Point-based polygonal models for random graphs

1993 ◽  
Vol 25 (02) ◽  
pp. 348-372 ◽  
Author(s):  
T. Arak ◽  
P. Clifford ◽  
D. Surgailis
Keyword(s):  
Computer Simulations ◽  
Random Graphs ◽  
Particle System ◽  
Two Dimensional ◽  
One Dimensional ◽  
Space And Time ◽  
Markov Random ◽  
Alternative Description ◽  
Polygonal Models ◽  
Birth Death

We define a class of two-dimensional Markov random graphs with I, V, T and Y-shaped nodes (vertices). These are termed polygonal models. The construction extends our earlier work [1]– [5]. Most of the paper is concerned with consistent polygonal models which are both stationary and isotropic and which admit an alternative description in terms of the trajectories in space and time of a one-dimensional particle system with motion, birth, death and branching. Examples of computer simulations based on this description are given.

Point-based polygonal models for random graphs

1993 ◽  
Vol 25 (2) ◽  
pp. 348-372 ◽  
Author(s):  
T. Arak ◽  
P. Clifford ◽  
D. Surgailis
Keyword(s):  
Computer Simulations ◽  
Random Graphs ◽  
Particle System ◽  
Two Dimensional ◽  
One Dimensional ◽  
Space And Time ◽  
Markov Random ◽  
Alternative Description ◽  
Polygonal Models ◽  
Birth Death

We define a class of two-dimensional Markov random graphs with I, V, T and Y-shaped nodes (vertices). These are termed polygonal models. The construction extends our earlier work [1]– [5]. Most of the paper is concerned with consistent polygonal models which are both stationary and isotropic and which admit an alternative description in terms of the trajectories in space and time of a one-dimensional particle system with motion, birth, death and branching. Examples of computer simulations based on this description are given.

scholarly journals On the Rate of Convergence for a Characteristic of Multidimensional Birth-Death Process

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 477 ◽  
Author(s):  
Alexander Zeifman ◽  
Yacov Satin ◽  
Ksenia Kiseleva ◽  
Victor Korolev
Keyword(s):  
Markov Process ◽  
Rate Of Convergence ◽  
State Vector ◽  
The State ◽  
Death Process ◽  
General Situation ◽  
Two Dimensional ◽  
One Dimensional ◽  
Whole Process ◽  
Birth Death

We consider a multidimensional inhomogeneous birth-death process. In this paper, a general situation is studied in which the intensity of birth and death for each coordinate (“each type of particle”) depends on the state vector of the whole process. A one-dimensional projection of this process on one of the coordinate axes is considered. In this case, a non-Markov process is obtained, in which the transitions to neighboring states are possible in small periods of time. For this one-dimensional process, by modifying the method previously developed by the authors of the note, estimates of the rate of convergence in weakly ergodic and null-ergodic cases are obtained. The simplest example of a two-dimensional process of this type is considered.

An experimental and theoretical study of a catalytic monolith to control automobile exhaust emissions

1992 ◽  
Vol 439 (1907) ◽  
pp. 465-483 ◽  
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Chemical Kinetics ◽  
Computer Simulations ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Two Dimensional Model ◽  
Inlet Conditions ◽  
The One

Experimental investigations of automobile exhaust emissions were examined by combusting a mixture of propane and air within a multi-channel monolith. Chemical kinetics, mass transfer and heat transfer effects were studied using appropriate temperature and flow conditions to separate the effects. The results were used to construct both a one- and two-dimensional mathematical model. Simulations of monolith behaviour were then compared with observed performance. First-order chemical kinetics were observed for the low hydrocarbon concentrations examined in the temperature range 557–648 K, while mass transfer limitation was apparent at temperatures between 736 K and 769 K. Perturbations to inlet concentration and temperature were effected while studying monolith performance, and the responses recorded. Computer simulations using the two mathematical models predicted correct trends, but did not agree quantitatively with the experimental results. The one-dimensional model predicts both concentration and temperature responses to a change in inlet conditions better than the more comprehensive two-dimensional model, even when heat losses are taken into account. This is because experimentally determined heat and mass transfer coefficients are used for computations relating to the one-dimensional model, whereas these parameters were calculated theoretically in the two-dimensional model. Further computer simulations revealed discontinuities in the values of Nusselt numbers, values depending on elapsed time following a step change in inlet conditions and axial position along the monolith channel. This unusual feature is accounted for by a reversal in heat transfer between wall and bulk fluid as the reaction develops along the monolith channel.

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.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

2012 ◽  
Vol 9 (1) ◽  
pp. 47-52
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Buzina
Keyword(s):  
Comparative Analysis ◽  
Numerical Model ◽  
Liquid Mixture ◽  
Phase Model ◽  
Test Problems ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Saturated Liquid ◽  
Two Phase ◽  
One Dimensional

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

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