Diffusion Boundary Conditions Research Articles

VALIDATION OF A FINITE–ELEMENT STORED GRAIN ECOSYSTEM MODEL

An axisymmetric finiteelement model was validated with respect to predicting the heat, mass, and momentumtransfer that occurred in upright corrugatedsteel storage bins due to conduction, diffusion, and natural convection usingrealistic boundary conditions. Hourly weather data that included hourly total solar radiation, wind speed, ambienttemperature, and relative humidity were used to model the corn temperature and moisture content during storage with noaeration, and with ambient and chilled aeration. Periods of aeration were simulated assuming a uniform airflow rate throughthe grain mass. Sixteen bins with a capacity of 11.7 t each and instrumented with temperature cables were available to validatethe model using two years of measured corn temperatures and moisture contents during summer storage. The averagestandard error between the experimental and predicted temperatures was 2.4C (1.1C to 5.7C range), and the standarderror between experimental and predicted moisture contents was 0.7 percentage points. The average standard error was 1.5Cin three nonaerated bins with sealed plenums when corn temperature was predicted as a function of the natural convectionequation. The predicted natural convection effect was not applicable unless the plenum was assumed sealed.

A rarefied gas flow caused by a discontinuous wall temperature

A flow of a rarefied gas caused by a discontinuous wall temperature is investigated on the basis of kinetic theory in the following situation. The gas is confined in a two-dimensional square container, and the left and right halves of the wall of the container are kept at different uniform temperatures, so that the temperatures of the top and bottom walls are discontinuous at their respective middle points. External forces are assumed to be absent. The steady flow of the gas induced in the container by the effect of the discontinuities is analyzed numerically on the basis of the Bhatnagar–Gross–Krook model of the Boltzmann equation and the diffuse reflection boundary condition by means of an accurate finite-difference method. The features of the flow are clarified for a wide range of the Knudsen number. In particular, it is shown that, as the Knudsen number becomes small (i.e., as the system approaches the continuum limit), the maximum flow speed tends to approach a finite value, but the region with appreciable flow shrinks to the points of discontinuity; thus, the overall flow in the container vanishes nonuniformly in the continuum limit. The behavior of the molecular velocity distribution function is also investigated in detail.

Discontinuous Finite Element Transport Solutions in Thick Diffusive Problems

The performance of discontinuous finite element methods (DFEMs) on problems that contain optically thick diffusive regions is analyzed and tested. The asymptotic analysis is quite general; it holds for an entire family of DFEMs in slab, XY, and XYZ geometries on arbitrarily connected polygonal or polyhedral spatial grids. The main contribution of the work is a theory that predicts and explains how DFEMs behave when applied to thick diffusive regions. It is well known that in the interior of such a region, the exact transport solution satisfies (to leading order) a diffusion equation, with boundary conditions that are known. Thus, in the interiors of such regions, the ideal discretized transport solution would satisfy (to leading order) an accurate discretization of the same diffusion equation and boundary conditions. The theory predicts that one class of DFEMs, which we call “zero-resolution” methods, fails dramatically in thick diffusive regions, yielding solutions that are completely meaningless. Another class—full-resolution methods—has leading-order solutions that satisfy discretizations of the correct diffusion equation. Full-resolution DFEMs are classified according to several categories of performance: continuity, robustness, accuracy, and boundary condition. Certain kinds of lumping, some of which are believed to be new, improve DFEM behavior in the continuity, robustness, and boundary-condition categories. Theoretical results are illustrated using different variations of linear and bilinear DFEMs on several test problems in XY geometry. In every case, numerical results agree precisely with the predictions of the asymptotic theory.

Carbonization mechanism of stabilized pitch-based spheres containing sulfur

A mathematical model has been developed for continuous cross-flow dryers operating in diffusion-controlled regime. In the model, a cross-flow dryer is treated as a series of gas-solid contact stages, each purged by a stream of drying gas while wet solids are passing through. By analyzing the gas-solid interactions in each stage, boundary conditions for intra-particle diffusion were established and model equations obtained. The model correlates the amount of moisture removed to a number of process variables (diffusivity, partition coefficient, particle size, residence time, total number of stages, solids loading, drying gas humidity and purge rate) and allows effects of these variables on drying to be studied. For drying fine powders, the effect of reduced mass transfer efficiency due to particle agglomeration and gas channeling is taken into account in the model by factoring an efficiency parameter into the Fourier number. Model predictions of product moisture concentration based on laboratory-measured partition coefficient, diffusivity, and efficiency factor were found to closely match data from a commercial cross-flow HDPE powder dryer.

Fracture Analysis of Hydrogen-Charged Nickel-Titanium Superelastic Alloy

Superelastic Ni–Ti alloys are widely used as engineering and medical materials. However, the alloy is susceptible to environmental embrittlement in a corrosive atmosphere. Accelerated tests of hydrogen embrittlement of the Ni–Ti alloy were carried out. The effect of electrolytic charging hydrogen on the properties of the alloy was measured. The rupture process in tension of the alloy with charged hydrogen was discussed on the basis of the tensile stress-strain curve, hardness in a cross-sectional area and fractography. The results of the measurements suggested that hydrogen concentration on the surface of the alloy and immersion time in an electrolytic bath had different effects on embrittlement. This will be related with the distribution of the hydrogen concentration, which was determined from the diffusion equation and boundary conditions.

Mean first passage times across a potential barrier in the lumped state approximation

The lumped state approximation (LSA) is a method for handling boundary conditions for diffusion on an interval which simplifies the description of transitions into and out of the interval. It was originally motivated by the problem of proton conduction through the ion channel gramicidin. This paper discusses the mean first passage time of a diffuser crossing a potential barrier in the lumped state approximation. The LSA mean first passage time is shown to be identical to a different quantity, the interior mean first passage time, clarifying the nature of the approximation. We also discuss a variant of the LSA in which dependence on an applied electrical potential is made explicit; an optimal value for an effective electrical distance is found. A detailed comparison is made of the LSA mean first passage time with several other formulations of the mean time to cross a barrier.

Upper Semicontinuity for Attractors of Parabolic Problems with Localized Large Diffusion and Nonlinear Boundary Conditions

The motivations to study the problem considered in this paper come from the theory of composite materials, where the heat diffusion properties can change from one part of the domain to another. Mathematically, this leads to a nonlinear second-order parabolic equation for which the diffusion coefficient becomes large in a subdomain Ω 0 ⊂Ω . The equation is supplemented by a nonlinear boundary condition on ∂Ω and an initial condition. The authors determine the form of the limit problem (the so-called shadow system), which involves an evolution equation for the averages of the density over Ω 0 . The main results include global-in-time existence of solutions and upper semicontinuity of the associated global attractors when the system approaches the shadow system.

Analysis of open-circuit potential transient and laser beam deflection transient simultaneously measured from Pd foil electrode pre-charged with hydrogen

In the present work open-circuit potential (OCP) transient and laser beam deflection transient were measured simultaneously from the impermeable Pd foil electrode pre-charged with hydrogen at −0.08–0.04 V (reversible hydrogen electrode (RHE)) in 0.1 M NaOH solution as a function of the pre-charging potential of hydrogen. The OCP is determined by a mixing of the potentials of two simultaneous reactions of anodic hydrogen oxidation MH ads+OH −=M+H 2O+e α and cathodic hydrogen underpotential deposition M+H 2O+e β=MH ads+OH − below 0.15 V (RHE) and oxygen reduction 1/2O 2+H 2O+2e β=2OH − above 0.15 V (RHE), coupled by a common corrosion rate. From the coincidence between the measured OCP transient and calculated corrosion potential transient, it is indicated that the plot of hydrogen oxidation rate versus reduced time calculated corresponds to the measured OCP transient and thus both transients are closely coupled each other. This means that the hydrogen self-discharge from the electrode proceeds with the rate of hydrogen oxidation at the electrode surface, calculated based upon the mixed potential theory from the measured Evans–Hoar diagram. By taking the value of self-discharge rate on one surface determined as a function of time and adopting the impermeable constraint on the other surface as the boundary condition for hydrogen diffusion through the electrode, hydrogen concentration profile across the electrode has been derived with time from the measured tensile deflection transient.

A Class of Discrete Kinetic Solutions for Non-Boundary-Driven Gas Flow

Discrete kinetic theory approach has been used to study dilute, monatomic, non-equilibrium gas flow between two walls in microdomains. A four-velocity coplanar model has been adopted, where the microscopic velocity-orientation angle and the Knudsen number are free parameters, which have to be prescribed. Diffusive reflection boundary condition has been incorporated to obtain the solution. A bounded range for the admissible orientation angle of the discrete velocity vectors for any given Knudsen number is identified. Consequently, the macroscopic velocity slip at the wall, the velocity profile across the walls and the volume flow rate is calculated as a function of the free parameters. The calculations based on a single model, 4-velocity, cover the transition flow regime between the continuum and the free-molecular flow. The calculated volume flow rate is compared with experimental data as well as with other theoretical models.

An assessment of the Geophysical Fluid Dynamics Laboratory ocean model with coarse resolution: Annual‐mean climatology

The Geophysical Fluid Dynamics Laboratory Modular Ocean Model 2.2 code with coarse resolution (4° × 3°) is assessed by performing three experiments and comparing their equilibrated solutions with recent observationally based analyses (OBAs). The first experiment (E1) uses subgrid‐scale horizontal diffusion and surface boundary conditions which relax surface temperature and salinity toward observations. The second (E2) replaces the physically incorrect heat and moisture flux boundary conditions of E1 by flux conditions taken from OBAs, plus a term relaxing surface temperatures toward observations. The third (E3) uses the same surface boundary conditions as E2 but replaces the horizontal diffusion by the Gent‐McWilliams (GM) parameterization of isopycnal diffusion. Under the restoring surface boundary conditions (E1), the North Atlantic overturning rate is about 17 Sv, smaller than in OBAs, the maximum poleward heat transport in the Northern Hemisphere is 1.2 Petawatts (PW), also smaller than in OBAs, and in the Antarctic Circumpolar Current (ACC) region the poleward heat transport is 1.3 PW, much larger than in OBAs. Under the more realistic flux boundary condition (E2) the overturning rate increases to an unrealistically large level of 40 Sv, and the poleward heat transports are only slightly improved. When the GM parameterization is employed (E3), the overturning is reduced to 28 Sv, and the poleward heat transport in the ACC region is reduced to 0.3 PW; both results are consistent with OBAs. However, there is only a slight further improvement in the poleward heat transport in the Northern Hemisphere, which now has a peak value of 1.6 PW, still about 0.5 PW less than in OBAs. The sea surface temperature errors in E3 are consistent with the conclusion that the heat transport in the Northern Hemisphere is still being underestimated. All the experiments show strong systematic biases in the salinity field.

Spectral Properties of a Streaming Operator with Diffuse Reflection Boundary Condition

In this paper, the spectrum of a streaming operator with diffuse reflection boundary condition arising in transport theory is observed in L1 space. We associate this unbounded operator with bounded integral operators which are determined by the boundary condition. It is shown that the spectrum of the streaming operator is completely determined by these integral operators and consists of countable isolated eigenvalues, each of which has finite algebraic multiplicity. Furthermore, under the assumption that the diffusion on the boundary is of Maxwell type, it is proved that the streaming operator has only one real eigenvalue which is simple and that each of the complex eigenvalues has geometry multiplicity one. A formula for computing these eigenvalues is also derived, by means of which the algebraic multiplicity of the complex eigenvalues is discussed.

On the stationary Povzner equation in $\mathbf{R}^n$

The stationary Povzner equation is considered in a bounded and strictly convex domain of $\mathbf{R}^{n}$. Existence theorems are established for a class of collision kernels in the case of hard forces and for diffuse reflection boundary conditions. Generalizations with respect to the collision kernel and boundary conditions are discussed.

A Ray Approximation to a PdE that Arises in the Study of Tandem Queues

We use singular perturbation methods to analyze a diffusion equation that arose in studying two tandem queues. Denoting by p(n1, n2) the probability that there are n1 customers in the first queue and n2 customers in the second queue, we obtain the approximation p(n1, n2)∼ɛ2P(X, Y)=ɛ2P(ɛn1, ɛn2), where ɛ is a small parameter. The diffusion approximation P satisfies an elliptic PDE with a nondiagonal diffusion matrix and boundary conditions that involve both normal and tangential derivatives. We analyze the boundary value problem using the ray method of geometrical optics and other singular perturbation techniques. This yields the asymptotic behavior of P(X, Y) for X and/or Y large.

The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate Method

In highly diffusive regimes, the transfer equation with anisotropic boundary conditions has an asymptotic behavior as the mean free path $\epsilon$ tends to zero that is governed by a diffusion equation and boundary conditions obtained through a matched asymptotic boundary layer analysis. A numerical scheme for solving this problem has an $\epsilon^{-1}$ contribution to the truncation error that generally gives rise to a nonuniform consistency with the transfer equation for small $\epsilon$, thus degrading its performance in diffusive regimes. In this paper we show that whenever the discrete-ordinate method has the correct diffusion limit, both in the interior and at the boundaries, its solutions converge to the solution of the transport equation uniformly in $\epsilon$. Our proof of the convergence is based on an asymptotic diffusion expansion and requires error estimates on a matched boundary layer approximation to the solution of the discrete-ordinate method.

The Boltzmann-Grad limit for a particle system in a slab with stochastic walls

It is shown that a stochastic system of N interacting particles in a slab approximates, in the Boltzmann–Grad limit, a one-dimensional Boltzmann equation with diffusive boundary conditions. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons, Ltd.

Stationary Particle Systems Approximating Stationary Solutions to the Boltzmann Equation

We show that a regularized stationary Boltzmann equation with diffusive boundary conditions can be rigorously derived from a suitable stochastic N-particle system. To do this, we prove that the L1 -distance between the k-particle density and the k-fold product of the solution to the stationary Boltzmann equation is of order 1/N.

Diffusion anormale pour le gaz de Knudsen

We show how a rough boundary described by a diffusive boundary condition may generate a diffusion process in a fluid. At variance with previous results obtained by probabilistic argument ( see [2]), our proof relies entirely on functional analysis as in the paper by Golse [3]. We prove the evolution of the density of a free molecular flow in thin channels bounded by parallel plane surfaces is described by a diffusion equation, on a time scale of ρ(ε) ~ ε 2¦ log ε 2¦ in the limit as the distance between the plates tends to 0.

Rectified Brownian movement in molecular and cell biology

A unified model is presented for rectified Brownian movement as the mechanism for a variety of putatively chemomechanical energy conversions in molecular and cell biology. The model is established by a detailed analysis of ubiquinone transport in electron transport chains and of allosteric conformation changes in proteins. It is applied to P-type ATPase ion transporters and to a variety of rotary arm enzyme complexes. It provides a basis for the dynamics of actin-myosin cross-bridges in muscle fibers. In this model, metabolic free energy does no work directly, but instead biases boundary conditions for thermal diffusion. All work is done by thermal energy, which is harnessed at the expense of metabolic free energy through the establishment of the asymmetric boundary conditions. @S1063-651X~98!13502-X#

Numerical simulation of electromagnetic wave attenuation in nonequilibrium chemically reacting flows

The effects of various gasdynamic phenomena on the attenuation of an electromagnetic (EM) wave propagating through the hypervelocity flow field generated by an aerodynamic body, are numerically investigated. The reacting flow field around a blunt wedge—consisting of nitric oxide ions, free electrons, and other species—is simulated using a computational fluid dynamics computer code. The computer code solves the Navier–Stokes equations including a nonequilibrium air kinetics model consisting of seven species and ten reactions, using a time-marching, explicit Runge–Kutta scheme. An EM wave, originating from within the wedge, is attenuated by the free electrons (plasma) in the chemically reacting flow. Attenuation analysis is performed separately (uncoupled) from the gasdynamic analysis using a series solution of Maxwell's equations valid for a long-wavelength plane wave and a thin (i.e. in comparison to wavelength) inhomogeneous plasma layer. The results of this computational study systematically demonstrate the importance of chemical kinetics, viscosity, mass diffusion and wall boundary conditions (adiabatic, isothermal, catalytic) for computer modeling of EM wave attenuation due to an aerodynamic plasma. Comparison is made with experimental data.

Boltzmann asymptotics with diffuse reflection boundary conditions

StrongL 1-convergence towards a stationary solution when time tends to infinity is established for the solutions of the time-dependent nonlinear Boltzmann equation in a bounded domain Ω ⊂ ℝ3 with constant temperature on the boundary. The collisionless case is first investigated in the varying temperature case.