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At least 73 records · Page 4Linked to original sources
PubMed2005

Master equation simulations of bistable and excitable dynamics in a model of a thermochemical system.

The effect of fluctuations on the dynamics of a model of a bistable thermochemical system is studied by means of the master equation. The system has three stationary states and exhibits two types of bistability: the coexistence of two stable focuses and the coexistence of a stable focus with a stable limit cycle separated by a saddle point. Stochastic effects are important when the system is close to the bifurcation, in which the stable limit cycle disappears through a homoclinic orbit. In this case the distribution of the first passage time from the stable limit cycle to the stable focus has a multipeak form. The dependence of this distribution on the number of particles is presented. Near the homoclinic orbit bifurcation, the system also exhibits excitability due to a particular shape of the basin of attraction of the stable focus.

Journal Article↗
PubMed2001

Unconditional pointer states from conditional master equations.

When part of the environment responsible for decoherence is used to extract information about the decohering system, the preferred pointer states remain unchanged. This conclusion--reached for a specific class of models--is investigated in a general setting of conditional master equations using suitable generalizations of predictability sieve. We also find indications that the einselected states are easiest to infer from the measurements carried out on the environment.

Journal Article↗
PubMed2004

Exciton migration dynamics in a dendritic molecule: quantum master equation approach using ab initio molecular orbital configuration interaction method.

We investigate the exciton migration dynamics in a dendritic molecular model composed of pi-conjugation linear-leg units (acetylenes and diacetylene) and a benzene ring (branching point) using the quantum master equation approach with the ab initio molecular orbital (MO) configuration interaction (CI) method. The efficient migration of exciton from short-length linear legs (acetylenes) to long-length linear leg (diacetylene) via a benzene ring is observed. As predicted in previous studies, the exciton (electron and hole) distributions are relatively well localized in each generation segmented by the meta-branching point (meta-substituted benzene ring) though the electron and hole distributions are delocalized and are somewhat spatially different from each other within each generation. It is found that the excitons localized in the generation composed of short linear legs occupy in higher-lying exciton states, while those in the generation composed of long linear legs do in lower-lying ones. These features suggest the decoupling of pi-conjugation at the meta-branching point. On the other hand, the relaxation effect between exciton states is found to be caused by the exciton-phonon coupling, in which the existence of common configurations (electron-hole pairs) in CI wave functions between adjacent exciton states (having primary distributions on short and long linear-leg regions, respectively) is important for the relaxation between their exciton states. This feature indicates the importance of partial penetration of pi-conjugation through the meta-substituted benzene ring in excited states for such exciton migration.

Journal Article↗
PubMed2006

Reduction and solution of the chemical master equation using time scale separation and finite state projection.

The dynamics of chemical reaction networks often takes place on widely differing time scales--from the order of nanoseconds to the order of several days. This is particularly true for gene regulatory networks, which are modeled by chemical kinetics. Multiple time scales in mathematical models often lead to serious computational difficulties, such as numerical stiffness in the case of differential equations or excessively redundant Monte Carlo simulations in the case of stochastic processes. We present a model reduction method for study of stochastic chemical kinetic systems that takes advantage of multiple time scales. The method applies to finite projections of the chemical master equation and allows for effective time scale separation of the system dynamics. We implement this method in a novel numerical algorithm that exploits the time scale separation to achieve model order reductions while enabling error checking and control. We illustrate the efficiency of our method in several examples motivated by recent developments in gene regulatory networks.

Biopolymers↗
PubMed2005

Master equation for a kinetic model of a trading market and its analytic solution.

We analyze an ideal-gas-like model of a trading market with quenched random saving factors for its agents and show that the steady state income (m) distribution P(m) in the model has a power law tail with Pareto index nu exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of P(m) . Precise solutions are then obtained in some special cases.

Journal Article↗
PubMed2006

Constraining the mechanism and kinetics of OH + NO2 and HO2 + NO using the multiple-well master equation.

Several recent experimental studies have provided substantial new constraints for the mechanisms on the HNO3 potential energy surface. These include observations of biexponential OH decay over short time scales from OH + NO2, which constrain key properties of the short-lived HOONO intermediate, observations of both conformers of the HOONO intermediate itself, isotopic scrambling data for 18OH + NO2, and observations of HONO2 production from the HO2 + NO reaction. We combine all of these recent data in a master-equation simulation of the system. This simulation is initialized with computational values for both stable species (wells) and transition states, but parameters are then adjusted to fit the observations. All parameters are kept within limits defined by experimental and theoretical uncertainty, and all converge away from their bounds. The primary fitting is carried out on the OH kinetic data-we first fit the biexponential kinetics, then address the isotopic scrambling. Isotopic scrambling is shown to be rapid but not complete at low pressure, while at least two parameter sets are shown to be consistent with the biexponential data. Of these two parameter sets, one is far more consistent with recent observations of trans-HOONO decay, isotopic scrambling, and HONO2 production from HO2 + NO. This we regard as the most probable potential energy surface for the reaction. On this PES, cis-trans isomerization for HOONO is slow but isomerization of trans-HOONO to HONO2 is rapid. This has significant implications for observed HOONO behavior and also HONO2 formation in the atmosphere from both HO2 + NO and OH + NO2.

Journal Article↗
PubMed2005

Calculation of photon-count number distributions via master equations.

Fitting of photon-count number histograms is a way of analysis of fluorescence intensity fluctuations, a successor to fluorescence correlation spectroscopy. First versions of the theory for calculating photon-count number distributions have assumed constant emission intensity by a molecule during a counting time interval. For a long time a question has remained unanswered: to what extent is this assumption violated in experiments? Here we present a theory of photon-count number distributions that takes account of intensity fluctuations during a counting time interval. Theoretical count-number distributions are calculated via a numerical solution of Master equations (ME), which is a set of differential equations describing diffusion, singlet-triplet transitions, and photon emission. Detector afterpulsing and dead-time corrections are also included. The ME-theory is tested by fitting a series of photon-count number histograms corresponding to different lengths of the counting time interval. Compared to the first version of fluorescence intensity multiple distribution analysis theory introduced in 2000, the fit quality is significantly improved. It is discussed how a theory of photon-count number distributions, which assumes constant emission intensity during a counting time interval, may also yield a good fit quality. We argue that the spatial brightness distribution used in calculations of the fit curve is not the true spatial brightness distribution. Instead, a number of dynamic processes, which cause fluorescence intensity fluctuations, are indirectly taken into account via the profile adjustment parameters.

Algorithms↗
PubMed2004

The dynamics of conformational isomerization in flexible biomolecules. II. Simulating isomerizations in a supersonic free jet with master equation dynamics.

Infrared-induced conformational isomerization of N-acetyl-tryptophan methyl amide is studied theoretically using a microcanonical Rice-Ramsperger-Kassel-Marcus description of the rates on potential energy surfaces calculated using the AMBER and OPLS-AA force fields. The results are compared with the experimental data from Dian et al. in the preceding paper [J. Chem. Phys. 120, 133 (2004)]. An exhaustive search of the potential energy surfaces locates all minima and transition states on these surfaces. A simple model is proposed for the vibrational cooling, and an appropriate cooling rate is chosen as the standard conditions for the master equation simulations by comparison with experiment. The two potential energy surfaces differ in the relative energies of minima and the heights of key transition states, leading to differences in the dominant pathways and rates of conformational isomerization. The predicted quantum yields depend sensitively on the cooling rate, varying from the slow cooling limit in which equilibrium populations are achieved to the fast quenching limit in which conformational isomerization is shut off. The excitation energy is varied from 5 to 20 kcal mol(-1). At the lowest energies, isomerization is completely quenched, while at the highest energies, equilibrium conditions are achieved. In between these extremes, the quantum yields are sensitive to the excitation energy, and can be used to locate the rate-limiting barriers to isomerization.

Computer Simulation↗
PubMed2005

Global and local relaxation of a spin chain under exact Schrödinger and master-equation dynamics.

We solve the Schrödinger equation for an interacting spin chain locally coupled to a quantum environment with a specific degeneracy structure. The reduced dynamics of the whole spin chain as well as of single spins is analyzed. We show that the total spin chain relaxes to a thermal equilibrium state independently of the internal interaction strength. In contrast, the asymptotic states of each individual spin are thermal for weak but nonthermal for stronger spin-spin coupling. The transition between both scenarios is found for couplings of the order of 0.1 x deltaE , with deltaE denoting the Zeeman splitting. We compare these results with a master-equation treatment; when time averaged, both approaches lead to the same asymptotic state and finally with analytical results.

Journal Article↗
PubMed2005

Correlation function and generalized master equation of arbitrary age.

We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation. These three methods yield exact expressions, thus coinciding with the recent result by Godrèche and Luck [J. Stat. Phys. 104, 489 (2001)]. Actually, non-Poisson statistics yields infinite memory at the probability level, thereby breaking any form of Markovian approximation, including the one adopted herein, to find an approximated analytical formula. For this reason, we check the accuracy of this approximated formula by comparing it with the numerical treatment of the second of the three exact expressions. We find that, although not exact, a simple analytical expression for the correlation function of arbitrary age is very accurate. We establish a connection between the correlation function and a generalized master equation of the same age. Thus this formalism, related to models used in glassy materials, allows us to illustrate an approach to the statistical treatment of blinking quantum dots, bypassing the limitations of the conventional Liouville treatment.

Journal Article↗
PubMed2001

Time-dependent master equation simulation of complex elementary reactions in combustion: application to the reaction of 1CH2 with C2H2 from 300-2000 K.

Computational simulations of the title reaction are presented, covering a temperature range from 300 to 2000 K. At lower temperatures we find that initial formation of the cyclopropene complex by addition of methylene to acetylene is irreversible, as is the stabilisation process via collisional energy transfer. Product branching between propargyl and the stable isomers is predicted at 300 K as a function of pressure for the first time. At intermediate temperatures (1200 K), complex temporal evolution involving multiple steady states begins to emerge. At high temperatures (2000 K) the timescale for subsequent unimolecular decay of thermalized intermediates begins to impinge on the timescale for reaction of methylene, such that the rate of formation of propargyl product does not admit a simple analysis in terms of a single time-independent rate constant until the methylene supply becomes depleted. Likewise, at the elevated temperatures the thermalized intermediates cannot be regarded as irreversible product channels. Our solution algorithm involves spectral propagation of a symmetrized version of the discretized master equation matrix, and is implemented in a high precision environment which makes hitherto unachievable low-temperature modelling a reality.

Journal Article↗
PubMed2003

Reaction of phenyl radicals with acetylene: quantum chemical investigation of the mechanism and master equation analysis of the kinetics.

The mechanism of the C(6)H(5) + C(2)H(2) reaction has been investigated by various quantum chemical methods. Electrophilic addition to the CC triple bond is found to be the only important mode of phenyl radical attack on acetylene. The initially formed chemically activated C(6)H(5)C(2)H(2) adducts may follow several isomerization pathways in competition with collisional stabilization and H-elimination. Thermochemistry of various decomposition and isomerization channels is evaluated by the G2M method. For key intermediates, the following standard enthalpies of formation have been deduced from isodesmic reactions: 94.2 +/- 2.0 kcal/mol (C(6)H(5)CHCH), 86.4 +/- 2.0 kcal/mol (C(6)H(5)CCH(2)), and 95.5 +/- 1.8 kcal/ mol (o-C(6)H(4)C(2)H(3)). The accuracy of theoretical predictions was examined through extensive comparisons with available experimental and theoretical data. The kinetics and product branching of the C(6)H(5) + C(2)H(2) reaction have been evaluated by weak collision master equation/Rice-Ramsperger-Kassel-Marcus (RRKM) analysis of the truncated kinetic model including only kinetically important transformations of the isomeric C(8)H(7) radicals. Available experimental kinetic data can be quantitatively reproduced by calculation with a minor adjustment of the C(6)H(5) addition barrier from 3.7 to 4.1 kcal/mol. Our predicted total rate constant, k(R1) = (1.29 x 10(10))T(0.834) exp(-2320/T) cm(3) mol(-)(1) s(-)(1), is weakly dependent on P and corresponds to the phenylation process under combustion conditions (T > 1000 K).

Journal Article↗
PubMed2005

Quantum chemical and master equation simulations of the oxidation and isomerization of vinoxy radicals.

The vinoxy radical, a common intermediate in gas-phase alkene ozonolysis, reacts with O2 to form a chemically activated alpha-oxoperoxy species. We report CBS-QB3 energetics for O2 addition to the parent (*CH2CHO, 1a), 1-methylvinoxy (*CH2COCH3, 1b), and 2-methylvinoxy (CH3*CHCHO, 1c) radicals. CBS-QB3 predictions for peroxy radical formation agree with experimental data, while the G2 method systematically overestimates peroxy radical stability. RRKM/master equation simulations based on CBS-QB3 data are used to estimate the competition between prompt isomerization and thermalization for the peroxy radicals derived from 1a, 1b, and 1c. The lowest energy isomerization pathway for radicals 4a and 4c (derived from 1a and 1c, respectively) is a 1,4-shift of the acyl hydrogen requiring 19-20 kcal/mol. The resulting hydroperoxyacyl radical decomposes quantitatively to form *OH. The lowest energy isomerization pathway for radical 4b (derived from 1b) is a 1,5-shift of a methyl hydrogen requiring 26 kcal/mol. About 25% of 4a, but only approximately 5% of 4c, isomerizes promptly at 1 atm pressure. Isomerization of 4b is negligible at all pressures studied.

Journal Article↗
PubMed2005

Thermal decomposition of ethylene oxide: potential energy surface, master equation analysis, and detailed kinetic modeling.

The unimolecular decomposition of ethylene oxide (oxirane) and the oxiranyl radial is examined by molecular orbital calculations, Rice-Ramsperger-Kassel-Marcus (RRKM)/Master Equation analysis, and detailed kinetic modeling of ethylene oxide pyrolysis in a single-pulse shock tube. It was found that the largest energy barrier to the decomposition of ethylene oxide lies in its initial isomerization to form acetaldehyde, and in agreement with previous studies, the isomerization was found to proceed through the *CH2CH2O* biradical. Because of the biradical nature of the transition states and intermediate, the energy barriers for the initial C-O rupture in ethylene oxide and the subsequent 1,2-H shift remain highly uncertain. An overall isomerization energy barrier of 59 +/- 2 kcal/mol was found to satisfactorily explain the available single pulse shock tube data. This barrier height is in line with the estimates made from an approximate spin-corrected procedure at the MP4/6-31+G(d) and QCISD(T)/6-31G(d) levels of theory. The dominant channel for the unimolecular decomposition of ethylene oxide was found to form CH3 + HCO at around the ambient pressure. It accounts for >90% of the total rate constant for T > 800 K. The high-pressure limit rate constant for the unimolecular decomposition of ethylene oxide was calculated as k(1,infinity)(s(-1)) = (3.74 x 10(10))T(1.298)e(-29990/T) for 600 < T < 2000 K.

Journal Article↗
PubMed2005

Quantum chemical and master equation studies of the methyl vinyl carbonyl oxides formed in isoprene ozonolysis.

Methyl vinyl carbonyl oxide is an important intermediate in the reaction of isoprene and ozone and may be responsible for most of the (*)OH formed in isoprene ozonolysis. We use CBS-QB3 calculations and RRKM/master equation simulations to characterize all the pathways leading to the formation of this species, all the interconversions among its four possible conformers, and all of its irreversible isomerizations. Our calculations, like previous studies, predict (*)OH yields consistent with experiment if thermalized syn-methyl carbonyl oxides form (*)OH quantitatively. Natural bond order analysis reveals that the vinyl group weakens the C=O bond of the carbonyl oxide, making rotation about this bond accessible to this chemically activated intermediate. The vinyl group also allows one conformer of the carbonyl oxide to undergo electrocyclization to form a dioxole, a species not previously considered in the literature. Dioxole formation, which has a CBS-QB3 reaction barrier of 13.9 kcal/mol, is predicted to be favored over vinyl hydroperoxide formation, dioxirane formation, and collisional stabilization. Our calculations also predict that two dioxole derivatives, 1,2-epoxy-3-butanone and 3-oxobutanal, should be major products of isoprene ozonolysis.

Journal Article↗
PubMed2006

Combined experimental and master equation investigation of the multiwell reaction H + SO2.

The temperature and pressure dependence of the rate coefficient for the reaction H + SO2 has been measured using a laser flash photolysis/laser-induced fluorescence technique, for 295 10(3) atm, the latter proceeds directly from H + SO2, via the energized states of HOSO. The derived rate coefficients rely heavily on measurements of the reverse reaction, OH + SO, which has only been determined at temperatures up to 700 K.

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