The impact of heat waves and cold spells on mortality rates in the Dutch population.

We conducted the study described in this paper to investigate the impact of ambient temperature on mortality in the Netherlands during 1979-1997, the impact of heat waves and cold spells on mortality in particular, and the possibility of any heat wave- or cold spell-induced forward displacement of mortality. We found a V-like relationship between mortality and temperature, with an optimum temperature value (e.g., average temperature with lowest mortality rate) of 16.5 degrees C for total mortality, cardiovascular mortality, respiratory mortality, and mortality among those [Greater and equal to] 65 year of age. For mortality due to malignant neoplasms and mortality in the youngest age group, the optimum temperatures were 15.5 degrees C and 14.5 degrees C, respectively. For temperatures above the optimum, mortality increased by 0.47, 1.86, 12.82, and 2.72% for malignant neoplasms, cardiovascular disease, respiratory diseases, and total mortality, respectively, for each degree Celsius increase above the optimum in the preceding month. For temperatures below the optimum, mortality increased 0.22, 1.69, 5.15, and 1.37%, respectively, for each degree Celsius decrease below the optimum in the preceding month. Mortality increased significantly during all of the heat waves studied, and the elderly were most effected by extreme heat. The heat waves led to increases in mortality due to all of the selected causes, especially respiratory mortality. Average total excess mortality during the heat waves studied was 12.1%, or 39.8 deaths/day. The average excess mortality during the cold spells was 12.8% or 46.6 deaths/day, which was mostly attributable to the increase in cardiovascular mortality and mortality among the elderly. The results concerning the forward displacement of deaths due to heat waves were not conclusive. We found no cold-induced forward displacement of deaths

On the Hyperbolicity of Lorenz Renormalization

We consider infinitely renormalizable Lorenz maps with real critical exponent $\alpha>1$ and combinatorial type which is monotone and satisfies a long return condition. For these combinatorial types we prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated unstable manifold. An unstable manifold defines a family of Lorenz maps and we prove that each infinitely renormalizable combinatorial type (satisfying the above conditions) has a unique representative within such a family. We also prove that each infinitely renormalizable map has no wandering intervals and that the closure of the forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure

No elliptic islands for the universal area-preserving map

A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} to prove the existence of a \textit{universal area-preserving map}, a map with hyperbolic orbits of all binary periods. The existence of a horseshoe, with positive Hausdorff dimension, in its domain was demonstrated in \cite{GJ1}. In this paper the coexistence problem is studied, and a computer-aided proof is given that no elliptic islands with period less than 20 exist in the domain. It is also shown that less than 1.5% of the measure of the domain consists of elliptic islands. This is proven by showing that the measure of initial conditions that escape to infinity is at least 98.5% of the measure of the domain, and we conjecture that the escaping set has full measure. This is highly unexpected, since generically it is believed that for conservative systems hyperbolicity and ellipticity coexist

Invariant measures for Cherry flows

We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we prove that there exists also an invariant probability measure supported on the quasi-minimal set, we discuss some situations when this other invariant measure is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.Comment: 12 pages; updated versio

How large is the spreading width of a superdeformed band?

Recent models of the decay out of superdeformed bands can broadly be divided into two categories. One approach is based on the similarity between the tunneling process involved in the decay and that involved in the fusion of heavy ions, and builds on the formalism of nuclear reaction theory. The other arises from an analogy between the superdeformed decay and transport between coupled quantum dots. These models suggest conflicting values for the spreading width of the decaying superdeformed states. In this paper, the decay of superdeformed bands in the five even-even nuclei in which the SD excitation energies have been determined experimentally is considered in the framework of both approaches, and the significance of the difference in the resulting spreading widths is considered. The results of the two models are also compared to tunneling widths estimated from previous barrier height predictions and a parabolic approximation to the barrier shape

Entropic particle transport: higher order corrections to the Fick-Jacobs diffusion equation

Transport of point-size Brownian particles under the influence of a constant and uniform force field through a three-dimensional channel with smoothly varying periodic cross-section is investigated. Here, we employ an asymptotic analysis in the ratio between the difference of the widest and the most narrow constriction divided through the period length of the channel geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. By use of the higher order corrections to the probability density we derive an expression for the spatially dependent diffusion coefficient D(x) which substitutes the constant diffusion coefficient present in the common Fick-Jacobs equation. In addition, we show that in the diffusion dominated regime the average transport velocity is obtained as the product of the zeroth-order Fick-Jacobs result and the expectation value of the spatially dependent diffusion coefficient . The analytic findings are corroborated with the precise numerical results of a finite element calculation of the Smoluchowski diffusive particle dynamics occurring in a reflection symmetric sinusoidal-shaped channel.Comment: 9 pages, 3 figure

Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly Simultaneous Measurement Process

The accuracy of the Arthurs-Kelly model of a simultaneous measurement of position and momentum is analysed using concepts developed by Braginsky and Khalili in the context of measurements of a single quantum observable. A distinction is made between the errors of retrodiction and prediction. It is shown that the distribution of measured values coincides with the initial state Husimi function when the retrodictive accuracy is maximised, and that it is related to the final state anti-Husimi function (the P representation of quantum optics) when the predictive accuracy is maximised. The disturbance of the system by the measurement is also discussed. A class of minimally disturbing measurements is characterised. It is shown that the distribution of measured values then coincides with one of the smoothed Wigner functions described by Cartwright.Comment: 12 pages, 0 figures. AMS-Latex. Earlier version replaced with final published versio

A Phase Transition for Circle Maps and Cherry Flows

We study $C^{2}$ weakly order preserving circle maps with a flat interval. The main result of the paper is about a sharp transition from degenerate geometry to bounded geometry depending on the degree of the singularities at the boundary of the flat interval. We prove that the non-wandering set has zero Hausdorff dimension in the case of degenerate geometry and it has Hausdorff dimension strictly greater than zero in the case of bounded geometry. Our results about circle maps allow to establish a sharp phase transition in the dynamics of Cherry flows

Biased Brownian motion in extreme corrugated tubes

Biased Brownian motion of point-size particles in a three-dimensional tube with smoothly varying cross-section is investigated. In the fashion of our recent work [Martens et al., PRE 83,051135] we employ an asymptotic analysis to the stationary probability density in a geometric parameter of the tube geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. Expression for the higher order corrections to the probability density are derived. Using this expansion orders we obtain that in the diffusion dominated regime the average particle current equals the zeroth-order Fick-Jacobs result corrected by a factor including the corrugation of the tube geometry. In particular we demonstrate that this estimate is more accurate for extreme corrugated geometries compared to the common applied method using the spatially dependent diffusion coefficient D(x,f). The analytic findings are corroborated with the finite element calculation of a sinusoidal-shaped tube.Comment: 10 pages, 4 figure