Numerical solutions of equations describing nonisothermal flows of a real gas in tubes

1967 ◽  
Vol 13 (4) ◽  
pp. 290-293
Author(s):  
B. L. Krivoshein ◽  
E. M. Minskii ◽  
V. P. Radchenko ◽  
I. E. Khodanovich ◽  
M. G. Khublaryan
Keyword(s):  
Numerical Solutions ◽  
Real Gas ◽  
Nonisothermal Flows ◽  
Solutions Of Equations

Numerical Solutions of Polynomial Equations for the Eight-Position Synthesis of the Cylindrical-Spherical Dyad

2012 ◽  
Author(s):  
Chintien Huang ◽  
Chenning Hung ◽  
Kuenming Tien
Keyword(s):  
Rigid Body ◽  
Numerical Solutions ◽  
Continuation Method ◽  
Quadratic Equation ◽  
Geometric Constraints ◽  
Numerical Continuation ◽  
Polynomial Equations ◽  
Quartic Polynomial ◽  
Solutions Of Equations ◽  
Position Synthesis

This paper investigates the numerical solutions of equations for the eight-position rigid-body guidance of the cylindrical-spherical (C-S) dyad. We seek to determine the number of finite solutions by using the numerical continuation method. We derive the design equations using the geometric constraints of the C-S dyad and obtain seven quartic polynomial equations and one quadratic equation. We then solve the system of equations by using the software package Bertini. After examining various specifications, including those with random complex numbers, we conclude that there are 804 finite solutions of the C-S dyad for guiding a body through eight prescribed positions. When designing spatial dyads for rigid-body guidance, the C-S dyad is one of the four dyads that result in systems of equal numbers of equations and unknowns if the maximum number of allowable positions is specified. The numbers of finite solutions in the syntheses of the other three dyads have been obtained previously, and this paper provides the computational kinematic result of the last unsolved problem, the eight-position synthesis of the C-S dyad.

SPATIOTEMPORAL IRREGULARITY IN A TWO-DIMENSIONAL MODEL OF CARDIAC TISSUE

1991 ◽  
Vol 01 (01) ◽  
pp. 219-225 ◽  
Author(s):  
A. V. PANFILOV ◽  
A. V. HOLDEN
Keyword(s):  
Cardiac Tissue ◽  
Numerical Solutions ◽  
Spiral Waves ◽  
Excitable Medium ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Dimensional Model ◽  
Solutions Of Equations

Meandering spiral waves are well-known solutions of equations that represent a two-dimensional excitable medium. Numerical solutions of a model for a sheet of cardiac tissue show transient meandering vortices that break down spontaneously into spatiotemporal irregularity.

scholarly journals Numerical Solutions of Three-Dimensional Non-Grey Gas Radiative Transfer Using the Statistical Narrow-Band Model

1999 ◽  
Vol 121 (1) ◽  
pp. 200-203 ◽  
Author(s):  
F. Liu
Keyword(s):  
Radiative Transfer ◽  
Numerical Solutions ◽  
Radiative Transfer Equation ◽  
Narrow Band ◽  
Pure Water ◽  
Three Dimensional ◽  
Band Model ◽  
Real Gas ◽  
Gas Radiation ◽  
Narrow Band Model

Three-dimensional non-grey gas radiation analyses were conducted using the statistical narrow-band model along with up-dated band parameters. The exact narrow-band averaged radiative transfer equation was solved using a ray-tracing method. Accurate numerical results were presented for non-grey real gas radiative transfer in a three-dimensional rectangular enclosure containing (i) an isothermal pure water vapor at 1000 K and 1 atm, (ii) an isothermal and inhomogeneous H2O/N2 mixture at 1000 K and 1 atm, and (iii) a nonisothermal and homogeneous mixture of CO2/H2O/N2 at 1 atm.

Large Deformation Analysis of Hyperelastic Membranes Containing a Hole or Inclusion

2010 ◽  
Vol 146-147 ◽  
pp. 696-700
Author(s):  
Wen Jia Wang ◽  
Bo Liu ◽  
Jian Bing Sang ◽  
Chen Hua Lu
Keyword(s):  
Large Deformation ◽  
Constitutive Relation ◽  
Numerical Solutions ◽  
Constitutive Models ◽  
Deformation Analysis ◽  
Large Deformation Analysis ◽  
Incompressible Materials ◽  
Strain Invariant ◽  
Solutions Of Equations ◽  
Constitutive Parameters

A large deformation analysis has been given by using a modified Gao’s second constitutive relation. In certain circumstances, the new constitutive relation may be simplified to the Mooney-Rivlin and Neo-Hookean models. With regard to incompressible materials, when the influence of the second strain invariant is neglected, the modified model brings a unified form of Gao’s two constitutive models. The new constitutive relation has been utilized to resolve a problem of a hyperelastic membrane containing a hole or rigid inclusion. The basic governing equations of incompressible materials have been obtained and numerical solutions of equations illustrate how constitutive parameters affect the result of membranes’ deformation. These conclusions may provide helps to practical problems.

scholarly journals Collapse and expansion of scalar thin-shell for a class of black holes

2019 ◽  
Vol 28 (03) ◽  
pp. 1950046 ◽  
Author(s):  
M. Sharif ◽  
Faisal Javed
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Thin Shell ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Massless Scalar ◽  
Massive Scalar ◽  
Exterior Regions ◽  
Rotation Parameters ◽  
Solutions Of Equations

This paper investigates the dynamics of thin-shell in the presence of perfect fluid as well as scalar field. We formulate the equations of motion using Israel thin-shell formalism by taking the interior and exterior regions of Schwarzschild, Kerr as well as Kerr–Newmann black hole. We find numerical solutions of equations of motion and effective potential to analyze the scalar shell for collapse and expansion. It is found that the rate of collapse and expansion of scalar shell through shell’s radius depend on charge and rotation parameters. We conclude that the massive scalar shell leads to collapse of thin-shell, while massless scalar shell indicates both collapse as well as expansion.

Mechanics of Texturing Thermoplastic Yarns

1977 ◽  
Vol 47 (4) ◽  
pp. 256-266 ◽  
Author(s):  
David Brookstein ◽  
Stanley Backer
Keyword(s):  
Steady State ◽  
Material Properties ◽  
Numerical Solutions ◽  
State Interaction ◽  
Cold Zone ◽  
Numerical Predictions ◽  
Steady State Model ◽  
Solutions Of Equations ◽  
False Twist ◽  
Good Agreement

A model is proposed to reflect the steady-state interaction between material properties of POY feed yarn and the false-twist draw-texturing process. Free filament migration is assumed for initial cold twisting, resulting in equal cold filament strains over the yarn section. No migration is assumed to occur during threadline uptwisting at the heater entry. Threadline torque in the cold zone is attributed to filament bending, twisting, and tensioning, while at the heater entry only the tensile components of yam torque prevail. Numerical solutions of equations of equilibrium and continuity provide predictions of threadline tension, torque, and zone twists. Results of experiments on a laboratory texturing device show good agreement with numerical predictions based on the steady-state model. Limitations of the model are considered.

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