Gravitational Collapse with Heat Flux and Gravitational Waves

In this paper, we investigated the cylindrical gravitational collapse with heat flux by considering the appropriate geometry of the interior and exterior spacetimes. For this purpose, we matched collapsing fluid to an exterior containing gravitational waves.The effects of heat flux on gravitational collapse are investigated and matched with the results obtained by Herrera and Santos (Class. Quantum Gravity 22:2407, 2005).     

Structure formation in the presence of relativistic heat conduction: corrections to the Jeans wave number with a stable, first order in the gradients, formalism

The problem of structure formation in relativistic dissipative fluids was analyzed in a previous work within Eckart’s framework, in which the heat flux is coupled to the hydrodynamic acceleration, additional to the usual temperature gradient term. It was shown that in such case, the pathological behavior of fluctuations leads to the disappearance of the gravitational instability responsible for structure formation (Mondragon-Suarez and Sandoval-Villalbazo in Gen Relativ Gravit 44:139–145, 2012). In the present work the problem is revisited using a constitutive equation derived from relativistic kinetic theory. This new relation, in which the heat flux is not coupled to the hydrodynamic acceleration, leads to a consistent first order in the gradients formalism. In this case the gravitational instability remains, and only relativistic corrections to the Jeans wave number are obtained. In the calculation here shown the non-relativistic limit is recovered, opposite to what happens in Eckart’s case (Hiscock and Lindblom in Phys Rev D 31:725–733, 1985).     

Monte Carlo simulation of a hard-sphere gas in the planar Fourier flow with a gravity field

By means of the Direct Simulation Monte Carlo (DSMC) method, the Boltzmann equation is numerically solved for a gas of hard spheres enclosed between two parallel plates kept at different temperatures and subject to the action of a gravity field normal to the plates. The profiles of pressure, density, temperature and heat flux are seen to be quite sensitive to the value of the gravity acceleration g. If the gravity field and the heat flux are parallel (g > 0), the magnitudes of both the temperature gradient and the heat flux are smaller than in the opposite case (g < 0). When considering the actual heat flux relative to the value predicted by the Fourier law, it is seen that, if g > 0, the ratio increases as the reduced local field strength increases, while the opposite happens if g < 0. The simulation results are compared with theoretical predictions for Maxwell molecules.     

Radiating stars with generalised Vaidya atmospheres

We model the gravitational behaviour of a radiating star when the exterior geometry is the generalised Vaidya spacetime. The interior matter distribution is shear-free and undergoing radial heat flow. The exterior energy momentum tensor is a superposition of a null fluid and a string fluid. An analysis of the junction conditions at the stellar surface shows that the pressure at the boundary depends on the interior heat flux and the exterior string density. The results for a relativistic radiating star undergoing nonadiabatic collapse are obtained as a special case. For a particular model we demonstrate that the radiating fluid sphere collapses without the appearance of the horizon at the boundary.     

Phonon relaxation and heat conduction in one-dimensional Fermiben Pastaben Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam (FPU) β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.     

Junction conditions at the boundary of a charged viscous-fluid sphere

Junction conditions are studied at the boundary of a sphere consisting of a charged viscous fluid with outgoing heat and radiation flux. The motion is anisotropic and the matching is done with the exterior Reissner-Nordström-Vaidya metric. A general relation in terms of the energy-momentum tensor componentsT ₁ ¹ andT ₄ ¹ is satisfied at the boundary hypersurface and this relation gives appropriate physical conditions in different special cases, some of which were obtained previously.     

Faint Young Sun,Planetary Paleoclimates and Varying Fundamental Constants

The effect of a cosmic time variation of the gravitational constant on the solar luminosity evolution is studied. It is demonstrated that a varying gravitational constant can substantially affect the solar flux at the planetary orbits on geological time scales. Mean surface temperatures well above the freezing point of water can be achieved in this way throughout the Archean and Hadean, without invoking an increased greenhouse effect or a lower albedo. Instead of a monotonous decline of the solar flux in look-back time, due to a dim early Sun, we infer a flux minimum during the Early Proterozoic and Late Archean. In this epoch, the solar flux is capable of generating mean surface temperatures between 7^∘C and 12^∘C, as compared to the present 15^∘C. The flux then steadily increases, culminating in temperatures between 12^∘C and 19^∘C some 4.5 Gry ago, depending on the parameters chosen for the ‘standard’ Sun. This explains the absence of polar caps, and even warm oceans in the Archean and Hadean are possible at these temperatures. No change of the present 33 K greenhouse effect is required. As for Mars, we show that the solar flux at the Martian orbit before 3.8 Gyr was at least 90% of the present-day flux, so that mean surface temperatures above the freezing point could have been generated by CO₂ greenhouse warming. The time variation of the gravitational constant is such that the moderate dimensionless ratio ħ² H₀/(k₀ cm_π³) stays constant in cosmic time. There are stringent bounds on the logarithmic time derivative of the gravitational constant from lunar laser ranging and helioseismology, which indicate that the first-order derivative at the present epoch is too small to noticeably affect the solar luminosity evolution within the age of the Earth. However, higher-order derivatives have to be taken into account, as they do affect the solar flux in geologic look-back time. We consider the impact of a varying gravitational constant on the redshift scaling of the linear size of radio galaxies. The observed scaling exponent also enters the solar luminosity evolution. The age of the universe has a substantial imprint on planetary paleoclimates.     

Gravitational model of the string

It is shown that an infinite gravitational flux tube solution in 5D Kaluza‐Klein gravity with the cross section in the Planck region after 5D ? 4D reduction and isometrical embedding in a Minkowski spacetime can be considered as a moving infinite string‐like object. Such an object carries an electric and a magnetic flux. The 4D gravitational waves on the tube are considered.     

Gravitational couplings and Z2 orientifolds

The interplay between gravitational couplings on branes and the occurrence of fractional flux in low-dimensional orientifolds is examined. It is argued that gravitational couplings need to be assigned not only to D-branes but also to orientifold planes. The fractional charges of the orientifold d-planes can be understood in terms of flux quantization of the d − 3 form potential and modified Bianchi identities. Detailed results are presented for the case of the type IIB orientifold on T⁶/Z₂, which is dual to F-theory on a complex 4-fold with terminal singularities.     

Scaling of heat transfer in gas-gas injector combustor

The scaling of heat transfer in gas-gas injector combustor is investigated theoretically, numerically and experimentally based on the previous study on the scaling of gas-gas combustion flowfield. The similarity condition of the gas-gas injector combustor heat transfer is obtained by conducting a formulation analysis of the boundary layer Navier-Stokes equations and a dimensional analysis of the corresponding heat transfer phenomenon. Then, a practicable engineering scaling criterion of the gas-gas injector combustor heat transfer is put forward. The criterion implies that when the similarity conditions of inner flowfield are satisfied, the size and the pressure of gas-gas combustion chamber can be changed, while the heat transfer can still be qualitatively similar to the distribution trend and quantitatively correlates well with the size and pressure as q ∝ pc0 .8d t-0.2. Based on the criterion, single-element injector chambers with different geometric sizes and at different chamber pressures ranging from 1 MPa to 20 MPa are numerically simulated. A single-element injector chamber is designed and hot-fire tested at seven chamber pressures from 0.92 MPa to 6.1 MPa. The inner wall heat flux are obtained and analysed. The numerical and experimental results both verified the scaling criterion in gas-gas injector combustion chambers under different chamber pressures and geometries.     

Variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states and its bridge function study

This paper is a research on the variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states by using theoretical analysis and numerical simulation methods. The newly developed near space hypersonic cruise vehicles have sharp noses and wingtips, which desires exact and relatively simple methods to estimate the stagnation point heat flux. With the decrease of the curvature radius of the leading edge, the flow becomes rarefied gradually, and viscous interaction effects and rarefied gas effects come forth successively, which results in that the classical Fay-Riddell equation under continuum hypothesis will become invalid and the variation of stagnation point heat flux is characterized by a new trend. The heat flux approaches the free molecular flow limit instead of an infinite value when the curvature radius of the leading edge tends to 0. The physical mechanism behind this phenomenon remains in need of theoretical study. Firstly, due to the fact that the whole flow regime can be described by Boltzmann equation, the continuum and rarefied flow are analyzed under a uniform framework. A relationship is established between the molecular collision insufficiency in rarefied flow and the failure of Fourier’s heat conduction law along with the increasing significance of the nonlinear heat flux. Then based on an inspiration drew from Burnett approximation, control factors are grasped and a specific heat flux expression containing the nonlinear term is designed in the stagnation region of hypersonic leading edge. Together with flow pattern analysis, the ratio of nonlinear to linear heat flux W _r is theoretically obtained as a parameter which reflects the influence of nonlinear factors, i.e. a criterion to classify the hypersonic rarefied flows. Ultimately, based on the characteristic parameter W _r , a bridge function with physical background is constructed, which predicts comparative reasonable results in coincidence well with DSMC and experimental data in the whole flow regime.     

Heat-transfer mechanisms in solar flares. 1: Classical and anomalous heat conduction

In the context of the problem of energy transport in solar flares, simplified analytical models have been developed that describe plasma heating in the solar atmosphere by heat fluxes from the super-hot (T _e ≳ 10⁸ K) reconnecting current layer. It is shown that the applicability conditions of common heat conduction produced by Coulomb collisions of electrons in plasma are not fulfilled in solar flares. The heat flux calculated using the classical Fourier’s law proves to be significantly higher than the real energy fluxes known from modern multi-wavelength observations of flares. The so called anomalous flux produced by interaction of free electrons with ion acoustic waves in a plasma is critically analyzed. The question of what the dominant mechanism of heat transfer in solar flares is requires additional consideration [1].     

Multipole analysis of kicks in collision of spinning binary black holes

Thorne and Kidder give expressions which allow for analytical estimates of the “kick”, i.e. the recoil, produced from asymmetrical gravitational radiation during the interaction of black holes, or in fact any gravitating compact bodies. (The Thorne-Kidder formula uses momentum flux calculations based on the linearized General Relativity of gravitational radiation). We specifically treat kicks arising in the binary interaction of equal mass black holes, when at least one of the black holes has significant spin, a. Such configurations can produce very large kicks in computational simulations. We consider both fly-by and quasicircular orbits. For fly-by orbits we find substantial kicks from those Thorne-Kidder terms which are linear in a. For the quasi-circular case, we consider in addition the nonlinear contribution (O(a ²)) to the kicks, and provide a dynamical explanation for such terms discovered and displayed by [2]. However, in the cases of maximal kick velocities, the dependence on spin is largely linear (reproduced in numerical results [6]).     

Extended Hydrodynamics from Enskog’s Equation for a Two-Dimensional System General Formalism

Balance equations are derived from Enskog’s kinetic equation for a two-dimensional system of hard disks using Grad’s moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional fluids. The set of independent hydrodynamic fields in the present formulations are: density, velocity, temperature and also—following Grad’s original idea—the symmetric and traceless pressure tensor p _ij and the heat flux vector q ^k . An approximation scheme similar in spirit to one made by Grad in his original work is made. Once the hydrodynamics is derived it is used to discuss the nature of a simple one-dimensional heat conduction problem. It is shown that, not too far from equilibrium, the nonequilibrium pressure in this case only depends on the density, temperature and heat flux vector. PACS: 51.10.+y, 05.20.Jj, 44.10.+i, 05.70.Ln     

Resolution of a Classical Gravitational Second-Law Paradox

Sheehan and coworkers have claimed [D. P. Sheehan et al., Found. Phys. 30, 1227 (2000); 32, 441 (2002); D. P. Sheehan, in Quantum Limits to the Second Law, AIP Conference Proceedings 643 (American Institute of Physics, Melville, NY, 2002), p. 391] that a dilute gas trapped between an external shell and a gravitator can support a steady state in which energy flux by particles in one direction is balanced by energy flux by radiation in the opposite direction, and in which work can be extracted from an isothermal heat reservoir, thereby violating the second law of thermodynamics. In this paper, we identify a fundamental error in their simulation and analysis of their model system that vitiates their conclusions. We analyze a simpler, exactly soluble, three-dimensional model of a very dilute gas in a gravitational field between two thermal reservoirs, and show that their conclusions are not supported for the simple model. We show that their method of simulation, when applied to either the simple model or their more complex model under simpler conditions where the answers are known, leads to unphysical results. We also show that, when appropriate sampling is done, their model gives results in accord with the second law and detailed balance.     

Forty Years to the Artemovsk Scintillation Detector for Neutrinos

The current status of the ASD (Artemovsk scintillation detector) experiment aimed at search for a neutrino flux from gravitational collapses of stellar cores is presented. Experimental data obtained for 40 years of operation of the detector situated in a salt mine at a depth of 570 mwe are processed. The results obtained by calculating the expected signal in the detector on the basis of two models of supernova explosion are described. No candidates for neutrino bursts from gravitational star collapses have been revealed: the limit on the frequency of gravitational collapses was found to be less than one event per 17.15 yr at a 90% confidence level (f_col < 0.058 yr^?1).     

On the role of dissipation in structure formation for dilute relativistic gases: the fluctuating static background case

A correction to the Jeans stability criterion due to dissipation is established for the case of dilute high temperature gases. This effect is only relevant in the relativistic scenario and includes additional terms due to a density gradient driven heat flux, a non-vanishing bulk viscosity and the space-time dependent gravitational potential first order fluctuations. The result is obtained by thoroughly analyzing the exponentially growing modes present in the dynamics of density fluctuations in the linearized relativistic Navier–Stokes regime. The corrections to the corresponding Jeans mass and wavenumber are explicitly obtained and are compared to the non-relativistic and non-dissipative values using the transport coefficients obtained in the BGK approximation.     

Plane symmetric self-gravitating fluids with pressure equal to energy density

Solutions of the Cauchy problem associated with the Einstein field equations which satisfy general initial conditions are obtained under the assumptions that (1) the source of the gravitational field is a perfect fluid with pressure,p, equal to energy density,w, and (2) the space-time admits the three parameter group of motions of the Euclidean plane, that is, the space-time is plane symmetric. The results apply to the situation where the source of the gravitational field is a massless scalar field since such a source has the same stress-energy tensor as an irrotational fluid withp=w. The relation between characteristic coordinates and comoving ones is discussed and used to interpret a number of special solutions. A solution involving a shock wave is discussed.     

Spectral energy balance in dry convective boundary layers

Three-dimensional large-eddy simulations (LES) of the convective boundary layer over a domain of approximately 6 km are performed with the UCLA LES model. Simulations are forced with a constant surface heat flux and prescribed subsidence, and are run to equilibrium. Sub-grid scale fluxes are parameterised with the Smagorinsky–Lilly scheme. A range of grid spacings from 40 down to 5 m are employed. Kinetic energy spectra and the various terms in the kinetic energy spectral budget – heat flux, nonlinear transfer, pressure, and dissipation – are computed using two-dimensional discrete Fourier transforms at every vertical level. Despite the fact that isotropic grid spacings of down to 5 m (grid sizes of 1152²×400) were used, an inertial range with a ?5/3 spectrum is not obtained. Rather, shallower energy spectral slopes that are closer to ?4/3 are found. The shallower spectra are shown to possibly result from the injection of kinetic energy over a wide range of scales via a very broad heat flux spectrum. Only with the highest resolution (Δx = 5 m) does the total heat flux begin to converge and the possibility of local isotropy emerge at small scales. Dependence on surface heat flux and domain size is considered. Preliminary sub-grid scale sensitivity results are obtained through comparison with the turbulent kinetic energy sub-grid scale model.     

Numerical investigation on properties of attack angle for opposing jet thermal protection system

The three-dimensional Navier-Stokes equation and the k-ε viscous model are used to simulate the attack angle characteristics of a hemisphere nose-tip with an opposing jet thermal protection system in supersonic flow condition. The numerical method is validated by the relevant experiment. The flow field parameters, aerodynamic forces, and surface heat flux distributions for attack angles of 0°, 2°, 5°, 7°, and 10° are obtained. The detailed numerical results show that the cruise attack angle has a great influence on the flow field parameters, aerodynamic force, and surface heat flux distribution of the supersonic vehicle nose-tip with opposing jet thermal protection system. When the attack angle reaches 10°, the heat flux on the windward generatrix is close to the maximal heat flux on the wall surface of the nose-tip without thermal protection system, thus the thermal protection is failure.