50,888 research outputs found
Analytic approximations, perturbation theory, effective field theory methods and their applications
We summarize the parallel session B4: 'Analytic approximations, perturbation
theory effective field theory methods and their applications' and the joint
session B2/B4: 'Approximate solutions to Einstein equations: Methods and
Applications', of the GR20 & Amaldi10 conference in Warsaw, July 2013. The
contributed talks reported significant advances on various areas of research in
gravity.Comment: 15 pages. Contribution to the Proceedings of GR20 - Amaldi1
Emergence of the second law out of reversible dynamics
Abstract If one demystifies entropy the second law of thermodynamics comes out as an emergent property entirely based on the simple dynamic mechanical laws that govern the motion and energies of system parts on a micro-scale. The emergence of the second law is illustrated in this paper through the development of a new, very simple and highly efficient technique to compare time-averaged energies in isolated conservative linear large scale dynamical systems. Entropy is replaced by a notion that is much more transparent and more or less dual called ectropy. Ectropy has been introduced before but we further modify the notion of ectropy such that the unit in which it is expressed becomes the unit of energy. The second law of thermodynamics in terms of ectropy states that ectropy decreases with time on a large enough time-scale and has an absolute minimum equal to zero. Zero ectropy corresponds to energy equipartition. Basically we show that by enlarging the dimension of an isolated conservative linear dynamical system and the dimension of the system parts over which we consider time-averaged energy partition, the tendency towards equipartition increases while equipartition is achieved in the limit. This illustrates that the second law is an emergent property of these systems. Finally from our large scale linear dynamic model we clarify Loschmidt’s paradox concerning the irreversible behavior of ectropy obtained from the reversible dynamic laws that govern motion and energy at the micro-scal
A comparison between observed Algol-type double stars in the Solar neighborhood and evolutionary computations of galactic case A binaries with a B-type primary at birth
We first discuss a large set of evolutionary calculations of close binaries
with a B-type primary at birth and with a period such that the Roche lobe
overflow starts during the core hydrogen burning phase of the primary
(intermediate mass and massive case A binaries). The evolution of both
components is followed simultaneously allowing us to check for the occurrence
of contact binaries. We consider various models to treat a contact system and
the influence of these models on the predicted Algol-type system population is
investigated. We critically discuss the available observations of Algol-type
binaries with a B-type primary at birth. Comparing these observations with the
predictions allows us to put constraints on the contact star physics. We find
that mass transfer in Algols is most probably not conservative, that contact
during this phase does not necessarily lead to a merger, and that angular
momentum loss must be moderate.Comment: 8 pages, 9 figures, accepted for publication in A&A; accepted versio
High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates
High-order reconstruction schemes for the solution of hyperbolic conservation
laws in orthogonal curvilinear coordinates are revised in the finite volume
approach. The formulation employs a piecewise polynomial approximation to the
zone-average values to reconstruct left and right interface states from within
a computational zone to arbitrary order of accuracy by inverting a
Vandermonde-like linear system of equations with spatially varying
coefficients. The approach is general and can be used on uniform and
non-uniform meshes although explicit expressions are derived for polynomials
from second to fifth degree in cylindrical and spherical geometries with
uniform grid spacing. It is shown that, in regions of large curvature, the
resulting expressions differ considerably from their Cartesian counterparts and
that the lack of such corrections can severely degrade the accuracy of the
solution close to the coordinate origin. Limiting techniques and monotonicity
constraints are revised for conventional reconstruction schemes, namely, the
piecewise linear method (PLM), third-order weighted essentially non-oscillatory
(WENO) scheme and the piecewise parabolic method (PPM).
The performance of the improved reconstruction schemes is investigated in a
number of selected numerical benchmarks involving the solution of both scalar
and systems of nonlinear equations (such as the equations of gas dynamics and
magnetohydrodynamics) in cylindrical and spherical geometries in one and two
dimensions. Results confirm that the proposed approach yields considerably
smaller errors, higher convergence rates and it avoid spurious numerical
effects at a symmetry axis.Comment: 37 pages, 12 Figures. Accepted for publication in Journal of
Compuational Physic
The Zeroth Law of Thermodynamics and Volume-Preserving Conservative Dynamics with Equilibrium Stochastic Damping
We propose a mathematical formulation of the zeroth law of thermodynamics and
develop a stochastic dynamical theory, with a consistent irreversible
thermodynamics, for systems possessing sustained conservative stationary
current in phase space while in equilibrium with a heat bath. The theory
generalizes underdamped mechanical equilibrium: , with and respectively
representing phase-volume preserving dynamics and stochastic damping. The
zeroth law implies stationary distribution . We find an
orthogonality as a hallmark of the system. Stochastic
thermodynamics based on time reversal
is formulated: entropy
production ; generalized "heat" ,
being "internal energy", and "free
energy" never increases.
Entropy follows . Our formulation is shown to
be consistent with an earlier theory of P. Ao. Its contradistinctions to other
theories, potential-flux decomposition, stochastic Hamiltonian system with even
and odd variables, Klein-Kramers equation, Freidlin-Wentzell's theory, and
GENERIC, are discussed.Comment: 25 page
Formulations of moist thermodynamics for atmospheric modelling
Internal energy, enthalpy and entropy are the key quantities to study
thermodynamic properties of the moist atmosphere, because they correspond to
the First (internal energy and enthalpy) and Second (entropy) Laws of
thermodynamics. The aim of this chapter is to search for analytical formulas
for the specific values of enthalpy and entropy and for the moist-air mixture
composing the atmosphere.
The Third Law of thermodynamics leads to the definition of absolute reference
values for thermal enthalpies and entropies of all atmospheric species. It is
shown in this Chapter 22 that it is possible to define and compute a general
moist-air entropy potential temperature, which is really an equivalent of the
moist-air specific entropy in all circumstances (saturated, or not saturated).
Similarly, it is shown that it is possible to define and compute the moist-air
specific enthalpy, which is different from the thermal part of what is called
Moist-Static-Energy in atmospheric studies.Comment: 44 pages, 8 figures,
URL:http://www.worldscientific.com/doi/abs/10.1142/9781783266913_002
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