Markovian master equation for a classical particle coupled with arbitrary strength to a harmonic bath

2014 ◽  
Vol 141 (21) ◽  
pp. 214109 ◽  
Author(s):  
Maxim F. Gelin
Keyword(s):  
Master Equation ◽  
Classical Particle ◽  
Arbitrary Strength ◽  
Harmonic Bath

A Primary Study on Classical Particle Modeling of Electron-Wave Interference Systems

2014 ◽  
Vol 1 ◽  
pp. 324-327 ◽  
Author(s):  
Keisuke Nagata ◽  
Wataru Nakashima ◽  
Hisato Fujisaka ◽  
Takeshi Kamio ◽  
Kazuhisa Haeiwa
Keyword(s):  
Classical Particle ◽  
Primary Study ◽  
Electron Wave ◽  
Wave Interference ◽  
Particle Modeling

scholarly journals Dynamic Indoor Localization Using Maximum Likelihood Particle Filtering

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1090
Author(s):  
Wenxu Wang ◽  
Damián Marelli ◽  
Minyue Fu
Keyword(s):  
Maximum Likelihood ◽  
Particle Filtering ◽  
Indoor Localization ◽  
Real Data ◽  
High Accuracy ◽  
Classical Particle ◽  
Popular Approach ◽  
Filtering Method ◽  
Essential Idea ◽  
Number Of Particles

A popular approach for solving the indoor dynamic localization problem based on WiFi measurements consists of using particle filtering. However, a drawback of this approach is that a very large number of particles are needed to achieve accurate results in real environments. The reason for this drawback is that, in this particular application, classical particle filtering wastes many unnecessary particles. To remedy this, we propose a novel particle filtering method which we call maximum likelihood particle filter (MLPF). The essential idea consists of combining the particle prediction and update steps into a single one in which all particles are efficiently used. This drastically reduces the number of particles, leading to numerically feasible algorithms with high accuracy. We provide experimental results, using real data, confirming our claim.

scholarly journals Direct Kinetic Measurements and Master Equation Modelling of the Unimolecular Decomposition of Resonantly-Stabilized CH2CHCHC(O)OCH3 Radical and an Upper Limit Determination for CH2CHCHC(O)OCH3 + O2 Reaction

2020 ◽  
Vol 234 (7-9) ◽  
pp. 1251-1268 ◽  
Author(s):  
Satya Prakash Joshi ◽  
Prasenjit Seal ◽  
Timo Theodor Pekkanen ◽  
Raimo Sakari Timonen ◽  
Arrke J. Eskola
Keyword(s):  
Master Equation ◽  
Density Functional ◽  
Rate Coefficient ◽  
Decomposition Kinetics ◽  
Basis Sets ◽  
Stationary Points ◽  
Unimolecular Decomposition ◽  
Kinetic Measurements ◽  
Point Energy ◽  
Upper Limit

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.

Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

2021 ◽  
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Density Matrix ◽  
Time Evolution ◽  
Reduced Density Matrix ◽  
Level System ◽  
Two Level Systems ◽  
Reduced Density ◽  
Harmonic Bath

We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates.

scholarly journals Integrodifference master equation describing actively growing blood vessels in angiogenesis

2020 ◽  
Vol 21 (7-8) ◽  
pp. 705-713 ◽  
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.

scholarly journals Unsteady dynamics of a classical particle-wave entity

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Rahil N. Valani ◽  
Anja C. Slim ◽  
David M. Paganin ◽  
Tapio P. Simula ◽  
Theodore Vo
Keyword(s):  
Classical Particle
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