Spatial Dissipative Structures in Excitable Media (Plankton, Soil Bacteria. . . .)

2019 ◽  
pp. 91-126
Keyword(s):  
Spatial Distribution ◽  
Phase Space ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
The Other ◽  
Excitable Media ◽  
Bifurcation Diagrams ◽  
Dimensional Phase Space ◽  
Liesegang Bands ◽  
Space Characteristic

A general, the simplest model of a spatial dissipative structure arising in an excitable medium is constructed, containing at least two components interacting with each other with their own mobility. One of these components (active) uses the other component as food. It is shown that such a model leads to a stationary stable spatial distribution of the components in the form of Liesegang bands. As specific examples of the formation of spatial dissipative structures, structures arising in plankton consisting of phytoplankton and zooplankton and in the soil containing the bacterial population and the nutrient substrate are considered. Bifurcation diagrams are constructed in the parameter space, characteristic for each of the considered excitable media, which determine the conditions for the formation of dissipative structures in these media. The existence in the plankton of a strange attractor of a previously unknown shape in four-dimensional phase space has been discovered.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

scholarly journals Geometric particle-in-cell methods for the Vlasov–Maxwell equations with spin effects

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Nicolas Crouseilles ◽  
Paul-Antoine Hervieux ◽  
Yingzhe Li ◽  
Giovanni Manfredi ◽  
Yajuan Sun
Keyword(s):  
Phase Space ◽  
Maxwell Equations ◽  
Stimulated Raman Scattering ◽  
Extended Phase ◽  
Five Dimensions ◽  
Particle In Cell ◽  
Spin Effects ◽  
Dimensional Phase Space ◽  
Spin Polarized ◽  
Underdense Plasma

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ , where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$ . It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$ . As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

scholarly journals Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Algebraic Characterization ◽  
Symmetric Hyperbolic System ◽  
Full Generality ◽  
Order Linear ◽  
First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

PROBING AWAY SIDE JET MODIFICATION WITH THREE PARTICLE CORRELATIONS

2007 ◽  
Vol 16 (07n08) ◽  
pp. 1982-1987
Author(s):  
◽  
N. N. AJITANAND
Keyword(s):  
Spatial Distribution ◽  
Correlation Functions ◽  
Theoretical Models ◽  
The Other ◽  
Experimental Investigations ◽  
Powerful Method ◽  
Particle Correlation ◽  
Low Viscosity ◽  
Jet Modification ◽  
Rhic Data

Recent experimental investigations have focussed on the abnormal spatial distribution of away side jet fragments as signals of significant medium induced effects. A variety of theoretical models including recent string-theory based efforts have supported the notion of Mach Cone like effects in the low viscosity QGP fluid. However, the presence of significant flow fields may deflect the fragmentation direction producing a significantly differing type of jet topology from that of the Mach cone. Three particle correlation functions constitute a powerful method whereby the predominance of one or the other type of mechanism can be differentiated. In this work the use of such an approach will be demonstrated via simulations and the results of its application to RHIC data will be presented.

Conservative generalized bifurcation diagrams and phase space properties for oval-like billiards

2022 ◽  
Vol 155 ◽  
pp. 111707
Author(s):  
Diogo Ricardo da Costa ◽  
André Fujita ◽  
Antonio Marcos Batista ◽  
Matheus Rolim Sales ◽  
José Danilo Szezech Jr
Keyword(s):  
Phase Space ◽  
Bifurcation Diagrams

scholarly journals Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years

2017 ◽  
Vol 24 (4) ◽  
pp. 713-725 ◽  
Author(s):  
Davide Faranda ◽  
Gabriele Messori ◽  
M. Carmen Alvarez-Castro ◽  
Pascal Yiou
Keyword(s):  
Phase Space ◽  
Sea Level ◽  
Northern Hemisphere ◽  
Atmospheric Dynamics ◽  
Complex Nature ◽  
Human Welfare ◽  
Sea Level Pressure ◽  
Level Pressure ◽  
Dimensional Phase Space ◽  
Dynamical Properties

Abstract. Atmospheric dynamics are described by a set of partial differential equations yielding an infinite-dimensional phase space. However, the actual trajectories followed by the system appear to be constrained to a finite-dimensional phase space, i.e. a strange attractor. The dynamical properties of this attractor are difficult to determine due to the complex nature of atmospheric motions. A first step to simplify the problem is to focus on observables which affect – or are linked to phenomena which affect – human welfare and activities, such as sea-level pressure, 2 m temperature, and precipitation frequency. We make use of recent advances in dynamical systems theory to estimate two instantaneous dynamical properties of the above fields for the Northern Hemisphere: local dimension and persistence. We then use these metrics to characterize the seasonality of the different fields and their interplay. We further analyse the large-scale anomaly patterns corresponding to phase-space extremes – namely time steps at which the fields display extremes in their instantaneous dynamical properties. The analysis is based on the NCEP/NCAR reanalysis data, over the period 1948–2013. The results show that (i) despite the high dimensionality of atmospheric dynamics, the Northern Hemisphere sea-level pressure and temperature fields can on average be described by roughly 20 degrees of freedom; (ii) the precipitation field has a higher dimensionality; and (iii) the seasonal forcing modulates the variability of the dynamical indicators and affects the occurrence of phase-space extremes. We further identify a number of robust correlations between the dynamical properties of the different variables.

scholarly journals Hydrochemical Characteristics of the Surgut Reservoir Water Area Littoral Sections

2018 ◽  
Author(s):  
Keyword(s):  
Spatial Distribution ◽  
Power Plants ◽  
Thermal Power ◽  
Water Area ◽  
The Other ◽  
Anthropogenic Pressure ◽  
Taiga Zone ◽  
Thermal Power Plants ◽  
Reservoir Water ◽  
First Time

Cooling reservoirs of thermal power plants represent the special class of natural/ engineering systems with, on the one hand, natural geo/systems as one subsystem and, on the other hand, production/technological units as the other subsystem. Studying of these ecosystems’ functioning regularities seems to be helpful for water quality management and rational organization of water use. Besides, it is topical due to the low level of the relevant knowledge in the North of the Western Siberia. The authors for the first time in the Middle Ob Region have carried out a two-year session of monitoring of hydro/chemical indicators and temperature regime of the thermal power plants cooling reservoirs in the riparian stripe of water area. All previous investigations were done only by industrial water users within the frameworks of production monitoring in terms of three indicators in three points of the cooling reservoir water area downstream the power plant dam. Spatial distribution of concentrations of biogenic ions, salt composition, pH, organic matter, and metals in specific natural/technological system of the Surgut hthermal power plants’ reservoirs has been analyzed for the first time for the conditions of the Western Siberian taiga zone. Sources of anthropogenic pressure upon a water body have been identified. According the results of the indicators’ spatial distribution analysis three sections of the Surgut reservoir water area have been separated: a background section of the Chernaya River; a section upstream the dam with predominantly recreational character of the anthropogenic pressure; and a sectio0n downstream the dam with anthropogenic pressure of technological origin. According the outcomes of the correlation analysis indicators of the anthropogenic pressure character have been reveald.

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