Stochastic methods for solving high-dimensional partial differential equations

We propose algorithms for solving high-dimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through Feynman-Kac representation, with sparse interpolation. Monte-Carlo methods and time-integration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms

Proof of principle of a high-spatial-resolution, resonant-response gamma-ray detector for Gamma Resonance Absorption in 14N

The development of a mm-spatial-resolution, resonant-response detector based on a micrometric glass capillary array filled with liquid scintillator is described. This detector was developed for Gamma Resonance Absorption (GRA) in 14N. GRA is an automatic-decision radiographic screening technique that combines high radiation penetration (the probe is a 9.17 MeV gamma ray) with very good sensitivity and specificity to nitrogenous explosives. Detailed simulation of the detector response to electrons and protons generated by the 9.17 MeV gamma-rays was followed by a proof-of-principle experiment, using a mixed gamma-ray and neutron source. Towards this, a prototype capillary detector was assembled, including the associated filling and readout systems. Simulations and experimental results indeed show that proton tracks are distinguishable from electron tracks at relevant energies, on the basis of a criterion that combines track length and light intensity per unit length.Comment: 18 pages, 16 figure

Macroscopic Quantum Coherence in a Magnetic Nanoparticle Above the Surface of a Superconductor

We study macroscopic quantum tunneling of the magnetic moment in a single-domain particle placed above the surface of a superconductor. Such a setup allows one to manipulate the height of the energy barrier, preserving the degeneracy of the ground state. The tunneling amplitude and the effect of the dissipation in the superconductor are computed.Comment: RevTeX, 4 pages, 1 figure. Submitted to Phys. Rev. Let

Recurrent triploidy due to a failure to complete maternal meiosis II: whole-exome sequencing reveals candidate variants

Triploidy is a relatively common cause of miscarriage; however, recurrent triploidy has rarely been reported. A healthy 34-year-old woman was ascertained because of 18 consecutive miscarriages with triploidy found in all 5 karyotyped losses. Molecular results in a sixth loss were also consistent with triploidy. Genotyping of markers near the centromere on multiple chromosomes suggested that all six triploid conceptuses occurred as a result of failure to complete meiosis II (MII). The proband's mother had also experienced recurrent miscarriage, with a total of 18 miscarriages. Based on the hypothesis that an inherited autosomal-dominant maternal predisposition would explain the phenotype, whole-exome sequencing of the proband and her parents was undertaken to identify potential candidate variants. After filtering for quality and rarity, potentially damaging variants shared between the proband and her mother were identified in 47 genes. Variants in genes coding for proteins implicated in oocyte maturation, oocyte activation or polar body extrusion were then prioritized. Eight of the most promising candidate variants were confirmed by Sanger sequencing. These included a novel change in the PLCD4 gene, and a rare variant in the OSBPL5 gene, which have been implicated in oocyte activation upon fertilization and completion of MII. Several variants in genes coding proteins playing a role in oocyte maturation and early embryonic development were also identified. The genes identified may be candidates for the study in other women experiencing recurrent triploidy or recurrent IVF failur

Propagation of Avalanches in Mn12_{12}-acetate: Magnetic Deflagration

Local time-resolved measurements of fast reversal of the magnetization of single crystals of Mn12-acetate indicate that the magnetization avalanche spreads as a narrow interface that propagates through the crystal at a constant velocity that is roughly two orders of magnitude smaller than the speed of sound. We argue that this phenomenon is closely analogous to the propagation of a flame front (deflagration) through a flammable chemical substance.Comment: 5 pages, 5 figure

A stochastic perturbation of inviscid flows

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a \holderspace{k}{\alpha} local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as $\nu \to 0$, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of $O(\sqrt{\nu t})$.Comment: 13 pages, no figures

The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of a Time Machine

We study the propagator of a non-relativistic, non-interacting particle in any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an external, flat spacetime in which two spatial regions, $V_-$ at time $t_-$ and $V_+$ at time $t_+$, are connected by two temporal wormholes, one leading from the past side of $V_-$ to t the future side of $V_+$ and the other from the past side of $V_+$ to the future side of $V_-$. We express the propagator explicitly in terms of those for ordinary, flat spacetime and for the two wormholes; and from that expression we show that the propagator satisfies completeness and unitarity in the initial and final ``chronal regions'' (regions without closed timelike curves) and its propagation from the initial region to the final region is unitary. However, within the time machine it satisfies neither completeness nor unitarity. We also give an alternative proof of initial-region-to-final-region unitarity based on a conserved current and Gauss's theorem. This proof can be carried over without change to most any non-relativistic time-machine spacetime; it is the non-relativistic version of a theorem by Friedman, Papastamatiou and Simon, which says that for a free scalar field, quantum mechanical unitarity follows from the fact that the classical evolution preserves the Klein-Gordon inner product

Preliminary studies for anapole moment measurements in rubidium and francium

Preparations for the anapole measurement in Fr indicate the possibility of performing a similar measurement in a chain of Rb. The sensitivity analysis based on a single nucleon model shows the potential for placing strong limits on the nucleon weak interaction parameters. There are values of the magnetic fields at much lower values than found before that are insensitive to first order changes in the field. The anapole moment effect in Rb corresponds to an equivalent electric field that is eighty times smaller than Fr, but the stability of the isotopes and the current performance of the dipole trap in the apparatus, presented here, are encouraging for pursuing the measurment.Comment: 16 pages, 6 figures. Accepted for publication in the J. Phys.