Robert F. Sekerka

Robert F. Sekerka
Carnegie Mellon University | CMU · Department of Physics

Bachelor of Science University of Pittsburgh 1960

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174
Publications
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11,220
Citations

Publications

Publications (174)
Article
The well-known Sauer-Freise flux equation is derived analytically for the general case of a multiphase, multicomponent diffusion couple with variable molar volume. Discontinuities in concentration versus distance data are specifically treated. Fluxes with respect to the local center of volume are employed if the partial molar volumes are constants....
Chapter
The theory of morphological stability provides a dynamical analysis of the stability of the interface that separates phases during a phase transformation. We focus on crystallization from either a pure or alloy melt. One solves the governing equations for heat flow, including diffusion for alloys, and uses perturbation theory to analyze the stabili...
Chapter
We give a unified treatment of ideal Fermi, Bose, and classical gases for temperatures sufficiently large that energy levels can be treated as a quasi-continuous. Sums can be converted to integrals over a density of quantum states to evaluate thermodynamic functions. Pressure is equal to two-thirds of the energy density for all three gases. Relevan...
Chapter
The first law of thermodynamics is stated in terms of the existence of an extensive function of state called the internal energy. For a chemically closed system, the internal energy changes when energy is added by heat transfer or work is done by the system. Heat and work are not state variables because they depend on a process. Reversible quasista...
Chapter
Cooperative phenomena are introduced via the simple Ising model in which spins having two states occupy a lattice and interact with nearest neighbors and an applied magnetic field. We study this model in the mean field approximation. Correlations among spin states are neglected, so each spin interacts with a self-consistent mean field. With no appl...
Chapter
Below a critical temperature, occupation of the ground state of a Bose gas becomes comparable to occupation of all excited states. This Bose condensation increases with decreasing temperature and affects thermodynamic functions. Only particles in excited states contribute to the pressure, internal energy, and entropy. Pressure remains equal to two-...
Chapter
Solid-fluid interfaces differ from fluid-fluid interfaces because a solid can be strained elastically. Surface area can change by stretching and by addition of new surface, each process giving rise to surface stress. Interfacial energy and adsorption can be referenced to the area of either the unstrained crystal surface or its actual strained surfa...
Chapter
The second law of thermodynamics is stated as the existence of an extensive function of state called the entropy that can only increase for an isolated system. Equilibrium is reached at maximum entropy. Reciprocal absolute temperature is defined as entropy change with energy. Entropy is additive for a composite system. Heat added to a chemically cl...
Chapter
The equilibrium criterion of maximum entropy for an isolated system is used to derive the equivalent criterion of minimum internal energy at constant entropy. Alternative equilibrium criteria for chemically closed systems are derived for other conditions and thermodynamic potentials: minimum Helmholtz free energy for constant temperature and no ext...
Chapter
According to the third law of thermodynamics, the entropy of a system in internal equilibrium approaches a constant independent of phase as the absolute temperature tends to zero. This constant value is taken to be zero for a non-degenerate ground state, in accord with statistical mechanics. Independence of phase is illustrated by extrapolation due...
Chapter
We derive a simplified version of the canonical ensemble developed in the next chapter. We treat a system of identical particles that can be distinguished, perhaps by position in a solid. We derive a statistical distribution of particles, each in a quantum state, by maximizing the number of ways they can be distributed among quantum states, subject...
Chapter
The grand canonical ensemble applies to a system at constant temperature and chemical potential; its number of particles is not fixed. We derive it from the microcanonical ensemble by contact with heat and particle reservoirs to form an isolated system. The probability of a system having a specified number of particles and being in a given stationa...
Chapter
Instead of the volume, could depend on a whole set of mechanical variables Yℓ if the system can do reversible work by means of generalized forces .
Chapter
An ensemble is a collection of microstates that are compatible with a specified macrostate of a thermodynamic system. The microcanonical ensemble represents an isolated system having fixed energy. For that ensemble, the fundamental assumption of statistical mechanics is that every compatible stationary quantum microstate is equally probable. Proper...
Chapter
The classical canonical ensemble employs a probability density function in phase space in which the energy in the Boltzmann factor for a quantum system is replaced by the classical Hamiltonian. The classical partition function is the integral of that Boltzmann factor over phase space. One can artificially divide the classical partition function by...
Chapter
Chemical reactions entail making or breaking of bonds, so energy is conserved for an isolated system. Reactions at constant volume or pressure exchange heat with the environment by change of internal energy or enthalpy, respectively. Reaction extent is measured by a progress variable; reactions progress until equilibrium is reached or some componen...
Chapter
Even at absolute zero, the Pauli exclusion principle forces fermions into high energy states, a degenerate gas. States fill to the Fermi energy, equivalent to about 50,000 K for a free electron gas. At laboratory temperatures, small excitation into higher energy states is calculated by using an asymptotic Sommerfeld expansion. Heat capacity is line...
Chapter
Phase equilibria for a monocomponent system require uniformity of temperature, pressure, and chemical potential. In the temperature-pressure plane, single-phase regions are separated from one another by two-phase coexistence curves that meet at the triple point where all three phases, crystalline solid, liquid, and vapor, are in mutual equilibrium....
Chapter
Since the 1800s and the work of Clausius and Boltzmann, it was believed that the entropy function, which can only increase for an isolated system, was a measure of a state of greater probability, a more disordered state in which information is lacking. In 1948, Shannon developed a quantitative measure of information in the context of communication...
Chapter
Open systems exchange particles with their environment in addition to work and heat. This exchange entails energy transfer. Internal energy becomes a function of entropy, volume, and moles of particles; its partial derivative with particle mole number is called chemical potential. This is extended to multicomponent systems. The chemical potential o...
Chapter
Classical many-particle systems are governed by continuous variables, the positions and momenta of all particles in multi-dimensional phase space. Total energy depends on these variables and is called the Hamiltonian. Hamilton’s equations govern dynamics. According to Liouville’s theorem, the time rate of change of the density of a given set of par...
Chapter
We derive equilibrium criteria in the presence of conservative external forces. For a chemically closed isothermal system with constant volume, equilibrium requires virtual variations of the Helmholtz free energy plus the external potential to be positive. For a uniform gravitational field, use of the calculus of variations shows that the gravitati...
Chapter
Surfaces or interfaces of discontinuity where phases meet are modeled by a Gibbs dividing surface of zero thickness. The differences between extensive variables of an actual system and one in which phases are uniform up to the dividing surface are defined to be surface excess quantities that depend on location of the dividing surface. The excess Kr...
Chapter
A binary solution constitutes two chemical components mutually dissolved on an atomic scale. We study its molar Gibbs free energy as a function of mole fraction at various temperatures and fixed pressure. Chemical potentials are calculated by the method of intercepts. Below a critical temperature, the common tangent construction demonstrates equili...
Chapter
The van der Waals model of a fluid exhibits a liquid-vapor phase transition. Isotherms in the volume-pressure plane depend on a parameter accounting for the finite size of molecules and another for molecular interactions. Below a critical temperature, the pressure of an isotherm is not monotonic. The locus of its maximum and minimum has an inverted...
Chapter
The canonical ensemble applies to a system held at constant temperature. We present two derivations based on the microcanonical ensemble by putting a system of interest in contact with a heat reservoir to form an isolated system. A third derivation employs the most probable distribution of ensemble members. The probability of a system being in a gi...
Chapter
Two types of averaging occur in quantum statistical mechanics, the first for pure quantum mechanical states and the second for a statistical ensemble of pure states. We define and exhibit the properties of density operators and their density matrix representation for both pure and statistical states. For equilibrium states, a statistical density op...
Chapter
We investigate whether a homogeneous system is stable with respect to breakup into a composite system of two or more homogeneous subsystems. Criteria to avoid breakup lead to requirements for the dependence of the entropy and thermodynamic potentials on their natural variables. For stability, the entropy must be a concave function of its natural va...
Article
We present a rigorous irreversible thermodynamics treatment of creep deformation of solid materials with interfaces described as geometric surfaces capable of vacancy generation and absorption and moving under the influence of local thermodynamic forces. The free energy dissipation rate derived in this work permits clear identification of thermodyn...
Article
In Thermal Physics: Thermodynamics and Statistical Mechanics for Scientists and Engineers, the fundamental laws of thermodynamics are stated precisely as postulates and subsequently connected to historical context and developed mathematically. These laws are applied systematically to topics such as phase equilibria, chemical reactions, external for...
Article
We modify a previous steady-state description developed by Genin [J. Appl. Phys. 77, 5130-5137 (1995)] for a grain boundary groove moving with a prescribed speed in a material subject to in-plane stress and a resultant grain boundary flux. The arbitrary assumption that the grain boundary flux is equally delivered to (or extracted from) the two adja...
Article
Full-text available
We develop an irreversible thermodynamics framework for the description of creep deformation in crystalline solids by mechanisms that involve vacancy diffusion and lattice site generation and annihilation. The material undergoing the creep deformation is treated as a non-hydrostatically stressed multi-component solid medium with non-conserved latti...
Article
Full-text available
We investigate generalized potentials for a mean-field density functional theory of a three-phase contact line. Compared to the symmetrical potential introduced in our previous article [Phys. Rev. E 85, 011120 (2012)], the three minima of these potentials form a small triangle located arbitrarily within the Gibbs triangle, which is more realistic f...
Article
A triple junction in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the triple junction. We employ a triangular grid and use a successive over-relaxation method to fin...
Article
Full-text available
A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive over-relaxation method...
Article
We develop the irreversible thermodynamic basis of the phase field model, which is a mesoscopic diffuse interface model that eliminates interface tracking during phase transformations. The phase field is an auxiliary parameter that identifies the phase; it is continuous but makes a transition over a thin region, the diffuse interface, from its cons...
Article
An eutectic alloy of antimony and manganese was directionally solidified to produce a composite of cylindrical fibers of MnSb aligned in a Sb matrix. The fibers were about 3 microns in diameter by 1 millimeter long and occupied 30% of the composite volume. Isothermal aging caused the fibers to develop undulations that had an average wavelength of 1...
Article
The appearance of an asymmetrical pattern that occurs when a disk crystal of ice grows from supercooled water was studied by using an analysis of growth rates for radius and thickness. The growth of the radius is controlled by transport of latent heat and is calculated by solving the diffusion equation for the temperature field surrounding the disk...
Article
Crystal growth morphology results from an interplay of crystallographic anisotropy and growth kinetics, the latter consisting of interfacial processes as well as long‐range transport. Mathematical modeling of crystal growth shapes is important to our understanding of fundamental crystal growth phenomena as well as to improvement and optimization of...
Article
We formulate a Lattice Boltzmann (LB) model for simulation of two-dimensional flow of nearly-immiscibile fluids between closely spaced parallel plates. We treat displacement of a more viscous fluid by a less viscous fluid, as in a Hele-Shaw cell. The nearly two dimensional flow leads to the well-known Saffman-Taylor instability. We use a binary (A-...
Article
We discuss wave propagation phenomena in a Lattice Boltzmann (LB) model of a binary diffusion couple for species having unequal masses. LB simulations reveal oscillations in the position of the global center of mass of the couple as it moves toward the center of the couple from its initial position located toward the more massive species. These osc...
Article
We present a numerical approach to modeling the deformation induced by the Kirkendall effect in binary alloys. The governing equations for isothermal binary diffusion are formulated with respect to inert markers and also with respect to the volume-averaged velocity. Relations necessary to convert between the two formulations are derived. Whereas th...
Article
Mass and thermal diffusivity measurements conducted on Earth are prone to contamination by uncontrollable convective contributions to the overall transport. Previous studies of mass and thermal diffusivities conducted on spacecraft have demonstration the gain in precision, and lower absolute values, resulting from the reduced convective transport p...
Article
We conduct a systematic study of the effect of various boundary conditions (bounce back and three versions of diffuse reflection) for the two-dimensional first-order upwind finite difference Lattice Boltzmann model. Simulation of Couette flow in a micro-channel using the diffuse reflection boundary condition reveals the existence of a slip velocity...
Article
Diffusion equations are derived for an isothermal lattice Boltzmann model with two components. The first-order upwind finite difference scheme is used to solve the evolution equations for the distribution functions. When using this scheme, the numerical diffusivity, which is a spurious diffusivity in addition to the physical diffusivity, is proport...
Article
We discuss the implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model for which the upwind finite difference scheme is used to solve the set of evolution equations recovered after discretization of the velocity space. Simulation of heat transport between two parallel walls at rest shows evidence of temperature...
Article
Since the death of Prof. Dr. Jan Czochralski nearly 50 years ago, crystals grown by the Czochralski method have increased remarkably in size and perfection, resulting today in the industrial production of silicon crystals about 30 cm in diameter and two meters in length. The Czochralski method is of great technological and economic importance for s...
Article
A model is used to describe the shape change of a binary diffusion couple when the diffusivities of the two species differ. The classical uniaxial Kirkendall shift is obtained only if the displacement is constrained to be in the diffusion direction. For traction-free conditions at the external surfaces of a diffusion couple, a more general displace...
Article
The equilibrium shape of a crystal is the shape that minimizes its anisotropic interfacial free energy subject to the constraint of constant volume. This shape can be determined geometrically by using the Wulff construction; it can have missing orientations, sharp edges and corners, and its faces can be rounded or flat (facets). In two dimensions,...
Article
We reexamine similarity solutions for composition in a very long binary diffusion couple for the case in which the diffusivity and the density are functions of composition. For such solutions, the composition depends for sufficiently short times only on a similarity variable x/t where x is distance and t is time. The classical Boltzmann–Matano trea...
Chapter
Crystal growth morphology is derived from an interplay of the crystallographic anisotropy and growth kinetics. The growth kinetics consist of interfacial processes as well as long-range transport. The equilibrium shape results from minimizing the anisotropic surface free energy of a crystal under the constraint of constant volume and serves as the...
Article
We examine Gibbs’ conditions for equilibrium of a non-hydrostatically stressed single component solid in equilibrium across one of its faces with a pure liquid at pressure pF. We show that the equilibrium melting temperature TN for the non-hydrostatically stressed solid in contact with a melt at pressure pF is below the equilibrium melting temperat...
Article
Over the last 50 years, there has been tremendous progress in the quantification of crystal growth morphology. In the 1950s, the dynamics of crystal growth from the melt was based on the sharp interface model (interface of zero thickness separating solid and liquid), often under the assumption of isotropy. Ivantsov had discovered analytical solutio...
Article
Facet formation during crystal growth is simulated by using the phase field model in two dimensions. Instead of moderate anisotropy of the often-used form , several functions having strong anisotropy are explored. For simplicity, the interfacial energy is assumed to be isotropic, so only the anisotropy in the kinetic coefficient is considered. This...
Article
This paper presents methodologies for measuring the thermal diffusivity using the difference between temperatures measured at two, essentially independent, locations. A heat pulse is applied for an arbitrary time to one region of the sample; either the inner core or the outer wall. Temperature changes are then monitored versus time. The thermal dif...
Article
Two-dimensional finite difference lattice Boltzmann models for single-component fluids are discussed and the corresponding macroscopic equations for mass and momentum conservation are derived by performing a Chapman–Enskog expansion. In order to recover the correct mass equation, characteristic-based finite difference schemes should be associated w...
Article
Mass and thermal diffusivity measurements conducted on Earth are prone to contamination by uncontrollable convective contributions to the overall transport. Previous studies of mass and thermal diffusivities conducted on spacecraft have demonstration the gain in precision, and lower absolute values, resulting from the reduced convective transport p...
Chapter
We develop a thermodynamically consistent phase field model for solidification of a multicomponent alloy, including hydrodynamics. The solid is treated as a very viscous fluid. The model is based on an entropy functional that includes gradient-entropy corrections for internal-energy density, partial-mass densities, and phase field. It allows for ex...
Article
We report some computational results obtained by using the phase field model for binary alloy solidification. We study directional solidification and concentrate on the transition between a planar interface and steady shallow cells near the onset of morphological instability at low growth speeds. The model is formulated on the principle of local po...
Conference Paper
We describe a methodology for determining thermal diffusivities in real time by using temperature measurements at only two locations in a cylindrical sample. The technique is based on an analytical solution of heat transfer in a circular cylinder. Starting with a heated cylindrical region having a unique fraction of the sample radius, the analytica...
Chapter
This chapter discusses the fundamentals of phase field theory. This theory provides an alternative method for solving dynamical problems involving crystallization from a melt. The sharp solid liquid interface of the classical model is replaced by a diffuse interface by introducing an auxiliary variable ( , the phase field, that indicates the phase....
Article
Two Bhatnagar–Gross–Krook (BGK) models for isothermal binary fluid systems—the classical single relaxation time model and a split collision term model—are discussed in detail, with emphasis on the diffusion process in perfectly miscible ideal gases. Fluid equations, as well as the constitutive equation for diffusion, are derived from the Boltzmann...
Article
The problem of a needle crystal having the shape of a paraboloid of revolution is re-examined. For this purpose, a dimensionless parabolic coordinate is employed. The solution obtained is demonstrated.
Article
We describe a methodology for determining thermal diffusivities in real time by using temperature measurements at only two locations in a cylindrical sample. The technique is based on an analytical solution of heat transfer in a circular cylinder. This methodology does not require knowing the initial temperature increase or any timing between the a...
Article
In previous work, approximate solutions were found for paraboloids having perturbations with four-fold axial symmetry in order to model dendritic growth in cubic materials. These solutions provide self-consistent corrections through second order in a shape parameter ε to the Peclet number vs supercooling relation of the Ivantsov solution. The param...
Article
We develop two analytical solutions for thermodynamic fluctuations that are present in the phase-field model of solidification. One solution deals with fluctuations in an isothermal single phase system. The other deals with fluctuations in a two-phase isothermal system having a planar diffuse interface. Explicit formulae are obtained in one, two an...
Article
The time evolution of a disk crystal of ice with radius R and thickness h growing from supercooled water is studied using a solution of an ordinary differential equation (ODE) for h with respect to R. The growth of thickness, i.e., growth along the c axis of ice, is governed by slow molecular rearrangements on the basal plane and is expressed as a...
Article
The Ivantsov solution for an isothermal paraboloid of revolution growing into a pure, supercooled melt provides a relation between the bulk supercooling and a dimensionless product (the Peclet number P) of the growth velocity and tip radius of a dendrite. Horvay and Cahn generalized this axisymmetric analytical solution to a paraboloid with ellipti...
Article
Full-text available
In previous work, we found approximate solutions for paraboloids having pertur-bations with four-fold axial symmetry in order to model dendritic growth in cubic materials. These solutions provide self-consistent corrections through second order in a shape parameter to the Peclet number { supercooling relation of the Ivantsov solution. The parameter...
Article
Variational models provide an alternative approach to standard sharp interface models for calculating the motion of phase boundaries during solidification. We present a correspondence between objective functions used in variational simulations and specific thermodynamic functions. We demonstrate that variational models with the proposed identificat...
Article
Stochastic forces due to thermodynamic fluctuations are derived for the anisotropic phase-field model of solidification. The stochastic forces turn out to be anisotropic. The derivation utilizes the general principles of irreversible thermodynamics. One of the forces is the divergence of the stochastic heat flux derived by Landau and Lifshitz (Stat...
Article
When a solid phase of uniform temperature TS∞ and composition CS∞ is brought into contact with a liquid phase of uniform temperature TL∞ and composition CL∞, there exist (under the assumption of local equilibrium at the solid–liquid interface) similarity solutions for which the position X of the interface is proportional to the square root of time...
Article
We develop a rather general thermodynamically consistent phase-field model for solidification of a binary alloy, based on an entropy functional that contains squared gradient terms in the energy density, the composition and the phase-field variable. By assuming positive local entropy production, we derive generalized phase-field equations for an al...
Article
We explore multiple similarity solutions in one spatial dimension during the solidification or melting of a binary alloy. The configuration is analogous to that of a diffusion couple, for which similarity multiple solutions in isothermal ternary alloys were discovered by Coates and Kirkaldy and explored further by Maugis et al. We proceed by findin...
Article
Advective nonsolenoidal (∇⋅v≠0) flow driven by diffusion-induced density changes in strictly zero gravity is studied in a two-dimensional rectangular box. Our model, which is more general than the Oberbeck–Boussinesq model, is a precursor for the study of fluid flow that occurs due to density changes during isothermal interdiffusion in a binary liq...
Article
We revisit our stagnant film model of the effect of natural convection on the dendrite operating state (velocity V and tip radius ϱ) and focus attention on possible effects of the container size used in the microgravity experiments of Glicksman et al. [Phys. Rev. Lett. 73 (1994) 573; ISIJ Int. 35 (1995) 604]. We find that the thickness, δ, of the s...
Article
This paper deals with numerical solutions of the phase field model of solidification in two dimensions in the context of dendritic growth. Finite difference methods associated with vectorized algorithms are employed to solve the phase field equations. The temperature equation is solved by an alternating direction implicit scheme and the equation fo...
Article
We develop a weakly nonlinear morphological stability analysis for an infinitely long right circular cylinder growing from its pure undercooled melt. For a cylinder perturbed by a specific planform consisting of sinusoids, we perform an expansion in the planform amplitude A to calculate the nonlinear critical radius (above which the chosen planform...
Article
The phase field model in two dimensions is used to calculate numerically the operating states (tip velocity v and tip radius rho) of dendrites grown from pure melts. At large supercoolings, a dendrite has a nearly hyperbolic envelope close to its tip, as opposed to being nearly parabolic, as at small supercoolings. The corresponding tip radius incr...
Article
We study the relationship of diffusion-limited aggregation (DLA) simulations to the solutions of a free-boundary problem that is used to model crystal growth in two spatial dimensions. The mathematical connection between the DLA hitting probability and the normal derivative to the boundary of a growing aggregate is made with particular attention to...
Article
We develop a simple model of the influence of natural convection on the selection of the operating state (dendrite tip velocity, V, and tip radius, ϱ) for dendritic growth of a pure material. We hypothesize that the important aspects of natural convection can be accounted for by considering the global convection that would occur in the vicinity of...
Article
We develop a model that allows interface kinetics to be incorporated in a simple way in the determination of the dendrite operating state. The model is based on an optimum stability conjecture, according to which the dendrite tip radius is related to the wavelength of the fastest growing Fourier component in a linear stability analysis that include...
Article
In this paper, we define flux, mass, density, and accumulation functions for the diffusion-limited aggregation (DLA) simulation. We assume time rescalings for each of these functions and for the radii that bring each of the graphs of these functions, separately, onto a curve that does not depend on time. We show, by comparison with DLA simulations...
Article
We develop a weakly nonlinear morphological stability analysis for a sphere growing from its pure undercooled melt. For a sphere perturbed by a specific planform (a single spherical harmonic) we perform an expansion in the planform amplitude, A, to calculate the nonlinear critical radius (above which the chosen planform will be unstable for finite...
Article
In an effort to unify the various phase-field models that have been used to study solidification, we have developed a class of phase-field models for crystallization of a pure substance from its melt. These models are based on an entropy functional, as in the treatment of Penrose and Fife, and are therefore thermodynamically consistent inasmuch as...
Article
We introduce a stochastic model to analyze in quantitative detail the effect of the high-frequency components of the residual accelerations onboard spacecraft (often called g jitter) on the motion of a fluid surface. The residual acceleration field is modeled as a narrow-band noise characterized by three independent parameters: its intensity, a dom...
Article
The inclusion of anisotropic surface free energy and anisotropic linear interface kinetics in phase-field models is studied for the solidification of a pure material. The formulation is described for a two-dimensional system with a smooth crystal-melt interface and for a surface free energy that varies smoothly with orientation, in which case a qui...
Article
The shapes of growing crystals are determined by an interplay of complex processes that include transport of energy and matter through bulk phases, capillarity-related processes that determine local equilibrium conditions at the crystal-nutrient interface, and non-equilibrium kinetic processes that take place locally to that interface. A mathematic...
Conference Paper
We introduce a stochastic model to analyze in quantitative detail the effect of the high frequency components of the residual accelerations onboard spacecraft (often called g-jitter) on fluid motion. The residual acceleration field is modeled as a narrow band noise characterized by three independent parameters: its intensity $G^{2}$, a dominant fre...
Article
We study the combined effect of anisotropic surface tension and interface kinetics on pattern formation during the growth of two-dimensional crystals under conditions such that the growth is governed by interfacial processes. For sinusoidal anisotropies having fourfold symmetry, we compute numerically the trajectories of elements of the interface h...
Article
We introduce a stochastic model to analyze in quantitative detail the effect of the high frequency components of the residual accelerations onboard spacecraft (often called g-jitter) on fluid motion. The residual acceleration field is modeled as a narrow band noise characterized by three independent parameters: its intensity $G^{2}$, a dominant fre...
Article
We examine in quantitative detail the effects of long-range crystalline order on the collective diffusion of an interstitial species that is dissolved in a coherent, binary hard-sphere crystal. A linear constitutive law relating the flux of diffusing interstitials to the chemical driving force for diffusion is derived within the framework of linear...
Article
The effects are studied of assumed random velocity fields on diffusion in a binary fluid. Random velocity fields can result, for example, from the high-frequency components of residual accelerations onboard spacecraft (often called g-jitter). An effective diffusion equation is derived for an average concentration which includes spatial and temporal...

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