From random walk to critical dynamics

2019 ◽  
pp. 421-450
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Brst Symmetry ◽  
Detailed Balance ◽  
Continuous Phase ◽  
Langevin Equations ◽  
Dynamic Scaling ◽  
Critical Dynamics ◽  
Dynamical Equations ◽  
Detailed Balance Condition ◽  
Wide Range ◽  
Dynamic Exponent

Chapter 22 studies stochastic dynamical equations, consistent with the detailed balance condition, which are generalized Langevin equations which describe a wide range of phenomena from Brownian motion to critical dynamics in continuous phase transitions. In the latter case, a dynamic action can be associated to the Langevin equation, which can be renormalized with the help of BRST symmetry. Dynamic renormalization group equations, describing critical dynamics, are then derived. Dynamic scaling follows, with a correlation time that exhibits critical slowing down governed by a dynamic exponent. In addition, Jarzinsky’s relation is derived in the case of a time–dependent driving force.

scholarly journals A NEW APPROACH TO DYNAMIC FINITE-SIZE SCALING

2003 ◽  
Vol 14 (07) ◽  
pp. 945-954 ◽  
Author(s):  
MEHMET DİLAVER ◽  
SEMRA GÜNDÜÇ ◽  
MERAL AYDIN ◽  
YİĞİT GÜNDÜÇ
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Taylor Series Expansion ◽  
Scaling Behavior ◽  
Dynamic Scaling ◽  
Finite Size Scaling ◽  
New Approach ◽  
Size Scaling ◽  
Dynamic Exponent ◽  
Good Agreement

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

Dynamic scaling for longitudinal critical dynamics of dilute Heisenberg and quantum XY chains

1986 ◽  
Vol 19 (10) ◽  
pp. 1927-1939 ◽  
Author(s):  
A C Maggs ◽  
L L Goncalves ◽  
R B Stinchcombe
Keyword(s):  
Dynamic Scaling ◽  
Critical Dynamics

Numerical Simulation of Droplet Generation in Series Co-Flow Capillaries

2009 ◽  
Author(s):  
Yanxi Song ◽  
Jinliang Xu
Keyword(s):  
Reynolds Number ◽  
Disperse Phase ◽  
Weber Number ◽  
Three Dimensional ◽  
Continuous Phase ◽  
Disperse Flow ◽  
Double Emulsions ◽  
Wide Range ◽  
In Series ◽  
Dispersed Phases

We study the production and motion of monodisperse double emulsions in microfluidics comprising series co-flow capillaries. Both two and three dimensional simulations are performed. Flow was determined by dimensionless parameters, i.e., Reynolds number and Weber number of continuous and dispersed phases. The co-flow generated droplets are sensitive to the Reynolds number and Weber number of the continuous phase, but insensitive to those of the disperse phase. Because the inner and outer drops are generate by separate co-flow processes, sizes of both inner and outer drops can be controlled by adjusting Re and We for the continuous phase. Meanwhile, the disperse phase has little effect on drop size, thus a desirable generation frequency of inner drop can be reached by merely adjusting flow rate of the inner fluid, leading to desirable number of inner drops encapsulated by the outer drop. Thus highly monodisperse double emulsions are obtained. It was found that only in dripping mode can droplet be of high mono-dispersity. Flow begins to transit from dripping regime to jetting regime when the Re number is decreased or Weber number is increased. To ensure that all the droplets are produced over a wide range of running parameters, tiny tapered tip outlet for the disperse flow should be applied. Smaller the tapered tip, wider range for Re and we can apply.

scholarly journals Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics

2021 ◽  
Vol 9 ◽  
Author(s):  
A. R. Ramos Ramos ◽  
O. Kühn
Keyword(s):  
Optimal Control ◽  
Gaussian Approximation ◽  
Gaussian Function ◽  
Dynamical Equations ◽  
Control Approach ◽  
Wide Range ◽  
Bistable Potential ◽  
Wavepacket Dynamics ◽  
Direct Optimal Control ◽  
Backward Propagation

Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets. Here, we propose direct optimal control as a robust and flexible alternative. It is based on a discretization of the dynamical equations resulting in a nonlinear optimization problem. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket is parameterized in terms of a single Gaussian function and field optimization is performed for a wide range of particle masses and lengths of the control interval. Using the optimized field in a full quantum propagation still yields reasonable control yields for most of the considered cases. Analysis of the deviations leads to conditions which have to be fulfilled to make the semiclassical single Gaussian approximation meaningful for field optimization.

scholarly journals Revisit on the thermodynamic stability of Hořava–Lifshitz black hole

2018 ◽  
Vol 27 (04) ◽  
pp. 1850048
Author(s):  
Xudong Meng ◽  
Ruihong Wang
Keyword(s):  
Black Hole ◽  
Thermodynamic Properties ◽  
Thermodynamic Stability ◽  
Detailed Balance ◽  
De Sitter ◽  
Thermodynamic Variable ◽  
Detailed Balance Condition ◽  
First Law Of Thermodynamics ◽  
Balance Condition ◽  
Lifshitz Black Hole

We study the thermodynamic properties of the black hole derived in Hořava–Lifshitz (HL) gravity without the detailed-balance condition. The parameter [Formula: see text] in the HL black hole plays the same role as that of the electric charge in the Reissner–Nordström-anti-de Sitter (RN-AdS) black hole. By analogy, we treat the parameter [Formula: see text] as the thermodynamic variable and obtain the first law of thermodynamics for the HL black hole. Although the HL black hole and the RN-AdS black hole have the similar mass and temperature, due to their very different entropy, the two black holes have very different thermodynamic properties. By calculating the heat capacity and the free energy, we analyze the thermodynamic stability of the HL black hole.

scholarly journals Measuring reaction rates at equilibrium with the isotope doping method

2019 ◽  
Vol 98 ◽  
pp. 13003
Author(s):  
Chen Zhu ◽  
Yilun Zhang ◽  
J Donald Rimstidt ◽  
Honglin Yuan
Keyword(s):  
Chemical Engineering ◽  
Experimental Testing ◽  
Detailed Balance ◽  
Reaction Rates ◽  
Irreversible Thermodynamics ◽  
Experimental Conditions ◽  
Special Cases ◽  
Wide Range ◽  
Long Time ◽  
Dissolution And Precipitation

Since the time of J. H. van’t Hoff [1], it has been known that chemical equilibrium is dynamic, meaning that at equilibrium, chemical reactions do not cease, but instead the forward and backward reaction rates are equal. The constant concentrations at equilibrium preclude the use of concentrations to measure reaction rates at equilibrium. Therefore, with the exception of a few special cases, no reaction rates at equilibrium have been published in the literature of chemistry, physics, or chemical engineering. Here we report dissolution and precipitation rates at equilibrium for quartz and barite with the isotope-doping method. Experimental data show that dissolution and precipitation rates are equal at equilibrium, indicating the principle of detailed balance (PDB) appear to be applicable at these experimental conditions. The PDB has been a cornerstone for irreversible thermodynamics and chemical kinetics for a long time, and its wide application in geochemistry has mostly been implicit and without experimental testing of its applicability. Nevertheless, many extrapolations based on PDB without experimental validation have far reaching impacts on society’s mega environmental enterprises. The isotope doping method appears to able to test its applicability for a variety of minerals at a wide range of conditions.

TWO-PHOTON ABSORPTION AND EMISSION PROCESS

2005 ◽  
Vol 08 (04) ◽  
pp. 573-591 ◽  
Author(s):  
FRANCO FAGNOLA ◽  
ROBERTO QUEZADA
Keyword(s):  
Detailed Balance ◽  
Photon Absorption ◽  
Positive Temperature ◽  
Stationary States ◽  
Emission Process ◽  
Absorption And Emission ◽  
Detailed Balance Condition ◽  
Two Photon Absorption ◽  
Two Photon ◽  
Invariant States

We analyze the two-photon absorption and emission process and characterize the stationary states at zero and positive temperature. We show that entangled stationary states exist only at zero temperature and, at positive temperature, there exists infinitely many commuting invariant states satisfying the detailed balance condition.

scholarly journals Statistical and probabilistic modeling of a cloud of particles coupled with a turbulent fluid

2019 ◽  
Vol 65 ◽  
pp. 401-424
Author(s):  
Ludovic Goudenège ◽  
Adam Larat ◽  
Julie Llobell ◽  
Marc Massot ◽  
David Mercier ◽  
...  
Keyword(s):  
Disperse Phase ◽  
Continuous Phase ◽  
Complex Situation ◽  
Gas Field ◽  
Strongly Coupled ◽  
Turbulent Fluid ◽  
Wide Range ◽  
Large Panel ◽  
Common Framework ◽  
Set Up

This paper exposes a novel exploratory formalism, the end goal of which is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Given the large panel of expertise of the list of authors, the content of this paper scans a wide range of connex notions, from the physics of turbulence to the rigorous definition of stochastic processes. Our approach is to develop reduced-order models for the dynamics of both carrying and carried phases which remain consistant within this formalism, and to set up a numerical process to validate these models. The novelties of this paper lie in the gathering of a large panel of mathematical and physical definitions and results within a common framework and an agreed vocabulary (sections 1 and 2), and in some preliminary results and achievements within this context, section 3. While the first three sections have been simplified to the context of a gas field providing that the disperse phase only retrieves energy through drag, the fourth section opens this study to the more complex situation when the disperse phase interacts with the continuous phase as well, in an energy conservative manner. This will allow us to expose the perspectives of the project and to conclude.

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