Pushing the Limit of Boltzmann Distribution in Cr3+-Doped CaHfO3 for Cryogenic Thermometry

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

Boltzmann Distributed Replicator Dynamics: Population Games in a Microgrid Context

Games ◽

10.3390/g12010008 ◽

2021 ◽

Vol 12 (1) ◽

pp. 8

Author(s):

Gustavo Chica-Pedraza ◽

Eduardo Mojica-Nava ◽

Ernesto Cadena-Muñoz

Keyword(s):

Control Method ◽

Optimization Problems ◽

Replicator Dynamics ◽

Boltzmann Distribution ◽

Full Information ◽

Multi Agent Systems ◽

Q Learning ◽

Population Games ◽

Distributed Approach ◽

Multi Agent

Multi-Agent Systems (MAS) have been used to solve several optimization problems in control systems. MAS allow understanding the interactions between agents and the complexity of the system, thus generating functional models that are closer to reality. However, these approaches assume that information between agents is always available, which means the employment of a full-information model. Some tendencies have been growing in importance to tackle scenarios where information constraints are relevant issues. In this sense, game theory approaches appear as a useful technique that use a strategy concept to analyze the interactions of the agents and achieve the maximization of agent outcomes. In this paper, we propose a distributed control method of learning that allows analyzing the effect of the exploration concept in MAS. The dynamics obtained use Q-learning from reinforcement learning as a way to include the concept of exploration into the classic exploration-less Replicator Dynamics equation. Then, the Boltzmann distribution is used to introduce the Boltzmann-Based Distributed Replicator Dynamics as a tool for controlling agents behaviors. This distributed approach can be used in several engineering applications, where communications constraints between agents are considered. The behavior of the proposed method is analyzed using a smart grid application for validation purposes. Results show that despite the lack of full information of the system, by controlling some parameters of the method, it has similar behavior to the traditional centralized approaches.

Energetics of mesoscale cell turbulence in two-dimensional monolayers

Communications Physics ◽

10.1038/s42005-021-00530-6 ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Shao-Zhen Lin ◽

Wu-Yang Zhang ◽

Dapeng Bi ◽

Bo Li ◽

Xi-Qiao Feng

Keyword(s):

Kinetic Energy ◽

Tumor Metastasis ◽

Cell Types ◽

Boltzmann Distribution ◽

Scaling Exponent ◽

Biological Processes ◽

Two Dimensional ◽

Cell Monolayers ◽

Wide Range ◽

Epithelial Cell Monolayers

AbstractInvestigation of energy mechanisms at the collective cell scale is a challenge for understanding various biological processes, such as embryonic development and tumor metastasis. Here we investigate the energetics of self-sustained mesoscale turbulence in confluent two-dimensional (2D) cell monolayers. We find that the kinetic energy and enstrophy of collective cell flows in both epithelial and non-epithelial cell monolayers collapse to a family of probability density functions, which follow the q-Gaussian distribution rather than the Maxwell–Boltzmann distribution. The enstrophy scales linearly with the kinetic energy as the monolayer matures. The energy spectra exhibit a power-decaying law at large wavenumbers, with a scaling exponent markedly different from that in the classical 2D Kolmogorov–Kraichnan turbulence. These energetic features are demonstrated to be common for all cell types on various substrates with a wide range of stiffness. This study provides unique clues to understand active natures of cell population and tissues.

EXPERIMENTAL INVESTIGATION OF LANGMUIR PROBES

Canadian Journal of Physics ◽

10.1139/p67-266 ◽

1967 ◽

Vol 45 (10) ◽

pp. 3199-3209 ◽

Cited By ~ 3

Author(s):

R. M. Clements ◽

H. M. Skarsgard

Keyword(s):

Magnetic Field ◽

Microwave Radiometer ◽

Resonant Cavity ◽

Boltzmann Distribution ◽

Probable Error ◽

Langmuir Probes ◽

Noticeable Effect ◽

Probe Field ◽

Probe Radius ◽

Weakly Ionized

Electron temperatures and densities measured in a weakly ionized helium afterglow with cylindrical double probes are compared with measurements obtained using a gated microwave radiometer and a microwave resonant cavity. The pressure was varied from 0.1 to 8.5 Torr. At low pressure, magnetic fields up to 0.11 T were applied. Independent of the values of the electron Larmor radii or particle mean free paths relative to the probe radius, the probes correctly measured the electron temperatures within an estimated random probable error of ±4% and a systematic error not exceeding ±4%. This demonstrates the validity, for the range of conditions studied, of a fundamental assumption of probe theory—that electrons in a retarding probe field are in a Maxwell–Boltzmann distribution at a temperature unaffected by the presence of the probe. Towards higher pressure the measurements show an increasing depression of the plasma density near the probe, associated with the diffusion to it. The applied magnetic field had no noticeable effect on the densities measured with the probes as compared with the cavity measurements.

DOES LIOUVILLE'S THEOREM IMPLY QUANTUM MECHANICS?

International Journal of Modern Physics B ◽

10.1142/s0217979299000114 ◽

1999 ◽

Vol 13 (02) ◽

pp. 161-189

Author(s):

C. SYROS

Keyword(s):

Quantum Mechanics ◽

Radiation Spectrum ◽

Black Body ◽

Boltzmann Distribution ◽

Black Body Radiation ◽

Planck Constant ◽

Klein Gordon ◽

Energy Variable ◽

Liouville’S Theorem ◽

Liouville’S Equation

The essentials of quantum mechanics are derived from Liouville's theorem in statistical mechanics. An elementary solution, g, of Liouville's equation helps to construct a differentiable N-particle distribution function (DF), F(g), satisfying the same equation. Reality and additivity of F(g): (i) quantize the time variable; (ii) quantize the energy variable; (iii) quantize the Maxwell–Boltzmann distribution; (iv) make F(g) observable through time-elimination; (v) produce the Planck constant; (vi) yield the black-body radiation spectrum; (vii) support chronotopology introduced axiomatically; (viii) the Schrödinger and the Klein–Gordon equations follow. Hence, quantum theory appears as a corollary of Liouville's theorem. An unknown connection is found allowing the better understanding of space-times and of these theories.

Simulated annealing for airborne EM inversion

Geophysics ◽

10.1190/1.2736195 ◽

2007 ◽

Vol 72 (4) ◽

pp. F189-F195 ◽

Cited By ~ 27

Author(s):

Changchun Yin ◽

Greg Hodges

Keyword(s):

Simulated Annealing ◽

Random Walk ◽

Boltzmann Distribution ◽

Model Parameters ◽

Local Minima ◽

Model Configuration ◽

Airborne Electromagnetic ◽

Starting Model ◽

Airborne Em ◽

Cooling Schedule

The traditional algorithms for airborne electromagnetic (EM) inversion, e.g., the Marquardt-Levenberg method, generally run only a downhill search. Consequently, the model solutions are strongly dependent on the starting model and are easily trapped in local minima. Simulated annealing (SA) starts from the Boltzmann distribution and runs both downhill and uphill searches, rendering the searching process to easily jump out of local minima and converge to a global minimum. In the SA process, the calculation of Jacobian derivatives can be avoided because no preferred searching direction is required as in the case of the traditional algorithms. We apply SA technology for airborne EM inversion by comparing the inversion with a thermodynamic process, and we discuss specifically the SA procedure with respect to model configuration, random walk for model updates, objective function, and annealing schedule. We demonstrate the SA flexibility for starting models by allowing the model parameters to vary in a large range (far away from the true model). Further, we choose a temperature-dependent random walk for model updates and an exponential cooling schedule for the SA searching process. The initial temperature for the SA cooling scheme is chosen differently for different model parameters according to their resolvabilities. We examine the effectiveness of the algorithm for airborne EM by inverting both theoretical and survey data and by comparing the results with those from the traditional algorithms.

Table of Values Based on a Maxwell‐Boltzmann Distribution for Calculations of the Kinetic Properties of Energized Molecules

The Journal of Chemical Physics ◽

10.1063/1.1732569 ◽

1962 ◽

Vol 36 (2) ◽

pp. 569-570 ◽

Cited By ~ 3

Author(s):

C. Sivertz ◽

D. Goldsack

Keyword(s):

Boltzmann Distribution ◽

Kinetic Properties

Cryogenic thermometry: a review of recent progress

Cryogenics ◽

10.1016/s0011-2275(70)80004-2 ◽

1970 ◽

Vol 10 (1) ◽

pp. 14-22 ◽

Cited By ~ 50

Author(s):

L.G. Rubin

Keyword(s):

Recent Progress ◽

Cryogenic Thermometry

The role of vibrationally excited oxygen and nitrogen in the ionosphere during the undisturbed and geomagnetic storm period of 6-12 April 1990

Annales Geophysicae ◽

10.1007/s00585-998-0589-5 ◽

1998 ◽

Vol 16 (5) ◽

pp. 589-601 ◽

Cited By ~ 33

Author(s):

A. V. Pavlov

Keyword(s):

Loss Rate ◽

Boltzmann Distribution ◽

Rate Coefficients ◽

Ion Chemistry ◽

Vibrationally Excited ◽

Model Calculations ◽

F Region ◽

Neutral Temperature ◽

The Difference ◽

Excited Nitrogen

Abstract. We present a comparison of the observed behavior of the F-region ionosphere over Millstone Hill during the geomagnetically quiet and storm periods of 6–12 April 1990 with numerical model calculations from the IZMIRAN time-dependent mathematical model of the Earth's ionosphere and plasmasphere. The major enhancement to the IZMIRAN model developed in this study is the use of a new loss rate of O+(4S) ions as a result of new high-temperature flowing afterglow measurements of the rate coefficients K1 and K2 for the reactions of O+(4S) with N2 and O2. The deviations from the Boltzmann distribution for the first five vibrational levels of O2(v) were calculated, and the present study suggests that these deviations are not significant. It was found that the difference between the non-Boltzmann and Boltzmann distribution assumptions of O2(v) and the difference between ion and neutral temperature can lead to an increase of up to about 3 or a decrease of up to about 4 of the calculated NmF2 as a result of a respective increase or a decrease in K2. The IZMIRAN model reproduces major features of the data. We found that the inclusion of vibrationally excited N2(v > 0) and O2(v > 0) in the calculations improves the agreement between the calculated NmF2 and the data on 6, 9, and 10 April. However, both the daytime and nighttime densities are reproduced by the IZMIRAN model without the vibrationally excited nitrogen and oxygen on 8 and 11 April better than the IZMIRAN model with N2(v > 0) and O2(v > 0). This could be due to possible uncertainties in model neutral temperature and densities, EUV fluxes, rate coefficients, and the flow of ionization between the ionosphere and plasmasphere, and possible horizontal divergence of the flux of ionization above the station. Our calculations show that the increase in the O+ + N2 rate factor due to N2(v > 0) produces a 5-36 decrease in the calculated daytime peak density. The increase in the O++ O2 loss rate due to vibrational-ly excited O2 produces 8-46 reductions in NmF2. The effects of vibrationally excited O2 and N2 on Ne and Te are most pronounced during the daytime.Key words. Ion chemistry and composition · Ionosphere – atmosphere interactions · Ionospheric disturbances

Observing the Maxwell–Boltzmann distribution in LED emission spectra

American Journal of Physics ◽

10.1119/1.3429980 ◽

2010 ◽

Vol 78 (9) ◽

pp. 933-935 ◽

Cited By ~ 5

Author(s):

Jed Brody ◽

Daniel Weiss ◽

Pearl Young

Keyword(s):

Emission Spectra ◽

Boltzmann Distribution