Structural Stability Theory and Phase Transitions Models

Global stability theory is introduced as a tool allowing the classification of mathematical models of phase transitions. The point of view is that a topological structure whose stability controls the transition, can be identified in the process of computation of the partition function. In particular we discuss mean field theories and the two dimensional Ising model. Interesting features are disclosed concerning the classification of the instabilities, such as the number of parameters and possible approximations.     

Pole placement controllers for linear time-delay systems with commensurate point delays

This paper investigates the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled diophantine equations of polynomials. An extra complexity is incorporated to the above design to cancel extra unsuitable dynamics being generated when solving the above diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delaydependent) closed-loop spectrum. However, if the controller is simplified by deleting the above mentioned extra complexity, then the robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is maintained. In the current approach, the finite spectrum assignment is only considered as a particular case to the designer‘s choice of a (delay-dependent) arbitrary spectrum assignment objective.     

Geometric Integration Methods that Preserve Lyapunov Functions

We consider ordinary differential equations (ODEs) with a known Lyapunov function V. To ensure that a numerical integrator reflects the correct dynamical behaviour of the system, the numerical integrator should have V as a discrete Lyapunov function. Only second-order geometric integrators of this type are known for arbitrary Lyapunov functions. In this paper we describe projection-based methods of arbitrary order that preserve any given Lyapunov function. AMS subject classification (2000) 65L05, 65L06, 65L20, 65P40     

Positron trapping in deformed Gd

Positron lifetime and Doppler broadening measurements have been used to study the annealing behaviour of deformed Gd between 290 and 700 K. The observed recovery stage at about 370 K is attributed to dislocations annealing.     

Covariant decomposition and polarizational selection rules for interaction among photons in a moving medium

Starting from the first principles we establish the symmetries under inversions and obtain relativistic tensorial decompositions for multiphoton amplitudes in moving isotropic homogeneous media. Basing on these decompositions we find universal selection rules with respect to polarizations for the processes of photon splitting and junction in a medium, as well as for photon-photon application to nonlinear wave processes.     

Excited-state absorption and 1064-nm end-pumped laser emission of Nd:YVO4 single-crystal fiber grown by laser-heated pedestal growth

We present an investigation of the excited-state absorption and laser emission of a 1.0-at. %-Nd3+-doped YVO4 single-crystal fiber grown by the low-cost and versatile laser-heated pedestal growth technique. Efficient laser emission at 1064 nm was achieved when the fiber was pumped, in an end-pump cavity, by a Ti:sapphire laser at 808 nm. A continuous-wave threshold of 10 mW was observed with an efficiency of 42% with respect to the absorbed pump power and the maximum output power of 200 mW. These results are excellent when compared with those of a commercial bulk crystal adapted to the same cavity (48% efficiency, 250-mW maximum output power). Thus the fibers are characterized as strong candidates for the construction of compact lasers that can also be pumped by low-cost diode lasers.     

Nonstochastic behavior of atomic surface diffusion on Cu(111) down to low temperatures

Atomic diffusion is usually understood as a succession of random, independent displacements of an adatom over the surface's potential energy landscape. Nevertheless, an analysis of molecular dynamics simulations of self-diffusion on Cu(111) demonstrates the existence of different types of correlations in the atomic jumps at all temperatures. Thus, the atomic displacements cannot be correctly described in terms of a random walk model. This fact has a profound impact on the determination and interpretation of diffusion coefficients and activation barriers.     

Enhanced self-diffusion on Cu(111) by trace amounts of s: chemical-reaction-limited kinetics

We find that less than 0.01 monolayer of S can enhance surface self-diffusion on Cu(111) by several orders of magnitude. The measured dependence of two-dimensional island decay rates on S coverage (theta(S)) is consistent with the proposal that Cu3S3 clusters are responsible for the enhancement. Unexpectedly, the decay and ripening are diffusion limited with very low and very high theta(S) but not for intermediate theta(S). To explain this result we propose that surface mass transport in the intermediate region is limited by the rate of reaction to form Cu3S3 clusters on the terraces.     

Direct measurement of decoherence for entanglement between a photon and stored atomic excitation

Violations of a Bell inequality are reported for an experiment where one of two entangled qubits is stored in a collective atomic memory for a user-defined time delay. The atomic qubit is found to preserve the violation of a Bell inequality for storage times up to 21 micros, 700 times longer than the duration of the excitation pulse that creates the entanglement. To address the question of the security of entanglement-based cryptography implemented with this system, an investigation of the Bell violation as a function of the cross correlation between the generated nonclassical fields is reported, with saturation of the violation close to the maximum value allowed by quantum mechanics.