Perturbative Treatment for Stationary State of Local Master Equation

AbstractMethyl-Crotonate (MC, (E)-methylbut-2-enoate, CH3CHCHC(O)OCH3) is a potential component of surrogate fuels that aim to emulate the combustion of fatty acid methyl ester (FAME) biodiesels with significant unsaturated FAME content. MC has three allylic hydrogens that can be readily abstracted under autoignition and combustion conditions to form a resonantly-stabilized CH2CHCHC(O)OCH3 radical. In this study we have utilized photoionization mass spectrometry to investigate the O2 addition kinetics and thermal unimolecular decomposition of CH2CHCHC(O)OCH3 radical. First we determined an upper limit for the bimolecular rate coefficient of CH2CHCHC(O)OCH3 + O2 reaction at 600 K (k ≤ 7.5 × 10−17 cm3 molecule−1 s−1). Such a small rate coefficient suggest this reaction is unlikely to be important under combustion conditions and subsequent efforts were directed towards measuring thermal unimolecular decomposition kinetics of CH2CHCHC(O)OCH3 radical. These measurements were performed between 750 and 869 K temperatures at low pressures (<9 Torr) using both helium and nitrogen bath gases. The potential energy surface of the unimolecular decomposition reaction was probed at density functional (MN15/cc-pVTZ) level of theory and the electronic energies of the stationary points obtained were then refined using the DLPNO-CCSD(T) method with the cc-pVTZ and cc-pVQZ basis sets. Master equation simulations were subsequently carried out using MESMER code along the kinetically important reaction pathway. The master equation model was first optimized by fitting the zero-point energy corrected reaction barriers and the collisional energy transfer parameters $\Delta{E_{{\text{down}},\;{\text{ref}}}}$ and n to the measured rate coefficients data and then utilize the constrained model to extrapolate the decomposition kinetics to higher pressures and temperatures. Both the experimental results and the MESMER simulations show that the current experiments for the thermal unimolecular decomposition of CH2CHCHC(O)OCH3 radical are in the fall-off region. The experiments did not provide definite evidence about the primary decomposition products.

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Master equation lumping for multi-well potential energy surfaces: a bridge between ab initio based rate constant calculations and large kinetic mechanisms

Chemical Engineering Journal ◽

10.1016/j.cej.2021.129954 ◽

2021 ◽

pp. 129954

Author(s):

Luna Pratali Maffei ◽

Matteo Pelucchi ◽

Carlo Cavallotti ◽

Andrea Bertolino ◽

Tiziano Faravelli

Keyword(s):

Potential Energy ◽

Ab Initio ◽

Master Equation ◽

Rate Constant ◽

Potential Energy Surfaces ◽

Kinetic Mechanisms ◽

Energy Surfaces

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Master Equation for the Finite State Space Planning Problem

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-021-01687-8 ◽

2021 ◽

Author(s):

Charles Bertucci ◽

Jean-Michel Lasry ◽

Pierre-Louis Lions

Keyword(s):

Master Equation ◽

State Space ◽

Planning Problem ◽

Space Planning ◽

Finite State ◽

Finite State Space ◽

State Space Planning

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A Discontinuity of the Energy of Quantum Walk in Impurities

Symmetry ◽

10.3390/sym13071134 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1134

Author(s):

Kenta Higuchi ◽

Takashi Komatsu ◽

Norio Konno ◽

Hisashi Morioka ◽

Etsuo Segawa

Keyword(s):

Unit Circle ◽

Stationary State ◽

Discrete Time ◽

Quantum Walk ◽

Time Limit ◽

The Other ◽

Unitary Matrix ◽

Initial State ◽

Time Quantum ◽

Long Time

We consider the discrete-time quantum walk whose local dynamics is denoted by a common unitary matrix C at the perturbed region {0,1,⋯,M−1} and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow ωn at time n(|ω|=1). From this expression, we compute the scattering on the surface of −1 and M and also compute the quantity how quantum walker accumulates in the perturbed region; namely, the energy of the quantum walk, in the long time limit. The frequency of the initial state of the influence to the energy is symmetric on the unit circle in the complex plain. We find a discontinuity of the energy with respect to the frequency of the inflow.

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Integrodifference master equation describing actively growing blood vessels in angiogenesis

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0094 ◽

2020 ◽

Vol 21 (7-8) ◽

pp. 705-713 ◽

Cited By ~ 1

Author(s):

Luis L. Bonilla ◽

Manuel Carretero ◽

Filippo Terragni

Keyword(s):

Master Equation ◽

Blood Vessels ◽

Transition Probabilities ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Birth Process ◽

Sink Term ◽

System Of Particles ◽

Vessel Network ◽

Tip Cells

AbstractWe study a system of particles in a two-dimensional geometry that move according to a reinforced random walk with transition probabilities dependent on the solutions of reaction-diffusion equations (RDEs) for the underlying fields. A birth process and a history-dependent killing process are also considered. This system models tumor-induced angiogenesis, the process of formation of blood vessels induced by a growth factor (GF) released by a tumor. Particles represent vessel tip cells, whose trajectories constitute the growing vessel network. New vessels appear and may fuse with existing ones during their evolution. Thus, the system is described by tracking the density of active tips, calculated as an ensemble average over many realizations of the stochastic process. Such density satisfies a novel discrete master equation with source and sink terms. The sink term is proportional to a space-dependent and suitably fitted killing coefficient. Results are illustrated studying two influential angiogenesis models.

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