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Rudi Schmitz

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Papers by Rudi Schmitz

Creeping flow about a sphere

Physica A: Statistical Mechanics and its Applications

We present the general solution of the linear Navier-Stokes equation for incompressible viscous f... more We present the general solution of the linear Navier-Stokes equation for incompressible viscous flow about a sphere with mixed slip-stick boundary conditions. Exphclt results are obtained in cartesian coordinates. The relation wRh Lamb's method is indicated. We derive expressions for a set of fundamental tensors, introduced by Brenner, describing the perturbed flow. Finally the force density induced on the sphere is evaluated.

Friction matrix for two spherical particles with hydrodynamic interaction

Physica A: Statistical Mechanics and its Applications

We solve the creeping flow equations for two spherically symmetric particles immersed in an incom... more We solve the creeping flow equations for two spherically symmetric particles immersed in an incompressible fluid. The flow pattern outside the particles is analyzed in a two-center expansion of spherical waves scattered from each of the particles. Hence we construct the friction matrix which relates the forces, the torques and symmetric force dipole moments to the imposed flow velocities and their linear derivatives at the particle centers.

Creeping flow about a spherical particle

Physica A: Statistical Mechanics and its Applications

We formulate the solution of the linear Navier-Stokes equations for steady, incompressible flow a... more We formulate the solution of the linear Navier-Stokes equations for steady, incompressible flow about a spherical particle as an expansion of scattered waves. The amplitudes of the outgoing waves are simply related to a set of spherical force multipoles. These multipoles are found from the amplitudes of the incident waves with the aid of a resistance matrix, which is expressed in terms of the scattering coefficients of the particle.

Driven Motion of Extended Defects Wetted by a New Phase

AIP Conference Proceedings

Moving extended defects can close to a bulk phase transition be coated by nuclei of a new phase. ... more Moving extended defects can close to a bulk phase transition be coated by nuclei of a new phase. Depending on the order of the transition and on the type of the defects, the co-moving nuclei display various types of non-equilibrium phase transitions and instabilities. These are expected to affect significantly the plastic behavior of real materials.

Positivity of transport coefficients for cellular automata

Physical Review a General Physics, Apr 1, 1990

Hydrodynamic interactions between two spherical particles

Simple dynamics in the presence of topological disorder

Physica A: Statistical Mechanics and its Applications, 1996

Dislocations and disclinations are classical examples of topological defects in condensed matter.... more Dislocations and disclinations are classical examples of topological defects in condensed matter. In this lecture, we will formulate pertinent questions concerning the dynamics of particles in the presence of these topological defects and provide answers to some of them. Some remarks about related quantum problems will be made, stressing the necessity of further thorough analysis.

Scattering of electrons on screw dislocations

Physical Review B, 1999

A previously established general framework for the description of long-wavelength quantum states ... more A previously established general framework for the description of long-wavelength quantum states of electrons in a crystal with topological defects is used to discuss the scattering of electrons on a screw dislocation. The corresponding Schrödinger equation contains contributions of the type of a vector potential as well as of a repulsive scalar potential. Together they give rise to modified Aharonov-Bohm interferences in the scattering amplitude, for which the far-field expression is calculated exactly. ͓S0163-1829͑99͒01121-2͔

Dislocation drag close to a phase transition

Physical Review B, 2003

The viscous drag of dislocations is known to increase when a phase transition of the host materia... more The viscous drag of dislocations is known to increase when a phase transition of the host material is approached. Previous discussions of this effect, however, have overlooked that, above the bulk transition point, the ordered phase can already nucleate along the dislocations. The viscous-drag component due to energy dissipation in such nuclei is shown to clearly dominate the previously known

Segregation instabilities of moving interfaces

Physical review letters, Jan 27, 2006

The segregation of solute particles on a moving interface leads to the appearance of two types of... more The segregation of solute particles on a moving interface leads to the appearance of two types of instabilities near competing velocity thresholds. This behavior is shown to occur in a variety of exactly solvable models where the interface motion is coupled to a diffusion process of the solute particles. These models directly apply to the propagation of internal domain walls, but can also be generalized to surfaces of growing crystals in the kinetics-limited regime.

Dynamic instability of dislocations due to nucleation of a new phase

Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

Dislocation lines in a crystal close to a bulk phase transition can be coated by nuclei of a new ... more Dislocation lines in a crystal close to a bulk phase transition can be coated by nuclei of a new phase which for a moving dislocation gives rise to a viscous friction force. In some range of the material parameters this force leads to a dynamic instability of the defect line, resulting from an intricate interplay between the shape fluctuations of the defect and the amplitude fluctuations of the nucleus. The instability shows up in the linear response of the dislocation to a periodic change of the driving force and in the structure factor of the order-parameter fluctuations of the nucleus.

Diffusion in the presence of topological disorder

Physical review letters, Jan 31, 1994

Light-scattering spectrum of supercooled liquids

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1996

... Rev., A [1992]. Stretching, mode coupling, and the glass transition. (PMID:9908334)Kim B. Phy... more

Periodic layer formation in the growth of dilute binary alloys

Physica A: Statistical Mechanics and its Applications, 2014

h i g h l i g h t s • A simple model for the banded-structure effect in alloys is presented. • Ou... more h i g h l i g h t s • A simple model for the banded-structure effect in alloys is presented. • Our theory is based on a capillary wave version of the phase-field model. • It describes an interesting case of pattern formation in a non-equilibrium state. • Our model might also explain the occurrence of striations during crystal growth.

Dynamics of metastable states: Mode-coupling theory and beyond

Transport Theory and Statistical Physics, 1995

Fluctuations in nonequilibrium fluids

Physics Reports, 1988

The extension of fluctuating hydrodynamics to nonequilibnum steady states is discussed. Fluctuati... more The extension of fluctuating hydrodynamics to nonequilibnum steady states is discussed. Fluctuations on the walls surrounding the system are systematically taken into account. Formal results for the correlation matrix and the spectral density matrix are derived. These results involve so-called mode-coupling terms, which yield important corrections to the local equilibrium expressions describing spatially long-range static correlations. As an application the dynamic structure factor of a simple fluid exposed to a temperature gradient is discussed.

Diffusion-Induced Oscillations of Extended Defects

Physical Review Letters, 2012

From a simple model for the driven motion of a planar interface under the influence of a diffusio... more From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is negative, we find limit-cycle solutions, describing an oscillatory propagation of the interface. In case of a growing solidification front this offers a transparent scenario for the formation of solute bands in binary alloys, and, taking into account the Mullins-Sekerka instability, of banded structures.

Single-Particle Quantum States in a Crystal with Topological Defects

Physical Review Letters, 1998

The influence of frozen-in topological defects in a crystal on the long-wavelength quantum states... more The influence of frozen-in topological defects in a crystal on the long-wavelength quantum states of a particle is considered. In the continuum limit of a conveniently defined tight-binding model one is led to a covariant Schrödinger equation on a Riemann-Cartan manifold. When the tight-binding transfer energies are assumed to depend on the local lattice deformations caused by the defects, additional noncovariant terms are generated in the Hamiltonian. These terms generate bound states of the particle to edge dislocations and enhance the scattering of particles on screw dislocations. [S0031-9007(98)05432-5]

Kinetic Wetting of a Moving Planar Defect by a New Phase

Physical Review Letters, 2003

Close to a bulk phase transition, a moving planar defect can be covered by a layer of the ordered... more Close to a bulk phase transition, a moving planar defect can be covered by a layer of the ordered phase. This, in fact, happens above the transition point in some finite region of the temperature-velocity diagram. In the case of a first-order transition this region is furnished with a net of nonequilibrium phase-transition lines. The topology of this net resembles that of the phase diagram of a first-order wetting transition in thermal equilibrium. In particular, there appears a kinetic complete-wetting line where a significant change of the drag coefficient of the defect is predicted.

Self-Induced Kinetic Roughening of Dislocations in the Vicinity of First-Order Phase Transitions

Physical Review Letters, 1999

The glide motion of a dislocation line is considered in a crystal undergoing a first-order phase ... more The glide motion of a dislocation line is considered in a crystal undergoing a first-order phase transition. Within the hysteresis temperature range a trail of a metastable phase can nucleate at the dislocation and act as a dry-friction force. The strength of this force depends on the angle between the Burgers vector and the local orientation of the defect line.

Creeping flow about a sphere

Physica A: Statistical Mechanics and its Applications

We present the general solution of the linear Navier-Stokes equation for incompressible viscous f... more We present the general solution of the linear Navier-Stokes equation for incompressible viscous flow about a sphere with mixed slip-stick boundary conditions. Exphclt results are obtained in cartesian coordinates. The relation wRh Lamb's method is indicated. We derive expressions for a set of fundamental tensors, introduced by Brenner, describing the perturbed flow. Finally the force density induced on the sphere is evaluated.

Friction matrix for two spherical particles with hydrodynamic interaction

Physica A: Statistical Mechanics and its Applications

We solve the creeping flow equations for two spherically symmetric particles immersed in an incom... more We solve the creeping flow equations for two spherically symmetric particles immersed in an incompressible fluid. The flow pattern outside the particles is analyzed in a two-center expansion of spherical waves scattered from each of the particles. Hence we construct the friction matrix which relates the forces, the torques and symmetric force dipole moments to the imposed flow velocities and their linear derivatives at the particle centers.

Creeping flow about a spherical particle

Physica A: Statistical Mechanics and its Applications

We formulate the solution of the linear Navier-Stokes equations for steady, incompressible flow a... more We formulate the solution of the linear Navier-Stokes equations for steady, incompressible flow about a spherical particle as an expansion of scattered waves. The amplitudes of the outgoing waves are simply related to a set of spherical force multipoles. These multipoles are found from the amplitudes of the incident waves with the aid of a resistance matrix, which is expressed in terms of the scattering coefficients of the particle.

Driven Motion of Extended Defects Wetted by a New Phase

AIP Conference Proceedings

Moving extended defects can close to a bulk phase transition be coated by nuclei of a new phase. ... more Moving extended defects can close to a bulk phase transition be coated by nuclei of a new phase. Depending on the order of the transition and on the type of the defects, the co-moving nuclei display various types of non-equilibrium phase transitions and instabilities. These are expected to affect significantly the plastic behavior of real materials.

Positivity of transport coefficients for cellular automata

Physical Review a General Physics, Apr 1, 1990

Hydrodynamic interactions between two spherical particles

Simple dynamics in the presence of topological disorder

Physica A: Statistical Mechanics and its Applications, 1996

Dislocations and disclinations are classical examples of topological defects in condensed matter.... more Dislocations and disclinations are classical examples of topological defects in condensed matter. In this lecture, we will formulate pertinent questions concerning the dynamics of particles in the presence of these topological defects and provide answers to some of them. Some remarks about related quantum problems will be made, stressing the necessity of further thorough analysis.

Scattering of electrons on screw dislocations

Physical Review B, 1999

A previously established general framework for the description of long-wavelength quantum states ... more A previously established general framework for the description of long-wavelength quantum states of electrons in a crystal with topological defects is used to discuss the scattering of electrons on a screw dislocation. The corresponding Schrödinger equation contains contributions of the type of a vector potential as well as of a repulsive scalar potential. Together they give rise to modified Aharonov-Bohm interferences in the scattering amplitude, for which the far-field expression is calculated exactly. ͓S0163-1829͑99͒01121-2͔

Dislocation drag close to a phase transition

Physical Review B, 2003

The viscous drag of dislocations is known to increase when a phase transition of the host materia... more The viscous drag of dislocations is known to increase when a phase transition of the host material is approached. Previous discussions of this effect, however, have overlooked that, above the bulk transition point, the ordered phase can already nucleate along the dislocations. The viscous-drag component due to energy dissipation in such nuclei is shown to clearly dominate the previously known

Segregation instabilities of moving interfaces

Physical review letters, Jan 27, 2006

The segregation of solute particles on a moving interface leads to the appearance of two types of... more The segregation of solute particles on a moving interface leads to the appearance of two types of instabilities near competing velocity thresholds. This behavior is shown to occur in a variety of exactly solvable models where the interface motion is coupled to a diffusion process of the solute particles. These models directly apply to the propagation of internal domain walls, but can also be generalized to surfaces of growing crystals in the kinetics-limited regime.

Dynamic instability of dislocations due to nucleation of a new phase

Physical review. E, Statistical, nonlinear, and soft matter physics, 2001

Dislocation lines in a crystal close to a bulk phase transition can be coated by nuclei of a new ... more Dislocation lines in a crystal close to a bulk phase transition can be coated by nuclei of a new phase which for a moving dislocation gives rise to a viscous friction force. In some range of the material parameters this force leads to a dynamic instability of the defect line, resulting from an intricate interplay between the shape fluctuations of the defect and the amplitude fluctuations of the nucleus. The instability shows up in the linear response of the dislocation to a periodic change of the driving force and in the structure factor of the order-parameter fluctuations of the nucleus.

Diffusion in the presence of topological disorder

Physical review letters, Jan 31, 1994

Light-scattering spectrum of supercooled liquids

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1996

... Rev., A [1992]. Stretching, mode coupling, and the glass transition. (PMID:9908334)Kim B. Phy... more

Periodic layer formation in the growth of dilute binary alloys

Physica A: Statistical Mechanics and its Applications, 2014

h i g h l i g h t s • A simple model for the banded-structure effect in alloys is presented. • Ou... more h i g h l i g h t s • A simple model for the banded-structure effect in alloys is presented. • Our theory is based on a capillary wave version of the phase-field model. • It describes an interesting case of pattern formation in a non-equilibrium state. • Our model might also explain the occurrence of striations during crystal growth.

Dynamics of metastable states: Mode-coupling theory and beyond

Transport Theory and Statistical Physics, 1995

Fluctuations in nonequilibrium fluids

Physics Reports, 1988

The extension of fluctuating hydrodynamics to nonequilibnum steady states is discussed. Fluctuati... more The extension of fluctuating hydrodynamics to nonequilibnum steady states is discussed. Fluctuations on the walls surrounding the system are systematically taken into account. Formal results for the correlation matrix and the spectral density matrix are derived. These results involve so-called mode-coupling terms, which yield important corrections to the local equilibrium expressions describing spatially long-range static correlations. As an application the dynamic structure factor of a simple fluid exposed to a temperature gradient is discussed.

Diffusion-Induced Oscillations of Extended Defects

Physical Review Letters, 2012

From a simple model for the driven motion of a planar interface under the influence of a diffusio... more From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is negative, we find limit-cycle solutions, describing an oscillatory propagation of the interface. In case of a growing solidification front this offers a transparent scenario for the formation of solute bands in binary alloys, and, taking into account the Mullins-Sekerka instability, of banded structures.

Single-Particle Quantum States in a Crystal with Topological Defects

Physical Review Letters, 1998

The influence of frozen-in topological defects in a crystal on the long-wavelength quantum states... more The influence of frozen-in topological defects in a crystal on the long-wavelength quantum states of a particle is considered. In the continuum limit of a conveniently defined tight-binding model one is led to a covariant Schrödinger equation on a Riemann-Cartan manifold. When the tight-binding transfer energies are assumed to depend on the local lattice deformations caused by the defects, additional noncovariant terms are generated in the Hamiltonian. These terms generate bound states of the particle to edge dislocations and enhance the scattering of particles on screw dislocations. [S0031-9007(98)05432-5]

Kinetic Wetting of a Moving Planar Defect by a New Phase

Physical Review Letters, 2003

Close to a bulk phase transition, a moving planar defect can be covered by a layer of the ordered... more Close to a bulk phase transition, a moving planar defect can be covered by a layer of the ordered phase. This, in fact, happens above the transition point in some finite region of the temperature-velocity diagram. In the case of a first-order transition this region is furnished with a net of nonequilibrium phase-transition lines. The topology of this net resembles that of the phase diagram of a first-order wetting transition in thermal equilibrium. In particular, there appears a kinetic complete-wetting line where a significant change of the drag coefficient of the defect is predicted.

Self-Induced Kinetic Roughening of Dislocations in the Vicinity of First-Order Phase Transitions

Physical Review Letters, 1999

The glide motion of a dislocation line is considered in a crystal undergoing a first-order phase ... more The glide motion of a dislocation line is considered in a crystal undergoing a first-order phase transition. Within the hysteresis temperature range a trail of a metastable phase can nucleate at the dislocation and act as a dry-friction force. The strength of this force depends on the angle between the Burgers vector and the local orientation of the defect line.