Families of periodic orbits for the spatial isosceles 3-body problem

We study the families of periodic orbits of the spatial isosceles 3-body problem (for small enough values of the mass lying on the symmetry axis) coming via the analytic continuation method from periodic orbits of the circular Sitnikov problem. Using the first integral of the angular momentum, we reduce the dimension of the phase space of the problem by two units. Since periodic orbits of the reduced isosceles problem generate invariant two-dimensional tori of the nonreduced problem, the analytic continuation of periodic orbits of the (reduced) circular Sitnikov problem at this level becomes the continuation of invariant two-dimensional tori from the circular Sitnikov problem to the nonreduced isosceles problem, each one filled with periodic or quasi-periodic orbits. These tori are not KAM tori but just isotropic, since we are dealing with a three-degrees-of-freedom system. The continuation of periodic orbits is done in two different ways, the first going directly from the reduced circular Sitnikov problem to the reduced isosceles problem, and the second one using two steps: first we continue the periodic orbits from the reduced circular Sitnikov problem to the reduced elliptic Sitnikov problem, and then we continue those periodic orbits of the reduced elliptic Sitnikov problem to the reduced isosceles problem. The continuation in one or two steps produces different results. This work is merely analytic and uses the variational equations in order to apply Poincar´e’s continuation method.

Matching stages of heavy-ion collision models

Heavy-ion reactions and other collective dynamical processes are frequently described by different theoretical approaches for the different stages of the process, like initial equilibration stage, intermediate locally equilibrated fluid dynamical stage, and final freeze-out stage. For the last stage, the best known is the Cooper-Frye description used to generate the phase space distribution of emitted, noninteracting particles from a fluid dynamical expansion or explosion, assuming a final ideal gas distribution, or (less frequently) an out-of-equilibrium distribution. In this work we do not want to replace the Cooper-Frye description, but rather clarify the ways of using it and how to choose the parameters of the distribution and, eventually, how to choose the form of the phase space distribution used in the Cooper-Frye formula. Moreover, the Cooper-Frye formula is used in connection with the freeze-out problem, while the discussion of transition between different stages of the collision is applicable to other transitions also. More recently, hadronization and molecular dynamics models have been matched to the end of a fluid dynamical stage to describe hadronization and freeze-out. The stages of the model description can be matched to each other on space-time hypersurfaces (just like through the frequently used freeze-out hypersurface). This work presents a generalized description of how to match the stages of the description of a reaction to each other, extending the methodology used at freeze-out, in simple covariant form which is easily applicable in its simplest version for most applications.

Diffusion in stationary flow from mesoscopic nonequilibrium thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of nonequilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation that is compared with others derived from the kinetic theory and projector operator techniques. This equation exhibits violation of the fluctuation-dissipation theorem. By implementing the hydrodynamic regime described by the first moments of the nonequilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose makes it applicable to more complex situations, often encountered in problems of soft-condensed matter, in which not only one but more degrees of freedom are coupled to a nonequilibrium bath.

Fluctuation relation for weakly ergodic aging systems

A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connection with the effective temperatures obtained from the fluctuation-dissipation theorem is discussed

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

Chaotic systems with a null conditional Lyapunov exponent under nonlinear driving.

Control of a chaotic system by homogeneous nonlinear driving, when a conditional Lyapunov exponent is zero, may give rise to special and interesting synchronizationlike behaviors in which the response evolves in perfect correlation with the drive. Among them, there are the amplification of the drive attractor and the shift of it to a different region of phase space. In this paper, these synchronizationlike behaviors are discussed, and demonstrated by computer simulation of the Lorentz model [E. N. Lorenz, J. Atmos. Sci. 20 130 (1963)] and the double scroll [T. Matsumoto, L. O. Chua, and M. Komuro, IEEE Trans. CAS CAS-32, 798 (1985)].

Deformation of Gabor systems

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames 'without inequalities' from lattices to non-uniform sets.

Minimum-uncertaity states and pseudoclassical dynamics. II

The set of initial conditions for which the pseudoclassical evolution algorithm (and minimality conservation) is verified for Hamiltonians of degrees N (N>2) is explicitly determined through a class of restrictions for the corresponding classical trajectories, and it is proved to be at most denumerable. Thus these algorithms are verified if and only if the system is quadratic except for a set of measure zero. The possibility of time-dependent a-equivalence classes is studied and its physical interpretation is presented. The implied equivalence of the pseudoclassical and Ehrenfest algorithms and their relationship with minimality conservation is discussed in detail. Also, the explicit derivation of the general unitary operator which linearly transforms minimum-uncertainty states leads to the derivation, among others, of operators with a general geometrical interpretation in phase space, such as rotations (parity, Fourier).

Variance reduction methods for simulation of densities on Wiener space

We develop a general error analysis framework for the Monte Carlo simulationof densities for functionals in Wiener space. We also study variancereduction methods with the help of Malliavin derivatives. For this, wegive some general heuristic principles which are applied to diffusionprocesses. A comparison with kernel density estimates is made.

Simple and fast methods based on solid-phase extraction coupled to liquid chromatography with UV detection for the monitoring of caffeine in natural and waste waters as marker of anthropogenic impact

Two concentration methods for fast and routine determination of caffeine (using HPLC-UV detection) in surface, and wastewater are evaluated. Both methods are based on solid-phase extraction (SPE) concentration with octadecyl silica sorbents. A common “offline” SPE procedure shows that quantitative recovery of caffeine is obtained with 2 mL of an elution mixture solvent methanol-water containing at least 60% methanol. The method detection limit is 0.1 μg L−1 when percolating 1 L samples through the cartridge. The development of an “online” SPE method based on a mini-SPE column, containing 100 mg of the same sorbent, directly connected to the HPLC system allows the method detection limit to be decreased to 10 ng L−1 with a sample volume of 100 mL. The “offline” SPE method is applied to the analysis of caffeine in wastewater samples, whereas the “on-line” method is used for analysis in natural waters from streams receiving significant water intakes from local wastewater treatment plants

Thickening of phase change materials (PCM) to avoid segregation

Estudi elaborat a partir d’una estada a Çukurova University, Turquia, al juliol del 2006. L’emmagatzematge d’energia tèrmica ha atret interès en aplicacions tèrmiques com l’aigua calenta, la calefacció i l’aire condicionat. Aquests sistemes són útils per corregir la no coincidència entre la oferta i la demanda d’energia. Principalment hi ha dos tipus de sistemes d’emmagatzematge d’energia tèrmica, emmagatzematge amb calor sensible i amb calor latent. L’emmagatzematge amb calor latent és particularment atractiu degut a la seva habilitat de donar una densitat d’emmagatzematge d’energia més alt i la seva característica d’emmagatzemar calor a una temperatura constant corresponent a la temperatura de transició de fase de la substància emmagatzemadora de calor. Les salts hidratades orgàniques tenen certes avantatges com a materials d’emmagatzematge de calor latent sobre els materials orgànics. En canvi, quan les salts hidratades s’utilitzen com a materials de canvi de fase (PCM) apareixen alguns problemes en les aplicacions d’emmagatzematge de calor latent. Aquests són el subrefredament de les salts hidratades quan es congelen degut a les seves dèbils propietats de nucleació, i la separació de fase que hi apareix degut a una fusió incongruent. En aquest estudi, s’estabilitza sal de Glauber (Na2SO4.10H2O) amb diferents concentracions de poliacrilamida i gelatina per prevenir la fusió incongruent. Per prevenir el subrefredament s’utilitza un agent nucleant amb una estructura cristal•lina semblant a la de la sal de Glauber. La capacitat d’emmagatzematge de calor de les mostres de PCM estabilitzades amb diferents concentracions de gels polimèrics es determinen amb DCS i amb el mètode T-history.

On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

A right to a national space of communication? : on Stateless nations, their right to a space of communication of their own

Hem establert les bases metodològiques i teòriques per investigar la pregunta “Tenen les nacions sense estat el dret de controlar el seu propi espai de comunicació?”. La investigació ajusta el concepte d’espai de comunicació a la teoria política, cercant els seus límits en els drets individuals i, des de la perspectiva del liberalisme 2, aportant la justificació del seu control en quant que plataforma que incideix en la conservació i supervivència d’una cultura nacional. El primer article i fase de la tesi és l’adaptació i definició del concepte espai de comunicació. Fins ara, la recerca ha proposat diferents models d’espai de comunicació entenent si es tracta d’una visió emfatitzant la distribució i la producció de material marcat amb els símbols de la identitat nacional de la societat emissora, o bé si emfatitza la idea d’un espai de circulació de fluxos comunicatiu ajustat a un territori tradicionalment vinculat a una identitat nacional o nació sense estat. Igualment, es distingeix la dimensió d’emissió –sortir del territori al món- i la de recepció –fluxos informatius rebuts des del món al territori, concretament, al ciutadà; el paper d’intervenció de les institucions democràtiques és diferent en una dimensió o una altra i, per tant, també són diferents els drets afectats i les teories o principis que neguen o justifiquen el control de l’espai de comunicació. També s’ha indagat en les teories sobre els efectes cognitius dels mitjans de comunicació per relacionar-los amb la construcció nacional com a cohesió simbòlica i cultural. Si bé els mitjans no poden fer canviar de pensament immediatament, sí que poden conformar a llarg termini una percepció nacional general. Una comunitat és imaginada, donada la distància física dels seus components, i la comunicació social és, juntament amb l’educació, el principal factor de construcció nacional, avui en dia.

Industrial Location and Space: New Insights

This paper tries to resolve some of the main shortcomings in the empirical literature of location decisions for new plants, i.e. spatial effects and overdispersion. Spatial effects are omnipresent, being a source of overdispersion in the data as well as a factor shaping the functional relationship between the variables that explain a firm’s location decisions. Using Count Data models, empirical researchers have dealt with overdispersion and excess zeros by developments of the Poisson regression model. This study aims to take this a step further, by adopting Bayesian methods and models in order to tackle the excess of zeros, spatial and non-spatial overdispersion and spatial dependence simultaneously. Data for Catalonia is used and location determinants are analysed to that end. The results show that spatial effects are determinant. Additionally, overdispersion is descomposed into an unstructured iid effect and a spatially structured effect. Keywords: Bayesian Analysis, Spatial Models, Firm Location. JEL Classification: C11, C21, R30.