Analytical Solutions for a Single Vertical Drain with Vacuum and Time-Dependent Surcharge Preloading in Membrane and Membraneless Systems

An analytical theory is developed to describe how negative pressure, (or ‘mud suction’, as it is sometimes referred to) develops underneath a body as it detaches itself from the ocean bottom. Biot's quasistatic equations of poro-elasticity are used to model the ocean bottom, and a general three-dimensional time-dependent analysis of the problem is worked out first using the boundary-layer approximation recently proposed by Mei and Foda. Then, explicit leading-order analytical solutions are presented for the problems of extrication of slender bodies as well as axisymmetric bodies from the ocean bottom.

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Analytical solutions for the time-dependent behaviour of composite beams with partial interaction

International Journal of Solids and Structures ◽

10.1016/j.ijsolstr.2005.03.032 ◽

2006 ◽

Vol 43 (13) ◽

pp. 3770-3793 ◽

Cited By ~ 43

Author(s):

G. Ranzi ◽

M.A. Bradford

Keyword(s):

Analytical Solutions ◽

Composite Beams ◽

Time Dependent ◽

Partial Interaction ◽

Time Dependent Behaviour ◽

Dependent Behaviour

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Analytical solutions for composite beams with slip, shear-lag and time-dependent effects

Engineering Structures ◽

10.1016/j.engstruct.2017.08.071 ◽

2017 ◽

Vol 152 ◽

pp. 559-578 ◽

Cited By ~ 12

Author(s):

Li Zhu ◽

R.K.L. Su

Keyword(s):

Analytical Solutions ◽

Composite Beams ◽

Time Dependent ◽

Shear Lag

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On the Unsteady Flow of Two Incompressible Immiscible Second Grade Fluids between Two Parallel Plates

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1016.546 ◽

2014 ◽

Vol 1016 ◽

pp. 546-553

Author(s):

Abdul M. Siddiqui ◽

Maya K. Mitkova ◽

Ali R. Ansari

Keyword(s):

Unsteady Flow ◽

Pressure Gradient ◽

Analytical Solutions ◽

Interface Velocity ◽

Time Dependent ◽

Second Grade ◽

Parallel Plates ◽

Governing Equations ◽

Layer Flow ◽

Second Grade Fluids

Unsteady, pressure driven in the gap between two parallel plates flow of two non-Newtonian incompressible second grade fluids is considered. The governing equations are established for the particular two-layer flow and analytical solutions of the equations that satisfy the imposed boundary conditions are obtained. The velocity of each fluid is expressed as function of the material constants, time dependent pressure gradient and other characteristics of the fluids. As part of the solution, an expression for the interface velocity is derived. We analyze the shift of the velocity maximum from one to another fluid as a function of variety of values of fluids’ parameters.

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Mathematical modeling of groundwater contamination with varying velocity field

Journal of Hydrology and Hydromechanics ◽

10.1515/johh-2017-0013 ◽

2017 ◽

Vol 65 (2) ◽

pp. 192-204 ◽

Cited By ~ 5

Author(s):

Pintu Das ◽

Sultana Begam ◽

Mritunjay Kumar Singh

Keyword(s):

Groundwater Contamination ◽

Analytical Solutions ◽

Diffusion Coefficients ◽

Numerical Solutions ◽

Finite Difference Methods ◽

Time Dependent ◽

Analytical Models ◽

Retardation Factor ◽

Hydrodynamic Dispersion ◽

The Impact

Abstract In this study, analytical models for predicting groundwater contamination in isotropic and homogeneous porous formations are derived. The impact of dispersion and diffusion coefficients is included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions are obtained using the Laplace Integral Transform Technique (LITT) and the concept of linear isotherm. For illustration, analytical solutions for linearly space- and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE).

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NUMERICAL SOLUTIONS OF QUANTUM MECHANICAL PROBLEMS USING THE BASIS-SPLINE COLLOCATION METHOD

International Journal of Modern Physics C ◽

10.1142/s0129183101002358 ◽

2001 ◽

Vol 12 (07) ◽

pp. 1093-1108 ◽

Cited By ~ 2

Author(s):

D. O. ODERO ◽

J. L. PEACHER ◽

D. H. MADISON

Keyword(s):

Collocation Method ◽

Analytical Solutions ◽

Numerical Solutions ◽

Time Dependent ◽

Quantum Mechanical ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Spline Collocation ◽

Spline Collocation Method

The time-dependent and time-independent Schrödinger equations have been numerically solved for several quantum mechanical problems with known analytical solutions using the basis-spline collocation algorithm. This algorithm has been demonstrated to be efficient and versatile. The results from these calculations illustrate the necessary numerical considerations required for solving both time-independent and time-dependent Schrödinger equations and form a basis that could be used for solving these and similar problems.

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