Inhomogeneous Fermi and quantum spin systems on lattices

We study the thermodynamic properties of a certain type of space-inhomogeneous Fermi and quantum spin systems on lattices. We are particularly interested in the case where the space scale of the inhomogeneities stays macroscopic, but very small as compared to the side-length of the box containing fermions or spins. The present study is however not restricted to "macroscopic inhomogeneities" and also includes the (periodic) microscopic and mesoscopic cases. We prove that - as in the homogeneous case - the pressure is, up to a minus sign, the conservative value of a two-person zero-sum game, named here thermodynamic game. Because of the absence of space symmetries in such inhomogeneous systems, it is not clear from the beginning what kind of object equilibrium states should be in the thermodynamic limit. However, we give rigorous statements on correlations functions for large boxes. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4763465]

Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.

Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

Reduced order adaptive models for systems of PDEs using POD

In this work we propose a method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory. The method is based on the combined use of such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations) and the integration of the reduced system, studying the evolution of the modal amplitudes. We integrate the reduced model until our a priori error estimator indicates that our approximation in not accurate. At this point we use again our original numerical code in a short time interval to adapt the POD manifold and continue then with the integration of the reduced model. Application will be made to two model problems: the Ginzburg-Landau equation in transient chaos conditions and the two-dimensional pulsating cavity problem, which describes the motion of liquid in a box whose upper wall is moving back and forth in a quasi-periodic fashion. Finally, we will discuss a way of improving the performance of the method using experimental data or information from numerical simulations

Effect of a variable delay in delayed dynamical systems

We report numerical evidence of the effects of a periodic modulation in the delay time of a delayed dynamical system. By referring to a Mackey-Glass equation and by adding a modula- tion in the delay time, we describe how the solution of the system passes from being chaotic to shadow periodic states. We analyze this transition for both sinusoidal and sawtooth wave mod- ulations, and we give, in the latter case, the relationship between the period of the shadowed orbit and the amplitude of the modulation. Future goals and open questions are highlighted.

Empirical and analytical study of instabilities in hybrid optical bistable systems

As it is well known from the work by Gibbs et al., optical turbulence and periodic oscillations are easily seen in hybrid optical bistable devices when a delay is added to the feedback. Such effects, as it was pointed out by Gibbs, may be used to convert cw laser power into a train of light pulses.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

Vortex pinning vs superconducting wire network: origin of periodic oscillations induced by applied magnetic fields in superconducting films with arrays of nanomagnets

Hybrid magnetic arrays embedded in superconducting films are ideal systems to study the competition between different physical (such as the coherence length) and structural length scales such as are available in artificially produced structures. This interplay leads to oscillation in many magnetically dependent superconducting properties such as the critical currents, resistivity and magnetization. These effects are generally analyzed using two distinct models based on vortex pinning or wire network. In this work, we show that for magnetic dot arrays, as opposed to antidot (i.e. holes) arrays, vortex pinning is the main mechanism for field induced oscillations in resistance R(H), critical current Ic(H), magnetization M(H) and ac-susceptibility χ ac(H) in a broad temperature range. Due to the coherence length divergence at Tc, a crossover to wire network behaviour is experimentally found. While pinning occurs in a wide temperature range up to Tc, wire network behaviour is only present in a very narrow temperature window close to Tc. In this temperature interval, contributions from both mechanisms are operational but can be experimentally distinguished.

Application of the homogenization techniques to the determination of the effective flexure constants of plate structural systems

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.

Frequency encoding in excitable systems with applications to calcium oscillations.

A number of excitable cell types respond to a constant hormonal stimulus with a periodic oscillation in intracellular calcium. The frequency of oscillation is often proportional to the hormonal stimulus, and one says that the stimulus is frequency encoded. Here we develop a theory of frequency encoding in excitable systems and apply it to intracellular calcium oscillations that results from increases in the intracellular level of inositol 1,4,5-triphosphate.

Tilted excitation implies odd periodic resonances

This work was supported by the Brazilian agencies FAPESP and CNPq. MSB also acknowledges the Engineering and Physical Sciences Research Council grant Ref. EP/I032606/1. GID thanks Felipe A. C. Pereira for fruitful discussions.

Automation of periodic reports. Preliminary user's manual.

Transportation Department, Office of the Assistant Secretary for Policy and International Affairs, Washington, D.C.

Data sources on probation, conditional discharge, supervision, and periodic imprisonment in Illinois /

Includes bibliographies.

Application of a coupled ground-surface water flow model to simulate periodic groundwater flow influenced by a sloping boundary, capillarity and vertical flows

Theoretical developments as well as field and laboratory data have shown the influence of the capillary fringe on water table fluctuations to increase with the fluctuation frequency. The numerical solution of a full, partially saturated flow equation can be computationally expensive. In this paper, the influence of the capillary fringe on water table fluctuations is simplified through its parameterisation into the storage coefficient of a fully-saturated groundwater flow model using the complex effective porosity concept [Nielsen, P., Perrochet, P., 2000. Water table dynamics under capillary fringes: experiments and modelling. Advances in Water Resources 23 (1), 503-515; Nielsen, P., Perrochet, P., 2000. ERRATA: water table dynamics under capillary fringes: experiments and modelling (Advances in Water Resources 23 (2000) 503-515). Advances in Water Resources 23, 907-908]. The model is applied to sand flume observations of periodic water table fluctuations induced by simple harmonic forcing across a sloping boundary, analogous to many beach groundwater systems. While not providing information on the moisture distribution within the aquifer, this approach can reasonably predict the water table fluctuations in response to periodic forcing across a sloping boundary. Furthermore, he coupled ground-surface water model accurately predicts the extent of the seepage face formed at the sloping boundary. (C) 2005 Elsevier Ltd. All rights reserved.

Periodic mesoporous organosilica hollow spheres with tunable wall thickness

Periodic mesoporous organosilica (PMO) hollow spheres with tunable wall thickness have been successfully synthesized by a new vesicle and a liquid crystal “dual templating” mechanism, which may be applicable for drug and DNA delivery systems, biomolecular encapsulation, as well as nanoreactors for conducting biological reactions at the molecular levels.