scholarly journals Exact Solutions of Fragmentation Equations with General Fragmentation Rates and Separable Particles Distribution Kernels

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
S. C. Oukouomi Noutchie ◽  
E. F. Doungmo Goufo
Keyword(s):  
Exact Solution ◽  
Evolution Equation ◽  
Laplace Transform ◽  
Exact Solutions ◽  
Method Of Characteristics ◽  
Open Problems ◽  
The Method Of Characteristics ◽  
Sudden Appearance ◽  
Many Particles

We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.

An Exact Solution for Flow Transients in Two-Phase Systems by the Method of Characteristics

1973 ◽  
Vol 95 (4) ◽  
pp. 470-476 ◽  
Author(s):  
J. M. Gonzalez-Santalo ◽  
R. T. Lahey
Keyword(s):  
Exact Solution ◽  
Method Of Characteristics ◽  
Accurate Analysis ◽  
Two Phase ◽  
Design Considerations ◽  
The Method Of Characteristics ◽  
System Flow ◽  
Hypothetical Accident ◽  
Phase Systems ◽  
Important Design

One of the important design considerations in modern water-cooled nuclear reactors is their thermal performance during hypothetical accident situations. However, an accurate analysis of the system thermal-hydraulics is required before the thermal margins can be appraised. In this paper, an analysis based on the method of characteristics has been developed by which the exact solution to flow decay transients in homogeneous two-phase systems can be obtained. The exact solution presented yields the system flow and quality at each point in space and time during an exponential flow decay transient. These parameters can then be combined with an appropriate CHF correlation to predict the occurrence of transient CHF.

scholarly journals Laplace-SBA Method for Solving Nonlinear Coupled Burger's Equations

2021 ◽  
Vol 14 (3) ◽  
pp. 842-862
Author(s):  
Joseph Bonazebi-Yindoula
Keyword(s):  
Fluid Dynamics ◽  
Exact Solution ◽  
Numerical Methods ◽  
Laplace Transform ◽  
Exact Solutions ◽  
Partial Derivative ◽  
Basic Principles ◽  
The Laplace Transform ◽  
Fluid Dynamics Equations ◽  
Burger's Equations

Burger’s equations, an extension of fluid dynamics equations, are typically solved by several numerical methods. In this article, the laplace-Somé Blaise Abbo method is used to solve nonlinear Burger equations. This method is based on the combination of the laplace transform and the SBA method. After reminders of the laplace transform, the basic principles of the SBA method are described. The process of calculating the Laplace-SBA algorithm for determining the exact solution of a linear or nonlinear partial derivative equation is shown. Thus, three examplesof PDE are solved by this method, which all lead to exact solutions. Our results suggest that this method can be extended to other more complex PDEs.

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

Non-symmetric flow in Laval type nozzles

1972 ◽  
Vol 273 (1232) ◽  
pp. 185-235 ◽  
Keyword(s):  
Steady State ◽  
Combustion Chamber ◽  
Method Of Characteristics ◽  
Three Dimensions ◽  
Symmetric Flow ◽  
Gaseous Flow ◽  
The Method Of Characteristics ◽  
Lateral Forces

The equations of the steady state, compressible inviscid gaseous flow are linearized in a form suitable for application to nozzles of the Laval type. The procedure in the supersonic phase is verified by comparing solutions so obtained with those derived by the method of characteristics in two and three dimensions. Likewise, the solutions in the transonic phase are com pared with those obtained by other investigators. The linearized equation is then used to investigate the nat re of non-symmetric flow in rocket nozzles. It is found that if the flow from the combustion chamber into the nozzle is non-symmetric, the magnitude and direction of the turning couple produced by the emergent jet is dependent on the profile of the nozzle and it is possible to design profiles such that the turning couples or lateral forces are zero. The optimum nozzle so designed is independent of the pressure and also of the magnitude of the non-symmetry of the entry flow. The formulae by which they are obtained have been checked by extensive static and projection tests with simulated rocket test vehicles which are described in this paper.

Boundary Layer Closure and Heat Transfer in Constant Base Pressure and Simple Wave Guns

1978 ◽  
Vol 100 (4) ◽  
pp. 690-696 ◽  
Author(s):  
A. D. Anderson ◽  
T. J. Dahm
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Momentum Equation ◽  
Base Pressure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Solutions of the two-dimensional, unsteady integral momentum equation are obtained via the method of characteristics for two limiting modes of light gas launcher operation, the “constant base pressure gun” and the “simple wave gun”. Example predictions of boundary layer thickness and heat transfer are presented for a particular 1 in. hydrogen gun operated in each of these modes. Results for the constant base pressure gun are also presented in an approximate, more general form.

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