6,270 research outputs found
Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States
Among various possible routes to extend entropy and thermodynamics to
nonequilibrium steady states (NESS), we take the one which is guided by
operational thermodynamics and the Clausius relation. In our previous study, we
derived the extended Clausius relation for NESS, where the heat in the original
relation is replaced by its "renormalized" counterpart called the excess heat,
and the Gibbs-Shannon expression for the entropy by a new symmetrized
Gibbs-Shannon-like expression. Here we concentrate on Markov processes
describing heat conducting systems, and develop a new method for deriving
thermodynamic relations. We first present a new simpler derivation of the
extended Clausius relation, and clarify its close relation with the linear
response theory. We then derive a new improved extended Clausius relation with
a "nonlinear nonequilibrium" contribution which is written as a correlation
between work and heat. We argue that the "nonlinear nonequilibrium"
contribution is unavoidable, and is determined uniquely once we accept the
(very natural) definition of the excess heat. Moreover it turns out that to
operationally determine the difference in the nonequilibrium entropy to the
second order in the temperature difference, one may only use the previous
Clausius relation without a nonlinear term or must use the new relation,
depending on the operation (i.e., the path in the parameter space). This
peculiar "twist" may be a clue to a better understanding of thermodynamics and
statistical mechanics of NESS.Comment: 31 pages, 4 figure
Multi-Dimensional Astrophysical Structural and Dynamical Analysis I. Development of a Nonlinear Finite Element Approach
A new field of numerical astrophysics is introduced which addresses the
solution of large, multidimensional structural or slowly-evolving problems
(rotating stars, interacting binaries, thick advective accretion disks, four
dimensional spacetimes, etc.). The technique employed is the Finite Element
Method (FEM), commonly used to solve engineering structural problems. The
approach developed herein has the following key features:
1. The computational mesh can extend into the time dimension, as well as
space, perhaps only a few cells, or throughout spacetime.
2. Virtually all equations describing the astrophysics of continuous media,
including the field equations, can be written in a compact form similar to that
routinely solved by most engineering finite element codes.
3. The transformations that occur naturally in the four-dimensional FEM
possess both coordinate and boost features, such that
(a) although the computational mesh may have a complex, non-analytic,
curvilinear structure, the physical equations still can be written in a simple
coordinate system independent of the mesh geometry.
(b) if the mesh has a complex flow velocity with respect to coordinate space,
the transformations will form the proper arbitrary Lagrangian- Eulerian
advective derivatives automatically.
4. The complex difference equations on the arbitrary curvilinear grid are
generated automatically from encoded differential equations.
This first paper concentrates on developing a robust and widely-applicable
set of techniques using the nonlinear FEM and presents some examples.Comment: 28 pages, 9 figures; added integral boundary conditions, allowing
very rapidly-rotating stars; accepted for publication in Ap.
Modeling Intra-Cluster Gas in Triaxial Dark Halos : An Analytical Approach
We present the first physical model for the non-spherical intra-cluster gas
distribution in hydrostatic equilibrium under the gravity of triaxial dark
matter halos. Adopting the concentric triaxial density profiles of the dark
halos with constant axis ratios proposed by Jing & Suto (2002), we derive an
analytical expression for the triaxial halo potential on the basis of the
perturbation theory, and find the hydrostatic solutions for the gas density and
temperature profiles both in isothermal and polytropic equations of state. The
resulting iso-potential surfaces are well approximated by triaxial ellipsoids
with the eccentricities dependent on the radial distance. We also find a
formula for the eccentricity ratio between the intra-cluster gas and the
underlying dark halo. Our results allow one to determine the shapes of the
underlying dark halos from the observed intra-cluster gas through the X-ray
and/or the Sunyaev-Zel'dovich effects clusters.Comment: accepted by ApJ, LaTex file, 22 pages, 8 postscript figure
University Student Learning in Everyday Life Activity: Place, Time, and Media
A lot of Japanese universities introduce some e-learning systems into their education. In this paper, we ask 22 female university/college students to report when, where, and what they do, and which kind of media/tool they use for their everyday life activities. We asked them to do this, every 15 minutes for a week. We also interview the students after their reporting everyday life activities, and analysis the log data of the system use. We describe students\u27 activities in their everyday life and learning. We discuss the meaning of students\u27 learning activities, especially activities using the e-learning system and other information and communication technology in their everyday life from the perspective of Vygotsky\u27s ideas of media/tool. Some implications for future research are outlined
Stationary structures of irrotational binary systems -- models for close binary systems of compact stars
We propose a new numerical method to calculate irrotational binary systems
composed of compressible gaseous stars in Newtonian gravity. Assuming
irrotationality, i.e. vanishing of the vorticity vector everywhere in the star
in the inertial frame, we can introduce the velocity potential for the flow
field. Using this velocity potential we can derive a set of basic equations for
stationary states which consist of (i) the generalized Bernoulli equation, (ii)
the Poisson equation for the Newtonian gravitational potential and (iii) the
equation for the velocity potential with the Neumann type boundary condition.
We succeeded in developing a new code to compute numerically exact solutions to
these equations for the first time. Such irrotational configurations of binary
systems are appropriate models for realistic neutron star binaries composed of
inviscid gases, just prior to coalescence of two stars caused by emission of
gravitational waves. Accuracies of our numerical solutions are so high that we
can compute reliable models for fully deformed final stationary configurations
and hence determine the inner most stable circular orbit of binary neutron star
systems under the approximations of weak gravity and inviscid limit.Comment: 32 pages, 25 bitmapped ps files, to appear in ApJ supplemen
Cosmological Lower Bound on Dark Matter Masses from the Soft Gamma-ray Background
Motivated by a recent detection of 511 keV photons from the center of our
Galaxy, we calculate the spectrum of the soft gamma-ray background of the
redshifted 511 keV photons from cosmological halos. Annihilation of dark matter
particles into electron-positron pairs makes a substantial contribution to the
gamma-ray background. Mass of such dark matter particles must be <~ 100 MeV so
that resulting electron-positron pairs are on-relativistic. On the other hand,
we show that in order for the annihilation not to exceed the observed
background, the dark matter mass needs to be >~ 20 MeV. We include the
contribution from the active galactic nuclei and supernovae. The halo
substructures may increase the lower bound to >~ 60 MeV.Comment: 5 pages, 5 figures; accepted for publication in PRD, Rapid
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