Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions

The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general co-variance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension $D = 2m$ and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in $D = 2m$. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, $R \sqrt{-g} = \partial_j R^j$ for a doublet of functions $R^j = (R^0,R^1)$ which depends only on the metric and its first derivatives. We explicitly construct families of such R^j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in $D = 4$. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.Comment: 15 pages, no figure

Self-phoretic oscillatory motion in a harmonic trap

We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with existing results for free particles or particles in a bounded domain, we find that the system exhibits a transition between an immobile phase, where the particle stays at the center of the trap, and an oscillatory state. We perform an exact analysis giving access to the bifurcation threshold, as well as the frequency of oscillations and their amplitude near the threshold. Our analysis also characterizes the shape of two-dimensional oscillations, that take place along a circle or a straight line. Our results are confirmed by numerical simulations.Comment: 10 pages 8 figure

Lorentz violating kinematics: Threshold theorems

Recent tentative experimental indications, and the subsequent theoretical speculations, regarding possible violations of Lorentz invariance have attracted a vast amount of attention. An important technical issue that considerably complicates detailed calculations in any such scenario, is that once one violates Lorentz invariance the analysis of thresholds in both scattering and decay processes becomes extremely subtle, with many new and naively unexpected effects. In the current article we develop several extremely general threshold theorems that depend only on the existence of some energy momentum relation E(p), eschewing even assumptions of isotropy or monotonicity. We shall argue that there are physically interesting situations where such a level of generality is called for, and that existing (partial) results in the literature make unnecessary technical assumptions. Even in this most general of settings, we show that at threshold all final state particles move with the same 3-velocity, while initial state particles must have 3-velocities parallel/anti-parallel to the final state particles. In contrast the various 3-momenta can behave in a complicated and counter-intuitive manner.Comment: V1: 32 pages, 6 figures, 3 tables. V2: 5 references adde

Observation of two-wave structure in strongly nonlinear dissipative granular chains

In a strongly nonlinear viscous granular chain under conditions of loading that exclude stationary waves (e.g., impact by a single grain) we observe a pulse that consists of two interconnected but distinct parts. One is a leading narrow "primary pulse" with properties similar to a solitary wave in a "sonic vacuum." It arises from strong nonlinearity and discreteness in the absence of dissipation, but now decays due to viscosity. The other is a broad, much more persistent shock-like "secondary pulse" trailing the primary pulse and caused by viscous dissipation. The medium behind the primary pulse is transformed from a "sonic vacuum" to a medium with finite sound speed. When the rapidly decaying primary pulse dies, the secondary pulse continues to propagate in the "sonic vacuum," with an oscillatory front if the viscosity is relatively small, until its eventual (but very slow) disintegration. Beyond a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shock-like attenuating pulse which now exhibits a nonoscillatory front

The Domination Number of Grids

In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.Comment: 12 pages, 4 figure

Spacetime Symmetries and Kepler's Third Law

The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler's third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a simple, covariant condition on the norm of the associated helical Killing vector field. This unusual derivation can be used to illustrate some concepts of prime importance in a general relativity course, including those of Killing field, covariance, coordinate dependence, and gravitational redshift.Comment: 11 pages, 3 figures; minor changes and text improvements; matches version to appear in Class. Quant. Gra

Resíduo desidratado de vitivinícolas do Vale do São Francisco associado a diferentes fontes energéticas na alimentação de ovinos: desempenho animal.

Objetivou-se com a realização deste trabalho avaliar o ganho de peso e conversão alimentar em ovinos confinados recebendo dietas contendo resíduo de vitivinícolas associado a diferentes fontes energéticas. Foram utilizados 18 ovinos sem padrão racial definido, não castrados, com peso médio de 23 kg e oito meses de idade. O período experimental constou de 63 dias, sendo as dietas compostas de 50% de resíduo de vitivinícolas e 50% de concentrados energéticos: grão de milho moído (Zea mays), raspa de mandioca (Manihot esculenta) enriquecida com 1,8% de uréia e farelo de palma forrageira (Opuntia ficus) enriquecido com 1,1% de uréia. Para determinação do ganho de peso os animais foram pesados no início do experimento e a cada sete dias e, para coversão alimentar foi feita a relação entre o consumo de matéria seca e ganho de peso total num período de 63 dias. Os ganhos de peso médio diários foram de 117, 71 e 132g; a conversão alimentar 9,50, 13,28 e 11,30, respectivamente para as combinações resíduo e grão de milho moído, raspa de mandioca e farelo de palma. As médias diárias de ganho de peso vivo obtido pelos ovinos ao longo do período de engorda revelaram um bom potencial forrageiro do resíduo de vitivinícolas combinado as diferentes fontes energéticas

Complex microwave conductivity of Na-DNA powders

We report the complex microwave conductivity, $\sigma=\sigma_1-i\sigma_2$, of Na-DNA powders, which was measured from 80 K to 300 K by using a microwave cavity perturbation technique. We found that the magnitude of $\sigma_1$ near room temperature was much larger than the contribution of the surrounding water molecules, and that the decrease of $\sigma_1$ with decreasing temperature was sufficiently stronger than that of the conduction of counterions. These results clearly suggest that the electrical conduction of Na-DNA is intrinsically semiconductive.Comment: 16 pages, 7 figure

Anomalous magnetic moment in parity-conserving QED3

In this article we derive the anomalous magnetic moment of fermions in (2+1)-dimensional parity-conserving QED3, in the presence of an externally applied constant magnetic field. We use a spectral representation of the photon propagator to avoid infrared divergences. We also discuss the scaling with the magnetic field intensity in the case of strong external fields, where there is dynamical mass generation for fermions induced by the magnetic field itself (magnetic catalysis). The results of this paper may be of relevance to the physics of high-temperature superconductors.Comment: 27 pages LATEX, three eps figures incorporate

Lectures on the functional renormalization group method

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scalar theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.Comment: 47 pages, 11 figures, final versio