Propagation and organization in lattice random media

We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a one-dimensional lattice whose sites are occupied by scatterers with the following properties: (i) the state of each site is defined by its spin (up or down); (ii) the particle arriving at a site is scattered forward (backward) if the spin is up (down); (iii) the state of the site is modified by the passage of the particle, i.e. the spin of the site where a scattering has taken place, flips ($\uparrow \Leftrightarrow \downarrow$). We consider one dimensional and triangular lattices, for which we give a microscopic description of the dynamics, prove the propagation of a particle through the scatterers, and compute analytically its statistical properties. In particular we prove that, in one dimension, the average propagation velocity is $= 1/(3-2q)$, with $q$ the probability that a site has a spin $\uparrow$, and, in the triangular lattice, the average propagation velocity is independent of the scatterers distribution: $= 1/8$. In both cases, the origin of the propagation is a blocking mechanism, restricting the motion of the particle in the direction opposite to the ultimate propagation direction, and there is a specific re-organization of the spins after the passage of the particle. A detailed mathematical analysis of this phenomenon is, to the best of our knowledge, presented here for the first time.Comment: 30 pages, 15 separate figures (in PostScript); submitted to J. Stat. Phy

Ionized Gas Motions and the Structure of Feedback Near a Forming Globular Cluster in NGC 5253

We observed Brackett $\alpha$ 4.05$\mu$m emission towards the supernebula in NGC 5253 with NIRSPEC on Keck II in adaptive optics mode, NIRSPAO, to probe feedback from its exciting embedded super star cluster (SSC). NIRSPEC's Slit-Viewing Camera was simultaneously used to image the K-band continuum at $\sim$$0.1''$ resolution. We register the IR continuum with HST imaging, and find that the visible clusters are offset from the K-band peak, which coincides with the Br $\alpha$ peak of the supernebula and its associated molecular cloud. The spectra of the supernebula exhibit Br $\alpha$ emission with a strong, narrow core. The linewidths are 65-76 km s$^{-1}$, FWHM, comparable to those around individual ultra-compact HII regions within our Galaxy. A weak, broad (FWHM$\simeq$150-175 km s$^{-1}$) component is detected on the base of the line, which could trace a population of sources with high-velocity winds. The core velocity of Br $\alpha$ emission shifts by +13 km s$^{-1}$ from NE to SW across the supernebula, possibly indicating a bipolar outflow from an embedded object, or linked to a foreground redshifted gas filament. The results can be explained if the supernebula comprises thousands of ionized wind regions around individual massive stars, stalled in their expansion due to critical radiative cooling and unable to merge to drive a coherent cluster wind. Based on the absence of an outflow with large mass loss, we conclude that feedback is currently ineffective at dispersing gas, and the SSC retains enriched material out of which it may continue to form stars.Comment: 24 pages, 9 figure

Jurisdicción multicultural en el Estado liberal: Una visión crítica

Este trabajo sostiene una actitud crítica respecto al llamado “nuevo pluralismo jurídico”.Comienza situando este concepto en una perspectiva histórica, para luego analizar losargumentos feministas a favor de la “acomodación transformativa” de la diversidad religiosaen un pluralismo jurídico basado en el estatus religioso. La aportación de la autora no se ciñea identificar los fallos del pluralismo jurídico, sino que ofrece además un modelo diferente deacomodación transformativa, que descansa en una mezcla de enfoques jurídicos respecto alos problemas que afrontan las mujeres religiosas en una democracia constitucional.Palabras claveIgualdad de género, minorías religiosas, multiculturalismo, pluralismo jurídico,constitucionalismo, derecho personal y de familia.Palabras clave: Igualdad de género, minorías religiosas, multiculturalismo, pluralismo jurídico,constitucionalismo, derecho personal y de familia.Abstract: This paper defends a critical view about the so called “new legal pluralism”. It begins byplacing this concept in an historical perspective, and then analyzing feminist arguments forthe “transformative accommodation” of religious diversity in the form of status based legalpluralism. The author’s contribution is not only the assessing of the flaws in the legal pluralistsolution, but also the offering of a different model of transformative accommodation that restson a mix of legal approaches to the problems faced by religious women in a constitutional democracy.Keywords: Gender equality, religious minorities, multiculturalism, legal pluralism,  constitutionalism, personal and family law

Repensando a privacidade: autonomia, identidade e a controvérsia sobre o aborto

Resumo A partir de um diálogo com a crítica feminista às dicotomias entre o público e o privado, a autora define os limites e contornos do direito à privacidade, considerado um aspecto central à autonomia e ao direito ao corpo. O comunitarismo e as correntes feministas que defendem a superação das fronteiras entre público e privado são criticados pela incapacidade de garantir o respeito às decisões autônomas dos indivíduos, sobretudo no que concerne seu corpo, sua vida afetiva e aspectos relevantes da sua identidade. A garantia da privacidade é vista como algo necessário à afirmação das identidades individuais e à proteção dos indivíduos em relação às práticas e valores majoritários na comunidade em que estão inseridos. O direito ao aborto constitui o direito à privacidade, assim definido. Palavras-chave: privacidade; autonomia; direito; identidades; aborto.   Abstract In a dialogue with feminist criticism to public-private dichotomies, the author defines limits and outlines of the right to privacy, considered as a core aspect of autonomy and the right to the body. Communitarianism and feminist streams that advocate overcoming boundaries between what is public and private are criticized for their inability to guarantee respect for individual’s autonomous decisions, especially regarding their bodies, their affective lives, and relevant aspects of their identities. Guarantee of privacy is seen as necessary to ascertain individual identities and protect individuals from majority values and practices within the communities they are part of. The right to abortion constitutes the right to privacy, thus defined. Key words: privacy; autonomy; rights; identities; abortion

Ewald Sums for One Dimension

We derive analytic solutions for the potential and field in a one-dimensional system of masses or charges with periodic boundary conditions, in other words Ewald sums for one dimension. We also provide a set of tools for exploring the system evolution and show that it's possible to construct an efficient algorithm for carrying out simulations. In the cosmological setting we show that two approaches for satisfying periodic boundary conditions, one overly specified and the other completely general, provide a nearly identical clustering evolution until the number of clusters becomes small, at which time the influence of any size-dependent boundary cannot be ignored. Finally we compare the results with other recent work with the hope of providing clarification over differences these issues have induced. We explain that modern formulations of physics require a well defined potential which is not available if the forces are screened directly.Comment: 2 figures added references expanded discussion of algorithm corrected figures added discussion of screened forc

Services within a busy period of an M/M/1 queue and Dyck paths

We analyze the service times of customers in a stable M/M/1 queue in equilibrium depending on their position in a busy period. We give the law of the service of a customer at the beginning, at the end, or in the middle of the busy period. It enables as a by-product to prove that the process of instants of beginning of services is not Poisson. We then proceed to a more precise analysis. We consider a family of polynomial generating series associated with Dyck paths of length 2n and we show that they provide the correlation function of the successive services in a busy period with (n+1) customers

Nonlinear dynamics of phase separation in thin films

We present a long-wavelength approximation to the Navier-Stokes Cahn-Hilliard equations to describe phase separation in thin films. The equations we derive underscore the coupled behaviour of free-surface variations and phase separation. We introduce a repulsive substrate-film interaction potential and analyse the resulting fourth-order equations by constructing a Lyapunov functional, which, combined with the regularizing repulsive potential, gives rise to a positive lower bound for the free-surface height. The value of this lower bound depends on the parameters of the problem, a result which we compare with numerical simulations. While the theoretical lower bound is an obstacle to the rupture of a film that initially is everywhere of finite height, it is not sufficiently sharp to represent accurately the parametric dependence of the observed dips or `valleys' in free-surface height. We observe these valleys across zones where the concentration of the binary mixture changes sharply, indicating the formation of bubbles. Finally, we carry out numerical simulations without the repulsive interaction, and find that the film ruptures in finite time, while the gradient of the Cahn--Hilliard concentration develops a singularity.Comment: 26 pages, 20 figures, PDFLaTeX with RevTeX4 macros. A thorough analysis of the equations is presented in arXiv:0805.103