Formation and evolution of the protoplanetary disk

A disk formation model during collapse of the protosolar nebula, yielding a low-mass protoplanetary disk is presented. The following subject areas are covered: (1) circumstellar disks; (2) conditions for the formation of stars with disks; (3) early evolution of the protoplanetary disk; and (4) temperature conditions and the convection in the protoplanetary disk

Expansionfree Fluid Evolution and Skripkin Model in f(R) Theory

We consider the modified $f(R)$ theory of gravity whose higher order curvature terms are interpreted as a gravitational fluid or dark source. The gravitational collapse of a spherically symmetric star, made up of locally anisotropic viscous fluid, is studied under the general influence of the curvature fluid. Dynamical equations and junction conditions are modified in the context of f(R) dark energy and by taking into account the expansionfree evolution of the self-gravitating fluid. As a particular example, the Skripkin model is investigated which corresponds to isotropic pressure with constant energy density. The results are compared with corresponding results in General Relativity.Comment: 18 pages, accepted for publication Int. J. Mod. Phys.

Spin Glass Computations and Ruelle's Probability Cascades

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC formulation of the functional are developed. They are used to derive continuity and monotonicity properties of the functional retrieving a theorem of Guerra. We also detail the connection between the Aizenman-Sims-Starr variational principle and the Parisi formula. As a final application of the techniques, we rederive the Almeida-Thouless line in the spirit of Toninelli but relying on the RPC structure.Comment: 20 page

Deep connection between f(R) gravity and the interacting dark sector model

We examine the conformal equivalence between the $f(R)$ gravity and the interacting dark sector model. We review the well-known result that the conformal transformation physically corresponds to the mass dilation which marks the strength of interaction between dark sectors. Instead of modeling f(R) gravity in the Jordan frame, we construct the $f(R)$ gravity in terms of mass dilation function in the Einstein frame. We find that the condition to keep $f(R)$ gravity consistent with CMB observations ensures the energy flow from dark energy to dark matter in the corresponding interacting model, which meets the requirement to alleviate the coincidence problem in the Einstein framework.Comment: 9 pages, 2 figures, revised version, accepted for publication in Phys. Rev.

Random matrices: Universality of local eigenvalue statistics up to the edge

This is a continuation of our earlier paper on the universality of the eigenvalues of Wigner random matrices. The main new results of this paper are an extension of the results in that paper from the bulk of the spectrum up to the edge. In particular, we prove a variant of the universality results of Soshnikov for the largest eigenvalues, assuming moment conditions rather than symmetry conditions. The main new technical observation is that there is a significant bias in the Cauchy interlacing law near the edge of the spectrum which allows one to continue ensuring the delocalization of eigenvectors.Comment: 24 pages, no figures, to appear, Comm. Math. Phys. One new reference adde

On analytical solutions of f(R) modified gravity theories in FLRW cosmologies

A novel analytical method for f(R) modified theories without matter in Friedmann-Lemaitre-Robertson-Walker spacetimes is introduced. The equation of motion for the scale factor in terms of cosmic time is reduced to the equation for the evolution of the Ricci scalar R with the Hubble parameter H. The solution of equation of motion for actions of the form of power law in Ricci scalar R, is presented with a detailed elaboration of the action quadratic in R. The reverse use of the introduced method is exemplified in finding functional forms f(R) which lead to specified scale factor functions. The analytical solutions are corroborated by numerical calculations with excellent agreement. Possible further applications to the phases of inflationary expansion and late-time acceleration as well as f(R) theories with radiation are outlined.Comment: 16 pages, 6 figures. v2: minor changes, references added. v3: minor changes, more references added. v4: version to appear in IJMPD. v5: DOI and journal reference adde

Excitation of MHD waves in magnetized anisotropic cosmologies

The excitation of cosmological perturbations in an anisotropic cosmological model and in the presence of a homogeneous magnetic field was studied, using the resistive magnetohydrodynamic (MHD) equations. We have shown that fast-magnetosonic modes, propagating normal to the magnetic field grow exponentially and saturated at high values, due to the resistivity. We also demonstrate that the jeans-like instabilities are enhanced inside a resistive and the formation of condensations formed within an anisotropic fluid influence the growing magnetosonic waves.Comment: 12 pages, RevTex, 5 figures ps, accepted for publication to Astronomy and Astrophysic

Dynamics of Circumstellar Disks II: Heating and Cooling

We present a series of 2-d ($r,\phi$) hydrodynamic simulations of marginally self gravitating disks around protostars using an SPH code. We implement simple dynamical heating and we cool each location as a black body, using a photosphere temperature obtained from the local vertical structure. We synthesize SEDs from our simulations and compare them to fiducial SEDs derived from observed systems. These simulations produce less distinct spiral structure than isothermally evolved systems, especially in the inner third of the disk. Pattern are similar further from the star but do not collapse into condensed objects. The photosphere temperature is well fit to a power law in radius with index $q\sim1.1$, which is very steep. Far from the star, internal heating ($PdV$ work and shocks) are not responsible for generating a large fraction of the thermal energy contained in the disk matter. Gravitational torques responsible for such shocks cannot transport mass and angular momentum efficiently in the outer disk. Within $\sim$5--10 AU of the star, rapid break up and reformation of spiral structure causes shocks, which provide sufficient dissipation to power a larger fraction of the near IR energy output. The spatial and size distribution of grains can have marked consequences on the observed near IR SED and can lead to increased emission and variability on $\lesssim 10$ year time scales. When grains are vaporized they do not reform into a size distribution similar to that from which most opacity calculations are based. With rapid grain reformation into the original size distribution, the disk does not emit near infrared photons. With a plausible modification to the opacity, it contributes much more.Comment: Accepted by ApJ, 60pg incl 24 figure