3,508 research outputs found
Perturbative Analysis of Universality and Individuality in Gravitational Waves from Neutron Stars
The universality observed in gravitational wave spectra of non-rotating
neutron stars is analyzed here. We show that the universality in the axial
oscillation mode can be reproduced with a simple stellar model, namely the
centrifugal barrier approximation (CBA), which captures the essence of the
Tolman VII model of compact stars. Through the establishment of scaled
co-ordinate logarithmic perturbation theory (SCLPT), we are able to explain and
quantitatively predict such universal behavior. In addition, quasi-normal modes
of individual neutron stars characterized by different equations of state can
be obtained from those of CBA with SCLPT.Comment: 29 pages, 10 figures, submitted to Astrophysical Journa
Methods and Approaches for Characterizing Learning Related Changes Observed in functional MRI Data — A Review
Brain imaging data have so far revealed a wealth of information about neuronal circuits involved in higher mental functions like memory, attention, emotion, language etc. Our efforts are toward understanding the learning related effects in brain activity during the acquisition of visuo-motor sequential skills. The aim of this paper is to survey various methods and approaches of analysis that allow the characterization of learning related changes in fMRI data. Traditional imaging analysis using the Statistical Parametric Map (SPM) approach averages out temporal changes and presents overall differences between different stages of learning. We outline other potential approaches for revealing learning effects such as statistical time series analysis, modelling of haemodynamic response function and independent component analysis. We present example case studies from our visuo-motor sequence learning experiments to describe application of SPM and statistical time series analyses. Our review highlights that the problem of characterizing learning induced changes in fMRI data remains an interesting and challenging open research problem
A Multi-disciplinary Approach to the Investigation of Aspects of Serial Order in Cognition
Serial order processing or Sequence processing underlies many human activities such as speech, language, skill learning, planning, problem solving, etc. Investigating the\ud
neural bases of sequence processing enables us to understand serial order in cognition and helps us building intelligent devices. In the current paper, various\ud
cognitive issues related to sequence processing will be discussed with examples. Some of the issues are: distributed versus local representation, pre-wired versus\ud
adaptive origins of representation, implicit versus explicit learning, fixed/flat versus hierarchical organization, timing aspects, order information embedded in sequences, primacy versus recency in list learning and aspects of sequence perception such as recognition, recall and generation. Experimental results that give evidence for the involvement of various brain areas will be described. Finally, theoretical frameworks based on Markov models and Reinforcement Learning paradigm will be presented. These theoretical ideas are useful for studying sequential phenomena in a principled way
Stability and evolution of wave packets in strongly coupled degenerate plasmas
We study the nonlinear propagation of electrostatic wave packets in a
collisional plasma composed of strongly coupled ions and relativistically
degenerate electrons. The equilibrium of ions is maintained by an effective
temperature associated with their strong coupling, whereas that of electrons is
provided by the relativistic degeneracy pressure. Using a multiple scale
technique, a (3+1)-dimensional coupled set of nonlinear Schr\"{o}dinger-like
equations with nonlocal nonlinearity is derived from a generalized viscoelastic
hydrodynamic model. These coupled equations, which govern the dynamics of wave
packets, are used to study the oblique modulational instability of a Stoke's
wave train to a small plane wave perturbation. We show that the wave packets,
though stable to the parallel modulation, becomes unstable against oblique
modulations. In contrast to the long-wavelength carrier modes, the wave packets
with short-wavelengths are shown to be stable in the weakly relativistic case,
whereas they can be stable or unstable in the ultra-relativistic limit.
Numerical simulation of the coupled equations reveals that a steady state
solution of the wave amplitude exists together with the formation of a
localized structure in (2+1) dimensions. However, in the (3+1)-dimensional
evolution, a Gaussian wave beam self-focuses after interaction and blows up in
a finite time. The latter is, however, arrested when the dispersion
predominates over the nonlinearities. This occurs when the Coulomb coupling
strength is higher or a choice of obliqueness of modulation, or a wavelength of
excitation is different. Possible application of our results to the interior as
well as in an outer mantle of white dwarfs are discussed.Comment: 18 pages, 7 figures; To appear in Phys. Rev. E (2012); The manuscript
has been revised with few discussions and citation of some relevant
reference
The spatial correlations in the velocities arising from a random distribution of point vortices
This paper is devoted to a statistical analysis of the velocity fluctuations
arising from a random distribution of point vortices in two-dimensional
turbulence. Exact results are derived for the correlations in the velocities
occurring at two points separated by an arbitrary distance. We find that the
spatial correlation function decays extremely slowly with the distance. We
discuss the analogy with the statistics of the gravitational field in stellar
systems.Comment: 37 pages in RevTeX format (no figure); submitted to Physics of Fluid
Determination of the internal structure of neutron stars from gravitational wave spectra
In this paper the internal structure of a neutron star is shown to be
inferrable from its gravitational-wave spectrum. Iteratively applying the
inverse scheme of the scaled coordinate logarithmic perturbation method for
neutron stars proposed by Tsui and Leung [Astrophys. J. {\bf 631}, 495 (2005)],
we are able to determine the mass, the radius and the mass distribution of a
star from its quasi-normal mode frequencies of stellar pulsation. In addition,
accurate equation of state of nuclear matter can be obtained from such
inversion scheme. Explicit formulas for the case of axial -mode oscillation
are derived here and numerical results for neutron stars characterized by
different equations of state are shown.Comment: 26 pages, 14 figures, submitted to Physical Review
The weakly perturbed Schwarzschild lens in the strong deflection limit
We investigate the strong deflection limit of gravitational lensing by a
Schwarzschild black hole embedded in an external gravitational field. The study
of this model, analogous to the Chang & Refsdal lens in the weak deflection
limit, is important to evaluate the gravitational perturbations on the
relativistic images that appear in proximity of supermassive black holes hosted
in galactic centers. By a simple dimensional argument, we prove that the tidal
effect on the light ray propagation mainly occurs in the weak field region far
away from the black hole and that the external perturbation can be treated as a
weak field quadrupole term. We provide a description of relativistic critical
curves and caustics and discuss the inversion of the lens mapping. Relativistic
caustics are shifted and acquire a finite diamond shape. Sources inside the
caustics produce four sequences of relativistic images. On the other hand,
retro-lensing caustics are only shifted while remaining point-like to the
lowest order.Comment: 12 pages, 1 figure
Stellar configurations in f(R) theories of gravity
We study stellar configurations and the space-time around them in metric
theories of gravity. In particular, we focus on the polytropic model of
the Sun in the model. We show how the stellar configuration in
the theory can, by appropriate initial conditions, be selected to be
equal to that described by the Lane-Emden -equation and how a simple scaling
relation exists between the solutions. We also derive the correct solution
analytically near the center of the star in theory. Previous analytical
and numerical results are confirmed, indicating that the space-time around the
Sun is incompatible with Solar System constraints on the properties of gravity.
Numerical work shows that stellar configurations, with a regular metric at the
center, lead to outside the star ie. the
Schwarzschild-de Sitter -space-time is not the correct vacuum solution for such
configurations. Conversely, by selecting the Schwarzschild-de Sitter -metric as
the outside solution, we find that the stellar configuration is unchanged but
the metric is irregular at the center. The possibility of constructing a
theory compatible with the Solar System experiments and possible new
constraints arising from the radius-mass -relation of stellar objects is
discussed.Comment: 8 pages, 7 figures; typos corrected, reference adde
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