Survival Probabilities at Spherical Frontiers

Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with an arbitrary power-law in time: $R(t)=R_0(1+t/t^*)^{\Theta}$, where $\Theta$ is a growth exponent, $R_0$ is the initial radius, and $t^*$ is a characteristic time for the growth, to be affected by the inflating geometry. We vary the parameters $t^*$ and $\Theta$ to capture a variety of possible growth regimes. Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier. Using analytical techniques, we calculate this probability for arbitrary $\Theta$. We compare our results to simulations of linearly inflating expansions ($\Theta=1$ spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling populations ($\Theta=0$, with cells in the interior removed by apoptosis or a similar process). We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more relative to mutations at treadmilling population frontiers. We also discuss the special properties of "marginally inflating" $(\Theta=1/2)$ expansions.Comment: 35 pages, 11 figures, revised versio

Electronically Variable Pressure Regulator (EVPR)

A new programmable electronically variable pressure regulator (EVPR) concept accurately controls the local outlet or remote system pressure. It uses an integral pulse width modulated rare earth permanent magnet motor operating in response to redundant pressure transducer feedback signals. The EVPR is a simple single stage device that does not use dynamic seals or pilot valving. Conversion of partial revolution motor torque to poppet lifting force is accomplished by pure flexure action to avoid using bearings. The flexure drive (called the ROTAX) has a variable lead to minimize motor weight and power consumption. Breadboard tests were completed successfully on two critical design elements of the EVPR: the ROTAX and the motor. The ROTAX cable system was tested for 250,000 cycles without failure. The breadboard motor met the basic design requirements including the design torque and power consumption. Prototype parts were fabricated, and testing of the prototype EVPR has started. It is PC computer controlled to facilitate programming, data acquisition and analysis. A lightweight dedicated microprocessor is planned for the flightweight EVPR

Models for the Observable System Parameters of Ultraluminous X-ray Sources

We investigate the evolution of the properties of model populations of ultraluminous X-ray sources (ULXs) consisting of a black-hole accretor in a binary with a donor star. We have computed models corresponding to three different populations of black-hole binaries; two invoke stellar-mass (~10 Msun) black hole accretors, and the third utilizes intermediate-mass (~1000 Msun) black holes (IMBHs). For each of the three populations, we computed 30,000 binary evolution sequences using a full Henyey stellar evolution code. The optical flux from the model ULXs includes contributions from the accretion disk, due to x-ray irradiation as well as intrinsic viscous heating, and that due to the donor star. We present "probability images" for the ULX systems in planes of color-magnitude, orbital period vs. X-ray luminosity, and luminosity vs. evolution time. Estimates of the numbers of ULXs in a typical galaxy as functions of time and of X-ray luminosity are also presented. Our model CMDs are compared with six ULX counterparts that have been discussed in the literature. Overall, the observed systems seem more closely related to model systems with very high-mass donors (> ~25 Msun) in binaries with IMBH accretors. However, significant difficulties remain with both the IMBH and stellar-mass black hole models.Comment: 15 pages, 8 figures, submitted to ApJ on Oct 05, 200

Translational Correlations in the Vortex Array at the Surface of a Type-II Superconductor

We discuss the statistical mechanics of magnetic flux lines in a finite-thickness slab of type-II superconductor. The long wavelength properties of a flux-line liquid in a slab geometry are described by a hydrodynamic free energy that incorporates the boundary conditions on the flux lines at the sample's surface as a surface contribution to the free energy. Bulk and surface weak disorder are modeled via Gaussian impurity potentials. This free energy is used to evaluate the two-dimensional structure factor of the flux-line tips at the sample surface. We find that surface interaction always dominates in determining the decay of translational correlations in the asymptotic long-wavelength limit. On the other hand, such large length scales have not been probed by the decoration experiments. Our results indicate that the translational correlations extracted from the analysis of the Bitter patterns are indeed representative of behavior of flux lines in the bulk.Comment: 23 pages, 1 figure (not included), harvmac.tex macro needed (e-mail requests to [email protected] SU-CM-92-01

Deranged calcium signaling and neurodegeneration in spinocerebellar ataxia type 3

Spinocerebellar ataxia type 3 (SCA3), also known as Machado-Joseph disease (MJD), is an autosomal-dominant neurodegenerative disorder caused by a polyglutamine expansion in ataxin-3 (SCA3, MJD1) protein. In biochemical experiments we demonstrate that mutant SCA3exp specifically associated with the type 1 inositol 1,4,5-trisphosphate receptor (InsP3R1), an intracellular calcium (Ca2+) release channel. In electrophysiological and Ca2+ imaging experiments we show that InsP3R1 are sensitized to activation by InsP3 in the presence of mutant SCA3exp. We found that feeding SCA3-YAC-84Q transgenic mice with dantrolene, a clinically relevant stabilizer of intracellular Ca2+ signaling, improved their motor performance and prevented neuronal cells loss in pontine nuclei and substantia nigra regions. Our results indicate that deranged Ca2+ signaling may play an important role in SCA3 pathology and that Ca2+ signaling stabilizers such as dantrolene may be considered as potential therapeutic drugs for treatment of SCA3 patients

Vortex Pinning and Non-Hermitian Quantum Mechanics

A delocalization phenomenon is studied in a class of non-Hermitian random quantum-mechanical problems. Delocalization arises in response to a sufficiently large constant imaginary vector potential. The transition is related to depinning of flux lines from extended defects in type-II superconductors subject to a tilted external magnetic field. The physical meaning of the complex eigenvalues and currents of the non-Hermitian system is elucidated in terms of properties of tilted vortex lines. The singular behavior of the penetration length describing stretched exponential screening of a perpendicular magnetic field (transverse Meissner effect), the surface transverse magnetization, and the trapping length are determined near the flux-line depinning point.Comment: 2-column 27-pages RevTex file with 35 eps figure files embedded. Minor errors amended. To be published in Phys. Rev.