Doubly stochastic matrices in quantum mechanics

The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Landé's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n!-space is surjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices.     

Emergent <Emphasis Type=Italic>SO</Emphasis>(3) Symmetry of the Frictionless Shear Jamming Transition

We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.     

Nearest-neighbor configuration in (GaIn)(NAs) probed by x-ray absorption spectroscopy

Ga(1-x)In(x)N(y)As(1-y) is a promising material system for the fabrication of inexpensive "last-mile" optoelectronic components. However, details of its atomic arrangement and the relationship to observed optical properties is not fully known. Particularly, a blueshift of emission wavelength is observed after annealing. In this work, we use x-ray absorption fine structure to study the chemical environment around N atoms in the material before and after annealing. We find that as-grown molecular beam epitaxy material consists of a nearly random distribution of atoms, while postannealed material shows segregation of In toward N. Ab initio simulations show that this short-range ordering creates a more thermodynamically stable alloy and is responsible for blueshifting the emission.     

Fiber bragg gratings made with a phase mask and 800-nm femtosecond radiation

High-quality retroreflecting fiber Bragg gratings were written in standard Ge-doped telecom fiber (Corning SMF-28) after a few minutes exposure with pulsed 800-nm, 120-fs laser radiation by use of a deep-etch silica zero-order nulled phase mask optimized for 800 nm. Induced index modulations of 1.9 x 10(-3) were achieved with peak power intensities of 1.2 x 10(13) W/cm2 without any fiber sensitization. The fiber gratings are stable and did not erase after 2 weeks at 300 degrees C. The primary mechanism of induced index change results from a structural modification to the fiber core.     

Source motion mitigation for adaptive matched field processing

Application of adaptive matched field processing to the problem of detecting quiet targets in shallow water is complicated by source motion, both the motion of the target and the motion of discrete interferers. Target motion causes spreading of the target peak, thereby reducing output signal power. Interferer motion increases the dimensionality of the interference subspace, reducing adaptive interference suppression. This paper presents three techniques that mitigate source motion problems in adaptive matched field processing. The first involves rank reduction, which enables adaptive weight computation over short observation intervals where motion effects are less pronounced. The other two techniques specifically compensate for source motion. Explicit target motion compensation reduces target motion mismatch by focusing snapshots according to a target velocity hypothesis. And time-varying interference filtering places time-varying nulls on moving interferers not otherwise suppressed by adaptive weights. The three techniques are applied to volumetric array data from the Santa Barbara Channel Experiment and are shown to improve output signal-to-background-plus-noise ratio by more than 3 dB over the standard minimum-variance, distortionless response adaptive beam-former. Application of the techniques in some cases proves to be the difference between detecting and not detecting the target.     

Assessing temporary threshold shift in a bottlenose dolphin (Tursiops truncatus) using multiple simultaneous auditory evoked potentials

Hearing sensitivity was measured in a bottlenose dolphin before and after exposure to an intense 20-kHz fatiguing tone in three different experiments. In each experiment, hearing was characterized using both the auditory steady-state response (ASSR) and behavioral methods. In experiments 1 and 2, ASSR stimuli consisted of seven frequency-modulated tones, each with a unique carrier and modulation frequency. The tones were simultaneously presented to the subject and the ASSR at each modulation rate measured to determine the effects of the sound exposure at the corresponding carrier frequency. In experiment 3 behavioral thresholds and ASSR input-output functions were measured at a single frequency before and after three exposures. Hearing loss was frequency-dependent, with the largest temporary threshold shifts occurring (in order) at 30, 40, and 20 kHz. ASSR threshold shifts reached 40-45 dB and were always larger than behavioral shifts (19-33 dB). The ASSR input-output functions were represented as the sum of two processes: a low threshold, saturating process and a higher threshold, linear process, that react and recover to fatigue at different rates. The loss of the near-threshold saturating process after exposure may explain the discrepancies between the ASSR and behavioral threshold shifts.     

Self-assembled alkanethiol structures on gold: A further insight into the origins of structural rearrangement phenomena

Self-assembled structures of alkanethiols that have been deposited on gold from ethanolic solutions are susceptible to both chemical and physical changes: ethanol provides a medium for the formation of S-alkyl hydrogen thiocarbonates and related compounds via reaction with dissolved, atmospheric, CO₂. Deposition from ethanolic solutions results in multilayered structures incorporating these compounds, which at room temperature are susceptible to time-dependent structural rearrangement and molecular migration.     

Universal quadratures for boundary integral equations on two-dimensional domains with corners

We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high-accuracy solution of Dirichlet boundary value problems for Laplace’s equation and the Helmholtz equation on such domains under a mild assumption on the boundary data. Our approach can be adapted to other boundary value problems and certain aspects of our scheme generalize to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.     

Understanding anomalous delays in a model of intracellular calcium dynamics

In many cell types, oscillations in the concentration of free intracellular calcium ions are used to control a variety of cellular functions. It has been suggested [J. Sneyd et al., "A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations," Proc. Natl. Acad. Sci. U.S.A. 103, 1675-1680 (2006)] that the mechanisms underlying the generation and control of such oscillations can be determined by means of a simple experiment, whereby a single exogenous pulse of inositol trisphosphate (IP(3)) is applied to the cell. However, more detailed mathematical investigations [M. Domijan et al., "Dynamical probing of the mechanisms underlying calcium oscillations," J. Nonlinear Sci. 16, 483-506 (2006)] have shown that this is not necessarily always true, and that the experimental data are more difficult to interpret than first thought. Here, we use geometric singular perturbation techniques to study the dynamics of models that make different assumptions about the mechanisms underlying the calcium oscillations. In particular, we show how recently developed canard theory for singularly perturbed systems with three or more slow variables [M. Wechselberger, "A propos de canards (Apropos canards)," Preprint, 2010] applies to these calcium models and how the presence of a curve of folded singularities and corresponding canards can result in anomalous delays in the response of these models to a pulse of IP(3).