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Master Equation (master + equation)

Distribution by Scientific Domains
Physics and Astronomy54%
Polymers and Materials Science18%

Selected Abstracts

Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2005
João Pedro Hespanha
Abstract A stochastic model for chemical reactions is presented, which represents the population of various species involved in a chemical reaction as the continuous state of a polynomial stochastic hybrid system (pSHS). pSHSs correspond to stochastic hybrid systems with polynomial continuous vector fields, reset maps, and transition intensities. We show that for pSHSs, the dynamics of the statistical moments of its continuous states, evolves according to infinite-dimensional linear ordinary differential equations (ODEs), which can be approximated by finite-dimensional nonlinear ODEs with arbitrary precision. Based on this result, a procedure to build this types of approximation is provided. This procedure is used to construct approximate stochastic models for a variety of chemical reactions that have appeared in literature. These reactions include a simple bimolecular reaction, for which one can solve the Master equation; a decaying,dimerizing reaction set which exhibits two distinct time scales; a reaction for which the chemical rate equations have a continuum of equilibrium points; and the bistable Schögl reaction. The accuracy of the approximate models is investigated by comparing with Monte Carlo simulations or the solution to the Master equation, when available. Copyright © 2005 John Wiley & Sons, Ltd. [source]

On the consistent interactions in D = 11 among a graviton, a massless gravitino and a three-form

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5-7 2009
E.M. Cioroianu
Abstract The couplings that can be introduced between a massless Rarita-Schwinger field, a Pauli-Fierz field and an Abelian three-form gauge field in eleven spacetime dimensions are analyzed in the context of the deformation of the solution of the master equation. [source]

Reaction of H + ketene to formyl methyl and acetyl radicals and reverse dissociations

INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 1 2003
Jongwoo Lee
Thermochemical properties for reactants, intermediates, products, and transition states important in the ketene (CH2CO) + H reaction system and unimolecular reactions of the stabilized formyl methyl (C·H2CHO) and the acetyl radicals (CH3C·O) were analyzed with density functional and ab initio calculations. Enthalpies of formation (,Hf°298) were determined using isodesmic reaction analysis at the CBS-QCI/APNO and the CBSQ levels. Entropies (S°298) and heat capacities (Cp°(T)) were determined using geometric parameters and vibrational frequencies obtained at the HF/6-311G(d,p) level of theory. Internal rotor contributions were included in the S and Cp(T) values. A hydrogen atom can add to the CH2 -group of the ketene to form the acetyl radical, CH3C·O (Ea = 2.49 in CBS-QCI/APNO, units: kcal/mol). The acetyl radical can undergo ,-scission back to reactants, CH2CO + H (Ea = 45.97), isomerize via hydrogen shift (Ea = 46.35) to form the slight higher energy, formyl methyl radical, C·H2CHO, or decompose to CH3 + CO (Ea = 17.33). The hydrogen atom also can add to the carbonyl group to form C·H2CHO (Ea = 6.72). This formyl methyl radical can undergo , scission back to reactants, CH2CO + H (Ea = 43.85), or isomerize via hydrogen shift (Ea = 40.00) to form the acetyl radical isomer, CH3C·O, which can decompose to CH3 + CO. Rate constants are estimated as function of pressure and temperature, using quantum Rice,Ramsperger,Kassel analysis for k(E) and the master equation for falloff. Important reaction products are CH3 + CO via decomposition at both high and low temperatures. A transition state for direct abstraction of hydrogen atom on CH2CO by H to form, ketenyl radical plus H2 is identified with a barrier of 12.27, at the CBS-QCI/APNO level. ,Hf°298 values are estimated for the following compounds at the CBS-QCI/APNO level: CH3C·O (,3.27), C·H2CHO (3.08), CH2CO (,11.89), HC·CO (41.98) (kcal/mol). © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 35: 20,44, 2003 [source]

The reaction between ethyl and molecular oxygen II: Further analysis

INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 11 2001
James A. Miller
The present investigation is a rather substantial extension and elaboration of our previous work on the same reaction. In this article we accomplish four primary objectives: 1.We show quantitatively how sensitive the high-temperature rate coefficient k(T) is to E02, the threshold energy of the transition state for direct molecular elimination of HO2 from ethylperoxy radical (C2H5O2), thus deducing a value of E02=,3.0 kcal/mol (measured from reactants). 2.We derive the result that k0(T) , k,,(T) in the high-temperature regime, where k0(T) is the zero-pressure rate coefficient, and k,,(T) is the infinite-pressure rate coefficient for the bimolecular channel. 3.Most importantly, we discuss the three different regimes of the reaction (low-temperature, transition, and high-temperature) in terms of the eigenvectors and eigenvalues of G, the transition matrix of the master equation. The transition regime is shown to be a region of avoided crossing between the two chemically significant eigenvalue curves in which the thermal rate coefficient k (T ,p) jumps from one eigenvalue to the other. This jump is accompanied by a "mixing" of the corresponding eigenvectors, through which both eigenvectors deplete the reactant. The onset of the high-temperature regime is triggered by reaching the "stabilization limit" of the ethylperoxy adduct, a limit that is induced by a shift in equilibrium of the stabilization reaction. Our identification of the prompt and secondary HO2 formed by the reaction with these eigenvalue/eigenvector pairs leads to good agreement between theory and the experiments of Clifford et al. (J Phys Chem A 2000, 104, 11549,11560). 4.Lastly, we describe the master equation results in terms of a set of elementary reactions and phenomenological rate coefficients. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 732,740, 2001 [source]

On the polarization properties of the micromaser pumped by the atoms with degenerate levels

LASER PHYSICS LETTERS, Issue 3 2004
V. A. Reshetov
Abstract The polarization properties of the micromaser field pumped by the atoms with the resonant levels, which are degenerate in the projections of the total angular momentum on the quantization axis, are studied numerically. The standard micromaser operation, when the atoms enter the cavity excited to the upper resonant level, and the micromaser operation under the coherent pump, when the atoms enter the cavity in a superposition of resonant atomic levels, are considered. The treatment is based on the master equation for the density matrix of the micromaser field, which takes into account the degeneracy of atomic levels. (© 2004 by HMS Consultants. Inc. Published exclusively by WILEY-VCH Verlag GmbH & Co.KGaA) [source]

Thermodynamic Modeling of Polymer Solution Interface

MACROMOLECULAR THEORY AND SIMULATIONS, Issue 2 2009
Majid Ghiass
Abstract A new method is presented to characterize the interfacial concentration field and interfacial tension between equilibrium polymer solution phases, using readily accessible equilibrium concentration data. The new method is tested and validated using experimental data from different polystyrene solutions and it consists of i) calculation of a universal expression for the concentration gradient coefficient based on the Cahn-Hilliard model and the Wolf interfacial tension master equation, and ii) development of a highly accurate algebraic function (Kappa distribution) that, for a given equilibrium polymer concentration set, yields the essentially exact interfacial profile predicted by the classical gradient theory for polymer solutions. [source]

Dynamical model for coherent optical manipulation of a single spin state in a charged quantum dot

PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 2 2009
Gabriela Slavcheva
Abstract The optically-induced coherent spin dynamics of a single spin confined in a charged quantum dot (QD) is theoretically studied employing coupled vector Maxwell-pseudospin formalism. Generalized pseudospin master equation is derived for description of the time evolution of spin coherences and spin populations including spin population transfer and dissipation in the system through spin relaxation processes. The equation is solved in the time domain self-consistently with the vector Maxwell equations for the optical wave propagation coupled to it via macroscopic medium polarisation. Using the model the long-lived electron spin coherence left behind a single resonant ultrashort optical excitation of the electron-trion transition in a charged QD is simulated in the low- and high-intensity Rabi oscillations regime. Signatures of the polarised photoluminescence (PL), predicted by the model, such as the appearance of a second echo pulse after the excitation and characteristic PL trace shape, are discussed for realization of high-fidelity schemes for coherent readout of a single spin polarisation state. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A study of electromagnetic induced transparency in dispersive band gap materials

PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 8 2005
Mahi R. SinghArticle first published online: 4 MAY 200
Abstract We study the electromagnetically induced transparency in dispersive band gap materials when an ensemble of non-interacting four-level atoms is doped. The system is interacting with a pump field, a probe field and a reservoir. The method of master equation and Lap lace transform has been used in calculating the expression for the susceptibility. Numerical simulations are performed on the susceptibility in dispersive band gap material (i.e. SiC). The phenomenon of electromagnetically induced transparency has been predicted in SiC. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

No cross-interactions between the Weyl graviton and the massless Rarita-Schwinger field

ANNALEN DER PHYSIK, Issue 6 2006
C. Bizdadea
Abstract The proof of the fact that there are no nontrivial, consistent cross-couplings that can be added between the Weyl graviton and the massless Rarita-Schwinger field is accomplished by means of a cohomological approach, based on the deformation of the solution to the master equation from the antifield-Becchi-Rouet-Stora-Tyutin (BRST) formalism. The procedure developed here relies on the assumptions of locality, smoothness, (background) Lorentz invariance, Poincaré invariance, and preservation of the number of derivatives with respect to each field (the last hypothesis was made only in antighost number zero). [source]

Four-dimensional couplings among BF and matter theories from BRST cohomology

ANNALEN DER PHYSIK, Issue 9 2003
C. Bizdadea
Abstract The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a "free" model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques. [source]

A Hybrid Galerkin,Monte-Carlo Approach to Higher-Dimensional Population Balances in Polymerization Kinetics

MACROMOLECULAR REACTION ENGINEERING, Issue 9-10 2010
Christof Schütte
Abstract Population balance models describing not only the chain-length distribution of a polymer but also additional properties like branching or composition are still difficult to solve numerically. For simulation of such systems two essentially different approaches are discussed in the literature: deterministic solvers based on rate equations and stochastic Monte-Carlo (MC) strategies based on chemical master equations. The paper presents a novel hybrid approach to polymer reaction kinetics that combines the best of these two worlds. We discuss the theoretical conditions of the algorithm, describe its numerical realization, and show that, if applicable, it is more efficient than full-scale MC approaches and leads to more detailed information in additional property indices than deterministic solvers. [source]