25,449 research outputs found
Two algorithms to construct a consistent first order theory of equilibrium figures of close binary systems
One of the main problems in celestial mechanics is the study of the shape adopted by extended deformable celestial bodies in its equilibrium configuration. In this paper, a new point of view about classical theories on equilibrium figures in close binary systems is offered.
Classical methods are based on the evaluation of the self-gravitational, centrifugal and tidal potentials. The most common technique used by classical methods shows convergence problems. To solve this problem up to first order in amplitudes two algorithms has been developed, the first one based on the Laplace method to develop the inverse of the distance and the second one based on the asymptotic properties of the numerical quadrature formulas.This research has been partially supported by Grant AICO/2015/037 from the Generalitat Valenciana
Numerical Models of Binary Neutron Star System Mergers. I.: Numerical Methods and Equilibrium Data for Newtonian Models
The numerical modeling of binary neutron star mergers has become a subject of
much interest in recent years. While a full and accurate model of this
phenomenon would require the evolution of the equations of relativistic
hydrodynamics along with the Einstein field equations, a qualitative study of
the early stages on inspiral can be accomplished by either Newtonian or
post-Newtonian models, which are more tractable. In this paper we offer a
comparison of results from both rotating and non-rotating (inertial) frame
Newtonian calculations. We find that the rotating frame calculations offer
significantly improved accuracy as compared with the inertial frame models.
Furthermore, we show that inertial frame models exhibit significant and
erroneous angular momentum loss during the simulations that leads to an
unphysical inspiral of the two neutron stars. We also examine the dependence of
the models on initial conditions by considering initial configurations that
consist of spherical neutron stars as well as stars that are in equilibrium and
which are tidally distorted. We compare our models those of Rasio & Shapiro
(1992,1994a) and New & Tohline (1997). Finally, we investigate the use of the
isolated star approximation for the construction of initial data.Comment: 32 pages, 19 gif figures, manuscript with postscript figures
available at http://www.astro.sunysb.edu/dswesty/docs/nspap1.p
Mean field theory of hard sphere glasses and jamming
Hard spheres are ubiquitous in condensed matter: they have been used as
models for liquids, crystals, colloidal systems, granular systems, and powders.
Packings of hard spheres are of even wider interest, as they are related to
important problems in information theory, such as digitalization of signals,
error correcting codes, and optimization problems. In three dimensions the
densest packing of identical hard spheres has been proven to be the FCC
lattice, and it is conjectured that the closest packing is ordered (a regular
lattice, e.g, a crystal) in low enough dimension. Still, amorphous packings
have attracted a lot of interest, because for polydisperse colloids and
granular materials the crystalline state is not obtained in experiments for
kinetic reasons. We review here a theory of amorphous packings, and more
generally glassy states, of hard spheres that is based on the replica method:
this theory gives predictions on the structure and thermodynamics of these
states. In dimensions between two and six these predictions can be successfully
compared with numerical simulations. We will also discuss the limit of large
dimension where an exact solution is possible. Some of the results we present
here have been already published, but others are original: in particular we
improved the discussion of the large dimension limit and we obtained new
results on the correlation function and the contact force distribution in three
dimensions. We also try here to clarify the main assumptions that are beyond
our theory and in particular the relation between our static computation and
the dynamical procedures used to construct amorphous packings.Comment: 59 pages, 25 figures. Final version published on Rev.Mod.Phy
Minimum and maximum entropy distributions for binary systems with known means and pairwise correlations
Maximum entropy models are increasingly being used to describe the collective
activity of neural populations with measured mean neural activities and
pairwise correlations, but the full space of probability distributions
consistent with these constraints has not been explored. We provide upper and
lower bounds on the entropy for the {\em minimum} entropy distribution over
arbitrarily large collections of binary units with any fixed set of mean values
and pairwise correlations. We also construct specific low-entropy distributions
for several relevant cases. Surprisingly, the minimum entropy solution has
entropy scaling logarithmically with system size for any set of first- and
second-order statistics consistent with arbitrarily large systems. We further
demonstrate that some sets of these low-order statistics can only be realized
by small systems. Our results show how only small amounts of randomness are
needed to mimic low-order statistical properties of highly entropic
distributions, and we discuss some applications for engineered and biological
information transmission systems.Comment: 34 pages, 7 figure
Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics
We present results of the application of the anisotropic hydrodynamics
(aHydro) framework to (2+1)-dimensional boost invariant systems. The necessary
aHydro dynamical equations are derived by taking moments of the Boltzmann
equation using a momentum-space anisotropic one-particle distribution function.
We present a derivation of the necessary equations and then proceed to
numerical solutions of the resulting partial differential equations using both
realistic smooth Glauber initial conditions and fluctuating Monte-Carlo Glauber
initial conditions. For this purpose we have developed two numerical
implementations: one which is based on straightforward integration of the
resulting partial differential equations supplemented by a two-dimensional
weighted Lax-Friedrichs smoothing in the case of fluctuating initial
conditions; and another that is based on the application of the Kurganov-Tadmor
central scheme. For our final results we compute the collective flow of the
matter via the lab-frame energy-momentum tensor eccentricity as a function of
the assumed shear viscosity to entropy ratio, proper time, and impact
parameter.Comment: 45 pages, 12 figures; v2 published versio
Optimal design and optimal control of structures undergoing finite rotations and elastic deformations
In this work we deal with the optimal design and optimal control of
structures undergoing large rotations. In other words, we show how to find the
corresponding initial configuration and the corresponding set of multiple load
parameters in order to recover a desired deformed configuration or some
desirable features of the deformed configuration as specified more precisely by
the objective or cost function. The model problem chosen to illustrate the
proposed optimal design and optimal control methodologies is the one of
geometrically exact beam. First, we present a non-standard formulation of the
optimal design and optimal control problems, relying on the method of Lagrange
multipliers in order to make the mechanics state variables independent from
either design or control variables and thus provide the most general basis for
developing the best possible solution procedure. Two different solution
procedures are then explored, one based on the diffuse approximation of
response function and gradient method and the other one based on genetic
algorithm. A number of numerical examples are given in order to illustrate both
the advantages and potential drawbacks of each of the presented procedures.Comment: 35 pages, 11 figure
U.S. stock market interaction network as learned by the Boltzmann Machine
We study historical dynamics of joint equilibrium distribution of stock
returns in the U.S. stock market using the Boltzmann distribution model being
parametrized by external fields and pairwise couplings. Within Boltzmann
learning framework for statistical inference, we analyze historical behavior of
the parameters inferred using exact and approximate learning algorithms. Since
the model and inference methods require use of binary variables, effect of this
mapping of continuous returns to the discrete domain is studied. The presented
analysis shows that binarization preserves market correlation structure.
Properties of distributions of external fields and couplings as well as
industry sector clustering structure are studied for different historical dates
and moving window sizes. We found that a heavy positive tail in the
distribution of couplings is responsible for the sparse market clustering
structure. We also show that discrepancies between the model parameters might
be used as a precursor of financial instabilities.Comment: 15 pages, 17 figures, 1 tabl
Basic Understanding of Condensed Phases of Matter via Packing Models
Packing problems have been a source of fascination for millenia and their
study has produced a rich literature that spans numerous disciplines.
Investigations of hard-particle packing models have provided basic insights
into the structure and bulk properties of condensed phases of matter, including
low-temperature states (e.g., molecular and colloidal liquids, crystals and
glasses), multiphase heterogeneous media, granular media, and biological
systems. The densest packings are of great interest in pure mathematics,
including discrete geometry and number theory. This perspective reviews
pertinent theoretical and computational literature concerning the equilibrium,
metastable and nonequilibrium packings of hard-particle packings in various
Euclidean space dimensions. In the case of jammed packings, emphasis will be
placed on the "geometric-structure" approach, which provides a powerful and
unified means to quantitatively characterize individual packings via jamming
categories and "order" maps. It incorporates extremal jammed states, including
the densest packings, maximally random jammed states, and lowest-density jammed
structures. Packings of identical spheres, spheres with a size distribution,
and nonspherical particles are also surveyed. We close this review by
identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal
of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298
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