3,898 research outputs found
Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids
The generalized Forchheimer flows are studied for slightly compressible
fluids in porous media with time-dependent Dirichlet boundary data for the
pressure. No restrictions on the degree of the Forchheimer polynomial are
imposed. We derive, for all time, the interior -estimates for the
pressure and its partial derivatives, and the interior -estimates for its
Hessian. The De Giorgi and Ladyzhenskaya-Uraltseva iteration techniques are
used taking into account the special structures of the equations for both
pressure and its gradient. These are combined with the uniform Gronwall-type
bounds in establishing the asymptotic estimates when time tends to infinity
A family of steady two-phase generalized Forchheimer flows and their linear stability analysis
We model multi-dimensional two-phase flows of incompressible fluids in porous
media using generalized Forchheimer equations and the capillary pressure.
Firstly, we find a family of steady state solutions whose saturation and
pressure are radially symmetric and velocities are rotation-invariant. Their
properties are investigated based on relations between the capillary pressure,
each phase's relative permeability and Forchheimer polynomial. Secondly, we
analyze the linear stability of those steady states.
The linearized system is derived and reduced to a parabolic equation for the
saturation. This equation has a special structure depending on the steady
states which we exploit to prove two new forms of the lemma of growth of
Landis-type in both bounded and unbounded domains. Using these lemmas,
qualitative properties of the solution of the linearized equation are studied
in details. In bounded domains, we show that the solution decays exponentially
in time. In unbounded domains, in addition to their stability, the solution
decays to zero as the spatial variables tend to infinity. The BernsteinComment: 33 page
Properties of Generalized Forchheimer Flows in Porous Media
The nonlinear Forchheimer equations are used to describe the dynamics of
fluid flows in porous media when Darcy's law is not applicable. In this
article, we consider the generalized Forchheimer flows for slightly
compressible fluids and study the initial boundary value problem for the
resulting degenerate parabolic equation for pressure with the time-dependent
flux boundary condition. We estimate -norm for pressure and its time
derivative, as well as other Lebesgue norms for its gradient and second spatial
derivatives. The asymptotic estimates as time tends to infinity are emphasized.
We then show that the solution (in interior -norms) and its gradient
(in interior -norms) depend continuously on the initial and
boundary data, and coefficients of the Forchheimer polynomials. These are
proved for both finite time intervals and time infinity. The De Giorgi and
Ladyzhenskaya-Uraltseva iteration techniques are combined with uniform
Gronwall-type estimates, specific monotonicity properties, suitable parabolic
Sobolev embeddings and a new fast geometric convergence result.Comment: 63 page
Predicting technology acceptance among student teachers in Malaysia: A structural equation modeling approach
In response towards the advances of technology in the Malaysian education system, the authors investigated the predictors of technology acceptance among a sample of student teachers. Data collected from 245 student teachers were tested against the Technology Acceptance Model using the structural equation modeling approach. The variables that were tested included perceived usefulness (PU), perceived ease of use (PEU), attitudes toward computer use (ATCU), and behavioural intentions to use the computer (BI). The results of the study showed that ATCU was significantly influenced by PU and PEU. PEU also influenced PU significantly and BI was jointly influenced by PU and ATCU
Importance sampling for quantum Monte Carlo in manifolds: Addressing the time scale problem in simulations of molecular aggregates
Several importance sampling strategies are developed and tested for stereographic projection diffusion Monte Carlo in manifolds. We test a family of one parameter trial wavefunctions for variational Monte Carlo in stereographically projected manifolds which can be used to produce importance sampling. We use the double well potential in one dimensional Euclidean space to study systematically sampling issues for diffusion Monte Carlo. We find that diffusion Monte Carlo with importance sampling in manifolds is orders of magnitude more efficient compared to unguided diffusion Monte Carlo. Additionally, diffusion Monte Carlo with importance sampling in manifolds can overcome problems with nonconfining potentials and can suppress quasiergodicity effectively. We obtain the ground state energy and the wavefunction for the Stokmayer trimer. (c) 2008 American Institute of Physics
- …