3D gravity and non-linear cosmology

By the inclusion of an additional term, non-linear in the scalar curvature $R$, it is tested if dark energy could rise as a geometrical effect in 3D gravitational formulations. We investigate a cosmological fluid obeying a non-polytropic equation of state (the van der Waals equation) that is used to construct the energy-momentum tensor of the sources, representing the hypothetical inflaton in gravitational interaction with a matter contribution. Following the evolution in time of the scale factor, its acceleration, and the energy densities of constituents it is possible to construct the description of an inflationary 3D universe, followed by a matter dominated era. For later times it is verified that, under certain conditions, the non-linear term in $R$ can generate the old 3D universe in accelerated expansion, where the ordinary matter is represented by the barotropic limit of the van der Waals constituent.Comment: 7 pages, to appear in Mod. Phys. Let

Non-linear terms in 2D cosmology

In this work we investigate the behavior of two-dimensional (2D) cosmological models, starting with the Jackiw-Teitelboim (JT) theory of gravitation. A geometrical term, non-linear in the scalar curvature $R$, is added to the JT dynamics to test if it could play the role of dark energy in a 2D expanding universe. This formulation makes possible, first, the description of an early (inflationary) 2D universe, when the van der Waals (vdW) equation of state is used to construct the energy-momentum tensor of the gravitational sources. Second, it is found that for later times the non-linear term in $R$ can generate an old 2D universe in accelerated expansion, where an ordinary matter dominated era evolves into a decelerated/accelerated transition, giving to the dark energy effects a geometrical origin. The results emerge through numerical analysis, following the evolution in time of the scale factor, its acceleration, and the energy densities of constituents.Comment: tex file plus figures in two zipped files. To appear in Europhys. Let

Large deviations for non-uniformly expanding maps

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average decays to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states. The corrections added to the published version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having pointed several errors in the statements and proofs, this is a correction to published article answering those comments. List of main changes in a new last sectio

NUMERICAL STUDY OF COOLING BY TANGENTIAL SYNTHETIC JET

Modern electronics are becoming more compact and with higher processing power, which translates into a demand for higher heat dissipation. Current electronic "coolers," which are based on the combination of fans and heat sinks, are becoming unable to provide sufficient heat dissipation since they rely primarily on generating large volumetric flowrates of air to achieve their results. As an alternative, synthetic jets are under consideration due to their known property to enhance turbulence and heat transfer. Synthetic jets are produced by the oscillation of a membrane in a sealed cavity equipped with an orifice. For this study, a numerical model of channel mounted with a heating element on one surface and a synthetic jet directed to blow along the wall was constructed on ANSYS CFX. Heat dissipation provided by the synthetic jet was analyzed with respect to changes in Reynolds number, pulsing frequency and placement of the heated element. Results were compared to a conventional technique represented by a steady channel flow of equivalent mass flow rate to the average flow induced by the synthetic jet. Results showed that the synthetic jet formed a thin layer of intense vorticity along the targeted surface with cooling greatly outperforming conventional techniques. Synthetic jet cooling was also determined to be most affected by jet velocity and Reynolds number while pulsing frequency and placement of the heated element were not as influential

The Dynamical State of Barnard 68: A Thermally Supported, Pulsating Dark Cloud

We report sensitive, high resolution molecular-line observations of the dark cloud Barnard 68 obtained with the IRAM 30-m telescope. We analyze spectral-line observations of C18O, CS(2--1), C34S(2--1), and N2H+(1--0) in order to investigate the kinematics and dynamical state of the cloud. We find extremely narrow linewidths in the central regions of the cloud. These narrow lines are consistent with thermally broadened profiles for the measured gas temperature of 10.5 K. We determine the thermal pressure to be a factor 4 -- 5 times greater than the non-thermal (turbulent) pressure in the central regions of the cloud, indicating that thermal pressure is the primary source of support against gravity in this cloud. This confirms the inference of a thermally supported cloud drawn previously from deep infrared extinction measurements. The rotational kinetic energy is found to be only a few percent of the gravitational potential energy, indicating that the contribution of rotation to the overall stability of the cloud is insignificant. Finally, our observations show that CS line is optically thick and self-reversed across nearly the entire projected surface of the cloud. The shapes of the self-reversed profiles are asymmetric and are found to vary across the cloud in such a manner that the presence of both inward and outward motions are observed within the cloud. Moreover, these motions appear to be globally organized in a clear and systematic alternating spatial pattern which is suggestive of a small amplitude, non-radial oscillation or pulsation of the outer layers of the cloud about an equilibrium configuration.Comment: To appear in the Astrophysical Journal; 23 pages, 8 figures; Manuscript and higher resolution images can be obtained at http://cfa-www.harvard.edu/~ebergin/pubs_html/b68_vel.htm

Error threshold in the evolution of diploid organisms

The effects of error propagation in the reproduction of diploid organisms are studied within the populational genetics framework of the quasispecies model. The dependence of the error threshold on the dominance parameter is fully investigated. In particular, it is shown that dominance can protect the wild-type alleles from the error catastrophe. The analysis is restricted to a diploid analogue of the single-peaked landscape.Comment: 9 pages, 4 Postscript figures. Submitted to J. Phy. A: Mat. and Ge

Modeling of tension–compression asymmetry and orthotropy on metallic materials: numerical implementation and validation

The details concerning the implementation of the yield criterion developed by Cazacu et al. 2006 (CPB06), which accounts for both tension–compression asymmetry and orthotropy of the plastic flow, in the fully implicit FE solver DD3IMP (contraction of ‘Deep Drawing 3-D IMPlicit') are presented in this work. The implemented constitutive model is extensively described, including the analytical first and second order derivatives required to the stress update algorithm. A set of anisotropy parameters describing the mechanical behavior of two metallic materials at room temperature, namely Zirconium and AZ31-Mg alloy, are identified with the DD3MAT (contraction for ‘Deep Drawing 3-D MATerial’) in-house code (Alves, 2004) [2]. The anisotropy parameters are identified for both the CPB06 and the Cazacu and Barlat (2001) (CB2001) yield criteria, in order to emphasize the importance and role of the strength differential effect. The results clearly show that the CPB06 yield criterion is able to accurately describe both the in-plane anisotropy and tension–compression asymmetry, as well a different anisotropic behavior in uniaxial tension and uniaxial compression. The numerical simulation of a four-point bending test is performed, considering different orientations of the beam, i.e. of the hard/soft to deform direction relatively to the load direction, allowing to validate the implementation. The results obtained with the CPB06 show its ability to describe with accuracy the strain fields in the beam's central cross-section, the distribution of the tensile and compressive layers and, consequently, the shift of the neutral layer. The comparison with the results obtained with CB2001 indicates that the strength differential effect affects the final deformed shape of the beam, particularly for materials exhibiting strong tension–compression asymmetry.The authors gratefully acknowledge the financial support of the Portuguese Foundation for Science and Technology (FCT), Portugal via the projects PTDC/EME-TME/118420/2010, UID/EMS/00285/2013 and by FEDER, Portugal funds through the program COMPETE - Programa Operational Factores de Competitividade, under the project CENTRO-07-0224-FEDER-002001 (MT4MOBI). The first author is also grateful to the FCT for the Ph.D. Grant SFRH/BD/98545/2013.info:eu-repo/semantics/publishedVersio