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 $\theta$. 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 $\theta m^2$. The stability or non-stability of the system may then be determined entirely by the $\phi^3$ coefficient in the potential. For higher-level solutions we find an ambiguity in extrapolating solutions to finite $\theta$ 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 $(p,q)$ 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 ${\cal N}=2$ supersymmetric Abelian-Higgs models also takes the square-root form. In contrast to string theory, the most general supersymmetric field theoretic model allows for $(p,q,r)$ 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