9,638 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
CPA for charge ordering in the extended Hubbard model
We study charge ordering in the extended Hubbard model with both on-site and
nearest neighbor Coulomb repulsion (U and V, respectively) within the Coherent
potential approximation (CPA). The phase boundary between the homogeneous and
charge ordered phase for the square lattice is obtained for different values of
U. It is shown that at quarter filling for all values of U the charge ordering
exists only if the inter-site Coulomb repulsion V exceeds certain critical
value which is of the order of the kinetic energy t. At finite temperature a
reentrant transition is found in some region of V.Comment: 5 pages, 4 figure
Evolution of structure of SiO2 nanoparticles upon cooling from the melt
Evolution of structure of spherical SiO2 nanoparticles upon cooling from the
melt has been investigated via molecular-dynamics (MD) simulations under
non-periodic boundary conditions (NPBC). We use the pair interatomic potentials
which have weak Coulomb interaction and Morse type short-range interaction. The
change in structure of SiO2 nanoparticles upon cooling process has been studied
through the partial radial distribution functions (PRDFs), coordination number
and bond-angle distributions at different temperatures. The core and surface
structures of nanoparticles have been studied in details. Our results show
significant temperature dependence of structure of nanoparticles. Moreover,
temperature dependence of concentration of structural defects in nanoparticles
upon cooling from the melt toward glassy state has been found and discussed.Comment: 12 pages, 6 figure
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
Stabilization Control of the Differential Mobile Robot Using Lyapunov Function and Extended Kalman Filter
This paper presents the design of a control model to navigate the
differential mobile robot to reach the desired destination from an arbitrary
initial pose. The designed model is divided into two stages: the state
estimation and the stabilization control. In the state estimation, an extended
Kalman filter is employed to optimally combine the information from the system
dynamics and measurements. Two Lyapunov functions are constructed that allow a
hybrid feedback control law to execute the robot movements. The asymptotical
stability and robustness of the closed loop system are assured. Simulations and
experiments are carried out to validate the effectiveness and applicability of
the proposed approach.Comment: arXiv admin note: text overlap with arXiv:1611.07112,
arXiv:1611.0711
The Capillary Pumped Loop Flight Experiment (CAPL): A pathfinder for EOS
The CAPL shuttle flight experiment will provide microgravity verification of the prototype capillary pumped loop (CPL) thermal control system for EOS. The design of the experiment is discussed with particular emphasis on the new technology areas in ammonia two-phase reservior design and heat pipe heat exchanger development. The thermal and hydrodynamic analysis techniques and results are also presented, including pressure losses, fluid flow, and non-orbit heat rejection capability. CAPL experiment results will be presented after the flight, presently planned for 1993
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
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