Soliton solutions and cosmological gravitational waves

We examine plane-symmetric cosmological solutions to Einstein's equations which can be generated by the "soliton" technique, using the homogeneous Bianchi solutions as seeds and arbitrary numbers of real or complex poles. In some circumstances, these solutions can be interpreted as "incipient" gravitational waves on the Bianchi background. At early times they look like nonlinear inhomogeneities propagating at nearly the speed of light ("gravisolitons"), while at late times they look like cosmological gravitational waves.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in three dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature (London) 409, 692 (2001)] that, even with no evidence of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas¿low-density-liquid (LDL) critical point, and the other in a gas¿high-density-liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the three-parameter space of the soft-core potential and perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram, we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.

On a class of exact solutions to the Fokker-Planck equations

In this paper we study under which circumstances there exists a general change of gross variables that transforms any FokkerPlanck equation into another of the OrnsteinUhlenbeck class that, therefore, has an exact solution. We find that any FokkerPlanck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo and Gompertz models.

Canonical formalism for path dependent Lagrangians. Coupling constant expansions

A canonical formalism obtained for path-dependent Lagrangians is applied to Fokker-type Lagrangians. The results are specialized for coupling constant expansions and later on are applied to relativistic systems of particles interacting through symmetric scalar and vector mesodynamics and electrodynamics.

Petrou types D and II perfect-fluid solutions in generalized Kerr-Schild form.

Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized KerrSchild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied. Finally, a detailed analysis of a new class of spherically symmetric static perfect-fluid metrics is given.

Valence-bond treatment of distortions in polyacene polymers

Distortions of polyacene polymers are studied within a many-body valence-bond framework using a powerful transfer-matrix technique for the valence-bond (or Heisenberg) model of the system. The computations suggest that the ground-state geometry is either totally symmetric or possibly exhibits a slight (A2 or B2 symmetry) bond-alternation distortion. The lowest-energy (nonsymmetric, in-plane) distortions are the A2 and B2 modes, which, within our approximations, are degenerate.

Asymmetric Little spin-Glass model

We study the static properties of the Little model with asymmetric couplings. We show that the thermodynamics of this model coincides with that of the Sherrington-Kirkpatrick model, and we compute the main finite-size corrections to the difference of the free energy between these two models and to some clarifying order parameters. Our results agree with numerical simulations. Numerical results are presented for the symmetric Little model, which show that the same conclusions are also valid in this case.

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

Polyconductivity in polypyrrole: the correlated electron glass

p-toluensulfonate doped polypyrrole ~PPy!, undergoes an electric-field induced reversible transition from an insulating state to a highly conductive one. The spatially average field can be as small as 200 V/cm, when the temperature of the sample is below 20 K. The applied electric field leads to a sharp jump in the value of the current to a value which is nearly five orders of magnitude higher than before. When the applied electric field is reduced to below a critical value, the system switches back to a low conductive state. The effect is reversible, symmetric in voltage, and reproducible for different samples. The switching is, we believe, an electronic glass melting transition and it is due to the disordered, highly charged granular nature of PPy.

Polyconductivity in polypyrrole: The correlated electron gas

p-toluensulfonate doped polypyrrole (PPy), undergoes an electric-field induced reversible transition from an insulating state to a highly conductive one. The spatially average field can be as small as 200 V/cm, when the temperature of the sample is below 20 K. The applied electric field leads to a sharp jump in the value of the current to a value which is nearly five orders of magnitude higher than before. When the applied electric field is reduced to below a critical value, the system switches back to a low conductive state. The effect is reversible, symmetric in voltage, and reproducible for different samples. The switching is, we believe, an electronic glass melting transition and it is due to the disordered, highly charged granular nature of PPy.

Financial Integration, Trade Openness and International Transmission

[cat] Com afecten l’obertura comercial i financera a la volatilitat macroeconòmica? La literatura existent, tant empírica com teòrica, no ha assolit encara un consens. Aquest article usa un model microfonamentat de dos països simètrics amb entrada endògena d’empreses per estudiar-ho. L’anàlisis es du a terme per tres règims econòmics diferents amb diferents nivells d’integració internacional: una economia tancada, una autarquia financera i una integració plena. Es consideren diversos nivells d’obertura comercial, en forma de biaix domèstic de la demanda i l’economia pot patir pertorbacions en la productivitat del treball i en innovació. El model conclou que la incertesa macroeconòmica, representada principalment per la volatilitat del consum, la producció i la relació real d’intercanvi internacional, depèn del grau d’obertura i del tipus de pertorbació.

An overall statistic for testing symmetry in social interactions

The present work focuses the attention on the skew-symmetry index as a measure of social reciprocity. This index is based on the correspondence between the amount of behaviour that each individual addresses to its partners and what it receives from them in return. Although the skew-symmetry index enables researchers to describe social groups, statistical inferential tests are required. The main aim of the present study is to propose an overall statistical technique for testing symmetry in experimental conditions, calculating the skew-symmetry statistic (Φ) at group level. Sampling distributions for the skew- symmetry statistic have been estimated by means of a Monte Carlo simulation in order to allow researchers to make statistical decisions. Furthermore, this study will allow researchers to choose the optimal experimental conditions for carrying out their research, as the power of the statistical test has been estimated. This statistical test could be used in experimental social psychology studies in which researchers may control the group size and the number of interactions within dyads.

Effects of anomalous propagation conditions on weather radar observations

In this chapter our objective is to provide an overview of the effects of anomalous propagation conditions on weather radar observations, based mostly on studies performed by the authors during the last decade, summarizing results from recent publications, presentations, or unpublished material. We believe this chapter may be useful as an introductory text for graduate students, or researchers and practitioners dealing with this topic. Throughout the text a spherical symmetric atmosphere is assumed and the focus is on the occurrence of ground and sea clutter and subsequent problems for weather radar applications. Other related topics such as long-path, over-the-horizon propagation and detection of radar targets (either clutter or weather systems) at long ranges is not considered here; however readers should be aware of the potential problems these phenomena may have as range aliasing may cause these echoes appear nearer than they are ¿ for more details see the discussion about second trip echoes by Zrnic, this volume.

A statistical procedure for testing social reciprocity at group, dyadic and individual levels

This paper examines statistical analysis of social reciprocity, that is, the balance between addressing and receiving behaviour in social interactions. Specifically, it focuses on the measurement of social reciprocity by means of directionality and skew-symmetry statistics at different levels. Two statistics have been used as overall measures of social reciprocity at group level: the directional consistency and the skew-symmetry statistics. Furthermore, the skew-symmetry statistic allows social researchers to obtain complementary information at dyadic and individual levels. However, having computed these measures, social researchers may be interested in testing statistical hypotheses regarding social reciprocity. For this reason, it has been developed a statistical procedure, based on Monte Carlo sampling, in order to allow social researchers to describe groups and make statistical decisions.