Martin Burschka - Academia.edu (original) (raw)
Papers by Martin Burschka
Physica D: Nonlinear Phenomena, May 1, 1982
We study stationary solutions of the Fokker-Planck equation for velocity and position of a Browni... more We study stationary solutions of the Fokker-Planck equation for velocity and position of a Brownian particle in the presence of a constant external field and a completely or selectively absorbing plane wall. Adapting a procedure used earlier for the field-free case, we determine analytically a set of boundary layer solutions and combine them numerically with the Chapman-Enskog solutions to satisfy
Journal of Statistical Physics, Dec 1, 1991
The one-dimensional single-species diffusion-limited-coagulation process with irreversible random... more The one-dimensional single-species diffusion-limited-coagulation process with irreversible random particle input (A~A + A reversibly and B~A irreversibly), under the influence of external fluctuations in the system parameters, is formulated in terms of a closed and linear partial-differential equation. Our theoretical treatment includes both internal fluctuations and external noise simultaneously and without approximation, allowing investigation of the interplay of their effects on the macroscopic behavior of this diffusion-reaction system. For the reversible model with the rate of the A~A+ A reaction fluctuating between two values as a Markov stochastic process, we solve the system exactly. We observe that spatially homogeneous macroscopic fluctuations in the system parameters can induce microscopic spatial correlations in the nonequilibrium steady state. Direct Monte Carlo simulations of the microscopic dynamics are presented, confirming the theoretical analysis and directly illustrating the externalnoise-induced spatial correlations.
Physical Review A, Apr 1, 1992
The one-dimensional single-species diffusion-limited-coagulation process with irreversible random... more The one-dimensional single-species diffusion-limited-coagulation process with irreversible random particle input (A~A + A reversibly and B~A irreversibly), under the influence of external fluctuations in the system parameters, is formulated in terms of a closed and linear partial-differential equation. Our theoretical treatment includes both internal fluctuations and external noise simultaneously and without approximation, allowing investigation of the interplay of their effects on the macroscopic behavior of this diffusion-reaction system. For the reversible model with the rate of the A~A+ A reaction fluctuating between two values as a Markov stochastic process, we solve the system exactly. We observe that spatially homogeneous macroscopic fluctuations in the system parameters can induce microscopic spatial correlations in the nonequilibrium steady state. Direct Monte Carlo simulations of the microscopic dynamics are presented, confirming the theoretical analysis and directly illustrating the externalnoise-induced spatial correlations.
Journal of Physics A: Mathematical and General, 1993
In a first-order wetting transition the decay of a metastable non-wet state occurs by nucleation ... more In a first-order wetting transition the decay of a metastable non-wet state occurs by nucleation and growth of supercritical droplets on the wall of the system. Based on an effective interface model for the wetting fluid the shape of the critical droplet is calculated outside a microscopic region near the wall for a class of long-range interface potentials. The solution has a surprisingly simple form if the dimension of the system coincides with the boundary dimension between the so-called strong and weak fluctuation regimes.
Journal of Statistical Physics, Sep 1, 1981
The Fokker-Planck equation for the distribution of position and velocity of a Brownian particle i... more The Fokker-Planck equation for the distribution of position and velocity of a Brownian particle is a particularly simple linear transport equation. Its normal solutions and an apparently complete set of stationary boundary layer solutions can be determined explicitly. By a numerical algorithm we select linear combinations of them that approximately fulfill the boundary condition for a completely absorbing plane wall, and that approach a linearly increasing position space density far from the wall. Various aspects of these approximate solutions are discussed. In particular we find that the extrapolated asymptotic density reaches zero at a distance x M beyond the wall. We find xM = 1.46 in units of the velocity persistence length of the Brownian particle. This study was motivated by certain problems in the theory of diffusion-controlled reactions, and the results might be used to test approximate theories employed in that field.
Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic descr... more Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic description. We show how the correlations dominate the dynamics by juxtaposing the macroscopic dynamics of a cellular automaton model for the diffusion-controlled limit to the deterministic diffusion-reaction rate equation for the same reaction. A more detailed N-body master equation is then presented in which explicit diffusion-controlled limits are explained. 1 What Is Special About Diffusion-Limited Reactions? Common diffusion-reaction-rate equations are similar in structure and concept to the hydrodynamic equations for simple fluids and appear to be a simpler paradigm for general purposes. To the statistical physicist, however, systems with ongoing chemical reactions pose a more fundamental challenge than simple fluids in that two familiar properties of fluctuations cannot be taken for granted there: a) slow variation in comparison to the fast microscopic (i.e. molecular) dynamics due to ...
Otology & Neurotology, 2007
HNO-Informationen (Kongressabstracts), 2005
Patienten fanden sich für das Hauptzielkriterium "Hörgewinn an Tag 7" zwar numerische Vorteile fü... more Patienten fanden sich für das Hauptzielkriterium "Hörgewinn an Tag 7" zwar numerische Vorteile für die HES-Gruppen gegenüber Placebo, jedoch keine statistisch signifikante Überlegenheit. Auffällig waren aber Unterschiede in der langfristigen Hörerholung zwischen Patienten, die innerhalb von 48 h nach dem Hörsturz zur Behandlung kamen (4,7% ohne Verbesserung innerhalb von 90 Tagen) und jenen, die erst später behandelt wurden (21,5 % nach 90 Tagen ohne Besserung). Auch Patienten mit einem systolischen Blutdruck >140 mmHg hatten geringere Chancen einer Erholung. Für jene Patienten, die diesen Risikofaktor aufwiesen und sich später als 48 h nach Symptombeginn in die Behandlung begeben hatten, waren in der Placebogruppe nach einer Woche 46 % noch ohne Hörbesserung, während in der 4%-HES-Gruppe nur 13 % ohne Besserung blieben (p=0,025 für eine zumindest partielle Hörerholung unter HES am Tag 7). Die neuartige HES-Lösung erwies sich insgesamt als nebenwirkungsarm, insbesondere trat der substanztypische Pruritus nur temporär bei 4 von 157 mit HES 130/0.4 Behandelten auf.
We present an exact closed formulation of the reversible diffusion-limited coagulation-growth rea... more We present an exact closed formulation of the reversible diffusion-limited coagulation-growth reactions 2A ↔ A with irreversible input B → A in one spatial dimension. The treatment here accommodates spatial as well as temporal variations in the particle density with a complete account of microscopic fluctuations and correlations. Moreover, spatial and/or temporal variations in the transport and reaction coefficients can be included in the model. A general solution to the reversible process is presented, and we explore the phenomenon of wavefront propagation.
Otology & Neurotology, 2007
Obtain and analyze first data on hydroxyethyl starch (HES 130/0.4) as monotherapy in acute idiopa... more Obtain and analyze first data on hydroxyethyl starch (HES 130/0.4) as monotherapy in acute idiopathic sudden sensorineural hearing loss (ISSNHL). Randomized, double-blind, Phase-II, dose-finding study. Twenty-five ENT centers in Germany, the Czech Republic, Romania, and Austria. Two hundred and ten inpatients with first-time ISSNHL of at least 20 dB at two or more frequencies and 95 dB or less at all of the speech frequencies (0.5, 1.0, 2.0, 3.0, and 4.0 kHz) with respect to the other (normal) ear for up to 7 days (d). Infusion of 750 mL/d with 45 (Group H), 30 (Group M), or 15 g/d HES (Group L), or glucose 5% (Group G) acting as "placebo" control during 6 days. MAIN ENDPOINT: Gain in average auditory threshold (in dB) from baseline to Day 7. RESULTS (MEDIANS): Average hearing loss at baseline was 24 dB, and infusions started 2 days after ISSNHL onset. No relevant group difference was observed in hearing gain or adverse treatment events, including pruritus. Half of all pat...
Physical Review A, 1992
The one-dimensional single-species diffusion-limited-coagulation process with irreversible random... more The one-dimensional single-species diffusion-limited-coagulation process with irreversible random particle input (A&lrarr2;A+A reversibly and B-->A irreversibly), under the influence of external fluctuations in the system parameters, is formulated in terms of a closed and linear partial-differential equation. Our theoretical treatment includes both internal fluctuations and external noise simultaneously and without approximation, allowing investigation of the interplay of their effects on the
Journal of Physics a Mathematical General, Nov 1, 1993
Journal of Physics a Mathematical and General, Feb 21, 1994
ABSTRACT In a first-order wetting transition it is possible to overheat a microscopic layer from ... more ABSTRACT In a first-order wetting transition it is possible to overheat a microscopic layer from below to above the wetting temperature Tw, and to undercool a macroscopic layer from above to below Tw. In both cases the transition to stable equilibrium occurs by formation and growth of supercritical nuclei. The critical nuclei for overheating are droplets on the wall of the system and for undercooling they are dents in the macroscopic layer. A recent calculation of the critical droplet in a special dimension d0 is now supplemented by the calculation of the critical dent for dewetting. Although the analytic expressions for the profiles are closely related, the nuclei above Tw are finite whereas they are infinitely large below Tw. The latter is to be expected since the system is infinitesimally close to coexistence of wet and non-wet states at all temperatures T<Tw.
Journal of Statistical Physics, Aug 31, 1990
We solve exactly the one-dimensional diffusion-limited single-species coagulation process (A+A-* ... more We solve exactly the one-dimensional diffusion-limited single-species coagulation process (A+A-* A) with back reactions (A ~A+A) and/or a steady input of particles (B-* A). The exact solution yields not only the steady-state concentration of particles, but also the exact time-dependent concentration as well as the time-dependent probability distribution for the distance between neighboring particles, i.e., the interparticle distribution function (IPDF). The concentration for this diffusion-limited reaction process does not obey the classical "mean-field" rate equation. Rather, the kinetics is described by a finite set of ordinary differential equations only in particular cases, with no such description holding in general. The reaction kinetics is linked to the spatial distribution of particles as reflected in the IPDFs. The spatial distribution of particles is totally random, i.e., the maximum entropy distribution, only in the steady state of the strictly reversible process A + A ~ A, a true equilibrium state with detailed balance. Away from this equilibrium state the particles display a static or dynamic self-organization imposed by the nonequilibrium reactions. The strictly reversible process also exhibits a sharp transition in its relaxation dynamics when switching between equilibria of different values of the system parameters. When the system parameters are suddenly changed so that the new equilibrium concentration is greater than exactly twice the old equilibrium concentration, the exponential relaxation time depends on the initial concentration.
Lecture Notes in Physics, May 5, 2007
Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic descr... more Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic description. We show how the correlations dominate the dynamics by juxtaposing the macroscopic dynamics of a cellular automaton model for the diffusion-controlled limit to the deterministic diffusion-reaction rate equation for the same reaction. A more detailed N-body master equation is then presented in which explicit diffusion-controlled limits are explained.
Epl, Jul 24, 2007
ABSTRACT We consider the many-body initial-value problem for the reversible single-species diffus... more ABSTRACT We consider the many-body initial-value problem for the reversible single-species diffusion-controlled reaction X + X X. A mapping to a dual process is identified which reduces the N-body problem to the dynamics of interfaces, which for general initial conditions is reduced to simple quadratures. The diffusion-controlled limit and the continuous space limit are taken as leading orders in power series expansions. The spectrum of the reaction operator is given explicitly and its use for the calculation of corrections to the diffusion-controlled limit is explained. A closed form is given for the time- and space-dependent concentration ρ(R, t) in one dimension following an arbitrary initial state.
Physical Review Letters
We sutdy a stochastic interacting particle system which displays a nonequilibrium transition in i... more We sutdy a stochastic interacting particle system which displays a nonequilibrium transition in its relaxation dynamics in the infinite volume limit. The transition is destroyed by restriction to a finite volume, but its remnants remain until a crossover time Tc(L,ε), where L is the system size and ε is the control parameter measuring the distance from the bulk transition. We find that the crossover time Tc(L,ε) diverges where ε-->0 in a fixed volume. Thus this finite volume system displays arbitrarily long time scales near the transition.
Journal of Statistical Physics
We develop a concise method to compute the corrections to the master equation for chemically reac... more We develop a concise method to compute the corrections to the master equation for chemically reacting systems in particle number space that arise if the system is not a well-stirred tank reactor, but the transport occurs by diffusion. Starting from the master equation in theRN space of all reactant particle positions, we expand in inverse powers of the diffusion constant and eliminate all transport modes adiabatically. It is found that the overall effect of spatially nonuniform fluctuations cannot be treated as a mere renormalization of the reaction rate constants. From second order on there appear correction terms with a new structure that corresponds formally to additional virtual reaction paths. An intuitive interpretation along this line is impeded, however, by the formal occurrence of negative reaction rate constants in these terms, i.e., the reaction rate may depend on the concentrations of the final products of the virtual reaction rather than on the ingoing products. We also...
Physica D: Nonlinear Phenomena, May 1, 1982
We study stationary solutions of the Fokker-Planck equation for velocity and position of a Browni... more We study stationary solutions of the Fokker-Planck equation for velocity and position of a Brownian particle in the presence of a constant external field and a completely or selectively absorbing plane wall. Adapting a procedure used earlier for the field-free case, we determine analytically a set of boundary layer solutions and combine them numerically with the Chapman-Enskog solutions to satisfy
Journal of Statistical Physics, Dec 1, 1991
The one-dimensional single-species diffusion-limited-coagulation process with irreversible random... more The one-dimensional single-species diffusion-limited-coagulation process with irreversible random particle input (A~A + A reversibly and B~A irreversibly), under the influence of external fluctuations in the system parameters, is formulated in terms of a closed and linear partial-differential equation. Our theoretical treatment includes both internal fluctuations and external noise simultaneously and without approximation, allowing investigation of the interplay of their effects on the macroscopic behavior of this diffusion-reaction system. For the reversible model with the rate of the A~A+ A reaction fluctuating between two values as a Markov stochastic process, we solve the system exactly. We observe that spatially homogeneous macroscopic fluctuations in the system parameters can induce microscopic spatial correlations in the nonequilibrium steady state. Direct Monte Carlo simulations of the microscopic dynamics are presented, confirming the theoretical analysis and directly illustrating the externalnoise-induced spatial correlations.
Physical Review A, Apr 1, 1992
The one-dimensional single-species diffusion-limited-coagulation process with irreversible random... more The one-dimensional single-species diffusion-limited-coagulation process with irreversible random particle input (A~A + A reversibly and B~A irreversibly), under the influence of external fluctuations in the system parameters, is formulated in terms of a closed and linear partial-differential equation. Our theoretical treatment includes both internal fluctuations and external noise simultaneously and without approximation, allowing investigation of the interplay of their effects on the macroscopic behavior of this diffusion-reaction system. For the reversible model with the rate of the A~A+ A reaction fluctuating between two values as a Markov stochastic process, we solve the system exactly. We observe that spatially homogeneous macroscopic fluctuations in the system parameters can induce microscopic spatial correlations in the nonequilibrium steady state. Direct Monte Carlo simulations of the microscopic dynamics are presented, confirming the theoretical analysis and directly illustrating the externalnoise-induced spatial correlations.
Journal of Physics A: Mathematical and General, 1993
In a first-order wetting transition the decay of a metastable non-wet state occurs by nucleation ... more In a first-order wetting transition the decay of a metastable non-wet state occurs by nucleation and growth of supercritical droplets on the wall of the system. Based on an effective interface model for the wetting fluid the shape of the critical droplet is calculated outside a microscopic region near the wall for a class of long-range interface potentials. The solution has a surprisingly simple form if the dimension of the system coincides with the boundary dimension between the so-called strong and weak fluctuation regimes.
Journal of Statistical Physics, Sep 1, 1981
The Fokker-Planck equation for the distribution of position and velocity of a Brownian particle i... more The Fokker-Planck equation for the distribution of position and velocity of a Brownian particle is a particularly simple linear transport equation. Its normal solutions and an apparently complete set of stationary boundary layer solutions can be determined explicitly. By a numerical algorithm we select linear combinations of them that approximately fulfill the boundary condition for a completely absorbing plane wall, and that approach a linearly increasing position space density far from the wall. Various aspects of these approximate solutions are discussed. In particular we find that the extrapolated asymptotic density reaches zero at a distance x M beyond the wall. We find xM = 1.46 in units of the velocity persistence length of the Brownian particle. This study was motivated by certain problems in the theory of diffusion-controlled reactions, and the results might be used to test approximate theories employed in that field.
Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic descr... more Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic description. We show how the correlations dominate the dynamics by juxtaposing the macroscopic dynamics of a cellular automaton model for the diffusion-controlled limit to the deterministic diffusion-reaction rate equation for the same reaction. A more detailed N-body master equation is then presented in which explicit diffusion-controlled limits are explained. 1 What Is Special About Diffusion-Limited Reactions? Common diffusion-reaction-rate equations are similar in structure and concept to the hydrodynamic equations for simple fluids and appear to be a simpler paradigm for general purposes. To the statistical physicist, however, systems with ongoing chemical reactions pose a more fundamental challenge than simple fluids in that two familiar properties of fluctuations cannot be taken for granted there: a) slow variation in comparison to the fast microscopic (i.e. molecular) dynamics due to ...
Otology & Neurotology, 2007
HNO-Informationen (Kongressabstracts), 2005
Patienten fanden sich für das Hauptzielkriterium "Hörgewinn an Tag 7" zwar numerische Vorteile fü... more Patienten fanden sich für das Hauptzielkriterium "Hörgewinn an Tag 7" zwar numerische Vorteile für die HES-Gruppen gegenüber Placebo, jedoch keine statistisch signifikante Überlegenheit. Auffällig waren aber Unterschiede in der langfristigen Hörerholung zwischen Patienten, die innerhalb von 48 h nach dem Hörsturz zur Behandlung kamen (4,7% ohne Verbesserung innerhalb von 90 Tagen) und jenen, die erst später behandelt wurden (21,5 % nach 90 Tagen ohne Besserung). Auch Patienten mit einem systolischen Blutdruck >140 mmHg hatten geringere Chancen einer Erholung. Für jene Patienten, die diesen Risikofaktor aufwiesen und sich später als 48 h nach Symptombeginn in die Behandlung begeben hatten, waren in der Placebogruppe nach einer Woche 46 % noch ohne Hörbesserung, während in der 4%-HES-Gruppe nur 13 % ohne Besserung blieben (p=0,025 für eine zumindest partielle Hörerholung unter HES am Tag 7). Die neuartige HES-Lösung erwies sich insgesamt als nebenwirkungsarm, insbesondere trat der substanztypische Pruritus nur temporär bei 4 von 157 mit HES 130/0.4 Behandelten auf.
We present an exact closed formulation of the reversible diffusion-limited coagulation-growth rea... more We present an exact closed formulation of the reversible diffusion-limited coagulation-growth reactions 2A ↔ A with irreversible input B → A in one spatial dimension. The treatment here accommodates spatial as well as temporal variations in the particle density with a complete account of microscopic fluctuations and correlations. Moreover, spatial and/or temporal variations in the transport and reaction coefficients can be included in the model. A general solution to the reversible process is presented, and we explore the phenomenon of wavefront propagation.
Otology & Neurotology, 2007
Obtain and analyze first data on hydroxyethyl starch (HES 130/0.4) as monotherapy in acute idiopa... more Obtain and analyze first data on hydroxyethyl starch (HES 130/0.4) as monotherapy in acute idiopathic sudden sensorineural hearing loss (ISSNHL). Randomized, double-blind, Phase-II, dose-finding study. Twenty-five ENT centers in Germany, the Czech Republic, Romania, and Austria. Two hundred and ten inpatients with first-time ISSNHL of at least 20 dB at two or more frequencies and 95 dB or less at all of the speech frequencies (0.5, 1.0, 2.0, 3.0, and 4.0 kHz) with respect to the other (normal) ear for up to 7 days (d). Infusion of 750 mL/d with 45 (Group H), 30 (Group M), or 15 g/d HES (Group L), or glucose 5% (Group G) acting as "placebo" control during 6 days. MAIN ENDPOINT: Gain in average auditory threshold (in dB) from baseline to Day 7. RESULTS (MEDIANS): Average hearing loss at baseline was 24 dB, and infusions started 2 days after ISSNHL onset. No relevant group difference was observed in hearing gain or adverse treatment events, including pruritus. Half of all pat...
Physical Review A, 1992
The one-dimensional single-species diffusion-limited-coagulation process with irreversible random... more The one-dimensional single-species diffusion-limited-coagulation process with irreversible random particle input (A&lrarr2;A+A reversibly and B-->A irreversibly), under the influence of external fluctuations in the system parameters, is formulated in terms of a closed and linear partial-differential equation. Our theoretical treatment includes both internal fluctuations and external noise simultaneously and without approximation, allowing investigation of the interplay of their effects on the
Journal of Physics a Mathematical General, Nov 1, 1993
Journal of Physics a Mathematical and General, Feb 21, 1994
ABSTRACT In a first-order wetting transition it is possible to overheat a microscopic layer from ... more ABSTRACT In a first-order wetting transition it is possible to overheat a microscopic layer from below to above the wetting temperature Tw, and to undercool a macroscopic layer from above to below Tw. In both cases the transition to stable equilibrium occurs by formation and growth of supercritical nuclei. The critical nuclei for overheating are droplets on the wall of the system and for undercooling they are dents in the macroscopic layer. A recent calculation of the critical droplet in a special dimension d0 is now supplemented by the calculation of the critical dent for dewetting. Although the analytic expressions for the profiles are closely related, the nuclei above Tw are finite whereas they are infinitely large below Tw. The latter is to be expected since the system is infinitesimally close to coexistence of wet and non-wet states at all temperatures T<Tw.
Journal of Statistical Physics, Aug 31, 1990
We solve exactly the one-dimensional diffusion-limited single-species coagulation process (A+A-* ... more We solve exactly the one-dimensional diffusion-limited single-species coagulation process (A+A-* A) with back reactions (A ~A+A) and/or a steady input of particles (B-* A). The exact solution yields not only the steady-state concentration of particles, but also the exact time-dependent concentration as well as the time-dependent probability distribution for the distance between neighboring particles, i.e., the interparticle distribution function (IPDF). The concentration for this diffusion-limited reaction process does not obey the classical "mean-field" rate equation. Rather, the kinetics is described by a finite set of ordinary differential equations only in particular cases, with no such description holding in general. The reaction kinetics is linked to the spatial distribution of particles as reflected in the IPDFs. The spatial distribution of particles is totally random, i.e., the maximum entropy distribution, only in the steady state of the strictly reversible process A + A ~ A, a true equilibrium state with detailed balance. Away from this equilibrium state the particles display a static or dynamic self-organization imposed by the nonequilibrium reactions. The strictly reversible process also exhibits a sharp transition in its relaxation dynamics when switching between equilibria of different values of the system parameters. When the system parameters are suddenly changed so that the new equilibrium concentration is greater than exactly twice the old equilibrium concentration, the exponential relaxation time depends on the initial concentration.
Lecture Notes in Physics, May 5, 2007
Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic descr... more Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic description. We show how the correlations dominate the dynamics by juxtaposing the macroscopic dynamics of a cellular automaton model for the diffusion-controlled limit to the deterministic diffusion-reaction rate equation for the same reaction. A more detailed N-body master equation is then presented in which explicit diffusion-controlled limits are explained.
Epl, Jul 24, 2007
ABSTRACT We consider the many-body initial-value problem for the reversible single-species diffus... more ABSTRACT We consider the many-body initial-value problem for the reversible single-species diffusion-controlled reaction X + X X. A mapping to a dual process is identified which reduces the N-body problem to the dynamics of interfaces, which for general initial conditions is reduced to simple quadratures. The diffusion-controlled limit and the continuous space limit are taken as leading orders in power series expansions. The spectrum of the reaction operator is given explicitly and its use for the calculation of corrections to the diffusion-controlled limit is explained. A closed form is given for the time- and space-dependent concentration ρ(R, t) in one dimension following an arbitrary initial state.
Physical Review Letters
We sutdy a stochastic interacting particle system which displays a nonequilibrium transition in i... more We sutdy a stochastic interacting particle system which displays a nonequilibrium transition in its relaxation dynamics in the infinite volume limit. The transition is destroyed by restriction to a finite volume, but its remnants remain until a crossover time Tc(L,ε), where L is the system size and ε is the control parameter measuring the distance from the bulk transition. We find that the crossover time Tc(L,ε) diverges where ε-->0 in a fixed volume. Thus this finite volume system displays arbitrarily long time scales near the transition.
Journal of Statistical Physics
We develop a concise method to compute the corrections to the master equation for chemically reac... more We develop a concise method to compute the corrections to the master equation for chemically reacting systems in particle number space that arise if the system is not a well-stirred tank reactor, but the transport occurs by diffusion. Starting from the master equation in theRN space of all reactant particle positions, we expand in inverse powers of the diffusion constant and eliminate all transport modes adiabatically. It is found that the overall effect of spatially nonuniform fluctuations cannot be treated as a mere renormalization of the reaction rate constants. From second order on there appear correction terms with a new structure that corresponds formally to additional virtual reaction paths. An intuitive interpretation along this line is impeded, however, by the formal occurrence of negative reaction rate constants in these terms, i.e., the reaction rate may depend on the concentrations of the final products of the virtual reaction rather than on the ingoing products. We also...