scholarly journals Dynamical analysis of an n−H−T cosmological quintessence real gas model with a general equation of state

2018 ◽  
Vol 33 (03) ◽  
pp. 1850025 ◽  
Author(s):  
Rossen I. Ivanov ◽  
Emil M. Prodanov
Keyword(s):  
Equation Of State ◽  
General Equation ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Dynamical Analysis ◽  
Real Gas ◽  
Cyclic Universe ◽  
Closed Orbits ◽  
Stable Periodic ◽  
Dimensional Dynamical System

The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. The cyclic solutions exhibit regions characterized by inflation and deflation, while the open trajectories are characterized by inflation in a “fly-by” near an unstable critical point.

scholarly journals Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

2021 ◽  
Vol 17 (1) ◽  
pp. 119-138
Author(s):  
M. R. Koroleva ◽  
◽  
O. V. Mishchenkova ◽  
V. A. Tenenev ◽  
T. Raeder ◽  
...  
Keyword(s):  
Equation Of State ◽  
Critical State ◽  
Stokes Equations ◽  
Safety Valve ◽  
Van Der Waals ◽  
Local Approximation ◽  
Critical Conditions ◽  
Nonlinear Processes ◽  
Real Gas ◽  
Van Der Waals Equation

The paper presents a modification of the digital method by S. K. Godunov for calculating real gas flows under conditions close to a critical state. The method is generalized to the case of the Van der Waals equation of state using the local approximation algorithm. Test calculations of flows in a shock tube have shown the validity of this approach for the mathematical description of gas-dynamic processes in real gases with shock waves and contact discontinuity both in areas with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with local approximation of the Van der Waals equation by a two-term equation of state was used for simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex shape, which is characteristic of the internal space of a safety valve. We have demonstrated that, under near-critical conditions, areas of nonclassical gas behavior may appear, which affects the nature of flows. We have studied nonlinear processes in a safety valve arising from the movement of the shut-off element, which are also determined by the device design features and the gas flow conditions.

Generalized van der Waals theory. I. Basic formulation and application to uniform fluids

1980 ◽  
Vol 33 (9) ◽  
pp. 2013 ◽  
Author(s):  
S Nordholm ◽  
ADJ Haymet
Keyword(s):  
Free Energy ◽  
Equation Of State ◽  
Particle Density ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Energy Functional ◽  
Coarse Grained ◽  
Uniform Structure ◽  
Free Energy Functional ◽  
Van Der Waals Theory

A generalized van der Waals theory is derived on the basis of simple physical and mathematical arguments. The derivation results in a free- energy functional wherein the independent variable is a coarse-grained particle density. It is assumed that a well defined particle density dominates the free energy and this density is to be obtained by minimizing the free energy functional. The variational theory so obtained can be applied to non-uniform fluids. In the present work the possibility of stable non-uniform structure is neglected and the theory is applied to uniform fluids. It then produces an equation of state identical in form to that proposed originally by van der Waals but the excluded volume is only about half as large in the three-dimensional case. Applications to several two- and three-dimensional systems indicate that the new equation of state is a distinct improvement over the traditional van der Waals theory when the full range of fluid densities is considered. The quantitative accuracy in the case of simple uniform fluids is sufficient to warrant further development and exploitation of the theory.

A Four-Leaf Chaotic Attractor of a Three-Dimensional Dynamical System

2015 ◽  
Vol 25 (02) ◽  
pp. 1530003 ◽  
Author(s):  
Tomoyuki Miyaji ◽  
Hisashi Okamoto ◽  
Alex D. D. Craik
Keyword(s):  
Dynamical System ◽  
Three Dimensional ◽  
Period Doubling ◽  
Numerical Verification ◽  
Unstable Periodic Orbits ◽  
Verification Method ◽  
Stable Periodic ◽  
Approach Infinity ◽  
Dimensional Dynamical System ◽  
Autonomous Dynamical System

A three-dimensional autonomous dynamical system proposed by Pehlivan is untypical in simultaneously possessing both unbounded and chaotic solutions. Here, this topic is studied in some depth, both numerically and analytically. We find, by standard methods, that four-leaf chaotic orbits result from a period-doubling cascade; we identify unstable fixed points and both stable and unstable periodic orbits; and we examine how initial data determines whether orbits approach infinity or a stable periodic orbit. Further, we describe and apply a strict numerical verification method that rigorously proves the existence of sequences of period doublings.

scholarly journals The Equation of State of Biogas

2017 ◽  
Vol 65 (2) ◽  
pp. 537-543
Author(s):  
Petr Trávníček ◽  
Tomáš Vítěz ◽  
Tomáš Koutný
Keyword(s):  
Equation Of State ◽  
Theoretical Approach ◽  
Van Der Waals ◽  
Compressibility Factor ◽  
Calculated Data ◽  
State Behavior ◽  
Real Gas ◽  
Van Der Waals Equation ◽  
Geometric Average ◽  
Pure Substances

The presented work deals with a state behavior of real gas, biogas. Theoretical approach was utilized for processing of this work. Compressibility factor was calculated with help of two equation of state – Van der Waals equation and Redlich‑Kwong equation. Constants a and b of both equations were calculated using geometric average of the constants of pure substances. On the basis of calculated data charts showing the dependence of compressibility factor and the pressure were created. These charts were created for temperatures 20 °C and 40 °C. Statistical analyses of data were carried out. The results showed that compressibility factor reached value from 0.997 to 0.97 (20 °C) and from 0.997 to 0.974 (40 °C) in the case Van der Waals equation and in the range of pressure from 100 kPa to 1000 kPa. In the case of Redlich‑Kwong equation these values were from 0.997 to 0.967 (20 °C) and from 0.997 to 0.974 (40 °C) in the same range of pressures.

Real gas flow fields about three dimensional configurations

1983 ◽  
Author(s):  
A. BALAKRISHNAN ◽  
C. LOMBARD ◽  
W.C. DAVY
Keyword(s):  
Gas Flow ◽  
Three Dimensional ◽  
Flow Fields ◽  
Real Gas

scholarly journals Superconducting contact and quantum interference between two-dimensional van der Waals and three-dimensional conventional superconductors

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Michael R. Sinko ◽  
Sergio C. de la Barrera ◽  
Olivia Lanes ◽  
Kenji Watanabe ◽  
Takashi Taniguchi ◽  
...  
Keyword(s):  
Quantum Interference ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Two Dimensional

Container port throughput analysis and active management using control theory

2021 ◽  
pp. 147509022110208
Author(s):  
Cuong Truong Ngoc ◽  
Xiao Xu ◽  
Hwan-Seong Kim ◽  
Duy Anh Nguyen ◽  
Sam-Sang You
Keyword(s):  
Control Theory ◽  
Time Series Data ◽  
Sliding Mode ◽  
Container Terminal ◽  
Three Dimensional ◽  
Maritime Transportation ◽  
Container Terminals ◽  
Active Management ◽  
Dynamical Analysis ◽  
Series Data

This paper deals with three-dimensional (3D) model of competitive Lotka-Volterra equation to investigate nonlinear dynamics and control strategy of container terminal throughput and capacity. Dynamical behaviors are intensely explored by using eigenvalue evaluation, bifurcation analysis, and time-series data. The dynamical analysis is to show the stability with bifurcation of the competition and collaboration of multiple container terminals in the maritime transportation. Based on the chaotic analysis, the sliding mode control theory has been utilized for optimization of port operations under disruptions. Extensive numerical simulations have been conducted to validate the efficacy and reliability of the presented control algorithms. Particularly, the closed-loop system has been assessed through chaotic suppression and synchronization strategies for port management. Finally, the presented fundamental techniques can be utilized to provide managerial insights and solutions on efficient seaport operations that allow more timely and cost-effective decision making for port authorities in such a highly competitive environment.

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