Phase growth in bistable systems with impurities

A system of coupled chaotic bistable maps on a lattice with randomly distributed impurities is investigated as a model for studying the phenomenon of phase growth in nonuniform media. The statistical properties of the system are characterized by means of the average size of spatial domains of equivalent spin variables that define the phases. It is found that the rate at which phase domains grow becomes smaller when impurities are present and that the average size of the resulting domains in the inhomogeneous state of the system decreases when the density of impurities is increased. The phase diagram showing regions where homogeneous, heterogeneous, and chessboard patterns occur on the space of parameters of the system is obtained. A critical boundary that separates the regime of slow growth of domains from the regime of fast growth in the heterogeneous region of the phase diagram is calculated. The transition between these two growth regimes is explained in terms of the stability properties of the local phase configurations. Our results show that the inclusion of spatial inhomogeneities can be used as a control mechanism for the size and growth velocity of phase domains forming in spatiotemporal systems.Comment: 7 pages, 12 figure

Firm Heterogeneity and International Trade: Implications for Agricultural and Food Industries

This article summarizes key insights from the firm heterogeneity and trade literature, the theme-day topic of the 2006 IATRC Annual Meeting, and draws their implications for the agricultural and food industriesInternational Relations/Trade,

Noncanonical Quantization of Gravity. I. Foundations of Affine Quantum Gravity

The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of constraints, a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel Hilbert space. Constraints are introduced following the projection operator method which involves no gauge fixing, no complicated moduli space, nor any auxiliary fields. The result, which is only qualitatively sketched in the present paper, involves another reproducing kernel with which inner products are defined for the physical Hilbert space and which is obtained through a reduction of the original reproducing kernel. Several of the steps involved in this general analysis are illustrated by means of analogous steps applied to one-dimensional quantum mechanical models. These toy models help in motivating and understanding the analysis in the case of gravity.Comment: minor changes, LaTeX, 37 pages, no figure

A note on the cylindrical collapse of counter-rotating dust

We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that--for the classes of solutions discussed herein--from regular initial data a curvature singularity inevitably develops, and no apparent horizons form, thus in accord with the spirit of the hoop conjecture.Comment: 8 pages, LaTeX, ijmpd macros (included), 1 eps figure; accepted for publication in Int. J. Mod. Phys.

Phase ordering induced by defects in chaotic bistable media

The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin variables that define the phases. It is found that spatial defects can induce the formation of domains in bistable spatiotemporal systems. The minimum distance between defects acts as parameter for a transition from a homogeneous state to a heterogeneous regime where two phases coexist The critical exponent of this transition also exhibits a transition when the coupling is increased, indicating the presence of a new class of domain where both phases coexist forming a chessboard pattern.Comment: 3 pages, 3 figures, Accepted in European Physics Journa

Nota sobre la pirofilita de Águilas (Murcia, SE de España)

Se hace un estudio previo del yacimiento de la pirofilita de Águilas (Provincia de Murcia, SE de España). Pirofilita, cuarzo, micas blancas y caolinita son los constituyentes de estas mineralizaciones filonianas que encajan enfisuras de las filitas del complejo Alpujárride. El origen de la pirofilita está relacionado con un proceso de metamorfismoregional de un material sedimentario rico en aluminio. La principal reacciónimplicada seria:1 Caolinita + 2 SiO2 = 1 Pirofilita + H2OSe contempla asimismo como posibilidad alternativa, un proceso de segregación metamórfica. Se dan datos ópticos, de análisis químico y de difracción de Rayos X

The role of the mother as a para-professional helper in the pre-school setting

The present study compared deployment of working—class mothers,\ud teachers and nursery nurses in day—to—day activities in pre—school set—\ud tings. Naturalistic observation was used in two pre—schools run on\ud free—play lines located in socially deprived areas. Mothers were\ud observed in the room their "Own" children attended. Teachers and mothers\ud were studied alone and with the other present in order to discover the\ud extent to which the presence of one affects the behaviour of the other.\ud Time spent by mothers in direct contact; indirect contact, dealing with\ud equipment, interaction with adults and not involved was compared with\ud that spent by the other two groups. Direct and indirect contact were\ud analysed at two different levels: (a) all time mothers spent with chil—\ud dren was considered, (b) time spent with "Own" children was disregarded.\ud Significantly larger within group differences were observed for mothers\ud when compared with teachers and nursery nurses in direct contact and no\ud activity. Significant differences in direct contact were observed for\ud mothers compared with the other two groups. Significant differences in\ud direct contact were due to: (a) wider within group differences for the\ud group of mothers than nursery nurses; (b) more time spent by teachers\ud than mothers. Time spent involved in no activity showed: (a) signifi—\ud cantly more varied behaviour than teachers, (b) significantly more time\ud than nursery nurses. Behaviours observed for mothers appeared to be\ud influenced by how they became involved; those invited by teachers show—\ud ing more time with the children and less not involved. It was also\ud found that teachers spent little time with "Own" children (large within\ud group differences were found). However, teacher—"Own" child interaction\ud was found to be somewhat lessened for some children due to the presence\ud of the mothers. Mothers in both conditions spent significantly more time\ud with their "Own" children than teachers and nursery nurses