Stability of coalescing binary stars against gravitational collapse: hydrodynamical simulations

We perform simulations of relativistic binary stars in post-Newtonian gravity to investigate their dynamical stability prior to merger against gravitational collapse in a tidal field. In general, our equations are only strictly accurate to first post-Newtonian order, but they recover full general relativity for spherical, static stars. We study both corotational and irrotational binary configurations of identical stars in circular orbits. We adopt a soft, adiabatic equation of state with $\Gamma = 1.4$, for which the onset of instability occurs at a sufficiently small value of the compaction $M/R$ that a post-Newtonian approximation is quite accurate. For such a soft equation of state there is no innermost stable circular orbit, so that we can study arbitrarily close binaries. This choice still allows us to study all the qualitative features exhibited by any adiabatic equation of state regarding stability against gravitational collapse. We demonstrate that, independent of the internal stellar velocity profile, the tidal field from a binary companion stabilizes a star against gravitational collapse.Comment: 13 pages, 10 figures, RevTex, to appear in Phys. Rev.

Impact of surface imperfections on the Casimir force for lenses of centimeter-size curvature radii

The impact of imperfections, which are always present on surfaces of lenses with centimeter-size curvature radii, on the Casimir force in the lens-plate geometry is investigated. It is shown that the commonly used formulation of the proximity force approximation is inapplicable for spherical lenses with surface imperfections, such as bubbles and pits. More general expressions for the Casimir force are derived that take surface imperfections into account. Using these expressions we show that surface imperfections can both increase and decrease the magnitude of the Casimir force up to a few tens of percent when compared with the case of a perfectly spherical lens. We demonstrate that the Casimir force between a perfectly spherical lens and a plate described by the Drude model can be made approximately equal to the force between a sphere with some surface imperfection and a plate described by the plasma model, and vice versa. In the case of a metallic sphere and semiconductor plate, approximately the same Casimir forces are obtained for four different descriptions of charge carriers in the semiconductor if appropriate surface imperfections on the lens surface are present. The conclusion is made that there is a fundamental problem in the interpretation of measurement data for the Casimir force, obtained by using spherical lenses of centimeter-size radii, and their comparison with theory.Comment: 28 pages, 7 figures, 1 table. To appear in Phys. Rev.

A spherical model with directional interactions: I. Static properties

We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting only between particles of different size. The small particles provide the bonds between the large ones. With a proper choice of the interaction parameters, as well as of the relative concentration of the two species, it is possible to control the effective valence. Here we focus on a specific choice of the parameters which favors tetrahedral ordering and study the equilibrium static properties of the system in a large window of densities and temperatures. Upon lowering the temperature we observe a progressive increase in local order, accompanied by the formation of a four-coordinated network of bonds. Three different density regions are observed: at low density the system phase separates into a gas and a liquid phase; at intermediate densities a network of fully bonded particles develops; at high densities -- due to the competition between excluded volume and attractive interactions -- the system forms a defective network. The very same behavior has been previously observed in numerical studies of non-spherical models for molecular liquids, such as water, and in models of patchy colloidal particles. Differently from these models, theoretical treatments devised for spherical potentials, e.g. integral equations and ideal mode coupling theory for the glass transition can be applied in the present case, opening the way for a deeper understanding of the thermodynamic and dynamic behavior of low valence molecules and particles.Comment: 11 pages, 11 figure

Modeling Forbidden Line Emission Profiles from Colliding Wind Binaries

This paper presents calculations for forbidden emission line profile shapes arising from colliding wind binaries. The main application is for systems involving a Wolf-Rayet (WR) star and an OB star companion. The WR wind is assumed to dominate the forbidden line emission. The colliding wind interaction is treated as an archimedean spiral with an inner boundary. Under the assumptions of the model, the major findings are as follows. (a) The redistribution of the WR wind as a result of the wind collision is not flux conservative but typically produces an excess of line emission; however, this excess is modest at around the 10% level. (b) Deviations from a flat-top profile shape for a spherical wind are greatest for viewing inclinations that are more nearly face-on to the orbital plane. At intermediate viewing inclinations, profiles display only mild deviations from a flat-top shape. (c) The profile shape can be used to constrain the colliding wind bow shock opening angle. (d) Structure in the line profile tends to be suppressed in binaries of shorter periods. (e) Obtaining data for multiple forbidden lines is important since different lines probe different characteristic radial scales. Our models are discussed in relation to ISO data for WR 147 and gamma Vel (WR11). The lines for WR 147 are probably not accurate enough to draw firm conclusions. For gamma Vel, individual line morphologies are broadly reproducible but not simultaneously so for the claimed wind and orbital parameters. Overall, the effort demonstrates how lines that are sensitive to the large-scale wind can help to deduce binary system properties and provide new tests of numerical simulations.Comment: to appear in MNRA

Competition of hydrophobic and Coulombic interactions between nano-sized solutes

The solvation of charged, nanometer-sized spherical solutes in water, and the effective, solvent-induced force between two such solutes are investigated by constant temperature and pressure Molecular Dynamics simulations of model solutes carrying various charge patterns. The results for neutral solutes agree well with earlier findings, and with predictions of simple macroscopic considerations: substantial hydrophobic attraction may be traced back to strong depletion (``drying'') of the solvent between the solutes. This hydrophobic attraction is strongly reduced when the solutes are uniformly charged, and the total force becomes repulsive at sufficiently high charge; there is a significant asymmetry between anionic and cationic solute pairs, the latter experiencing a lesser hydrophobic attraction. The situation becomes more complex when the solutes carry discrete (rather than uniform) charge patterns. Due to antagonistic effects of the resulting hydrophilic and hydrophobic ``patches'' on the solvent molecules, water is once more significantly depleted around the solutes, and the effective interaction reverts to being mainly attractive, despite the direct electrostatic repulsion between solutes. Examination of a highly coarse-grained configurational probability density shows that the relative orientation of the two solutes is very different in explicit solvent, compared to the prediction of the crude implicit solvent representation. The present study strongly suggests that a realistic modeling of the charge distribution on the surface of globular proteins, as well as the molecular treatment of water are essential prerequisites for any reliable study of protein aggregation.Comment: 20 pages, 25 figure

Comparison between experiment and theory for the thermal Casimir force

We analyze recent experiments on measuring the thermal Casimir force with account of possible background effects. Special attention is paid to the validity of the proximity force approximation (PFA) used in the comparison between the experimental data and computational results in experiments employing a sphere-plate geometry. The PFA results are compared with the exact results where they are available. The possibility to use fitting procedures in theory-experiment comparison is discussed. On this basis we reconsider experiments exploiting spherical lenses of centimeter-size radii.Comment: Plenary talk at the 10th International Conference "Quantum Field Theory Under the Influence of External Conditions" (Benasque, Spain, 2011); 16 pages, 5 figure

Contributions to the Power Spectrum of Cosmic Microwave Background from Fluctuations Caused by Clusters of Galaxies

We estimate the contributions to the cosmic microwave background radiation (CMBR) power spectrum from the static and kinematic Sunyaev-Zel'dovich (SZ) effects, and from the moving cluster of galaxies (MCG) effect. We conclude, in agreement with other studies, that at sufficiently small scales secondary fluctuations caused by clusters provide important contributions to the CMBR. At $\ell \gtrsim 3000$, these secondary fluctuations become important relative to lensed primordial fluctuations. Gravitational lensing at small angular scales has been proposed as a way to break the ``geometric degeneracy'' in determining fundamental cosmological parameters. We show that this method requires the separation of the static SZ effect, but the kinematic SZ effect and the MCG effect are less important. The power spectrum of secondary fluctuations caused by clusters of galaxies, if separated from the spectrum of lensed primordial fluctuations, might provide an independent constraint on several important cosmological parameters.Comment: LateX, 41 pages and 10 figures. Accepted for publication in the Astrophysical Journa

Modelling of Phase Separation in Alloys with Coherent Elastic Misfit

Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) of alloys. If the elastic moduli are different in the two phases, the elastic interactions may accelerate, slow down or even stop the phase separation process. If the material is elastically anisotropic, the precipitates can be shaped like plates or needles instead of spheres and can form regular precipitate superlattices. Tensions or compressions applied externally to the specimen may have a strong effect on the shapes and arrangement of the precipitates. In this paper, we review the main theoretical approaches that have been used to model these effects and we relate them to experimental observations. The theoretical approaches considered are (i) `macroscopic' models treating the two phases as elastic media separated by a sharp interface (ii) `mesoscopic' models in which the concentration varies continuously across the interface (iii) `microscopic' models which use the positions of individual atoms.Comment: 106 pages, in Latex, figures available upon request, e-mail addresses: [email protected], [email protected], [email protected], submitted to the Journal of Statistical Physic