Angular momentum distribution during the collapse of primordial star-forming clouds

It is generally believed that angular momentum is distributed during the gravitational collapse of the primordial star forming cloud. However, so far there has been little understanding of the exact details of the distribution. We use the modified version of the Gadget-2 code, a three-dimensional smoothed-particle hydrodynamics simulation, to follow the evolution of the collapsing gas in both idealized as well as more realistic minihalos. We find that, despite the lack of any initial turbulence and magnetic fields in the clouds the angular momentum profile follows the same characteristic power-law that has been reported in studies that employed fully self-consistent cosmological initial conditions. The fit of the power-law appears to be roughly constant regardless of the initial rotation of the cloud. We conclude that the specific angular momentum of the self-gravitating rotating gas in the primordial minihalos maintains a scaling relation with the gas mass as $L \propto M^{1.125}$. We also discuss the plausible mechanisms for the power-law distribution.Comment: Accepted for publication in Astrophysics and Space Science (ASTR

Bayes Model Selection with Path Sampling: Factor Models and Other Examples

We prove a theorem justifying the regularity conditions which are needed for Path Sampling in Factor Models. We then show that the remaining ingredient, namely, MCMC for calculating the integrand at each point in the path, may be seriously flawed, leading to wrong estimates of Bayes factors. We provide a new method of Path Sampling (with Small Change) that works much better than standard Path Sampling in the sense of estimating the Bayes factor better and choosing the correct model more often. When the more complex factor model is true, PS-SC is substantially more accurate. New MCMC diagnostics is provided for these problems in support of our conclusions and recommendations. Some of our ideas for diagnostics and improvement in computation through small changes should apply to other methods of computation of the Bayes factor for model selection.Comment: Published in at http://dx.doi.org/10.1214/12-STS403 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Lifshitz tricritical point and its relation to the FFLO superconducting state

We study the phase diagram of spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) superconducting state using the Ginzburg-Landau(GL) free energy, derived from the microscopic Hamiltonian of the system, and notice that it has a very clear Lifshitz tricritical point. We find the specific heat jumps abruptly near the first-order line in the emergent phase diagram which is very similar to the recent experimental observation in layered organic superconductor. Comparison with experimental data allows us to obtain quantitative relations between the parameters of phenomenological free energy. The region of the phase diagram where the specific heat jumps can be probed by doing a dynamical analysis of the free energy.Comment: Published versio

Dynamical Structure Factor of Fulde-Ferrell-Larkin-Ovchinnikov Superconductors

Superconductor with a spatially-modulated order parameter is known as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor. Using the time-dependent Ginzburg-Landau (TDGL) formalism we have theoretically studied the temporal behaviour of the equal-time correlation function, or the structure factor, of a FFLO superconductor following a sudden quench from the unpaired, or normal, state to the FFLO state. We find that quenching into the ordered FFLO phase can reveal the existence of a line in the mean-field phase diagram which cannot be accessed by static properties.Comment: 2 pages, Poster presented at 57TH DAE SOLID STATE PHYSICS SYMPOSIUM, 2012. Mainly based on arXiv:1210.220

Search for chaos in neutron star systems: Is Cyg X-3 a black hole?

The accretion disk around a compact object is a nonlinear general relativistic system involving magnetohydrodynamics. Naturally the question arises whether such a system is chaotic (deterministic) or stochastic (random) which might be related to the associated transport properties whose origin is still not confirmed. Earlier, the black hole system GRS 1915+105 was shown to be low dimensional chaos in certain temporal classes. However, so far such nonlinear phenomena have not been studied fairly well for neutron stars which are unique for their magnetosphere and kHz quasi-periodic oscillation (QPO). On the other hand, it was argued that the QPO is a result of nonlinear magnetohydrodynamic effects in accretion disks. If a neutron star exhibits chaotic signature, then what is the chaotic/correlation dimension? We analyze RXTE/PCA data of neutron stars Sco X-1 and Cyg X-2, along with the black hole Cyg X-1 and the unknown source Cyg X-3, and show that while Sco X-1 and Cyg X-2 are low dimensional chaotic systems, Cyg X-1 and Cyg X-3 are stochastic sources. Based on our analysis, we argue that Cyg X-3 may be a black hole.Comment: 9 pages including 6 figures; to appear in The Astrophysical Journa

On the effects of rotation during the formation of population III protostars

It has been suggested that turbulent motions are responsible for the transport of angular momentum during the formation of Population III stars, however the exact details of this process have never been studied. We report the results from three dimensional SPH simulations of a rotating self-gravitating primordial molecular cloud, in which the initial velocity of solid-body rotation has been changed. We also examine the build-up of the discs that form in these idealized calculations.Comment: 4 pages, AIP Conference Proceedings, First Stars IV from Hayashi to the Future (Kyoto, Japan

Hierarchical Feature Learning

The success of many tasks depends on good feature representation which is often domain-specific and hand-crafted requiring substantial human effort. Such feature representation is not general, i.e. unsuitable for even the same task across multiple domains, let alone different tasks.To address these issues, a multilayered convergent neural architecture is presented for learning from repeating spatially and temporally coincident patterns in data at multiple levels of abstraction. The bottom-up weights in each layer are learned to encode a hierarchy of overcomplete and sparse feature dictionaries from space- and time-varying sensory data. Two algorithms are investigated: recursive layer-by-layer spherical clustering and sparse coding to learn feature hierarchies. The model scales to full-sized high-dimensional input data and to an arbitrary number of layers thereby having the capability to capture features at any level of abstraction. The model learns features that correspond to objects in higher layers and object-parts in lower layers.Learning features invariant to arbitrary transformations in the data is a requirement for any effective and efficient representation system, biological or artificial. Each layer in the proposed network is composed of simple and complex sublayers motivated by the layered organization of the primary visual cortex. When exposed to natural videos, the model develops simple and complex cell-like receptive field properties. The model can predict by learning lateral connections among the simple sublayer neurons. A topographic map to their spatial features emerges by minimizing the wiring length simultaneously with feature learning.The model is general-purpose, unsupervised and online. Operations in each layer of the model can be implemented in parallelized hardware, making it very efficient for real world applications