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PubMed2002

Static configurations of gravitating dusty plasmas.

Plasma and dust are key ingredients of the universe, and in larger astrophysical systems the gravitational and electrostatic forces can become comparable, thus prompting a careful revision of stationary configurations of self-gravitating dusty plasmas. An overview of some physically acceptable models is given, with applications to relevant structures in space and astrophysical plasmas. For those cases where explicit solutions can be obtained, the scales over which the system is inhomogeneous are of the order of the Jeans lengths, determined in the usual way by studying local perturbations of a uniform equilibrium.

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PubMed2003

Radiation-condensation instability in a self-gravitating dusty astrophysical plasma.

Properties of radiation-condensation instability in a partially-ionized self-gravitating dusty astrophysical plasmas are studied. For this purpose, new dispersion relations for coupled dusty plasma and condensation modes in both unmagnetized and magnetized plasmas are derived. The dispersion relations are numerically analyzed to investigate the interplay between self-gravitation and impurity losses, as well as to study the effects of the external magnetic field and finite plasma beta on instabilities we found.

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PubMed2003

Stability analysis of mean-field-type nonlinear Fokker-Planck equations associated with a generalized entropy and its application to the self-gravitating system.

Multidimensional nonlinear Fokker-Planck equations of mean-field type are proposed within the framework of generalized thermostatistics to develop a general formulation of stability analysis of their solutions. Two types of eigenvalue equations are studied. The nonlinear Fokker-Planck equations are shown to exhibit an H theorem with a Liapunov functional that takes the form of a free energy involving generalized entropies of Tsallis. The second-order variation of the Liapunov functional is computed to conduct local stability analysis and the associated eigenvalue equation is derived for an arbitrary form of mean-field coupling potential. Assuming quasiequilibrium for the velocity distribution, the reduced eigenvalue equation with space coordinates alone is also obtained. The alternative type of eigenvalue equation based on the linearization of the nonlinear Fokker-Planck equations is presented. Taking the mean-field coupling potential to be the gravitational one, the nonlinear Fokker-Planck equation in terms of three-dimensional velocity and space coordinates together with the framework of stability analysis is shown to be applicable to a mean-field model of self-gravitating system. By solving the eigenvalue equation for the eigenfunction with 0 eigenvalue, the occurrence of stability change of the equilibrium probability density with spherical symmetry is discussed.

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PubMed2003

Models of spatial and orientational self-organization of microtubules under the influence of gravitational fields.

Tabony and co-workers [C. Papaseit, N. Pochon, and J. Tabony, Proc. Natl. Acad. Sci. U.S.A. 97, 8364 (2000)] showed that the self-organization of microtubules from purified tubulin solutions is sensitive to gravitational conditions. In this paper, we propose two models of spatial and orientational self-organization of microtubules in a gravitational field. First, the spatial model is based on the dominant chemical kinetics. The pattern formation of microtubule concentration is obtained (1) in terms of a moving kink in the limit when the disassembly rate is negligible, and (2) for the case of no free tubulin and only assembled microtubules present. Second, the orientational pattern of striped microtubule domains is consistent with predictions from a phenomenological Landau-Ginzburg free energy expansion in terms of an orientational order parameter.

Animals↗
PubMed2004

Gravitational force in weakly correlated particle spatial distributions.

We study the statistics of the gravitational (Newtonian) force in a particular class of weakly correlated spatial distributions of pointlike and unitary mass particles generated by the so-called Gauss-Poisson point processes. In particular we extend to these distributions the analysis that Chandrasekhar introduced for purely Poisson processes. In this way we can find the explicit asymptotic behavior of the probability density function of the force for both large and small values of the field as a generalization of the Holtzmark statistics. In particular, we show how the modifications at large fields depend on the density correlations introduced at small scales. The validity of the introduced approximations is positively tested through a direct comparison with the analysis of the statistics of the gravitational force in numerical simulations of Gauss-Poisson processes.

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PubMed2004

Postcollapse dynamics of self-gravitating Brownian particles and bacterial populations.

We address the postcollapse dynamics of a self-gravitating gas of Brownian particles in D dimensions in both canonical and microcanonical ensembles. In the canonical ensemble, the postcollapse evolution is marked by the formation of a Dirac peak with increasing mass. The density profile outside the peak evolves self-similarly with decreasing central density and increasing core radius. In the microcanonical ensemble, the postcollapse regime is marked by the formation of a "binarylike" structure surrounded by an almost uniform halo with high temperature. These results are consistent with thermodynamical predictions in astrophysics. We also show that the Smoluchowski-Poisson system describing the collapse of self-gravitating Brownian particles in a strong-friction limit is isomorphic to a simplified version of the Keller-Segel equations describing the chemotactic aggregation of bacterial populations. Therefore, our study has direct applications in this biological context.

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PubMed2005

Universal non-Gaussian velocity distribution in violent gravitational processes.

We study the velocity distribution in spherical collapses and cluster-pair collisions by use of N -body simulations. Reflecting the violent gravitational processes, the velocity distribution of the resultant quasistationary state generally becomes non-Gaussian. Through the strong mixing of the violent process, there appears a universal non-Gaussian velocity distribution, which is a democratic (equal-weighted) superposition of many Gaussian distributions (DT distribution). This is deeply related with the local virial equilibrium and the linear mass-temperature relation which characterize the system. We show the robustness of this distribution function against various initial conditions which leads to the violent gravitational process. The DT distribution has a positive correlation with the energy fluctuation of the system. On the other hand, the coherent motion such as the radial motion in the spherical collapse and the rotation with the angular momentum suppress the appearance of the DT distribution.

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PubMed2005

Self-gravitating Brownian systems and bacterial populations with two or more types of particles.

We study the thermodynamical properties of a self-gravitating gas with two or more types of particles. Using the method of linear series of equilibria, we determine the structure and stability of statistical equilibrium states in both microcanonical and canonical ensembles. We show how the critical temperature (Jeans instability) and the critical energy (Antonov instability) depend on the relative mass of the particles and on the dimension of space. We then study the dynamical evolution of a multicomponent gas of self-gravitating Brownian particles in the canonical ensemble. Self-similar solutions describing the collapse below the critical temperature are obtained analytically. We find particle segregation, with the scaling profile of the slowest collapsing particles decaying with a nonuniversal exponent that we compute perturbatively in different limits. These results are compared with numerical simulations of the two-species Smoluchowski-Poisson system. Our model of self-attracting Brownian particles also describes the chemotactic aggregation of a multi-species system of bacteria in biology.

Bacteria↗
PubMed2006

Dynamics of the Bose-Einstein condensation: analogy with the collapse dynamics of a classical self-gravitating Brownian gas.

We consider the dynamics of a gas of free bosons within a semiclassical Fokker-Planck equation for which we give a physical justification. In this context, we find a striking similarity between the Bose-Einstein condensation in the canonical ensemble, and the gravitational collapse of a gas of classical self-gravitating Brownian particles. The paper is mainly devoted to the complete study of the Bose-Einstein "collapse" within this model. We find that at the Bose-Einstein condensation temperature Tc, the chemical potential mu(t) vanishes exponentially with a universal rate that we compute exactly. Below Tc, we show analytically that square root mu(t) vanishes linearly in a finite time t coll. After t coll, the mass of the condensate grows linearly with time and saturates exponentially to its equilibrium value for large time. We also give analytical results for the density scaling functions, for the corrections to scaling, and for the exponential relaxation time. Finally, we find that the equilibration time (above Tc) and the collapse time T coll(below Tc) both behave like -T -3 c ln|T-Tc|, near Tc.

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PubMed2000

Radiative tail of realistic rotating gravitational collapse

An astrophysically realistic model of wave dynamics in black-hole spacetimes must involve a nonspherical background geometry with angular momentum. We consider the evolution of gravitational (and electromagnetic) perturbations in rotating Kerr spacetimes. We show that a rotating Kerr black hole becomes "bald" slower than the corresponding spherically symmetric Schwarzschild black hole. Moreover, our results turn over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal. Our results are also of importance both to the study of the no-hair conjecture and the mass-inflation scenario (stability of Cauchy horizons).

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PubMed2000

Generalization of the regge-wheeler equation for self-gravitating matter fields

It is shown that the dynamical evolution of perturbations on a static spacetime is governed by a standard pulsation equation for the extrinsic curvature tensor. The centerpiece of the pulsation equation is a wave operator whose spatial part is manifestly self-adjoint. In contrast to metric formulations, the curvature-based approach to perturbation theory generalizes in a natural way to self-gravitating matter fields, including non-Abelian gauge fields and perfect fluids. As an example, the pulsation equations for self-gravitating, non-Abelian gauge fields are explicitly shown to be symmetric.

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PubMed2000

Gravitational wave bursts from cosmic strings

Cusps of cosmic strings emit strong beams of high-frequency gravitational waves (GW). As a consequence of these beams, the stochastic ensemble of gravitational waves generated by a cosmological network of oscillating loops is strongly non-Gaussian, and includes occasional sharp bursts that stand above the rms GW background. These bursts might be detectable by the planned GW detectors LIGO/VIRGO and LISA for string tensions as small as G&mgr; approximately 10(-13). The GW bursts discussed here might be accompanied by gamma ray bursts.

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PubMed2001

Solving the characteristic initial-value problem for colliding plane gravitational and electromagnetic waves.

A method is presented for solving the characteristic initial-value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromy-transform approach to fields with nonanalytic behavior on the characteristics inherent to waves with distinct wave fronts. The crux of the method is in a reformulation of the main nonlinear symmetry reduced field equations as linear integral equations whose solutions are determined by generalized ("dynamical") monodromy data which evolve from data specified on the initial characteristics (the wave fronts).

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PubMed2001

Possibility of direct measurement of the acceleration of the universe using 0.1 Hz band laser interferometer gravitational wave antenna in space.

It may be possible to construct a laser interferometer gravitational wave antenna in space with h(rms) approximately 10(-27) at f approximately 0.1 Hz in this century. Using this antenna, (1) typically 10(5) chirp signals of coalescing binary neutron stars per year may be detected with S/N approximately 10(4); (2) we can directly measure the acceleration of the universe by a 10 yr observation of binary neutron stars; and (3) the stochastic gravitational waves of Omega(GW) > or similar to 10(-20) predicted by the inflation may be detected by correlation analysis. Our formula for phase shift due to accelerating motion might be applied for binary sources of LISA.

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PubMed2002

Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection.

Interferometric gravitational wave detectors are expected to be limited by shot noise at some frequencies. We experimentally demonstrate that a power recycled Michelson with squeezed light injected into the dark port can overcome this limit. An improvement in the signal-to-noise ratio of 2.3 dB is measured and locked stably for long periods of time. The configuration, control, and signal readout of our experiment are compatible with current gravitational wave detector designs. We consider the application of our system to long baseline interferometer designs such as LIGO.

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PubMed2002

Separation of gravitational-wave and cosmic-shear contributions to cosmic microwave background polarization.

Inflationary gravitational waves (GW) contribute to the curl component in the polarization of the cosmic microwave background (CMB). Cosmic shear--gravitational lensing of the CMB--converts a fraction of the dominant gradient polarization to the curl component. Higher-order correlations can be used to map the cosmic shear and subtract this contribution to the curl. Arcminute resolution will be required to pursue GW amplitudes smaller than those accessible by the Planck surveyor mission. The blurring by lensing of small-scale CMB power leads with this reconstruction technique to a minimum detectable GW amplitude corresponding to an inflation energy near 10(15) GeV.

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PubMed2002

Three-wave interaction in a self-gravitating fluid.

Nonlinear three-wave interaction is investigated in rotating self-gravitating astrophysical fluids. Both direct and inverse cascades are found. The latter should be of importance for the formation of structures in rotating astrophysical objects like protogalaxies and galaxies. Linear gravitational instability is shown to be a process that develops on much longer time scales, compared to the nonlinear wave interaction, and the nonlinear precipitation of energy from the linearly unstable, slowly contracting mode towards smaller spatial and time scales is shown to be possible.

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PubMed2002

Determination of the gravitational constant with a beam balance.

The Newtonian gravitational constant G was determined by means of a novel beam-balance experiment with an accuracy comparable to that of the most precise torsion-balance experiments. The gravitational force of two stainless steel tanks filled with 13 521 kg mercury on 1.1 kg test masses was measured using a commercial mass comparator. A careful analysis of the data and the experimental error yields G=6.674 07(22)x10(-11) m(3) kg(-1) s(-2). This value is in excellent agreement with most values previously obtained with different methods.

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