Solution of the Percus-Yevick equation for hard discs

We solve the Percus-Yevick equation in two dimensions by reducing it to a set of simple integral equations. We numerically obtain both the pair correlation function and the equation of state for a hard disc fluid and find good agreement with available Monte-Carlo calculations. The present method of resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure

The spectrum of large powers of the Laplacian in bounded domains

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.Comment: 13 pages, 2 figure

Finite-distance singularities in the tearing of thin sheets

We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.Comment: 4 pages, 4 figure

Scale calculus and the Schrodinger equation

We introduce the scale calculus, which generalizes the classical differential calculus to non differentiable functions. The new derivative is called the scale difference operator. We also introduce the notions of fractal functions, minimal resolution, and quantum representation of a non differentiable function. We then define a scale quantization procedure for classical Lagrangian systems inspired by the Scale relativity theory developped by Nottale. We prove that the scale quantization of Newtionian mechanics is a non linear Schrodinger equation. Under some specific assumptions, we obtain the classical linear Schrodinger equation.Comment: 49 page

Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions

We solve the Percus-Yevick equation in even dimensions by reducing it to a set of simple integro-differential equations. This work generalizes an approach we developed previously for hard discs. We numerically obtain both the pair correlation function and the virial coefficients for a fluid of hyper-spheres in dimensions $d=4,6$ and 8, and find good agreement with available exact results and Monte-Carlo simulations. This paper confirms the alternating character of the virial series for $d \ge 6$, and provides the first evidence for an alternating character for $d=4$. Moreover, we show that this sign alternation is due to the existence of a branch point on the negative real axis. It is this branch point that determines the radius of convergence of the virial series, whose value we determine explicitly for $d=4,6,8$. Our results complement, and are consistent with, a recent study in odd dimensions [R.D. Rohrmann et al., J. Chem. Phys. 129, 014510 (2008)].Comment: Accepted for publication in J. Chem. Phys. (11 pages, 6 figures

Continuum field description of crack propagation

We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching and fragmentation.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett. Additional information can be obtained from http://gershwin.msd.anl.gov/theor

Feasibility of low-dose coronary CT angiography: first experience with prospective ECG-gating

AIMS: To determine the feasibility of prospective electrocardiogram (ECG)-gating to achieve low-dose computed tomography coronary angiography (CTCA). METHODS AND RESULTS: Forty-one consecutive patients with suspected (n = 35) or known coronary artery disease (n = 6) underwent 64-slice CTCA using prospective ECG-gating. Individual radiation dose exposure was estimated from the dose-length product. Two independent readers semi-quantitatively assessed the overall image quality on a five-point scale and measured vessel attenuation in each coronary segment. One patient was excluded for atrial fibrillation. Mean effective radiation dose was 2.1 +/- 0.6 mSv (range, 1.1-3.0 mSv). Image quality was inversely related to heart rate (HR) (57.3 +/- 6.2, range 39-66 b.p.m.; r = 0.58, P 63 b.p.m. (P < 0.001). CONCLUSION: This first experience documents the feasibility of prospective ECG-gating for CTCA with diagnostic image quality at a low radiation dose (1.1-3.0 mSv), favouring HR <63 b.p.

Feasibility of low-dose coronary CT angiography: first experience with prospective ECG-gating

AIMS: To determine the feasibility of prospective electrocardiogram (ECG)-gating to achieve low-dose computed tomography coronary angiography (CTCA). METHODS AND RESULTS: Forty-one consecutive patients with suspected (n = 35) or known coronary artery disease (n = 6) underwent 64-slice CTCA using prospective ECG-gating. Individual radiation dose exposure was estimated from the dose-length product. Two independent readers semi-quantitatively assessed the overall image quality on a five-point scale and measured vessel attenuation in each coronary segment. One patient was excluded for atrial fibrillation. Mean effective radiation dose was 2.1 +/- 0.6 mSv (range, 1.1-3.0 mSv). Image quality was inversely related to heart rate (HR) (57.3 +/- 6.2, range 39-66 b.p.m.; r = 0.58, P 63 b.p.m. (P < 0.001). CONCLUSION: This first experience documents the feasibility of prospective ECG-gating for CTCA with diagnostic image quality at a low radiation dose (1.1-3.0 mSv), favouring HR <63 b.p.