24,627 research outputs found
Equation of state for hard sphere fluids with and without Kac tails
In this note, we propose a simple derivation of the one dimensional hard rod
equation of state, with and without a Kac tail (appended long range and weak
potential). The case of hard spheres in higher dimension is also addressed and
it is shown there that our arguments --which avoid any mathematical
complication-- allow to recover the virial form of the equation of state in a
direct way.Comment: pedagogical pape
A Paraconsistent Higher Order Logic
Classical logic predicts that everything (thus nothing useful at all) follows
from inconsistency. A paraconsistent logic is a logic where an inconsistency
does not lead to such an explosion, and since in practice consistency is
difficult to achieve there are many potential applications of paraconsistent
logics in knowledge-based systems, logical semantics of natural language, etc.
Higher order logics have the advantages of being expressive and with several
automated theorem provers available. Also the type system can be helpful. We
present a concise description of a paraconsistent higher order logic with
countable infinite indeterminacy, where each basic formula can get its own
indeterminate truth value (or as we prefer: truth code). The meaning of the
logical operators is new and rather different from traditional many-valued
logics as well as from logics based on bilattices. The adequacy of the logic is
examined by a case study in the domain of medicine. Thus we try to build a
bridge between the HOL and MVL communities. A sequent calculus is proposed
based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker,
Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte
Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature
We prove convergence results for expanding curvature flows in the Euclidean
and hyperbolic space. The flow speeds have the form , where and
is a positive, strictly monotone and 1-homogeneous curvature function. In
particular this class includes the mean curvature . We prove that a
certain initial pinching condition is preserved and the properly rescaled
hypersurfaces converge smoothly to the unit sphere. We show that an example due
to Andrews-McCoy-Zheng can be used to construct strictly convex initial
hypersurfaces, for which the inverse mean curvature flow to the power
loses convexity, justifying the necessity to impose a certain pinching
condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and
pinching. In the third version we dropped the concavity assumption on F.
Comments are welcom
How to measure the Bogoliubov quasiparticle amplitudes in a trapped condensate
We propose an experiment, based on two consecutive Bragg pulses, to measure
the momentum distribution of quasiparticle excitations in a trapped Bose gas at
low temperature. With the first pulse one generates a bunch of excitations
carrying momentum , whose Doppler line is measured by the second pulse. We
show that this experiment can provide direct access to the amplitudes
and characterizing the Bogoliubov transformations from particles to
quasiparticles. We simulate the behavior of the nonuniform gas by numerically
solving the time dependent Gross-Pitaevskii equation.Comment: 12 pages, 4 figures include
Herschel evidence for disk flattening or gas depletion in transitional disks
Transitional disks are protoplanetary disks characterized by reduced near-
and mid-infrared emission with respect to full disks. This characteristic
spectral energy distribution indicates the presence of an optically thin inner
cavity within the dust disk believed to mark the disappearance of the
primordial massive disk. We present new Herschel Space Observatory PACS spectra
of [OI] 63 micron for 21 transitional disks. Our survey complements the larger
Herschel GASPS program "Gas in Protoplanetary Systems" (Dent et al. 2013) by
quadrupling the number of transitional disks observed with PACS at this
wavelength. [OI] 63 micron traces material in the outer regions of the disk,
beyond the inner cavity of most transitional disks. We find that transitional
disks have [OI] 63 micron line luminosities two times fainter than their full
disk counterparts. We self consistently determine various stellar properties
(e.g. bolometric luminosity, FUV excess, etc.) and disk properties (e.g. disk
dust mass, etc.) that could influence the [OI] 63 micron line luminosity and we
find no correlations that can explain the lower [OI] 63 micron line
luminosities in transitional disks. Using a grid of thermo-chemical
protoplanetary disk models, we conclude that either transitional disks are less
flared than full disks or they possess lower gas-to-dust ratios due to a
depletion of gas mass. This result suggests that transitional disks are more
evolved than their full disk counterparts, possibly even at large radii.Comment: Accepted for publication in ApJ; 52 pages, 16 figures, 8 table
Effect of atmospheric turbulence on propagation properties of optical vortices formed by using coherent laser beam arrays
In this paper, we consider the effect of the atmospheric turbulence on the
propagation of optical vertex formed from the radial coherent laser beam array,
with the initially well-defined phase distribution. The propagation formula of
the radial coherent laser array passing through the turbulent atmosphere is
analytically derived by using the extended Huygens-Fresnel diffraction
integral. Based on the derived formula, the effect of the atmospheric
turbulence on the propagation properties of such laser arrays has been studied
in great detail. Our main results show that the atmospheric turbulence may
result in the prohibition of the formation of the optical vortex or the
disappearance of the formed optical vortex, which are very different from that
in the free space. The formed optical vortex with the higher topological charge
may propagate over a much longer distance in the moderate or weak turbulent
atmosphere. After the sufficient long-distance atmospheric propagation, all the
output beams (even with initially different phase distributions) finally lose
the vortex property and gradually become the Gaussian-shaped beams, and in this
case the output beams actually become incoherent light fields due to the
decoherence effect of the turbulent atmosphere.Comment: 10 pages, 5 figure
Interparticle interactions:Energy potentials, energy transfer, and nanoscale mechanical motion in response to optical radiation
In the interactions between particles of material with slightly different electronic levels, unusually large shifts in the pair potential can result from photoexcitation, and on subsequent electronic excitation transfer. To elicit these phenomena, it is necessary to understand the fundamental differences between a variety of optical properties deriving from dispersion interactions, and processes such as resonance energy transfer that occur under laser irradiance. This helps dispel some confusion in the recent literature. By developing and interpreting the theory at a deeper level, one can anticipate that in suitable systems, light absorption and energy transfer will be accompanied by significant displacements in interparticle separation, leading to nanoscale mechanical motion
Vortex Waves in a Cloud of Bose Einstein - Condensed, Trapped Alkali - Metal Atoms
We consider the vortex state solution for a rotating cloud of trapped, Bose
Einstein - condensed alkali atoms and study finite temperature effects. We find
that thermally excited vortex waves can distort the vortex state significantly,
even at the very low temperatures relevant to the experiments.Comment: to appear in Phys. Rev.
New connection formulae for some q-orthogonal polynomials in q-Askey scheme
New nonlinear connection formulae of the q-orthogonal polynomials, such
continuous q-Laguerre, continuous big q-Hermite, q-Meixner-Pollaczek and
q-Gegenbauer polynomials, in terms of their respective classical analogues are
obtained using a special realization of the q-exponential function as infinite
multiplicative series of ordinary exponential function
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