scholarly journals Anisotropic Jüttner (relativistic Boltzmann) distribution

2016 ◽  
Vol 34 (9) ◽  
pp. 737-738 ◽  
Author(s):  
Rudolf A. Treumann ◽  
Wolfgang Baumjohann

Abstract. A rigorous derivation of the Jüttner (covariant Boltzmann) distribution is provided for anisotropic pressure (or temperature) tensors. It was in similar form anticipated first by Gladd (1983). Its manifestly covariant version follows straightforwardly from its scalar property.

2018 ◽  
Author(s):  
Igor Baburin

The paper calls attention to the most symmetric interpenetration patterns of honeycomb layers. To the best of my knowledge, such patterns remained unknown so far. In my contribution a rigorous derivation of such patterns is given that makes use of a new approach to interpenetrating nets. The results are presented in a broad context of structural chemistry and crystal engineering.


1970 ◽  
Vol 22 ◽  
Author(s):  
R. Goossens ◽  
J. De Schuyter

In  this article, we tried to perform the drawing of forest maps, together with  the calculations involved, automatically by means of relatively simple aids.      The computer unit used is an office computer Olivetti P203. As an example  the growing stock (in m3/ha) was mapped out. The proper inventory in the field is done  according to the classical method by means of a previously fixed network of  squares (70,7 m x 70,7 m), which corresponds to two plots a ha.     The quantity which is measured and mapped out (in this case the growing  stock) is in a similar form not very useful in mapping. Therefore a division  in classes (Ku) numbered from 0 to 9, is set up. An appropriate program  calculates for a certain number of points within this elementary square, to which  class they have to be assigned, whereas the typewriter prints the  corresponding code number on the right place.     Fig. 1 and the formulas (1), (2) and (3) represent the principle o[ the  calculations while fig. 2A and B reproduce the results printed by the  typewriter for a elementary square of respective 1” X 1” and 2” X 2”. The  whole of similar network of squares eventually results in a basical document,  on which the existing forest map with an adapted scale is laid (see appendix  3) and the class limits are drawn.     If desirable, the scale may be adapted when the forest map under discussion  is definitely reproduced.


Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen

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.


Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 8
Author(s):  
Gustavo Chica-Pedraza ◽  
Eduardo Mojica-Nava ◽  
Ernesto Cadena-Muñoz

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.


2017 ◽  
Vol 3 (1) ◽  
pp. 63-67 ◽  
Author(s):  
Alexander Brensing ◽  
Roman Ruff ◽  
Benjamin Fischer ◽  
Sascha L. Wien ◽  
Klaus-Peter Hoffmann

Abstract:The usability of flexible electrodes in moving environment is limited due to different mechanical characteristics of their metallic and polymeric components. To achieve structure compatible electrodes, all used materials need to have similar Young’s moduli as the surrounding tissue. This paper describes the characterization of macroscopic as well as miniaturized electrodes entirely made out of modified silicone (PDMS). Electrochemical, mechanical, biological, optical, and applicative methods were used. It could be shown, that PDMS electrodes are capable to be used for recording electrocardiograms with similar form and amplitude as with standard electrodes.


2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Shao-Zhen Lin ◽  
Wu-Yang Zhang ◽  
Dapeng Bi ◽  
Bo Li ◽  
Xi-Qiao Feng

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.


1955 ◽  
Vol 59 (540) ◽  
pp. 850-852 ◽  
Author(s):  
R. E. D. Bishop

A convenient method is pointed out for calculating the response of a damped linear system with one degree of freedom to harmonic excitation. Results of such calculations are usually represented by the familiar “ resonance curves ”—one curve being plotted for each intensity of damping. These curves are not particularly convenient to use and Yates has overcome several of their defects by throwing them into a nomographic form. Yates' nomogram is based upon the concept of viscous damping and it does not give the information of a conventional set of resonance curves in that it relates to the velocity of vibration. By changing over to hysteretic damping, a nomogram of somewhat similar form may be constructed such that it gives amplitudes and phase angles of displacements while retaining the advantages, over resonance curves, of this form of representation.


1967 ◽  
Vol 45 (10) ◽  
pp. 3199-3209 ◽  
Author(s):  
R. M. Clements ◽  
H. M. Skarsgard

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.


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