40 resultados para 1137
em Queensland University of Technology - ePrints Archive
Resumo:
In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.
Resumo:
The transition of cubic indium hydroxide to cubic indium oxide has been studied by thermogravimetric analysis complimented with hot stage Raman spectroscopy. Thermal analysis shows the transition of In(OH)3 to In2O3 occurs at 219°C. The structure and morphology of In(OH)3 synthesised using a soft chemical route at low temperatures was confirmed by X-ray diffraction and scanning electron microscopy. A topotactical relationship exists between the micro/nano-cubes of In(OH)3 and In2O3. The Raman spectrum of In(OH)3 is characterised by an intense sharp band at 309 cm-1 attributed to ν1 In-O symmetric stretching mode, bands at 1137 and 1155 cm-1 attributed to In-OH δ deformation modes, bands at 3083, 3215, 3123 and 3262 cm-1 assigned to the OH stretching vibrations. Upon thermal treatment of In(OH)3 new Raman bands are observed at 125, 295, 488 and 615 cm-1 attributed to In2O3. Changes in the structure of In(OH)3 with thermal treatment is readily followed by hot stage Raman spectroscopy.
Resumo:
A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.
Resumo:
The uniformization method (also known as randomization) is a numerically stable algorithm for computing transient distributions of a continuous time Markov chain. When the solution is needed after a long run or when the convergence is slow, the uniformization method involves a large number of matrix-vector products. Despite this, the method remains very popular due to its ease of implementation and its reliability in many practical circumstances. Because calculating the matrix-vector product is the most time-consuming part of the method, overall efficiency in solving large-scale problems can be significantly enhanced if the matrix-vector product is made more economical. In this paper, we incorporate a new relaxation strategy into the uniformization method to compute the matrix-vector products only approximately. We analyze the error introduced by these inexact matrix-vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost. Numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications.
Resumo:
We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.