Exact solution of Smoluchowski’s equation for reorientational motion in Maier–Saupe potential

Analytical Solutions for Composition-Dependent Coagulation

Mathematical Problems in Engineering ◽

10.1155/2016/1735897 ◽

2016 ◽

Vol 2016 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Manli Yang ◽

Zhiming Lu ◽

Jie Shen

Keyword(s):

Exact Solution ◽

Particle Size ◽

Conditional Distribution ◽

Gaussian Function ◽

Initial Distribution ◽

Initial Particle ◽

Initial Particle Size ◽

Large Particles ◽

The Laplace Transform ◽

Smoluchowski’S Equation

Exact solutions of the bicomponent Smoluchowski’s equation with a composition-dependent additive kernelK(va,vb;va′,vb′)=α(va+va′)+(vb+vb′)are derived by using the Laplace transform for any initial particle size distribution. The exact solution for an exponential initial distribution is then used to analyse the effects of parameterαon mixing degree of such bicomponent mixtures and the conditional distribution of the first component for particles with given mass. The main finding is that the conditional distribution of large particles at larger time is a Gaussian function which is independent of the parameterα.

Exact solution of a four-site crystal model for an intermediate-valence system

Journal de Physique ◽

10.1051/jphys:019860047060102900 ◽

1986 ◽

Vol 47 (6) ◽

pp. 1029-1034 ◽

Cited By ~ 25

Author(s):

J.C. Parlebas ◽

R.H. Victora ◽

L.M. Falicov

Keyword(s):

Exact Solution ◽

Intermediate Valence ◽

Crystal Model

The Exact Solution of the Highest Wave Derived from a Universal Wave Model

Coastal Engineering 1984 ◽

10.1061/9780872624382.071 ◽

1985 ◽

Author(s):

Yang Yih Chen ◽

Frederick L. W. Tang

Keyword(s):

Exact Solution ◽

Wave Model

Unsteady Exact Solution for Flows of Fluids with Pressure-Dependent Viscosities

Mathematical Proceedings of the Royal Irish Academy ◽

10.3318/pria.2006.106.2.115 ◽

2006 ◽

Vol 106 (2) ◽

pp. 115-130 ◽

Cited By ~ 11

Author(s):

K. R. Rajagopal ◽

G. Saccomandi

Keyword(s):

Exact Solution

An Exact Solution for Fully Developed Temperature Distribution in Laminar Steady Forced Convection Inside Circular Tubes with Uniform Wall Temperature

Heat Transfer Research ◽

10.1615/heattransres.v34.i3-4.130 ◽

2003 ◽

Vol 34 (3-4) ◽

pp. 11

Author(s):

Kamel Hooman

Keyword(s):

Exact Solution ◽

Temperature Distribution ◽

Forced Convection ◽

Wall Temperature ◽

Circular Tubes ◽

Uniform Wall Temperature ◽

Uniform Wall

AN EXACT SOLUTION FOR THERMAL ANALYSIS OF A CYLINDRICAL OBJECT USING A HYPERBOLIC HEAT CONDUCTION MODEL

Heat Transfer Research ◽

10.1615/heattransres.2012005537 ◽

2012 ◽

Vol 43 (5) ◽

pp. 405-423

Author(s):

Seyfolah Saedodin ◽

Mohammad Sadegh Motaghedi Barforoush

Keyword(s):

Thermal Analysis ◽

Exact Solution ◽

Heat Conduction ◽

Hyperbolic Heat Conduction ◽

Conduction Model ◽

Heat Conduction Model ◽

Cylindrical Object

COMPUTATIONAL NEAR-FIELD RADIATIVE HEAT TRANSFER: CONVERGENCE ANALYSIS OF THE THERMAL DISCRETE DIPOLE APPROXIMATION USING THE EXACT SOLUTION FOR TWO SPHERES

Proceeding of Proceedings of CHT-15. 6th International Symposium on ADVANCES IN COMPUTATIONAL HEAT TRANSFER , May 25-29, 2015, Rutgers University, New Brunswick, NJ, USA ◽

10.1615/ichmt.2015.intsympadvcomputheattransf.290 ◽

2015 ◽

Author(s):

Sheila Edalatpour ◽

Martin Cuma ◽

Tyler Trueax ◽

Roger Backman ◽

Mathieu Francoeur

Keyword(s):

Heat Transfer ◽

Exact Solution ◽

Convergence Analysis ◽

Radiative Heat Transfer ◽

Radiative Heat ◽

Near Field ◽

Dipole Approximation ◽

Discrete Dipole Approximation

EXACT SOLUTION TO THE TWO-DIMENSIONAL APPROACH OF THE REWETTING BY A FALLING FILM

Proceeding of International Heat Transfer Conference 8 ◽

10.1615/ihtc8.1750 ◽

1986 ◽

Cited By ~ 1

Author(s):

Francesco Castiglia ◽

E. Oliveri ◽

S. Taibi ◽

G. Vella

Keyword(s):

Exact Solution ◽

Falling Film ◽

Two Dimensional ◽

Dimensional Approach

TEST-CASE NO 34: TWO-DIMENSIONAL SLOSHING IN CAVITY - AN EXACT SOLUTION (PA)

Multiphase Science and Technology ◽

10.1615/multscientechn.v16.i1-3.320 ◽

2004 ◽

Vol 16 (1-3) ◽

pp. 251-257

Author(s):

J.-L. Estivalezes ◽

G. Chanteperdrix

Keyword(s):

Exact Solution ◽

Test Case ◽

Two Dimensional

Difference Schemes for Nonlinear BVPS on the Semiaxis

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2007-0002 ◽

2007 ◽

Vol 7 (1) ◽

pp. 25-47 ◽

Cited By ~ 4

Author(s):

I.P. Gavrilyuk ◽

M. Hermann ◽

M.V. Kutniv ◽

V.L. Makarov

Keyword(s):

Differential Equation ◽

Exact Solution ◽

Boundary Value Problem ◽

Difference Scheme ◽

Adaptive Algorithm ◽

Order Differential Equation ◽

Constructive Method ◽

Numerical Examples ◽

Exact Difference ◽

The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.