The Height of a Giraffe

A minor modification of the arguments of Press and Lightman leads to an estimate of the height of the tallest running, breathing organism on a habitable planet as the Bohr radius multiplied by the three-tenths power of the ratio of the electrical to gravitational forces between two protons (rather than the one-quarter power that Press got for the largest animal that would not break in falling over, after making an assumption of unreasonable brittleness). My new estimate gives a height of about 3.6 meters rather than Press's original estimate of about 2.6 cm. It also implies that the number of atoms in the tallest runner is very roughly of the order of the nine-tenths power of the ratio of the electrical to gravitational forces between two protons, which is about 3 x 10^32.Comment: 12 pages, LaTe

Numerical computation of real or complex elliptic integrals

Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind). Numerical check values, consistency checks, and relations to Legendre's integrals and Bulirsch's integrals are included

Matrix product representation of gauge invariant states in a Z_2 lattice gauge theory

The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. In this work, we propose an efficient variational method based on the matrix product ansatz for a Z_2 lattice gauge theory on a spatial ladder chain. Gauge invariant low-lying states are identified by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian.Comment: 15 pages, 6 figures, minor corrections, accepted for publication in JHE

Customized design of hearing aids using statistical shape learning

3D shape modeling is a crucial component of rapid prototyping systems that customize shapes of implants and prosthetic devices to a patient’s anatomy. In this paper, we present a solution to the problem of customized 3D shape modeling using a statistical shape analysis framework. We design a novel method to learn the relationship between two classes of shapes, which are related by certain operations or transformation. The two associated shape classes are represented in a lower dimensional manifold, and the reduced set of parameters obtained in this subspace is utilized in an estimation, which is exemplified by a multivariate regression in this paper.We demonstrate our method with a felicitous application to estimation of customized hearing aid devices

Superradiant instabilities of rotating black branes and strings

Black branes and strings are generally unstable against a certain sector of gravitational perturbations. This is known as the Gregory-Laflamme instability. It has been recently argued that there exists another general instability affecting many rotating extended black objects. This instability is in a sense universal, in that it is triggered by any massless field, and not just gravitational perturbations. Here we investigate this novel mechanism in detail. For this instability to work, two ingredients are necessary: (i) an ergo-region, which gives rise to superradiant amplification of waves, and (ii) ``bound'' states in the effective potential governing the evolution of the particular mode under study. We show that the black brane Kerr_4 x R^p is unstable against this mechanism, and we present numerical results for instability timescales for this case. On the other hand, and quite surprisingly, black branes of the form Kerr_d x R^p are all stable against this mechanism for d>4. This is quite an unexpected result, and it stems from the fact that there are no stable circular orbits in higher dimensional black hole spacetimes, or in a wave picture, that there are no bound states in the effective potential. We also show that it is quite easy to simulate this instability in the laboratory with acoustic black branes.Comment: 19 pages, 10 figures. v2: Enlarged discussion on the necessary conditions for the existence of instabilit

Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field

This paper continues a study on Choptuik scaling in gravitational collapse of a complex scalar field at the threshold for black hole formation. We perform a linear perturbation analysis of the previously derived complex critical solution, and calculate the critical exponent for black hole mass, $\gamma \approx 0.387106$. We also show that this critical solution is unstable via a growing oscillatory mode.Comment: 15 pages of latex/revtex; added details of numerics, in press in Phys Rev D; 1 figure included, or available by anonymous ftp to ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-58.ep

Towards the realistic fermion masses with a single family in extra dimensions

In a class of multidimensional models, topology of a thick brane provides three chiral fermionic families with hierarchical masses and mixings in the effective four-dimensional theory, while the full model contains a single vector-like generation. We carry out numerical simulations and reproduce all known Standard Model fermion masses and mixings in one of these models.Comment: 12 pages, 2 figures, uses JHEP3.cls. Some minor corrections are mad

Is the present expansion of the universe really accelerating?

The current observations are usually explained by an accelerating expansion of the present universe. However, with the present quality of the supernovae Ia data, the allowed parameter space is wide enough to accommodate the decelerating models as well. This is shown by considering a particular example of the dark energy equation-of-state $w_\phi\equiv p_\phi/\rho_\phi=-1/3$, which is equivalent to modifying the \emph{geometrical curvature} index $k$ of the standard cosmology by shifting it to $(k-\alpha)$ where $\alpha$ is a constant. The resulting decelerating model is consistent with the recent CMB observations made by WMAP, as well as, with the high redshift supernovae Ia data including SN 1997ff at $z= 1.755$. It is also consistent with the newly discovered supernovae SN 2002dc at $z=0.475$ and SN 2002dd at $z=0.95$ which have a general tendency to improve the fit.Comment: Replaced with the accepted version to appear in MNRA

Choosing integration points for QCD calculations by numerical integration

I discuss how to sample the space of parton momenta in order to best perform the numerical integrations that lead to a calculation of three jet cross sections and similar observables in electron-positron annihilation.Comment: 25 pages with 8 figure

Instabilities of Twisted Strings

A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory -- an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry -- is carried out. Here the twist refers to a relative phase between the two complex scalars (with linear dependence on, say, the $z$ coordinate), and importantly it leads to a global current flowing along the the string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO) solution embedded in the semilocal theory. Our numerical investigations of the small fluctuation spectrum confirm previous results that twisted strings exhibit instabilities whose amplitudes grow exponentially in time. More precisely twisted strings with a single magnetic flux quantum admit a continuous family of unstable eigenmodes with harmonic $z$ dependence, indexed by a wavenumber $k\in[-k_{\rm m},k_{\rm m}]$. Carrying out a perturbative semi-analytic analysis of the bifurcation, it is found that the purely numerical results are very well reproduced. This way one obtains not only a good qualitative description of the twisted solutions themselves as well as of their instabilities, but also a quantitative description of the numerical results. Our semi-analytic results indicate that in close analogy to the known instability of the embedded ANO vortex a twisted string is also likely to expand in size caused by the spreading out of its magnetic flux.Comment: 27 pages, 18 figures. Typos corrected, references adde