Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure

Whittaker-Hill equation and semifinite-gap Schroedinger operators

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.Comment: Revised versio

Results of the life sciences DSOs conducted aboard the space shuttle 1981-1986

Results are presented for a number of life sciences investigations sponsored by the Space Biomedical Research Institute at the NASA Lyndon B. Johnson Space Center and conducted as Detailed Supplementary Objectives (DSOs) on Space Shuttle flights between 1981 and 1986. An introduction and a description of the DSO program are followed by summary reports on the investigations. Reports are grouped into the following disciplines: Biochemistry and Pharmacology, Cardiovascular Effects and Fluid Shifts, Equipment Testing and Experiment Verification, Microbiology, Space Motion Sickness, and Vision. In the appendix, the status of every medical/life science DSO is presented in graphical form, which enables the flight history, the number of subjects tested, and the experiment results to be reviewed at a glance

Adaptive walks on time-dependent fitness landscapes

The idea of adaptive walks on fitness landscapes as a means of studying evolutionary processes on large time scales is extended to fitness landscapes that are slowly changing over time. The influence of ruggedness and of the amount of static fitness contributions are investigated for model landscapes derived from Kauffman's $NK$ landscapes. Depending on the amount of static fitness contributions in the landscape, the evolutionary dynamics can be divided into a percolating and a non-percolating phase. In the percolating phase, the walker performs a random walk over the regions of the landscape with high fitness.Comment: 7 pages, 6 eps-figures, RevTeX, submitted to Phys. Rev.

Relations Between QRS|T Angle, Cardiac Risk Factors, and Mortality in the Third National Health and Nutrition Examination Survey (NHANES III)

On the surface electrocardiogram, an abnormally wide QRS|T angle reflects changes in the regional action potential duration profiles and in the direction of the repolarization sequence, which is thought to increase the risk of ventricular arrhythmia. We investigated the relation between an abnormal QRS|T angle and mortality in a nationally representative sample of subjects without clinically evident heart disease. We studied 7,052 participants ≥40 years old in the third National Health and Nutrition Examination Survey with 12-lead electrocardiograms. Those with self-reported or electrocardiographic evidence of a previous myocardial infarction, QRS duration of ≥120 ms, or history of heart failure were excluded. Borderline and abnormal spatial QRS|T angles were defined according to gender-specific 75th and 95th percentiles of frequency distributions. All-cause (1,093 women and 1,191 men) and cardiovascular (462 women and 455 men) mortality during the 14-year period was assessed through linkage with the National Death Index. On multivariate analyses, an abnormal spatial QRS|T angle was associated with an increased hazard ratio (HR) for cardiovascular mortality in women (HR 1.82, 95% confidence interval 1.05 to 3.14) and men (HR 2.21, 95% confidence interval 1.32 to 3.68). Also, the multivariate adjusted HR for all-cause mortality associated with an abnormal QRS|T angle was 1.30 (95% confidence interval 0.95 to 1.78) for women and 1.87 (95% confidence interval 1.29 to 2.7) for men. A borderline QRS|T angle was not associated with an increased risk of all-cause or cardiovascular mortality. In conclusion, an abnormal QRS|T angle, as measured on a 12-lead electrocardiogram, was associated with an increased risk of cardiovascular and all-cause mortality in this population-based sample without known heart disease

Pulsating star products from the Palomar Transient Factory: Ultra-long period Cepheids in M31 and RR Lyrae in Kepler field

The Palomar Transient Factory (PTF) and its successor, the intermediate PTF (iPTF), are wide-field synoptic sky surveys aimed to detect transients. Even though the main science goal for PTF/iPTF is to detect various types of transients, the synoptic nature of the surveys can also be used for the study of variable stars. In this proceedings contribution, I will first give a brief introduction to PTF/iPTF, followed by the two pulsating stars studies using the PTF/iPTF data: the Ultra-Long Period Cepheids (ULPC) in M31 and the RR Lyrae in the Kepler field. For the formal study, we searched the M31’s ULPC using PTF imaging data, and follow up the candidates with other telescopes. Our finding revealed that there are only two ULPC in M31. I will give a brief implication of our finding in distance scale studies. For the latter study, I will present our work on the derivation of metallicity-light curve relation in native PTF/iPTF R-band using the RRab stars in the Kepler field

Calcium, magnesium and potassium intake and mortality in women with heart failure: The Women\u27s Health Initiative

Although diet is thought to affect the natural history of heart failure (HF), nutrient intake in HF patients has not been well studied. Based on prior research linking high intake of Ca, Mg and K to improved cardiovascular health, we hypothesised that these nutrients would be inversely associated with mortality in people with HF. Of the 161 808 participants in the Women\u27s Health Initiative (WHI), we studied 3340 who experienced a HF hospitalisation. These participants were followed for post-hospitalisation all-cause mortality. Intake was assessed using questionnaires on food and supplement intake. Hazard ratios (HR) and 95 % CI were calculated using Cox proportional hazards models adjusted for demographics, physical function, co-morbidities and dietary covariates. Over a median of 4·6 years of follow-up, 1433 (42·9 %) of the women died. HR across quartiles of dietary Ca intake were 1·00 (referent), 0·86 (95 % CI 0·73, 1·00), 0·88 (95 % CI 0·75, 1·04) and 0·92 (95 % CI 0·76, 1·11) (P for trend = 0·63). Corresponding HR were 1·00 (referent), 0·86 (95 % CI 0·71, 1·04), 0·88 (95 % CI 0·69, 1·11) and 0·84 (95 % CI 0·63, 1·12) (P for trend = 0·29), across quartiles of dietary Mg intake, and 1·00 (referent), 1·20 (95 % CI 1·01, 1·43), 1·06 (95 % CI 0·86, 1·32) and 1·16 (95 % CI 0·90, 1·51) (P for trend = 0·35), across quartiles of dietary K intake. Results were similar when total (dietary plus supplemental) nutrient intakes were examined. In summary, among WHI participants with incident HF hospitalisation, intakes of Ca, Mg and K were not significantly associated with subsequent mortality

Genuine converging solution of self-consistent field equations for extended many-electron systems

Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set of equations, one believes in the iterative method for the solution that should consist in consecutive improvement of the potential and the electron density until the self-consistency is attained. Though this approach exists for a long time there are two grave problems accompanying its implementation to infinitely extended systems. The first of them is related with the Poisson equation and lies in possible incompatibility of the boundary conditions for the potential with the electron density distribution. The analysis of this difficulty and suggested resolution are presented for both infinite conducting systems in jellium approximation and periodic solids. It provides the existence of self-consistent solution for the potential at every iteration step due to realization of a screening effect. The second problem results from the existence of continuous spectrum of Hamiltonian eigenvalues for unbounded systems. It needs to have a definition of Hilbert space basis with eigenfunctions of continuous spectrum as elements, which would be convenient in numerical applications. The definition of scalar product specifying the Hilbert space is proposed that incorporates a limiting transition. It provides self-adjointness of Hamiltonian and, respectively, the orthogonality of eigenfunctions corresponding to the different eigenvalues. In addition, it allows to normalize them effectively to delta-function and to prove in the general case the orthogonality of the 'right' and 'left' eigenfunctions belonging to twofold degenerate eigenvalues.Comment: 12 pages. Reported on Interdisciplinary Workshop "Nonequilibrium Green's Functions III", August 22 - 26, 2005, University Kiel, Germany. To be published in Journal of Physics: Conference Series, 2006; Typos in Eqs. (37), (53) and (54) are corrected. The content of the footnote is changed. Published version available free online at http://www.iop.org/EJ/abstract/1742-6596/35/1/01

INTRINSIC MECHANISM FOR ENTROPY CHANGE IN CLASSICAL AND QUANTUM EVOLUTION

It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively pure state can evolve under the usual unitary evolution to an effectively mixed state.Comment: 20 pages. For more information or comments contact E. Eisenberg at [email protected] (internet)