75,407 research outputs found
Gravity from a Modified Commutator
We show that a suitably chosen position-momentum commutator can elegantly
describe many features of gravity, including the IR/UV correspondence and
dimensional reduction (`holography'). Using the most simplistic example based
on dimensional analysis of black holes, we construct a commutator which
qualitatively exhibits these novel properties of gravity. Dimensional reduction
occurs because the quanta size grow quickly with momenta, and thus cannot be
"packed together" as densely as naively expected. We conjecture that a more
precise form of this commutator should be able to quantitatively reproduce all
of these features.Comment: 8 pages; Honorable Mention in the 2005 Gravity Research Foundation
Essay Competition; v2: acknowledgments adde
The Stability of Noncommutative Scalar Solitons
We determine the stability conditions for a radially symmetric noncommutative
scalar soliton at finite noncommutivity parameter . We find an
intriguing relationship between the stability and existence conditions for all
level-1 solutions, in that they all have nearly-vanishing stability eigenvalues
at critical . The stability or non-stability of the system may then
be determined entirely by the coefficient in the potential. For
higher-level solutions we find an ambiguity in extrapolating solutions to
finite which prevents us from making any general statements. For these
stability may be determined by comparing the fluctuation eigenvalues to
critical values which we calculate.Comment: 12 pages, corrected typo
A Note on Cosmic (p,q,r) Strings
The spectrum of bound states of F- and D-strings has a distinctive
square-root tension formula that is hoped to be a hallmark of fundamental
cosmic strings. We point out that the Bogomol'nyi-Prasad-Sommerfield (BPS)
bound for vortices in supersymmetric Abelian-Higgs models also
takes the square-root form. In contrast to string theory, the most general
supersymmetric field theoretic model allows for strings, with three
classes of strings rather than two. Unfortunately, we find that there do not
exist BPS solutions except in the trivial case. The issue of whether there
exist non-BPS solutions which may closely resemble the square-root form is left
as an open question.Comment: 4 pages; v2: references adde
Feynman-Jackson integrals
We introduce perturbative Feynman integrals in the context of q-calculus
generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide
analytic as well as combinatorial interpretations for the Feynman-Jackson
integrals.Comment: Final versio
Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics
We present a generalized van der Waals theory for a lyotropic cholesteric
system of chiral spherocylinders based on the classical Onsager theory for hard
anisometric bodies. The rods consist of a hard spherocylindrical backbone
surrounded with a square-well potential to account for attractive (or soft
repulsive) interactions. Long-ranged chiral interactions are described by means
of a simple pseudo-scalar potential which is appropriate for weak chiral forces
of a predominant electrostatic origin. Based on the formalism proposed by
Straley [Phys. Rev. A {\bf 14}, 1835 (1976)] we derive explicit algebraic
expressions for the twist elastic modulus and the cholesteric pitch for rods as
a function of density and temperature. The pitch varies non-monotonically with
density, with a sharp decrease at low packing fractions and a marked increase
at higher packing fractions. A similar trend is found for the temperature
dependence. The unwinding of the helical pitch at high densities (or low
temperatures) originates from a marked increase in the local nematic order and
a steep increase of the twist elastic resistance associated with near-parallel
local rod configurations. This contrasts with the commonly held view that the
increase in pitch with decreasing temperature as often observed in cholesterics
is due to layer formation resulting from pre-smectic fluctuations. The increase
in pitch with increasing temperature is consistent with an entropic unwinding
as the chiral interaction becomes less and less significant than the thermal
energy. The variation of the pitch with density, temperature and contour length
is in qualitative agreement with recent experimental results on colloidal {\em
fd} rods.Comment: 17 pages, 6 figures, to appear in J. Chem. Phy
A hybrid computer program for the visual display of compensatory system model parameters
A hybrid computer identification program has been developed which determines and displays those parameter values of a model of the compensatory control system that existed over the last fifteen seconds of operation. These values are up-dated every 0.05 sec so that a visual display of the parameters appears to be continuous. Presently, a closed loop crossover model is being used as the compensatory system model with the parameters K and tau displayed, however, any suitable model could be used in its place
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