U. Titulaer - Academia.edu (original) (raw)
Papers by U. Titulaer
Physica A: Statistical Mechanics and its Applications, 1984
ABSTRACT
Physica A: Statistical Mechanics and its Applications, 1980
The normal mode analysis of systems of linear macroscopic equations in irreversible thermodynamic... more The normal mode analysis of systems of linear macroscopic equations in irreversible thermodynamics is extended in several ways. When the characteristic equation has multiple roots, there may appear normal solutions that do not decay purely exponentially, but a closed form for the Green function and the autocorrelation function can still be given. Furthermore, nonexponential decay is associated only with accidental, not with systematic degeneracy. We also discuss the case of external parameters that break microscopic time reversibility. In this case the orthonormality relations between the normal mode vectors are replaced by biorthonormality relations between the normal modes of the system studied and those of the system with reversed external parameters. Finally we discuss systems in which the second order energy is only positive semi-definite.
Physica A: Statistical Mechanics and its Applications, 1996
We consider a collection of droplets growing from a supersaturated vapor or (in general fluid) so... more We consider a collection of droplets growing from a supersaturated vapor or (in general fluid) solution for the time well after the nucleation. Its coarsening is driven by surface energy and leads asymptotically to a linear growth of the mean droplet volume with time (Ostwald ripening). The droplets grow either from the supersaturated uncondensed phase (coalescence) or by collisions with subsequent fusion (coagulation). We derive the evolution equation for a scaled size distribution of the droplets, which includes both mechanisms, and obtain the temporal behavior of the average size, variance and skewness by a cumulant expansion method. Since the cumulant expansion contains the boundary value at zero droplet radius, an assumption about this value must be made. In this context we use a piecewise linear approximation of the distribution. A comparison with earlier results and with the calculated asymptotic distribution shows that such an expansion in low order reproduces the main features of the system for the whole time evolution in most cases.
Journal of Statistical Physics, 1988
It has been known for some time that small deviations from the Onsager-Casimir symmetry relations... more It has been known for some time that small deviations from the Onsager-Casimir symmetry relations are introduced when one passes from a given description of a system to a less detailed one by adiabatic elimination of fast variables. Exact validity is preserved, however, for a slightly modified form of these relations. In this paper the question is considered whether this modified Onsager symmetry is also preserved by the transition from a microscopic to a mesoscopic description, the step that introduces manifest irreversibility into the equations of motion. This question is examined in detail for a system of a few heavy oscillators coupled to a bath, a model discussed in a recent paper by van Kampen. The modified Onsager symmetry survives the transition to an irreversible description via the dense spectrum approximation. This is shown explicitly by inspection of the results obtained by van Kampen; some arguments favoring a more general validity are also briefly discussed.
Physica A: Statistical Mechanics and its Applications, 1989
We consider the motion of a Brownlan pamcle in a medium with lnhomogeneous temperature in the pre... more We consider the motion of a Brownlan pamcle in a medium with lnhomogeneous temperature in the presence of an external potential We start from the Kleln-Kramers equation, m this equation a thermophoretlc force, proportional to the temperature gradient, should in general be included to obtain a correct description of thermodlffUSlOn effects in the hydrodynamic stage of the evolution With the Chapman-Enskog method we derive the correct form for the Smoluchowskl equation, which reduces to van Kampen's recent result in the absence of thermophoretlc forces We also give the first correction to this equation caused by deviations from local thermal equilibrium For the system considered, such devlatmns persist even in the steady state
Physica, 1973
Abstract The behaviour in time of a local phase function in a large system of harmonic oscillator... more Abstract The behaviour in time of a local phase function in a large system of harmonic oscillators approaches that of an ergodic phase function when the size of the system increases. This fact was established in a previous paper for the case in which periodic boundary conditions are imposed upon the system. In the present paper we give a more abstract approach to the same problem and show that the result is largely independent of the precise boundary conditions used. Moreover we prove some additional asymptotic ergodic properties of local phase functions, in particular that they form a K system in the sense of Kolmogorov and Sinai. In all of this the restriction to local phase functions is essential. The physical meaning of the result is that a large system acts as a good heat bath for a small subsystem. It is not claimed that the large system as a whole approaches ergodic behaviour.
Physica A: Statistical Mechanics and its Applications, 1991
The transfer of heat between an object not too large compared to a mean free path and a gas surro... more The transfer of heat between an object not too large compared to a mean free path and a gas surrounding it is influenced considerably by the structure of the kinetic bounda D, layer around the object. We calculate this effect for a spherical object in a dilute gas ~ app!)1ng a recently developed variant of the moment method to .solve the stationaD linearized Boltzmann equation for the gas surrounding the sphere. From the solut)on we deterrmne the temperature jump coefficient, which occurs in the boundary, condition to be used for the beat conduction equation at the surface of the sphere. We study the dependence of this quantity on the radius and on the thermal accommodatton coefficient We find that t)pical boundar) layer effects become less important as the accommodatton cocfficten decreases, and propo.~ a simple approximate formula, whtch describes the results for large spheres to w~thm al-,out hall a percent.
Journal of Molecular Liquids, 2000
We analyze the exact solution of the recombination probability of a radical pair with the Δg mech... more We analyze the exact solution of the recombination probability of a radical pair with the Δg mechanism for the spin dynamics and diffusion for translational motion. This reproduces the B12 dependence of the recombination probability in a small magnetic field and the saturation effect in a strong magnetic field.
Physics Letters A, 1985
We study the stationary density profile of brownian particles near a partially absorbing plane wa... more We study the stationary density profile of brownian particles near a partially absorbing plane wall. This profile is nonanalytic; the simplest possibility is a variation with a fractional power of the distance. If particles not absorbed are reflected specularly, then the exponent is a continuous function of the absorption coefficient.
Physica A: Statistical Mechanics and its Applications, 1985
The Chapman-Enskog method for the adiabatic elimination of fast variables is applied to a general... more The Chapman-Enskog method for the adiabatic elimination of fast variables is applied to a general Fokker-Planck equation linear in the fast variables. This equation is the counterpart of the generalized Haken-Zwanzig model, a system of coupled Langevin equations often encountered in quantum optics and in the theory of non-equilibrium phase transitions. After a few equilibration times for the fast variables
Condensed Matter Physics, 1999
We discuss a statistical model for antibody-antigen binding. The two macromolecules are assumed t... more We discuss a statistical model for antibody-antigen binding. The two macromolecules are assumed to be linked by a number of relatively weak bonds (or groups of correlated bonds) that are assumed to open and close statistically. We use the model for a preliminary analysis of experiments performed in the Institute of Biophysics at the Johannes Kepler University. In these experiments the two molecules are brought into contact using an atomic force microscope; then a prescribed time dependent force is applied to the bond and the distribution of times needed to pull the molecules completely apart is measured. This quantity is calculated with our model; its dependence on the model parameters (binding free energies, number of groups of correlated elementary bonds, force dependence of the binding free energy) is determined.
Physica A: Statistical Mechanics and its Applications, 1978
The motion of a Brownian particle in an external field can be described on two levels: by a Fokke... more The motion of a Brownian particle in an external field can be described on two levels: by a Fokker-Planck equation for the joint probability distribution of position and velocity, and by a Smoluchowski equation for the distribution in position space only. We derive the second description, with corrections, from the first by means of a systematic expansion procedure of the Chapman-Enskog type in terms of the inverse friction coefficient. We also derive equations describing the initial period, when the Smoluchowski description is not yet valid; in particular we find formulae connecting the initial value to be used for the Smoluchowski equation with that of the full Fokker-Planck equation. The special case of an harmonically bound Brownian particle can be solved exactly; the results are used to check and to illustrate our expressions for general potential.
Physica A: Statistical Mechanics and its Applications, 1980
We show that the linear equations of irreversible thermodynamics possess normal mode solutions al... more We show that the linear equations of irreversible thermodynamics possess normal mode solutions allowing a simple spectral decomposition of the Green function and of the timecorrelation function of thermal fluctuations. In the nondegenerate case it is possible to introduce normal coordinates with exponential behavior in time. As an application we consider the normal mode analysis of damped mechanical systems.
Physica A: Statistical Mechanics and its Applications, 1983
We consider linear dynamical systems with motions characterized by two different timescales. In p... more We consider linear dynamical systems with motions characterized by two different timescales. In practice the dynamical matrix in the phenomenological equations of motion often exhibits a strong coupling of the slow and fast variables. It is shown on the basis of the Onsager symmetry relations that a simple transformation of variables leads to a weak coupling. After the transformation one can use perturbation theory to derive reduced matrices describing the slow (fast) motions of the slow (fast) subsystem.
The Journal of Chemical Physics, 1982
ABSTRACT
Physica A: Statistical Mechanics and its Applications, 1991
ABSTRACT
Physica A: Statistical Mechanics and its Applications, 1984
ABSTRACT
Physica A: Statistical Mechanics and its Applications, 1980
The normal mode analysis of systems of linear macroscopic equations in irreversible thermodynamic... more The normal mode analysis of systems of linear macroscopic equations in irreversible thermodynamics is extended in several ways. When the characteristic equation has multiple roots, there may appear normal solutions that do not decay purely exponentially, but a closed form for the Green function and the autocorrelation function can still be given. Furthermore, nonexponential decay is associated only with accidental, not with systematic degeneracy. We also discuss the case of external parameters that break microscopic time reversibility. In this case the orthonormality relations between the normal mode vectors are replaced by biorthonormality relations between the normal modes of the system studied and those of the system with reversed external parameters. Finally we discuss systems in which the second order energy is only positive semi-definite.
Physica A: Statistical Mechanics and its Applications, 1996
We consider a collection of droplets growing from a supersaturated vapor or (in general fluid) so... more We consider a collection of droplets growing from a supersaturated vapor or (in general fluid) solution for the time well after the nucleation. Its coarsening is driven by surface energy and leads asymptotically to a linear growth of the mean droplet volume with time (Ostwald ripening). The droplets grow either from the supersaturated uncondensed phase (coalescence) or by collisions with subsequent fusion (coagulation). We derive the evolution equation for a scaled size distribution of the droplets, which includes both mechanisms, and obtain the temporal behavior of the average size, variance and skewness by a cumulant expansion method. Since the cumulant expansion contains the boundary value at zero droplet radius, an assumption about this value must be made. In this context we use a piecewise linear approximation of the distribution. A comparison with earlier results and with the calculated asymptotic distribution shows that such an expansion in low order reproduces the main features of the system for the whole time evolution in most cases.
Journal of Statistical Physics, 1988
It has been known for some time that small deviations from the Onsager-Casimir symmetry relations... more It has been known for some time that small deviations from the Onsager-Casimir symmetry relations are introduced when one passes from a given description of a system to a less detailed one by adiabatic elimination of fast variables. Exact validity is preserved, however, for a slightly modified form of these relations. In this paper the question is considered whether this modified Onsager symmetry is also preserved by the transition from a microscopic to a mesoscopic description, the step that introduces manifest irreversibility into the equations of motion. This question is examined in detail for a system of a few heavy oscillators coupled to a bath, a model discussed in a recent paper by van Kampen. The modified Onsager symmetry survives the transition to an irreversible description via the dense spectrum approximation. This is shown explicitly by inspection of the results obtained by van Kampen; some arguments favoring a more general validity are also briefly discussed.
Physica A: Statistical Mechanics and its Applications, 1989
We consider the motion of a Brownlan pamcle in a medium with lnhomogeneous temperature in the pre... more We consider the motion of a Brownlan pamcle in a medium with lnhomogeneous temperature in the presence of an external potential We start from the Kleln-Kramers equation, m this equation a thermophoretlc force, proportional to the temperature gradient, should in general be included to obtain a correct description of thermodlffUSlOn effects in the hydrodynamic stage of the evolution With the Chapman-Enskog method we derive the correct form for the Smoluchowskl equation, which reduces to van Kampen's recent result in the absence of thermophoretlc forces We also give the first correction to this equation caused by deviations from local thermal equilibrium For the system considered, such devlatmns persist even in the steady state
Physica, 1973
Abstract The behaviour in time of a local phase function in a large system of harmonic oscillator... more Abstract The behaviour in time of a local phase function in a large system of harmonic oscillators approaches that of an ergodic phase function when the size of the system increases. This fact was established in a previous paper for the case in which periodic boundary conditions are imposed upon the system. In the present paper we give a more abstract approach to the same problem and show that the result is largely independent of the precise boundary conditions used. Moreover we prove some additional asymptotic ergodic properties of local phase functions, in particular that they form a K system in the sense of Kolmogorov and Sinai. In all of this the restriction to local phase functions is essential. The physical meaning of the result is that a large system acts as a good heat bath for a small subsystem. It is not claimed that the large system as a whole approaches ergodic behaviour.
Physica A: Statistical Mechanics and its Applications, 1991
The transfer of heat between an object not too large compared to a mean free path and a gas surro... more The transfer of heat between an object not too large compared to a mean free path and a gas surrounding it is influenced considerably by the structure of the kinetic bounda D, layer around the object. We calculate this effect for a spherical object in a dilute gas ~ app!)1ng a recently developed variant of the moment method to .solve the stationaD linearized Boltzmann equation for the gas surrounding the sphere. From the solut)on we deterrmne the temperature jump coefficient, which occurs in the boundary, condition to be used for the beat conduction equation at the surface of the sphere. We study the dependence of this quantity on the radius and on the thermal accommodatton coefficient We find that t)pical boundar) layer effects become less important as the accommodatton cocfficten decreases, and propo.~ a simple approximate formula, whtch describes the results for large spheres to w~thm al-,out hall a percent.
Journal of Molecular Liquids, 2000
We analyze the exact solution of the recombination probability of a radical pair with the Δg mech... more We analyze the exact solution of the recombination probability of a radical pair with the Δg mechanism for the spin dynamics and diffusion for translational motion. This reproduces the B12 dependence of the recombination probability in a small magnetic field and the saturation effect in a strong magnetic field.
Physics Letters A, 1985
We study the stationary density profile of brownian particles near a partially absorbing plane wa... more We study the stationary density profile of brownian particles near a partially absorbing plane wall. This profile is nonanalytic; the simplest possibility is a variation with a fractional power of the distance. If particles not absorbed are reflected specularly, then the exponent is a continuous function of the absorption coefficient.
Physica A: Statistical Mechanics and its Applications, 1985
The Chapman-Enskog method for the adiabatic elimination of fast variables is applied to a general... more The Chapman-Enskog method for the adiabatic elimination of fast variables is applied to a general Fokker-Planck equation linear in the fast variables. This equation is the counterpart of the generalized Haken-Zwanzig model, a system of coupled Langevin equations often encountered in quantum optics and in the theory of non-equilibrium phase transitions. After a few equilibration times for the fast variables
Condensed Matter Physics, 1999
We discuss a statistical model for antibody-antigen binding. The two macromolecules are assumed t... more We discuss a statistical model for antibody-antigen binding. The two macromolecules are assumed to be linked by a number of relatively weak bonds (or groups of correlated bonds) that are assumed to open and close statistically. We use the model for a preliminary analysis of experiments performed in the Institute of Biophysics at the Johannes Kepler University. In these experiments the two molecules are brought into contact using an atomic force microscope; then a prescribed time dependent force is applied to the bond and the distribution of times needed to pull the molecules completely apart is measured. This quantity is calculated with our model; its dependence on the model parameters (binding free energies, number of groups of correlated elementary bonds, force dependence of the binding free energy) is determined.
Physica A: Statistical Mechanics and its Applications, 1978
The motion of a Brownian particle in an external field can be described on two levels: by a Fokke... more The motion of a Brownian particle in an external field can be described on two levels: by a Fokker-Planck equation for the joint probability distribution of position and velocity, and by a Smoluchowski equation for the distribution in position space only. We derive the second description, with corrections, from the first by means of a systematic expansion procedure of the Chapman-Enskog type in terms of the inverse friction coefficient. We also derive equations describing the initial period, when the Smoluchowski description is not yet valid; in particular we find formulae connecting the initial value to be used for the Smoluchowski equation with that of the full Fokker-Planck equation. The special case of an harmonically bound Brownian particle can be solved exactly; the results are used to check and to illustrate our expressions for general potential.
Physica A: Statistical Mechanics and its Applications, 1980
We show that the linear equations of irreversible thermodynamics possess normal mode solutions al... more We show that the linear equations of irreversible thermodynamics possess normal mode solutions allowing a simple spectral decomposition of the Green function and of the timecorrelation function of thermal fluctuations. In the nondegenerate case it is possible to introduce normal coordinates with exponential behavior in time. As an application we consider the normal mode analysis of damped mechanical systems.
Physica A: Statistical Mechanics and its Applications, 1983
We consider linear dynamical systems with motions characterized by two different timescales. In p... more We consider linear dynamical systems with motions characterized by two different timescales. In practice the dynamical matrix in the phenomenological equations of motion often exhibits a strong coupling of the slow and fast variables. It is shown on the basis of the Onsager symmetry relations that a simple transformation of variables leads to a weak coupling. After the transformation one can use perturbation theory to derive reduced matrices describing the slow (fast) motions of the slow (fast) subsystem.
The Journal of Chemical Physics, 1982
ABSTRACT
Physica A: Statistical Mechanics and its Applications, 1991
ABSTRACT