General discussion

1990 ◽  
Vol 330 (1615) ◽  
pp. 679-681
Keyword(s):  
Environmental Changes ◽  
Mean Field ◽  
Climatic Changes ◽  
Archaeological Record ◽  
Large Fluctuation ◽  
Axis Of Rotation ◽  
The Mean ◽  
Earth’S Climate ◽  
Newcastle Upon Tyne ◽  
Interesting Analogy

S. K. Runcorn, F. R. S. ( University of Newcastle upon Tyne, U. K. ). In examining whether there is evidence in the records of the Earth’s climate for small variations with periods of about 200 years, the geophysicists suppose that the large fluctuation from year to year (of which we are very conscious) due to the instabilities of the atmosphere-ocean system may average out over long periods so as to reveal shorter-period changes in solar activity. There is an interesting analogy with the Earth’s magnetic field, which varies considerably on a shorter timescale, yet over longer time spans the mean field is exactly that of a dipole aligned along the axis of rotation. Can we tell, from the archaeological record, whether climatic changes, resulting for instance in the migration of peoples, are short lived, or whether they might be produced by longer-term environmental changes?

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Collection of Environmental Variables and Bacterial Community Compositions in Marian Cove, Antarctica, during Summer 2018

Data ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 27
Author(s):  
Hyo-Ryeon Kim ◽  
Jae-Hyun Lim ◽  
Ju-Hyoung Kim ◽  
Il-Nam Kim
Keyword(s):  
Bacterial Community ◽  
Community Composition ◽  
Marine Bacteria ◽  
Environmental Variables ◽  
Environmental Changes ◽  
Bacterial Community Composition ◽  
Composition Data ◽  
Decomposition Of Organic Matter ◽  
Class Level ◽  
Earth’S Climate

Marine bacteria, which are known as key drivers for marine biogeochemical cycles and Earth’s climate system, are mainly responsible for the decomposition of organic matter and production of climate-relevant gases (i.e., CO₂, N₂O, and CH₄). However, research is still required to fully understand the correlation between environmental variables and bacteria community composition. Marine bacteria living in the Marian Cove, where the inflow of freshwater has been rapidly increasing due to substantial glacial retreat, must be undergoing significant environmental changes. During the summer of 2018, we conducted a hydrographic survey to collect environmental variables and bacterial community composition data at three different layers (i.e., the seawater surface, middle, and bottom layers) from 15 stations. Of all the bacterial data, 17 different phylum level bacteria and 21 different class level bacteria were found and Proteobacteria occupy 50.3% at phylum level following Bacteroidetes. Gammaproteobacteria and Alphaproteobacteria, which belong to Proteobacteria, are the highest proportion at the class level. Gammaproteobacteria showed the highest relative abundance in all three seawater layers. The collection of environmental variables and bacterial composition data contributes to improving our understanding of the significant relationships between marine Antarctic regions and marine bacteria that lives in the Antarctic.

scholarly journals The Mean-field Behavior of Processor Sharing Systems with General Job Lengths Under the SQ(d) Policy

2019 ◽  
Vol 46 (3) ◽  
pp. 54-55
Author(s):  
Thirupathaiah Vasantam ◽  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar
Keyword(s):  
Mean Field ◽  
Processor Sharing ◽  
Field Behavior ◽  
The Mean

scholarly journals The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation

2020 ◽  
Vol 31 (1) ◽  
Author(s):  
Hui Huang ◽  
Jinniao Qiu
Keyword(s):  
Existence Of Solutions ◽  
Particle System ◽  
Mean Field ◽  
Field Limit ◽  
Mean Field Limit ◽  
Unique Existence ◽  
Interacting Particle ◽  
Microscopic Derivation ◽  
The Mean ◽  
Limit Result

AbstractIn this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions $$d=2,3$$ d = 2 , 3 . Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.

scholarly journals Asymptotic expansion of low-energy excitations for weakly interacting bosons

2021 ◽  
Vol 9 ◽  
Author(s):  
Lea Boßmann ◽  
Sören Petrat ◽  
Robert Seiringer
Keyword(s):  
Asymptotic Expansion ◽  
Coulomb Potential ◽  
Mean Field ◽  
Low Energy ◽  
Energy Eigenstates ◽  
Bogoliubov Theory ◽  
Weakly Interacting ◽  
Repulsive Coulomb ◽  
The Mean

Abstract We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in $1/N$ .

scholarly journals Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Phan Thành Nam ◽  
Marcin Napiórkowski
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Mean Field ◽  
Interaction Strength ◽  
Bose Gas ◽  
Body Density ◽  
The Mean ◽  
The One ◽  
Mean Field Regime ◽  
Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

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