Mathematical model for predicting human vertebral fracture

Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam

Transition to Reconstructibility in Weakly Coupled Networks

Across scientific disciplines, thresholded pairwise measures of statistical dependence between time series are taken as proxies for the interactions between the dynamical units of a network. Yet such correlation measures often fail to reflect the underlying physical interactions accurately. Here we systematically study the problem of reconstructing direct physical interaction networks from thresholding correlations. We explicate how local common cause and relay structures, heterogeneous in-degrees and non-local structural properties of the network generally hinder reconstructibility. However, in the limit of weak coupling strengths we prove that stationary systems with dynamics close to a given operating point transition to universal reconstructiblity across all network topologies.Comment: 15 pages, 4 figures, supplementary material include

Generating Generalized Distributions from Dynamical Simulation

We present a general molecular-dynamics simulation scheme, based on the Nose' thermostat, for sampling according to arbitrary phase space distributions. We formulate numerical methods based on both Nose'-Hoover and Nose'-Poincare' thermostats for two specific classes of distributions; namely, those that are functions of the system Hamiltonian and those for which position and momentum are statistically independent. As an example, we propose a generalized variable temperature distribution that designed to accelerate sampling in molecular systems.Comment: 10 pages, 3 figure

Plateau Inflation from Random Non-Minimal Coupling

A generic non-minimal coupling can push any higher-order terms of the scalar potential sufficiently far out in field space to yield observationally viable plateau inflation. We provide analytic and numerical evidence that this generically happens for a non-minimal coupling strength $\xi$ of the order $N_e^2$. In this regime, the non-minimally coupled field is sub-Planckian during inflation and is thus protected from most higher-order terms. For larger values of $\xi$, the inflationary predictions converge towards the sweet spot of PLANCK. The latter includes $\xi\simeq 10^4$ obtained from CMB normalization arguments, thus providing a natural explanation for the inflationary observables measured.Comment: 9 pages, twocolumn, some figures; v2: 1 figure and appendix added, jcap layou

Bogoliubov excitation spectrum of an elongated condensate from quasi-one-dimensional to three-dimensional transition

The quasiparticle excitation spectra of a Bose gas trapped in a highly anisotropic trap is studied with respect to varying total number of particles by numerically solving the effective one-dimensional (1D) Gross-Pitaevskii (GP) equation proposed recently by Mateo \textit{et al.}. We obtain the static properties and Bogoliubov spectra of the system in the high energy domain. This method is computationally efficient and highly accurate for a condensate system undergoing a 1D to three-dimensional (3D) cigar-shaped transition, as is shown through a comparison our results with both those calculated by the 3D-GP equation and analytical results obtained in limiting cases. We identify the applicable parameter space for the effective 1D-GP equation and find that this equation fails to describe a system with large number of atoms. We also identify that the description of the transition from 1D Bose-Einstein condensate (BEC) to 3D cigar-shaped BEC using this equation is not smooth, which highlights the fact that for a finite value of $a_\perp/a_s$ the junction between the 1D and 3D crossover is not perfect.Comment: 17 pages, 6 figure

A Revised Textual Tree Trace Notation for Prolog

This paper describes a ''textual tree trace'' (TTT) notation for representing the execution of Prolog programs. Compact, textual and non-linear, it provides detailed information about variable binding and execution history, and distinguishes several modes of goal failure. The revised form given here, yet to be empirically tested, is partly informed by Paul Mulholland's empirical comparisons of Prolog trace notations, in which an earlier version of the TTT notation was amongst those studied and criticised. The work presented here is an updated version of a previous workshop paper (Taylor, du Boulay, & Patel, 1994)