scholarly journals Time-Dependent Surface Elevation of an ice Slope

1980 ◽  
Vol 25 (92) ◽  
pp. 247-266 ◽  
Author(s):  
Kolumban Hutter
Keyword(s):  
Differential Equation ◽  
Accumulation Rate ◽  
Wave Theory ◽  
Viscous Medium ◽  
Time Dependent ◽  
Field Equations ◽  
Diffusion Term ◽  
Creep Flow ◽  
The Mean ◽  
Flow Law

AbstractBy introducing a coordinate stretching, the governing field equations of the creep flow of a non-Newtonian viscous medium down a uniform slope are solved to determine the differential equation describing the propagation of long surface waves caused by initial disturbances and/or time-dependent accumulation-rate The differential equation for the surface wave depends on the flow law of the non-Newtonian fluid, the boundary condition at the ice-bedrock interface, the bedrock topography and the thickness–wavelength ratio. For moderately long waves and small elevation above the mean thickness the results agree in their essentials with those of the kinematic wave theory and the forward wave equation with a diffusion term is derived, but when improving this by allowing higher elevations the Burger's equation and even more complex equations are obtained. To derive these results Glen’s flow law must be generalized to avoid infinitely fast changes in stress deviators close to zero Strain-rates, The range of applicability of the various equations is discussed.

scholarly journals Time-Dependent Surface Elevation of an ice Slope

1980 ◽  
Vol 25 (92) ◽  
pp. 247-266 ◽  
Author(s):  
Kolumban Hutter
Keyword(s):  
Differential Equation ◽  
Accumulation Rate ◽  
Wave Theory ◽  
Viscous Medium ◽  
Time Dependent ◽  
Field Equations ◽  
Diffusion Term ◽  
Creep Flow ◽  
The Mean ◽  
Flow Law

AbstractBy introducing a coordinate stretching, the governing field equations of the creep flow of a non-Newtonian viscous medium down a uniform slope are solved to determine the differential equation describing the propagation of long surface waves caused by initial disturbances and/or time-dependent accumulation-rate The differential equation for the surface wave depends on the flow law of the non-Newtonian fluid, the boundary condition at the ice-bedrock interface, the bedrock topography and the thickness–wavelength ratio. For moderately long waves and small elevation above the mean thickness the results agree in their essentials with those of the kinematic wave theory and the forward wave equation with a diffusion term is derived, but when improving this by allowing higher elevations the Burger's equation and even more complex equations are obtained. To derive these results Glen’s flow law must be generalized to avoid infinitely fast changes in stress deviators close to zero Strain-rates, The range of applicability of the various equations is discussed.

scholarly journals The Large Number Hypothesis and Einstein's Theory of Gravitation

1985 ◽  
Vol 38 (4) ◽  
pp. 547 ◽  
Author(s):  
Yun-Kau Lau
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Matter Density ◽  
Time Dependent ◽  
Field Equations ◽  
Large Number Hypothesis ◽  
Theory Of Gravitation ◽  
The Mean ◽  
Limiting Case ◽  
The Universe

In an attempt to reconcile the large number hypothesis (LNH) with Einstein's theory of gravitation, a tentative generalization of Einstein's field equations with time-dependent cosmological and gravitational constants is proposed. A cosmological model consistent with the LNH is deduced. The coupling formula of the cosmological constant with matter is found, and as a consequence, the time-dependent formulae of the cosmological constant and the mean matter density of the Universe at the present epoch are then found. Einstein's theory of gravitation, whether with a zero or nonzero cosmological constant, becomes a limiting case of the new generalized field equations after the early epoch.

An Incremental Criterion for Time-Dependent Failure of Materials

1976 ◽  
Vol 98 (2) ◽  
pp. 140-145 ◽  
Author(s):  
S. R. Bodner ◽  
U. S. Lindholm
Keyword(s):  
Failure Criterion ◽  
Strain Energy ◽  
Hydrostatic Stress ◽  
Time Dependent ◽  
Accumulation Of Damage ◽  
The Mean ◽  
Flow Law ◽  
Dependent Failure

A criterion for the time-dependent failure of materials is developed based upon the concept that failure results from an incremental accumulation of damage. The failure criterion is thereby explicitly tied to the incremental flow law describing the inelastic deformations. The damage increment is assumed as a product of functions of the stored strain energy due to inelastic deformations, the mean hydrostatic stress, and the damage itself. The consequences of the failure criterion for various types of loading are discussed.

Electronic dynamics in chains with Ornstein–Uhlenbeck correlated disorder

2020 ◽  
Vol 31 (12) ◽  
pp. 2050176
Author(s):  
J. L. S. Soares ◽  
R. D. dos Santos ◽  
F. J. S. Sousa ◽  
M. O. Sales ◽  
F. A. B. F. Moura
Keyword(s):  
Differential Equation ◽  
Evolution Operator ◽  
Mean Square Displacement ◽  
Time Dependent ◽  
Mean Square ◽  
Strong Correlations ◽  
Uhlenbeck Process ◽  
Electronic Dynamics ◽  
Ornstein Uhlenbeck Process ◽  
The Mean

In this paper, we present a detailed study of the electronic dynamics in systems with correlated disorder generated from the Ornstein–Uhlenbeck process (OU). In short, we used numeric methods for solving the time-dependent Schrödinger equation. We apply a Taylor’s expansion of the evolution operator in order to solve the differential equation. We calculate some typical tools, such as the participation function [Formula: see text], the mean square displacement [Formula: see text] and the probability of return [Formula: see text]. In our analysis, we show that for low correlations the system behaves as in the standard Anderson model (i.e. all eigenstates are localized). For strong correlations, our results suggest the existence of a quasi-ballistic dynamics.

Qxygen transfer in gravity flow sewers

2000 ◽  
Vol 42 (3-4) ◽  
pp. 417-422 ◽  
Author(s):  
T.Y. Pai ◽  
C.F. Ouyang ◽  
Y.C. Liao ◽  
H.G. Leu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dissolved Oxygen ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Partial Differential ◽  
Diffusion Term ◽  
Sewer Pipes ◽  
Gravity Sewer

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

FRW viscous fluid cosmological model with time-dependent inhomogeneous equation of state

2017 ◽  
Vol 15 (01) ◽  
pp. 1830001 ◽  
Author(s):  
G. S. Khadekar ◽  
Deepti Raut
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Quadratic Form ◽  
State Parameter ◽  
The Other ◽  
Time Dependent ◽  
Inhomogeneous Equation ◽  
Field Equations ◽  
Equation Of State Parameter ◽  
Viscous Models

In this paper, we present two viscous models of non-perfect fluid by avoiding the introduction of exotic dark energy. We consider the first model in terms of deceleration parameter [Formula: see text] has a viscosity of the form [Formula: see text] and the other model in quadratic form of [Formula: see text] of the type [Formula: see text]. In this framework we find the solutions of field equations by using inhomogeneous equation of state of form [Formula: see text] with equation of state parameter [Formula: see text] is constant and [Formula: see text].

scholarly journals Sequential eigenfunction expansion for a problem in combustion theory

2003 ◽  
Vol 45 (1) ◽  
pp. 35-48 ◽  
Author(s):  
M. Al-Refai ◽  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Eigenfunction Expansion ◽  
Time Dependent ◽  
Linear Parabolic Equation ◽  
System Of Equations ◽  
Multiple Steady State ◽  
Definitive Answer ◽  
Combustion Theory ◽  
The Galerkin Method ◽  
Steady State Solutions

AbstractA method of sequential eigenfunction expansion is developed for a semi-linear parabolic equation. It allows the time-dependent coefficients of the eigenfunctions to be determined sequentially and iterated to reach convergence. At any stage, only a single ordinary differential equation needs to be considered, in contrast to the Galerkin method which requires the consideration of a system of equations. The method is applied to a central problemin combustion theory to provide a definitive answer to the question of the influence of the initial data in determining whether the solution is sub- or super-critical, in the case of multiple steady-state solutions. It is expected this method will prove useful in dealing with similar problems.

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