Dynamics of viscous dissipative gravitational collapse: A full causal approach

The Misner and Sharp approach to the study of gravitational collapse is extended to the viscous dissipative case in, both, the streaming out and the diffusion approximations. The dynamical equation is then coupled to causal transport equations for the heat flux, the shear and the bulk viscosity, in the context of Israel--Stewart theory, without excluding the thermodynamics viscous/heat coupling coefficients. The result is compared with previous works where these later coefficients were neglected and viscosity variables were not assumed to satisfy causal transport equations. Prospective applications of this result to some astrophysical scenarios are discussed.Comment: 22 pages Latex. To appear in Int. J. Mod. Phys. D. Typos correcte

On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks

Most of our knowledge on the nonlinear development of the magneto-rotational instability (MRI) relies on the results of numerical simulations employing the shearing box (SB) approximation. A number of difficulties arising from this approach have recently been pointed out in the literature. We thoroughly examine the effects of the assumptions made and numerical techniques employed in SB simulations. This is done in order to clarify and gain better understanding of those difficulties as well as of a number of additional serious problems, raised here for the first time, and of their impact on the results. Analytical derivations and estimates as well as comparative analysis to methods used in the numerical study of turbulence are used. Numerical experiments are performed to support some of our claims and conjectures. The following problems, arising from the (virtually exclusive) use of the SB simulations as a tool for the understanding and quantification of the nonlinear MRI development in disks, are analyzed and discussed: (i) inconsistencies in the application of the SB approximation itself; (ii) the limited spatial scale of the SB; (iii) the lack of convergence of most ideal MHD simulations; (iv) side-effects of the SB symmetry and the non-trivial nature of the linear MRI; (v) physical artifacts arising on the too small box scale due to periodic boundary conditions. The computational and theoretical challenge posed by the MHD turbulence problem in accretion disks cannot be met by the SB approximation, as it has been used to date. A new strategy to confront this challenge is proposed, based on techniques widely used in numerical studies of turbulent flows - developing (e.g., with the help of local numerical studies) a sub-grid turbulence model and implementing it in global calculations.Comment: Accepted for publication in Astronomy and Astrophysic

The Sagnac Phase Shift suggested by the Aharonov-Bohm effect for relativistic matter beams

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a a formal analogy with the the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.Comment: 18 pages, LaTeX, 2 EPS figures. To appear in General Relativity and Gravitatio

Strong-field dynamo action in rapidly rotating convection with no inertia

The earth's magnetic field is generated by dynamo action driven by convection in the outer core. For numerical reasons, inertial and viscous forces play an important role in geodynamo models; however, the primary dynamical balance in the earth's core is believed to be between buoyancy, Coriolis, and magnetic forces. The hope has been that by setting the Ekman number to be as small as computationally feasible, an asymptotic regime would be reached in which the correct force balance is achieved. However, recent analyses of geodynamo models suggest that the desired balance has still not yet been attained. Here we adopt a complementary approach consisting of a model of rapidly rotating convection in which inertial forces are neglected from the outset. Within this framework we are able to construct a branch of solutions in which the dynamo generates a strong magnetic field that satisfies the expected force balance. The resulting strongly magnetized convection is dramatically different from the corresponding solutions in which the field is weak

Conservation laws for vacuum tetrad gravity

Ten conservation laws in useful polynomial form are derived from a Cartan form and Exterior Differential System (EDS) for the tetrad equations of vacuum relativity. The Noether construction of conservation laws for well posed EDS is introduced first, and an illustration given, deriving 15 conservation laws of the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS and tetrad gravity EDS have parallel structures, with their numbers of dependent variables, numbers of generating 2-forms and generating 3-forms, and Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding symmetries with the same Lorentz algebra, and 10 corresponding conservation laws.Comment: Final version with additional reference

Oscillations and secondary bifurcations in nonlinear magnetoconvection

Complicated bifurcation structures that appear in nonlinear systems governed by partial differential equations (PDEs) can be explained by studying appropriate low-order amplitude equations. We demonstrate the power of this approach by considering compressible magnetoconvection. Numerical experiments reveal a transition from a regime with a subcritical Hopf bifurcation from the static solution, to one where finite-amplitude oscillations persist although there is no Hopf bifurcation from the static solution. This transition is associated with a codimension-two bifurcation with a pair of zero eigenvalues. We show that the bifurcation pattern found for the PDEs is indeed predicted by the second-order normal form equation (with cubic nonlinearities) for a Takens-Bogdanov bifurcation with Z2 symmetry. We then extend this equation by adding quintic nonlinearities and analyse the resulting system. Its predictions provide a qualitatively accurate description of solutions of the full PDEs over a wider range of parameter values. Replacing the reflecting (Z2) lateral boundary conditions with periodic [O(2)] boundaries allows stable travelling wave and modulated wave solutions to appear; they could be described by a third-order system

Odorant-Binding Proteins and Chemosensory Proteins in Spodoptera frugiperda: From Genome-Wide Identification and Developmental Stage-Related Expression Analysis to the Perception of Host Plant Odors, Sex Pheromones, and Insecticides

Spodoptera frugiperda is a worldwide generalist pest with remarkable adaptations to environments and stresses, including developmental stage-related behavioral and physiological adaptations, such as diverse feeding preferences, mate seeking, and pesticide resistance. Insects' odorant-binding proteins (OBPs) and chemosensory proteins (CSPs) are essential for the chemical recognition during behavioral responses or other physiological processes. The genome-wide identification and the gene expression patterns of all these identified OBPs and CSPs across developmental stage-related S. frugiperda have not been reported. Here, we screened for genome-wide SfruOBPs and SfruCSPs, and analyzed the gene expression patterns of SfruOBPs and SfruCSPs repertoires across all developmental stages and sexes. We found 33 OBPs and 22 CSPs in the S. frugiperda genome. The majority of the SfruOBP genes were most highly expressed in the adult male or female stages, while more SfruCSP genes were highly expressed in the larval or egg stages, indicating their function complementation. The gene expression patterns of SfruOBPs and SfruCSPs revealed strong correlations with their respective phylogenic trees, indicating a correlation between function and evolution. In addition, we analyzed the chemical-competitive binding of a widely expressed protein, SfruOBP31, to host plant odorants, sex pheromones, and insecticides. Further ligands binding assay revealed a broad functional related binding spectrum of SfruOBP31 to host plant odorants, sex pheromones, and insecticides, suggesting its potential function in food, mate seeking, and pesticide resistance. These results provide guidance for future research on the development of behavioral regulators of S. frugiperda or other environmentally friendly pest-control strategies

On the Significance of the Weyl Curvature in a Relativistic Cosmological Model

The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolutions of propagations manifest explicit solutions of gravitational waves. We see that models with purely Newtonian field are inconsistent with relativistic models and obstruct sounding solutions. Therefore, both fields are necessary for the nonlocal nature and radiative solutions of gravitation.Comment: 15 pages, incorporating proof correction

Lagrange structure and quantization

A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the Lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in $d+1$ dimensions, being localized on the boundary, are proved to be equivalent to the original theory in $d$ dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily Lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.Comment: Minor corrections, format changed, 40 page