2,609 research outputs found
Thermodynamic Entropy And The Accessible States of Some Simple Systems
Comparison of the thermodynamic entropy with Boltzmann's principle shows that
under conditions of constant volume the total number of arrangements in simple
thermodynamic systems with temperature-independent heat capacities is TC/k. A
physical interpretation of this function is given for three such systems; an
ideal monatomic gas, an ideal gas of diatomic molecules with rotational motion,
and a solid in the Dulong-Petit limit of high temperature. T1/2 emerges as a
natural measure of the number of accessible states for a single particle in one
dimension. Extension to N particles in three dimensions leads to TC/k as the
total number of possible arrangements or microstates. The different microstates
of the system are thus shown a posteriori to be equally probable, with
probability T-C/k, which implies that for the purposes of counting states the
particles of the gas are distinguishable. The most probable energy state of the
system is determined by the degeneracy of the microstates.Comment: 9 pages, 1 figur
Observer with a constant proper acceleration
Relying on the equivalence principle, a first approach of the general theory
of relativity is presented using the spacetime metric of an observer with a
constant proper acceleration. Within this non inertial frame, the equation of
motion of a freely moving object is studied and the equation of motion of a
second accelerated observer with the same proper acceleration is examined. A
comparison of the metric of the accelerated observer with the metric due to a
gravitational field is also performed.Comment: 5 figure
Ideal Gas in a strong Gravitational field: Area dependence of Entropy
We study the thermodynamic parameters like entropy, energy etc. of a box of
gas made up of indistinguishable particles when the box is kept in various
static background spacetimes having a horizon. We compute the thermodynamic
variables using both statistical mechanics as well as by solving the
hydrodynamical equations for the system. When the box is far away from the
horizon, the entropy of the gas depends on the volume of the box except for
small corrections due to background geometry. As the box is moved closer to the
horizon with one (leading) edge of the box at about Planck length (L_p) away
from the horizon, the entropy shows an area dependence rather than a volume
dependence. More precisely, it depends on a small volume A*L_p/2 of the box,
upto an order O(L_p/K)^2 where A is the transverse area of the box and K is the
(proper) longitudinal size of the box related to the distance between leading
and trailing edge in the vertical direction (i.e in the direction of the
gravitational field). Thus the contribution to the entropy comes from only a
fraction O(L_p/K) of the matter degrees of freedom and the rest are suppressed
when the box approaches the horizon. Near the horizon all the thermodynamical
quantities behave as though the box of gas has a volume A*L_p/2 and is kept in
a Minkowski spacetime. These effects are: (i) purely kinematic in their origin
and are independent of the spacetime curvature (in the sense that Rindler
approximation of the metric near the horizon can reproduce the results) and
(ii) observer dependent. When the equilibrium temperature of the gas is taken
to be equal to the the horizon temperature, we get the familiar A/L_p^2
dependence in the expression for entropy. All these results hold in a D+1
dimensional spherically symmetric spacetime.Comment: 19 pages, added some discussion, matches published versio
Incoherent dynamics in neutron-matter interaction
Coherent and incoherent neutron-matter interaction is studied inside a
recently introduced approach to subdynamics of a macrosystem. The equation
describing the interaction is of the Lindblad type and using the Fermi
pseudopotential we show that the commutator term is an optical potential
leading to well-known relations in neutron optics. The other terms, usually
ignored in optical descriptions and linked to the dynamic structure function of
the medium, give an incoherent contribution to the dynamics, which keeps
diffuse scattering and attenuation of the coherent beam into account, thus
warranting fulfilment of the optical theorem. The relevance of this analysis to
experiments in neutron interferometry is briefly discussed.Comment: 15 pages, revtex, no figures, to appear in Phys. Rev.
Direct evidence for the magnetic ordering of Nd ions in NdFeAsO by high resolution inelastic neutron scattering
We investigated the low energy excitations in the parent compound NdFeAsO of
the Fe-pnictide superconductor in the eV range by a back scattering
neutron spectrometer. The energy scans on a powder NdFeAsO sample revealed
inelastic peaks at E = 1.600 eV at T = 0.055 K on both energy
gain and energy loss sides. The inelastic peaks move gradually towards lower
energy with increasing temperature and finally merge with the elastic peak at
about 6 K. We interpret the inelastic peaks to be due to the transition between
hyperfine-split nuclear level of the Nd and Nd isotopes with
spin . The hyperfine field is produced by the ordering of the
electronic magnetic moment of Nd at low temperature and thus the present
investigation gives direct evidence of the ordering of the Nd magnetic
sublattice of NdFeAsO at low temperature
The Minkowski metric in non-inertial observer radar coordinates
We give a closed expression for the Minkowski (1+1)-dimensional metric in the
radar coordinates of an arbitrary non-inertial observer O in terms of O's
proper acceleration. Knowledge of the metric allows the non-inertial observer
to perform experiments in spacetime without making reference to inertial
frames. To clarify the relation between inertial and non-inertial observers the
coordinate transformation between radar and inertial coordinates, also is
given. We show that every conformally flat coordinate system can be regarded as
the radar coordinate system of a suitable observer for a suitable
parametrization of the observer worldline. Therefore, the coordinate
transformation between arbitrarily moving observers is a conformal
transformation and conformally invariant (1+1)-dimensional theories lead to the
same physics for all observers, independently of their relative motion.Comment: Revtex4, 6 pages, 1 figur
Using state space differential geometry for nonlinear blind source separation
Given a time series of multicomponent measurements of an evolving stimulus,
nonlinear blind source separation (BSS) seeks to find a "source" time series,
comprised of statistically independent combinations of the measured components.
In this paper, we seek a source time series with local velocity cross
correlations that vanish everywhere in stimulus state space. However, in an
earlier paper the local velocity correlation matrix was shown to constitute a
metric on state space. Therefore, nonlinear BSS maps onto a problem of
differential geometry: given the metric observed in the measurement coordinate
system, find another coordinate system in which the metric is diagonal
everywhere. We show how to determine if the observed data are separable in this
way, and, if they are, we show how to construct the required transformation to
the source coordinate system, which is essentially unique except for an unknown
rotation that can be found by applying the methods of linear BSS. Thus, the
proposed technique solves nonlinear BSS in many situations or, at least,
reduces it to linear BSS, without the use of probabilistic, parametric, or
iterative procedures. This paper also describes a generalization of this
methodology that performs nonlinear independent subspace separation. In every
case, the resulting decomposition of the observed data is an intrinsic property
of the stimulus' evolution in the sense that it does not depend on the way the
observer chooses to view it (e.g., the choice of the observing machine's
sensors). In other words, the decomposition is a property of the evolution of
the "real" stimulus that is "out there" broadcasting energy to the observer.
The technique is illustrated with analytic and numerical examples.Comment: Contains 14 pages and 3 figures. For related papers, see
http://www.geocities.com/dlevin2001/ . New version is identical to original
version except for URL in the bylin
Symmetric airfoil geometry effects on leading edge noise
Computational aeroacoustic methods are applied to the modeling of noise due to interactions between gusts and the leading edge of real symmetric airfoils. Single frequency harmonic gusts are interacted with various airfoil geometries at zero angle of attack. The effects of airfoil thickness and leading edge radius on noise are investigated systematically and independently for the first time, at higher frequencies than previously used in computational methods. Increases in both leading edge radius and thickness are found to reduce the predicted noise. This noise reduction effect becomes greater with increasing frequency and Mach number. The dominant noise reduction mechanism for airfoils with real geometry is found to be related to the leading edge stagnation region. It is shown that accurate leading edge noise predictions can be made when assuming an inviscid meanflow, but that it is not valid to assume a uniform meanflow. Analytic flat plate predictions are found to over-predict the noise due to a NACA 0002 airfoil by up to 3 dB at high frequencies. The accuracy of analytic flat plate solutions can be expected to decrease with increasing airfoil thickness, leading edge radius, gust frequency and Mach number
Flight Determination of Drag of Normal-shock Nose Inlets with Various Cowling Profiles at Mach Numbers from 0.9 to 1.5
Nuclear Incompressibility in Asymmetric Systems at Finite Temperature and Entropy
The nuclear incompressibility is investigated in asymmetric systems
in a mean field model. The calculations are done at zero and finite
temperatures and include surface, Coulomb and symmetry energy terms for several
equations of state. Also considered is the behavior of the incompressibility at
constant entropy which is shown to have a very different behavior
than the isothermal . Namely, decreases with increasing
entropy while the isothermal increases with increasing . A duality
is found between the adiabatic and the T=0 isothermal .
Analytic and also simple approximate expressions for are given.Comment: 11 page
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