Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.

Numerical coupling of thermal-electric network models and energy-transport equations including optoelectronic semiconductor devices

In this work the numerical coupling of thermal and electric network models with model equations for optoelectronic semiconductor devices is presented. Modified nodal analysis (MNA) is applied to model electric networks. Thermal effects are modeled by an accompanying thermal network. Semiconductor devices are modeled by the energy-transport model, that allows for thermal effects. The energy-transport model is expandend to a model for optoelectronic semiconductor devices. The temperature of the crystal lattice of the semiconductor devices is modeled by the heat flow eqaution. The corresponding heat source term is derived under thermodynamical and phenomenological considerations of energy fluxes. The energy-transport model is coupled directly into the network equations and the heat flow equation for the lattice temperature is coupled directly into the accompanying thermal network. The coupled thermal-electric network-device model results in a system of partial differential-algebraic equations (PDAE). Numerical examples are presented for the coupling of network- and one-dimensional semiconductor equations. Hybridized mixed finite elements are applied for the space discretization of the semiconductor equations. Backward difference formluas are applied for time discretization. Thus, positivity of charge carrier densities and continuity of the current density is guaranteed even for the coupled model.

A study of finite-difference methods as applied to hypersonic viscous shock-layer equations

"Contract no. Nonr 2653(00)."

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Partial regularity of minimizers of a functional involving forms and maps

We discuss the partial regularity of minimizers of energy functionals such as (1)/(p)integral(Omega)[sigma(u)dA(p) + (1)/(2)delu(2p)]dx, where u is a map from a domain Omega is an element of R-n into the m-dimensional unit sphere of Rm+1 and A is a differential one-form in Omega.

Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function

We consider the existence and uniqueness problem for partial differential-functional equations of the first order with the initial condition for which the right-hand side depends on the derivative of unknown function with deviating argument.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Retention force of T-bar clasps for titanium and cobalt-chromium removable partial dentures

The objective of this study was to evaluate the retention force of T-bar clasps made from commercially pure titanium (CP Ti) and cobalt-chromium (Co-Cr) alloy by the insertion/removal test simulating 5 years use. Thirty-six frameworks were cast from CP Ti (n=18) and Co-Cr alloy (n=18) with identical prefabricated patterns on refractory casts from a distal extension mandibular hemi-arch segment. The castings were made on a vacuum-pressure machine, under vacuum and argon atmosphere. Each group was subdivided in three, corresponding to 0.25 mm, 0.50 mm and 0.75 mm undercuts, respectively. No polishing procedures were performed to ensure uniformity. The specimens were subjected to an insertion/removal test and data was analyzed statistically to compare CP Ti and Co-Cr alloy in the same undercut (Student's t-test for independent samples) and each material in different undercuts (one-way ANOVA) (p=0.05). Comparisons between materials revealed significant differences (p=0.017) only for the 0.50-mm undercut. No significant differences (p>0.05) were found when comparing the same material for the undercuts. It may be concluded that for different undercuts, both Co-Cr alloy and CP Ti had no significant differences for T-bar clasps; CP Ti showed the lowest retention force values when compared to Co-Cr alloy in each undercut, but with significant difference only for the 0.50-mm undercut; and both materials maintained the retentive capacity during the simulation test.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.