A computational strategy for multiscale systems with applications to Lorenz 96 model

Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.     

The Asymmetric Avalanche Process

An asymmetric stochastic process describing the avalanche dynamics on a ring is proposed. A general kinetic equation which incorporates the exclusion and avalanche processes is considered. The Bethe ansatz method is used to calculate the generating function for the total distance covered by all particles. It gives the average velocity of particles which exhibits a phase transition from an intermittent to continuous flow. We calculated also higher cumulants and the large deviation function for the particle flow. The latter has the universal form obtained earlier for the asymmetric exclusion process and conjectured to be common for all models of the Kardar–Parisi–Zhang universality class.     

Enhancement of the Kerr effect for a quantum dot in a cavity

Nonlinear susceptibility of a quantum dot (QD) embedded in a two-sided cavity, is studied theoretically from a weak-coupling to a strong-coupling regime. In the relevance of a quantum logic gate, the corresponding nonlinear phase shifts (Kerr effect) are estimated for coherent wavepackets including one photon on average. In the weak-coupling regime, the phase shift enhances strongly as a function of a coupling constant between the cavity photon and QD, and eventually saturates in the strong-coupling regime. We also show transmission spectra to evaluate the efficiency of the phase shift. Although the efficiency decreases monotonically in the weak-coupling regime, it rises in the strong-coupling regime.     

Comparison of XYZ Model Fitting Functions for 111Cd in In3La

The XYZ model describes the interaction between nuclear probes and an electric field gradient that fluctuates among three orthogonal directions. The model presents a means to calculate the perturbation function that represents spectra obtained using perturbed angular correlation spectroscopy. Three analytic approximations of the perturbation function have been developed previously, and they are evaluated in the present paper in the context of Cd jumping among In-lattice sites in In₃La.     

Cold compaction of ceramic powder: Computational analysis of the effect of pressing method and die shape

This paper deals with a computational analysis of the influence of the pressing method and part geometry on the final density distribution in the cold compaction process of ceramic alumina powders. The analysis is based on the explicit finite-element model proposed and validated in a previous study. The mechanical behavior of the processing material is described using a multisurface elastoplastic model, the modified Drucker-Prager/Cap model Published in Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 129–134, October 2007.     

Analysis of heterojunction resonant cavity-enhanced Schottky photodiodes by using two-valley transport model

The article concerns heterojunction resonant cavity-enhanced (RCE) Schottky photodiodes with GaAs in the absorption layer. The quantum efficiency and linear pulse response have thoroughly been analysed. For the first time, the response of a heterojunction photodiode has been modelled by the phenomenological model for a two-valley semiconductor. The results obtained have shown that the satellite valleys, as well as the parasitic time constant, significantly influence the response and, accordingly, have to be taken into account when analysing and optimizing RCE photodetectors.     

Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type

We consider two classes of integrable nonlinear hyperbolic systems on Lie algebras. These systems generalize the principal chiral model. Each system is related to a pair of compatible Lie brackets and has a Lax representation, which is determined by the direct sum decomposition of the Lie algebra of Laurent series into the subalgebra of Taylor series and the complementary subalgebra corresponding to the pair. New examples of compatible Lie brackets are given.     

Global and exploding solutions in a model of self-gravitating systems

We study asymptotic properties of solutions to an extension to arbitrary dimensions of the astrophysical model proposed by Chavanis et al. to explain phenomena of gravitational collapse in clouds of self-gravitating particles. In particular, we show that in the two-dimensional case the solutions can be continued to global ones, while in three space dimensions large data of negative energy blow up in a finite time. Relations between isothermal, Streater's energy-transport and the present models are also studied.     

Confidence regions in a multivariate regression model with constraints II

The multivariate model, where not only parameters of the mean value of the observation matrix, but also some other parameters occur in constraints, is considered in the paper. Some basic inference is presented under the condition that the covariance matrix is either unknown, or partially unknown, or known. Supported by the grant of the Council of Czech Republic MSM 6 198 959 214.