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 $L^\infty$-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 $L^\infty$-norms) and its gradient (in interior $L^{2-\delta}$-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

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

An isogeometric analysis for elliptic homogenization problems

A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational expenses while using traditional finite element methods. The isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in this paper is regarded as an alternative approach to the standard Finite Element Heterogeneous Multiscale Method (FE-HMM) which is currently an effective framework to solve these problems. The method utilizes non-uniform rational B-splines (NURBS) in both macro and micro levels instead of standard Lagrange basis. Beside the ability to describe exactly the geometry, it tremendously facilitates high-order macroscopic/microscopic discretizations thanks to the flexibility of refinement and degree elevation with an arbitrary continuity level provided by NURBS basis functions. A priori error estimates of the discretization error coming from macro and micro meshes and optimal micro refinement strategies for macro/micro NURBS basis functions of arbitrary orders are derived. Numerical results show the excellent performance of the proposed method

A Renormalization Group Improved Calculation of Top Quark Production near Threshold

The top quark cross section close to threshold in $e^+e^-$ annihilation is computed including the summation of logarithms of the velocity at next-to-next-to-leading-logarithmic order in QCD. The remaining theoretical uncertainty in the normalization of the total cross section is at the few percent level, an order of magnitude smaller than in previous next-to-next-to-leading order calculations. This uncertainty is smaller than the effects of a light standard model Higgs boson.Comment: changed figures, added reference

A High Efficiency Lateral Light Emitting Device on SOI

The infrared light emission of lateral p/sup +/-p-n/sup +/ diodes realized on SIMOX-SOI (separation by implantation of oxygen - silicon on insulator) substrates has been studied. The confinement of the free carriers in one dimension due to the buried oxide was suggested to be a key point to increase the band-to-band recombination probability in silicon light emitters. We found in our devices an external quantum efficiency comparable to previous results presented in the literature. The wavelength range of the emission was found to be 900-1300 nm which is common for indirect band to band recombination in Si. The SOI technology incorporates an insulating layer between the thin single crystal silicon layer and the much thicker substrate. This electrically insulating layer is also a thermal isolator and so self-heating effects are common in devices fabricated on SOI wafers. Investigation of its influence on the light emission and the light distribution in the device has been carried out in our research. In this paper, the characteristics of the device with different active region lengths were investigated and explained quantitatively based on the recombination rate of carriers inside the active area by using the simulation model in Silvaco

Effect of Disorder in the Frustrated Ising FCC Antiferromagnet: Phase Diagram and Stretched Exponential Relaxation

We study the phase transition in a face-centered-cubic antiferromagnet with Ising spins as a function of the concentration $p$ of ferromagnetic bonds randomly introduced into the system. Such a model describes the spin-glass phase at strong bond disorder. Using the standard Monte Carlo simulation and the powerful Wang-Landau flat-histogram method, we carry out in this work intensive simulations over the whole range of $p$. We show that the first-order transition disappears with a tiny amount of ferromagnetic bonds, namely $p\sim 0.01$, in agreement with theories and simulations on other 3D models. The antiferromagnetic long-range order is also destroyed with a very small $p$ ($\simeq 5$). With increasing $p$, the system changes into a spin glass and then to a ferromagnetic phase when $p>0.65$. The phase diagram in the space ($T_c,p$) shows an asymmetry, unlike the case of the $\pm J$ Ising spin glass on the simple cubic lattice. We calculate the relaxation time around the spin-glass transition temperature and we show that the spin autocorrelation follows a stretched exponential relaxation law where the factor $b$ is equal to $\simeq 1/3$ at the transition as suggested by the percolation-based theory. This value is in agreement with experiments performed on various spin glasses and with Monte Carlo simulations on different SG models

A new scenario of dynamical heterogeneity in supercooled liquid and glassy states of 2D monatomic system

Via analysis of spatio-temporal arrangements of atoms based on their dynamics in supercooled liquid and glassy states of 2D monatomic system with a double-well Lennard-Jones-Gauss (LJG) interaction potential, we find a new scenario of dynamical heterogeneity. Atoms with the same or very close mobility have a tendency to aggregate into clusters. Number of atoms with high mobility (and size of their clusters) increases with decreasing temperature passing over a maximum before decreasing downto zero. Position of the peak moves toward a lower temperature if mobility of atoms in clusters is lower together with an enhancement of height of the peak. In contrast, number of atoms with very low mobility or solidlike atoms (and size of their clusters) has a tendency to increase with decreasing temperature and then it suddenly increases in the vicinity of glass transition temperature leading to the formation of a glassy state. A sudden increase in the number of strongly correlated solidlike atoms in the vicinity of a glass transition temperature ( ) may be an origin of a drastical increase in viscosity of the glass-forming systems approaching glass transition. The fact, we find that diffusion coefficient decays exponentially with fraction of solidlike atoms exhibiting a sudden decrease in the vicinity of glass transition region

Top quark mass definition and top quark pair production near threshold at the NLC

We suggest an infrared-insensitive quark mass, defined by subtracting the soft part of the quark self energy from the pole mass. We demonstrate the deep relation of this definition with the static quark-antiquark potential. At leading order in 1/m this mass coincides with the PS mass which is defined in a completely different manner. Going beyond static limit, the small normalization point introduces recoil corrections which are calculated here as well. Using this mass concept and other concepts for the quark mass we calculate the cross section of e+ e- -> t t-bar near threshold at NNLO accuracy adopting three alternative approaches, namely (1) fixing the pole mass, (2) fixing the PS mass, and (3) fixing the new mass which we call the PS-bar mass. We demonstrate that perturbative predictions for the cross section become much more stable if we use the PS or the PS-bar mass for the calculations. A careful analysis suggests that the top quark mass can be extracted from a threshold scan at NLC with an accuracy of about 100-200 MeV.Comment: published version, 21 pages in LaTeX including 11 PostScript figure