A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

Radiator design system computer programs

Minimum weight space radiator subsystems which can operate over heat load ranges wider than the capabilities of current subsystems are investigated according to projected trends of future long duration space vehicles. Special consideration is given to maximum heat rejection requirements of the low temperature radiators needed for environmental control systems. The set of radiator design programs that have resulted from this investigation are presented in order to provide the analyst with a capability to generate optimum weight radiator panels or sets of panels from practical design considerations, including transient performance. Modifications are also provided for existing programs to improve capability and user convenience

Multiple Transition States and Roaming in Ion-Molecule Reactions: a Phase Space Perspective

We provide a dynamical interpretation of the recently identified `roaming' mechanism for molecular dissociation reactions in terms of geometrical structures in phase space. These are NHIMs (Normally Hyperbolic Invariant Manifolds) and their stable/unstable manifolds that define transition states for ion-molecule association or dissociation reactions. The associated dividing surfaces rigorously define a roaming region of phase space, in which both reactive and nonreactive trajectories can be trapped for arbitrarily long times.Comment: 20 pages, 6 figure

Contrast‐Enhanced Diagnostic Ultrasound Causes Renal Tissue Damage in a Porcine Model

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135402/1/jum201029101391.pd

Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium

The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The problem can be solved either under some non-resonance hypotheses on the spectrum of the linear part or if the non-linear term is assumed to be (slowly) decaying in time. This paper "completes" a pioneering work of Pustil'nikov in which, despite under weaker non-resonance hypotheses, the nonlinearity is required to be asymptotically autonomous. The result is obtained as a consequence of the existence of a strong normal form for a suitable class of real-analytic Hamiltonians with non-autonomous perturbations.Comment: 10 page

The role of dredge-up in double white dwarf mergers

We present the results of an investigation of the dredge-up and mixing during the merger of two white dwarfs with different chemical compositions by conducting hydrodynamic simulations of binary mergers for three representative mass ratios. In all the simulations, the total mass of the two white dwarfs is $\lesssim1.0~{\rm M_\odot}$. Mergers involving a CO and a He white dwarf have been suggested as a possible formation channel for R Coronae Borealis type stars, and we are interested in testing if such mergers lead to conditions and outcomes in agreement with observations. Even if the conditions during the merger and subsequent nucleosynthesis favor the production of $^{18}{\mathrm O}$, the merger must avoid dredging up large amounts of $^{16}{\mathrm O}$, or else it will be difficult to produce sufficient $^{18}{\mathrm O}$ to explain the oxygen ratio observed to be of order unity. We performed a total of 9 simulations using two different grid-based hydrodynamics codes using fixed and adaptive meshes, and one smooth particle hydrodynamics (SPH) code. We find that in most of the simulations, $>10^{-2}~{\rm M_\odot}$ of $^{16}{\mathrm O}$ is indeed dredged up during the merger. However, in SPH simulations where the accretor is a hybrid He/CO white dwarf with a $\sim 0.1~{\rm M_\odot}$ layer of helium on top, we find that no $^{16}{\mathrm O}$ is being dredged up, while in the $q=0.8$ simulation $<10^{-4}~{\rm M_\odot}$ of $^{16}{\mathrm O}$ has been brought up, making a WD binary consisting of a hybrid CO/He WD and a companion He WD an excellent candidate for the progenitor of RCB stars.Comment: Accepted for publication in Ap

The role of body rotation in bacterial flagellar bundling

In bacterial chemotaxis, E. coli cells drift up chemical gradients by a series of runs and tumbles. Runs are periods of directed swimming, and tumbles are abrupt changes in swimming direction. Near the beginning of each run, the rotating helical flagellar filaments which propel the cell form a bundle. Using resistive-force theory, we show that the counter-rotation of the cell body necessary for torque balance is sufficient to wrap the filaments into a bundle, even in the absence of the swirling flows produced by each individual filament

Toward a better understanding of the comparatively high prostate cancer incidence rates in Utah

BACKGROUND: This study assesses whether comparatively high prostate cancer incidence rates among white men in Utah represent higher rates among members of the Church of Jesus Christ of Latter-day Saints (LDS or Mormons), who comprise about 70% of the state's male population, and considers the potential influence screening has on these rates. METHODS: Analyses are based on 14,693 histologically confirmed invasive prostate cancer cases among men aged 50 years and older identified through the Utah Cancer Registry between 1985 and 1999. Cancer records were linked to LDS Church membership records to determine LDS status. Poisson regression was used to derive rate ratios of LDS to nonLDS prostate cancer incidence, adjusted for age, disease stage, calendar time, and incidental detection. RESULTS: LDS men had a 31% (95% confidence interval, 26% – 36%) higher incidence rate of prostate cancer than nonLDS men during the study period. Rates were consistently higher among LDS men over time (118% in 1985–88, 20% in 1989–92, 15% in 1993–1996, and 13% in 1997–99); age (13% in ages 50–59, 48% in ages 60–69, 28% in ages 70–79, and 16% in ages 80 and older); and stage (36% in local/regional and 17% in unstaged). An age- and stage-shift was observed for both LDS and nonLDS men, although more pronounced among LDS men. CONCLUSIONS: Comparatively high prostate cancer incidence rates among LDS men in Utah are explained, at least in part, by more aggressive screening among these men

Twirling Elastica: Kinks, Viscous Drag, and Torsional Stress

Biological filaments such as DNA or bacterial flagella are typically curved in their natural states. To elucidate the interplay of viscous drag, twisting, and bending in the overdamped dynamics of such filaments, we compute the steady-state torsional stress and shape of a rotating rod with a kink. Drag deforms the rod, ultimately extending or folding it depending on the kink angle. For certain kink angles and kink locations, both states are possible at high rotation rates. The agreement between our macroscopic experiments and the theory is good, with no adjustable parameters.Comment: 4 pages, 4 figure