An ALE ESFEM for Solving PDEs on Evolving Surfaces

Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite elements on evolving triangulated surfaces are presented. In the ALE ESFEM the vertices of the triangles evolve with a velocity which is normal to the hypersurface whilst having a tangential velocity which is arbitrary. This is in contrast to the original evolving surface finite element method in which the nodes move with a material velocity. Numerical experiments are presented which illustrate the value of choosing the arbitrary tangential velocity to improve mesh quality. Simulations of two applications arising in material science and biology are presented which couple the evolution of the surface to the solution of the surface partial differential equation.     

Positive Definite Toeplitz Completions

The problem of completing a partially prescribed Toeplitz matrixto a positive definite Toeplitz matrix is considered. The mainresult is a characterization of the patterns of specified entriesthat guarantee the existence of a positive definite Toeplitzcompletion of a partial positive definite Toeplitz matrix. Thischaracterization resolves affirmatively a conjecture of C. R.Johnson and L. Rodman.     

Postural Complexity during Listening in Young and Middle-Aged Adults

Postural behavior has traditionally been studied using linear assessments of stability (e.g., center of pressure ellipse area). While these assessments may provide valuable information, they neglect the nonlinear nature of the postural system and often lead to the conflation of variability with pathology. Moreover, assessing postural behavior in isolation or under otherwise unrealistic conditions may obscure the natural dynamics of the postural system. Alternatively, assessing postural complexity during ecologically valid tasks (e.g., conversing with others) may provide unique insight into the natural dynamics of the postural system across a wide array of temporal scales. Here, we assess postural complexity using Multiscale Sample Entropy in young and middle-aged adults during a listening task of varying degrees of difficulty. It was found that middle-aged adults exhibited greater postural complexity than did young adults, and that this age-related difference in postural complexity increased as a function of task difficulty. These results are inconsistent with the notion that aging is universally associated with a loss of complexity, and instead support the notion that age-related differences in complexity are task dependent.     

Chain Lengths in Certain Random Directed Graphs

We study the random directed graph with vertex set {1, …, n} in which the directed edges (i, j) occur independently with probability c_n/n for i<j and probability zero for i ? j. Let M_n (resp., L_n) denote the length of the longest path (resp., longest path starting from vertex 1). When c_n is bounded away from 0 and ∞ as n→∞, the asymptotic behavior of M_n was analyzed in previous work of the author and J. E. Cohen. Here, all restrictions on c_n are eliminated and the asymptotic behavior of L_n is also obtained. In particular, if c_n/ln(n)→∞ while c_n/n→0, then both M_n/c_n and L_n/c_n are shown to converge in probability to the constant e.     

Molecular dynamics by the Backward-Euler method

This paper introduces a new computational method for molecular dynamics. The method combines the Backward-Euler scheme for the solution of stiff differential equations with a Langevin-equation approach to the establishment of thermal equilibrium. The method allows the user to choose a cutoff frequency ω_c. Vibrational modes with frequencies below ω_c will be fully excited (receive a mean energy of kT per mode), while modes with frequencies greater than ω_c will be effectively frozen by the method. By setting ω_c = kT/h, one can obtain reasonable agreement with the quantum-mechanical energy distribution among the various modes, despite the classical character of the computation.     

Existence of the Møller wave operators for V(r)=γ sin(μrα)rβ

We prove the existence of the Møller wave operators and the unitarity of the S operator for quantum mechanical potential scattering by potentials of the form

This includes the Special case $\text{V(r) =}\text{sin}\text{(r)}\text{r}$.     

Upstream ionization instability associated with a current-free double layer

A low frequency instability has been observed using various electrostatic probes in a low-pressure expanding helicon plasma. The instability is associated with the presence of a current-free double layer (DL). The frequency of the instability increases linearly with the potential drop of the DL, and simultaneous measurements show their coexistence. A theory for an upstream ionization instability has been developed, which shows that electrons accelerated through the DL increase the ionization upstream and are responsible for the observed instability. The theory is in good agreement with the experimental results.     

T2-shortening of 3He gas by magnetic microspheres

In a gas-filled material like the lung parenchyma, the transverse relaxation time (T2) for 3He is shortened by the deposition of magnetic microspheres and rapid molecular diffusion through induced field distortions. Here, this unique relaxation process is described theoretically and predicted T2-shortening is validated using pressurized 3He gas in a foam model of alveolar airways. Results demonstrate that: (1) significant T2-shortening is induced by microsphere deposition, (2) shortened 3He T2s are accurately predicted, and (3) measured relaxation times are exploitable for quantifying local deposition patterns. Based on these findings the feasibility of imaging inhaled particulates in vivo with hyperpolarized 3He is examined and performance projections are formulated.     

Observation of the decay B+/--->pi+/-pi0, study of B+/--->K+/-pi0, and search for B0-->pi0pi0

We present results for the branching fractions and charge asymmetries in B+/--->h(+/-)pi(0) (where h(+/-)=pi(+/-),K+/-) and a search for the decay B0-->pi(0)pi(0) using a sample of approximately 88 x 10(6) BBmacr; pairs collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We measure B(B+/--->pi(+/-)pi(0))=(5.5(+1.0)(-0.9)+/-0.6)x10(-6), where the first error is statistical and the second is systematic. The B+/--->pi(+/-)pi(0) signal has a significance of 7.7sigma including systematic uncertainties. We simultaneously measure the K+/-pi(0) branching fraction to be B(B+/--->K+/-pi(0))=(12.8(+1.2)(-1.1)+/-1.0)x10(-6). The charge asymmetries are Api(+/-)(pi(0))=-0.03(+0.18)(-0.17)+/-0.02 and AK+/-(pi(0))=-0.09+/-0.09+/-0.01. We place a 90% confidence-level upper limit on the branching fraction B(B0-->pi(0)pi(0)) of 3.6 x 10(-6).     

Sooting tendencies of nonvolatile aromatic hydrocarbons

We have measured sooting tendencies of 72 nonvolatile aromatic hydrocarbons, only five of which have been previously reported in the literature. The tested compounds include long-chain alkylbenzenes up to tridecylbenzene, methyl-substituted benzenes, naphthalenes, biaryls, and polycyclic aromatic hydrocarbons (PAH) with up to four rings. Sooting tendency was defined as the maximum soot concentration f_v,max in a methane/air coflow nonpremixed flame with 5-80 ppm of the aromatic added to the fuel. The f_v,max were converted into Yield Sooting Indices (YSI’s) by the equation YSI = C^∗f_v,max + D, where C and D are constants chosen so that YSI-2-heptanone = 17 and YSI-phenanthrene = 191. The aromatics were dissolved in 2-heptanone and added to the fuel mixture with a syringe pump. Soot concentrations were measured with laser-induced incandescence (LII). The burner and fuel lines were heated; time-resolved soot measurements verified that all of the test compounds were quantitatively transmitted to the flame without losses to the walls. The uncertainties in the results range from ±3 to ±10%.