Dynamics and transport near quantum-critical points

The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N)-symmetric, relativistic, quantum field theory of a N-component scalar field in $d$ spatial dimensions. A great deal of insight is gained from a simple, exact solution of the long-time dynamics for the N=1 d=1 case: this model describes the critical point of the Ising chain in a transverse field, and the dynamics in all the distinct, limiting, physical regions of its finite temperature phase diagram is obtained. The N=3, d=1 model describes insulating, gapped, spin chain compounds: the exact, low temperature value of the spin diffusivity is computed, and compared with NMR experiments. The N=3, d=2,3 models describe Heisenberg antiferromagnets with collinear N\'{e}el correlations, and experimental realizations of quantum-critical behavior in these systems are discussed. Finally, the N=2, d=2 model describes the superfluid-insulator transition in lattice boson systems: the frequency and temperature dependence of the the conductivity at the quantum-critical coupling is described and implications for experiments in two-dimensional thin films and inversion layers are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical properties of unconventional magnetic systems", Geilo, Norway, April 2-12, 1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be published. 46 page

Finite temperature bosonization

Finite temperature properties of a non-Fermi liquid system is one of the most challenging probelms in current understanding of strongly correlated electron systems. The paradigmatic arena for studying non-Fermi liquids is in one dimension, where the concept of a Luttinger liquid has arisen. The existence of a critical point at zero temperature in one dimensional systems, and the fact that experiments are all undertaken at finite temperature, implies a need for these one dimensional systems to be examined at finite temperature. Accordingly, we extended the well-known bosonization method of one dimensional electron systems to finite temperatures. We have used this new bosonization method to calculate finite temperature asymptotic correlation functions for linear fermions, the Tomonaga-Luttinger model, and the Hubbard model.Comment: REVTex, 48 page

Quasi-static imaged-based immersed boundary-finite element model of human left ventricle in diastole

SUMMARY: Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid–structure interaction simulations of the heart

Modelling and identification of non-linear deterministic systems in the delta-domain

This paper provides a formulation for using the delta-operator in the modelling of non-linear systems. It is shown that a unique representation of a deterministic non-linear auto-regressive with exogenous input (NARX) model can be obtained for polynomial basis functions using the delta-operator and expressions are derived to convert between the shift- and delta- domain. A delta-NARX model is applied to the identification of a test problem (a Van-der-Pol oscillator): a comparison is made with the standard shift operator non-linear model and it is demonstrated that the delta-domain approach improves the numerical properties of structure detection, leads to a parsimonious description and provides a model that is closely linked to the continuous-time non-linear system in terms of both parameters and structure

Whitham Averaged Equations and Modulational Stability of Periodic Traveling Waves of a Hyperbolic-Parabolic Balance Law

In this note, we report on recent findings concerning the spectral and nonlinear stability of periodic traveling wave solutions of hyperbolic-parabolic systems of balance laws, as applied to the St. Venant equations of shallow water flow down an incline. We begin by introducing a natural set of spectral stability assumptions, motivated by considerations from the Whitham averaged equations, and outline the recent proof yielding nonlinear stability under these conditions. We then turn to an analytical and numerical investigation of the verification of these spectral stability assumptions. While spectral instability is shown analytically to hold in both the Hopf and homoclinic limits, our numerical studies indicates spectrally stable periodic solutions of intermediate period. A mechanism for this moderate-amplitude stabilization is proposed in terms of numerically observed "metastability" of the the limiting homoclinic orbits.Comment: 27 pages, 5 figures. Minor changes throughou