Explicit solutions of quasi-static problems in the coupled theory of poroelasticity

2021 ◽  
Author(s):  
Lamara Bitsadze
Keyword(s):  
Explicit Solutions ◽  
Coupled Theory

scholarly journals ON p – q DUALITY AND EXPLICIT SOLUTIONS IN c ≤ 1 2D GRAVITY MODELS

1995 ◽  
Vol 10 (08) ◽  
pp. 1219-1236 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MARSHAKOV
Keyword(s):  
String Theory ◽  
Exact Solutions ◽  
2D Gravity ◽  
Integral Formula ◽  
Integral Representations ◽  
Gravity Models ◽  
Explicit Solutions ◽  
String Equation ◽  
Duality Transformation

We study the role of integral representations in the description of nonperturbative solutions to c ≤ 1 string theory. A generic solution is determined by two functions, W(x) and Q(x), which behave at infinity like xp and xq respectively. The integral formula for arbitrary (p, q) models is derived, which explicitly realizes a duality transformation between (p, q) and (q, p) 2D gravity solutions. We also discuss the exact solutions to the string equation and reduction condition and present several explicit examples.

Explicit Solutions of the Coupled Bogoyavlensky Lattice 1(2) Hierarchy

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Xianguo Geng ◽  
Wei Liu ◽  
Bo Xue
Keyword(s):  
Explicit Solutions

Stress Singularity of Edge Delamination in Angle-Ply and Cross-Ply Laminates

1997 ◽  
Vol 64 (3) ◽  
pp. 525-531 ◽  
Author(s):  
Wen-Hwa Chen ◽  
Tain-Fu Huang
Keyword(s):  
Transverse Shear ◽  
Axial Strain ◽  
Stress Singularity ◽  
Shear Stresses ◽  
Explicit Solutions ◽  
Real Constant ◽  
Stress Singularities ◽  
General Solutions ◽  
Transverse Shear Stresses ◽  
Edge Delamination

By utilizing the general solutions derived for the plies with arbitrary fiber orientations under uniform axial strain (Huang and Chen, 1994), the explicit solutions of the edge-delamination stress singularities for the angle-ply and cross-ply laminates are obtained. The dominant edge-delamination stress singularities for the angle-ply laminates are found to be a real constant, −1/2, and a pair of complex conjugates, −1/2±i/2πln{(b+b2−a2)/a}. For the cross-ply laminates, the significant effect of transverse shear stresses of the laminate is considered and the dominant edge-delamination stress singularities are shown as −1/2 and −1/2±i/2πln{(c2+c22−4c1c3)/2c1}. a, b, cl, c2, and c3 are the corresponding combined complex constants. In addition, two elementary forms of edge-delamination stress singularity, say, r−1/2 and rδr(lnr)n(δr=n−3/2,n=1,2...) exist for both the angle-ply and cross-ply laminates. Excellent correlations between the present results and available solutions show the validity of the approach. The deficiencies of the solutions available in the literature are compensated. New results for other angle-ply and cross-ply laminates are also provided.

The use of Riemann problems in solving a class of transcendental equations

1973 ◽  
Vol 73 (1) ◽  
pp. 111-118 ◽  
Author(s):  
E. E. Burniston ◽  
C. E. Siewert
Keyword(s):  
Boundary Value Problem ◽  
Closed Form ◽  
Boundary Value ◽  
Explicit Solutions ◽  
Riemann Boundary Value Problem ◽  
Riemann Problems ◽  
Riemann Boundary ◽  
Canonical Solution ◽  
Transcendental Equations ◽  
Explicit Expressions

AbstractA method of finding explicit expressions for the roots of a certain class of transcendental equations is discussed. In particular it is shown by determining a canonical solution of an associated Riemann boundary-value problem that expressions for the roots may be derived in closed form. The explicit solutions to two transcendental equations, tan β = ωβ and β tan β = ω, are discussed in detail, and additional specific results are given.

scholarly journals Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

2012 ◽  
Vol 45 (4) ◽  
pp. 045206 ◽  
Author(s):  
Jun-ichi Inoguchi ◽  
Kenji Kajiwara ◽  
Nozomu Matsuura ◽  
Yasuhiro Ohta
Keyword(s):  
Kdv Equation ◽  
Plane Curves ◽  
Explicit Solutions ◽  
Modified Kdv Equation

scholarly journals Coagulation Processes with Gibbsian Time Evolution

2012 ◽  
Vol 49 (03) ◽  
pp. 612-626
Author(s):  
Boris L. Granovsky ◽  
Alexander V. Kryvoshaev
Keyword(s):  
Stochastic Process ◽  
Recurrence Relation ◽  
Time Evolution ◽  
Nonnegative Function ◽  
Gibbs Distribution ◽  
Time Dependent ◽  
Explicit Solutions ◽  
Gibbs Distributions ◽  
Giant Cluster ◽  
Positive Integers

We prove that a stochastic process of pure coagulation has at any timet≥ 0 a time-dependent Gibbs distribution if and only if the rates ψ(i,j) of single coagulations are of the form ψ(i;j) =if(j) +jf(i), wherefis an arbitrary nonnegative function on the set of positive integers. We also obtain a recurrence relation for weights of these Gibbs distributions that allow us to derive the general form of the solution and the explicit solutions in three particular cases of the functionf. For the three corresponding models, we study the probability of coagulation into one giant cluster by timet> 0.

Explicit solutions for a SWCNT collapse

2011 ◽  
Vol 82 (6) ◽  
pp. 767-776 ◽  
Author(s):  
Jianlin Liu
Keyword(s):  
Explicit Solutions
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