系数与所需时间成反比;偏摩尔体积增大时,达到临界屈曲力所需时间减少;随着LISF绝对值增大,完全锂化时轴向力降低.     

A linear relativistic model of processes with causal faster-than-light effects

To get a synthesis of causal faster-than-light effects and signals that do not propagate faster than light by using local, covariant, linear equations of motion, we propose the following hypothesis. Free fields that propagate signals according to the Klein-Gordon, Dirac, Proca or Maxwell equations, are actually describing only smoothed-out, average properties of underlying causal transport processes of point like entities with arbitrary four-momenta, the states of which are described by a scalar, spinor or four-vector field that satisfies a local, covariant, linear transport equation. An example of such a linear, causal, covariant transport process is shown to display causal faster-than-light effects, to propagate signals not faster than light, and to contain the Klein-Gordon equation as a limiting case. An analogous transport model displays causal, four-vector, faster-than-light effects, and also distinctive four-vector, long-range and short-range effects that do not propagate faster than light.     

Anomalous scaling in epitaxial growth on vicinal surfaces: meandering and mounding instabilities in a linear growth equation with spatiotemporally correlated noise

We have undertaken an extensive analytical and kinetic Monte Carlo study of the (2+1) dimensional discrete growth model on a vicinal surface. A non-local, phenomenological continuum equation describing surface growth in unstable systems with anomalous scaling is presented. The roughness produced by unstable growth is first studied considering various effects in surface diffusion processes (corresponding to temperature, flux, diffusion anisotropy). We found that the thermally activated roughness is well-described by a generalized Lai–Das Sarma–Villain model with non linear growth continuum equation and uncorrelated noise. The corresponding critical exponents are computed analytically for the first time and show a continuous variation in agreement with simulation results of a solid-on-solid model. However, the roughness related to the meandering instability is found, unexpectedly, to be well described by a linear continuum equation with spatiotemporally correlated noise.     

Differential constants of motion for systems of free gravitating particles. I. Newton's theory

Differential constants of motion for systems of free gravitating particles in the Newtonian frame are first defined and then determined. It is shown that they are all implied by the existence of the first integral invariants of Poincaré known from classical mechanics, or by the circulation theorem known from hydrodynamics. It is proved further that the restriction to vacuum conditions does not change the set of differential constants of motion. Another consequence is that nothing can be inferred from local (in space and time) measurements about the displacement, velocity, and orientation of a laboratory in free fall relative to a fixed Galilean frame.     

MAXWELL-Theorie (in Medien) und Quantentheorie in einem rotierenden Bezugssystem

On the basis of our 3-dimensional conceptions of the electromagnetic quantities [1] the MAXWELL theory is represented in a rotating frame of reference. For such a frame the MAXWELL equations obtain additional terms depending on the angular velocity (analogous to the CORIOLIS term etc. in NEWTON ian mechanics). Using these results with the help of the DIRAC equation we investigate quantum mechanics in a rotating frame of reference. Also in this case we obtain interesting additional terms depending on the angular velocity. The need for such a theory is obvious for many reasons: 1. Our Earth is such a rotating laboratory. Later the rotation effects must not be neglected. 2. In magnetic resonance physics theoretical questions with respect to rotating systems are important. 3. Interesting statements result for a rotational JOSEPHSON effect of superconductors. — All our calculations are carried out up to the first order in the angular velocity.     

Transport of volume in a binary liquid

In this paper, the transport of volume in a binary liquid mixture is theoretically investigated in three steps, with strong implications for the measurement of mutual diffusivities in non-dilute mixtures. In a first step, the velocity of volume transport is determined from the transport velocities of the two components and the thermodynamic relation of state of the liquid mixture in equilibrium. The role played by Galilean invariance and the choice of a rigid frame of reference for reckoning current densities is highlighted. The divergence of the volume-transport velocity field is found to involve the isothermal compressibility and the thermal expansivity of the liquid together with the spatiotemporal variations of pressure and temperature. In a second step, a linear-response relation is introduced between the interdiffusion current density and the gradient of composition; this relation phenomenologically defines the mutual diffusivity of the binary liquid in a manifestly Galilean-invariant way. In a third step, it is examined whether the practical measurement of that diffusivity in a constant-volume container entails a vanishing mass-transport or volume-transport velocity. From a singular-perturbation analysis of the hydrodynamic equations, it is shown that the mass-transport velocity vanishes in the limit of a diffusion of composition that is much slower than the diffusion of momentum. As a consequence, the volume-transport velocity does not vanish during interdiffusion even though the law of additive volumes of the components holds. The physical meaning of the non-vanishing volume velocity is interpreted by means of the thermodynamic results obtained in the second step. Some of the conclusions carry over to multicomponent liquid mixtures.     

Stress influence on high temperature oxide scale growth: Modeling and investigation on a thermal barrier coating system

In thermal barrier coating (TBC) systems, an oxide layer develops at high temperature below the ceramic coating, leading in the long term to the mechanical failure of the structure upon cooling. The mechanism of stress-affected oxidation likely to induce the growth of a non-uniform oxide scale detrimental to the TBC lifetime was investigated. A continuum thermodynamics formulation is derived accounting for the influence of the stress and strain situation at the sharp metal/oxide phase boundary on the local oxidation kinetics. It specially includes the contributions of the large volumetric strain and the mass consumption associated with metal oxidation. A continuum mechanics/mass diffusion framework is used along with the developed formulation for the interface evolution to study the growth of an oxide layer coupled with local stress development. The implementation of the model has required the development of a specific simulation tool, based on a finite element method completed with an external routine for the phase boundary propagation. Results on an electron-beam physical vapor deposited (EB-PVD) TBC case are presented. The processes resulting in a non-uniform oxide scale growth are analyzed and the main influences are discussed.     

Nonequilibrium processes in condensed media: Part 1. Experimental studies in light of nonlocal transport theory

Based on experimental research in shock loading of solid-state materials it is shown that among the important dynamic characteristics of the process, like spatial-temporal mass velocity profiles of shock waves, are the mass velocity variation, velocity defect, and structural instability threshold recorded in real time. Analysis of these characteristics depending on the strain rate, target thickness, and structural state of material demonstrates that conventional approaches of continuum mechanics fail to provide their adequate interpretation and simulation of shock wave processes. A new concept of shock wave processes in condensed media is proposed. The concept, being based on nonlocal nonequilibrium transport theory, allows describing the transition from elastic to hydrodynamic response of a medium depending on the loading rate and time. A nonstationary elastoplastic wave model is proposed for describing the relaxation of an elastic precursor and formation of a retarded plastic front during the wave propagation in a medium with regard to structural evolution. Analysis of the experimental data shows that the division of stresses and strains into elastic and plastic components is incorrect for shock loading.     

Continuity and momentum equations for moist atmospheres

The moist atmosphere with occurring precipitation is considered to be a multiphase fluid composed of dry air, water vapor and hydrometeors. These compositions move with different velocities: they take a macroscopic motion with a reference velocity and a relative motion with a velocity deviated from the reference velocity. The reference velocity can be chosen as the velocities of dry air, a gas mixture and the total air mixture. The budget equations of continuity and momentum are formulated in the three reference-velocity frames. It is shown that the resulting equations are dependent on the chosen reference velocity. The diffusive flux due to compositions moving with velocities deviated from the reference velocity and the internal sources due to the phase transitions of water substances result in additional source terms in continuity and momentum equations. A continuity equation of the total mass is conserved and free of diffusive flux divergence if the reference velocity is referred to the velocity of the total air mixture. However, continuity equations in the dry-air and gasmixture frames are not conserved due to the mass diffusive flux divergence. The diffusive flux introduces additional source terms in the momentum equation. In the dry-air frame, the diffusive flux of water substances and the phase transitions of water substances contribute to the change of the total momentum. The additional sources of total momentum in the frame of a gas mixture are associated with the diffusive flux of hydrometeors, the phase transitions of hydrometeors and the gasmixture diffusive flux. In the frame of total air mixture, the contribution to the total momentum comes from the diffusive flux of all atmospheric compositions instead of the phase transitions. The continuity and momentum equations derived here are more complicated than the traditional model equations. With increasing computing power, it becomes possible to simulate atmospheric processes with these sophisticated equations. It is helpful to the improvement of precipitation forecast.     

Transmission through biased graphene strip

We solve the 2D Dirac equation describing graphene in the presence of a linear vector potential. The discretization of the transverse momentum due to the infinite mass boundary condition reduced our 2D Dirac equation to an effective massive 1D Dirac equation with an effective mass equal to the quantized transverse momentum. We use both a numerical Poincaré map approach, based on space discretization of the original Dirac equation, and a direct analytical method. These two approaches have been used to study tunneling phenomena through a biased graphene strip. The numerical results generated by the Poincaré map are in complete agreement with the analytical results.     

HL-1M装置弹丸和分子束加料的粒子输运研究

研究了IL-1M装置上弹丸和分子束加料的粒子输运。在研究粒子输运时拟合了粒子源分布,利用调制送气模型研究了分子束送气时的粒子输运。由弹丸注入后较长时间内密度的自然衰减研究了粒子输运,给出了一种简单的研究弹丸注入后粒子输运的方法。计算表明,分子束和弹丸注入改善了等离子体的粒子输运特性。将计算结果与实验测量进行了比较。     

An exponential integrator for advection-dominated reactive transport in heterogeneous porous media

We present an exponential time integrator in conjunction with a finite volume discretisation in space for simulating transport by advection and diffusion including chemical reactions in highly heterogeneous porous media representative of geological reservoirs. These numerical integrators are based on the variation of constants solution and solving the linear system exactly. This is at the expense of computing the exponential of the stiff matrix comprising the finite volume discretisation. Using real Léja points or a Krylov subspace technique compared to standard finite difference-based time integrators. We observe for a variety of example applications that numerical solutions with exponential methods are generally more accurate and require less computational cost. They hence comprise an efficient and accurate method for simulating non-linear advection-dominated transport in geological formations.     

Nonlinear nonautonomous discrete dynamical systems from a general discrete isomonodromy problem

Nonlinear nonautonomous discrete dynamical systems (DDS) whose continuum limits are the well-known Painlevé equations, have recently arisen in models of quantum gravity. The Painlevé equations are believed integrable because each is the isomonodromy condition for an associated linear differential equation. However, not every DDS with an integrable continuum limit is necessarily integrable. Which of the many discrete versions of the Painlevé equations inherit their integrability is not known. How to derive all their integrable discrete versions is also not known. We provide a systematic method of attacking these questions by giving a general discrete isomonodromy problem. Discrete versions of the first and second Painlevé equations are deduced from this general problem.