Multiple vacancy inclusive probabilities for the scattering system 16 MeV S{^16+} on Ar

To evaluate single and double K-shell inclusive charge transfer probabilities in ion-atom collisions we solve the time-dependent Dirac equation. By expanding the timedependent wavefunction in a set of molecular basis states the time-dependent equation reduces to a set of coupled-channel equations. The energy eigenvalues and matrix elements are taken from self-consistent relativistic molecular many-electron Dirac-Fock-Slater calculations. We present many-electron inclusive probabilities for different final configurations as a function of impact parameter for single and double K-shell vacancy production in collisions of bare S on Ar.

Realistic many electron coupled channel calculations in heavy ion scattering

The time dependent Dirac equation which describes a heavy ion-atom collision system is solved via a set of coupled channel equations with energy eigenvalues and matrix elements which are given by a selfconsistent field many electron calculation. After a brief discussion of the theoretical approximations and the connection of the many particle with the one particle interpretation we discuss first results for the systems F{^8+} - Ne and F{^6+} - Ne. The resulting P(b) curves for the creation of a Ne K-hole are in good agreement with the experimental results.

A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

The PML for rough surface scattering

In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

A well-posed integral equation formulation for three-dimensional rough surface scattering

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space L-2 (Gamma) when the scattering surface G does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, kappa, for kappa > 0, if the coupling parameter h is chosen proportional to the wave number. In the case when G is a plane, we show that the choice eta = kappa/2 is nearly optimal in terms of minimizing the condition number.

Acoustic scattering by mildly rough unbounded surfaces in three dimensions

For a nonlocally perturbed half- space we consider the scattering of time-harmonic acoustic waves. A second kind boundary integral equation formulation is proposed for the sound-soft case, based on a standard ansatz as a combined single-and double-layer potential but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half- space Green's function. Due to the unboundedness of the surface, the integral operators are noncompact. In contrast to the two-dimensional case, the integral operators are also strongly singular, due to the slow decay at infinity of the fundamental solution of the three-dimensional Helmholtz equation. In the case when the surface is sufficiently smooth ( Lyapunov) we show that the integral operators are nevertheless bounded as operators on L-2(Gamma) and on L-2(Gamma G) boolean AND BC(Gamma) and that the operators depend continuously in norm on the wave number and on G. We further show that for mild roughness, i.e., a surface G which does not differ too much from a plane, the boundary integral equation is uniquely solvable in the space L-2(Gamma) boolean AND BC(Gamma) and the scattering problem has a unique solution which satisfies a limiting absorption principle in the case of real wave number.

Radar scattering by aggregate snowflakes

The radar scattering properties of realistic aggregate snowflakes have been calculated using the Rayleigh-Gans theory. We find that the effect of the snowflake geometry on the scattering may be described in terms of a single universal function, which depends only on the overall shape of the aggregate and not the geometry or size of the pristine ice crystals which compose the flake. This function is well approximated by a simple analytic expression at small sizes; for larger snowflakes we fit a curve to Our numerical data. We then demonstrate how this allows a characteristic snowflake radius to be derived from dual wavelength radar measurements without knowledge of the pristine crystal size or habit, while at the same time showing that this detail is crucial to using such data to estimate ice water content. We also show that the 'effective radius'. characterizing the ratio of particle volume to projected area, cannot be inferred from dual wavelength radar data for aggregates. Finally, we consider the errors involved in approximating snowflakes by 'air-ice spheres', and show that for small enough aggregates the predicted dual wavelength ratio typically agrees to within a few percent, provided some care is taken in choosing the radius of the sphere and the dielectric constant of the air-ice mixture; at larger sizes the radar becomes more sensitive to particle shape, and the errors associated with the sphere model are found to increase accordingly.

Energy separation of neutrons scattered at small angles from silicon using time-of-flight techniques

The time-of-flight technique is used on a small-angle neutron scattering instrument to separate the energies of the scattered neutrons, in order to determine the origin of the temperature-dependent scattering observed from silicon at Q > similar to 0.1 angstrom(-1). A quantitative analysis of the results in comparison with the phonon dispersion curves, determined by Dolling using a triple-axis neutron spectrometer, shows that the temperature-dependent scattering can be understood in terms of Umklapp processes whereby neutrons gain energy from phonons.

Molecular aluminum hydrides identified by inelastic neutron scattering during H-2 regeneration of catalyst-doped NaAlH4

Catalyst-doped sodium aluminum hydrides have been intensively studied as solid hydrogen carriers for onboard proton-exchange membrane (PEM) fuel cells. Although the importance of catalyst choice in enhancing kinetics for both hydrogen uptake and release of this hydride material has long been recognized, the nature of the active species and the mechanism of catalytic action are unclear. We have shown by inelastic neutron scattering (INS) spectroscopy that a volatile molecular aluminum hydride is formed during the early stage of H-2 re-eneration of a depleted, catalyst-doped sodium aluminum hydride. Computational modeling of the INS spectra suggested the formation of AlH3 and oligomers (AlH3)(n) (Al2H6, Al3H9, and Al4H12 clusters), which are pertinent to the mechanism of hydrogen storage. This paper demonstrates, for the first time, the existence of these volatile species.

Crystallization in poly(L-lactide)-b-poly(epsilon-caprolactone) double crystalline diblock copolymers: a study using X-ray scattering, differential scanning calorimetry, and polarized optical microscopy

The crystallization of well-defined poly(L-lactide)-b-poly(epsilon-caprolactone) diblock copolymers, PLLA-b-PCL, was investigated by time-resolved X-ray techniques, polarized optical microscopy (POM), and differential scanning calorimetry (DSC). Two compositions were studied that contained 44 and 60 wt % poly(L-lactide), PLLA (they are referred to as (L44C5614)-C-11 and (L60C409)-C-12, respectively, with the molecular weight of each block in kg/mol as superscript). The copolymers were found to be initially miscible in the melt according to small-angle X-ray scattering measurements (SAXS). Their thermal behavior was also indicative of samples whose crystallization proceeds from a mixed melt. Sequential isothermal crystallization from the melt at 100 degreesC (for 30 min) and then at 30 degreesC (for 15 min) was measured. At 100 degreesC only the PLLA block is capable of crystallization, and its crystallization kinetics was followed by both WAXS and DSC; comparable results were obtained that indicated an instantaneous nucleation with three-dimensional superstructures (Avrami index of approximately 3). The spherulitic nature of the superstructure was confirmed by POM. When the temperature was decreased to 30 degreesC, the PCL block was able to crystallize within the PLLA negative spherulites (with an Avrami index of 2, as opposed to 3 in homo-PCL), and its crystallization rate was much slower than an equivalent homo-PCL. Time-resolved SAXS experiments in (L60C409)-C-12 revealed an initial melt mixed morphology at 165 degreesC that upon cooling transformed into a transient microphase-separated lamellar structure prior to crystallization at 100 degreesC.

Dihydrogen in zeolite CaX: an inelastic neutron scattering study

We report an inelastic neutron scattering (INS) study of the rotational–vibrational spectrum of dihydrogen sorbed by zeolite CaX. In the low energy (<200 cm−1) INS spectrum of adsorbed H2 we observe the rotational–vibrational spectrum of H2, where the vibration is that of the H2 molecule against the binding site (i.e. H2–X, not H–H). We have observed for the first time the vibrational overtones of the hydrogen molecule against the adsorption surface up to sixth order. These vibrations are usually forbidden in INS spectroscopy because of the selection rules imposed by the spin flip event required. In our case we are able to observe such a vibration because the rotational transition J(1 ← 0) convolutes the vibrational spectrum. This paper reports the effect for the first time.

Small-angle x-ray scattering study of flow alignment of a thermotropic liquid crystal in the nematic and smectic phases

WThe capillary flow alignment of the thermotropic liquid crystal 4-n-octyl-4′-cyanobiphenyl in the nematic and smectic phases is investigated using time-resolved synchrotron small-angle x-ray scattering. Samples were cooled from the isotropic phase to erase prior orientation. Upon cooling through the nematic phase under Poiseuille flow in a circular capillary, a transition from the alignment of mesogens along the flow direction to the alignment of layers along the flow direction (mesogens perpendicular to flow) appears to occur continuously at the cooling rate applied. The transition is centered on a temperature at which the Leslie viscosity coefficient α3 changes sign. The configuration with layers aligned along the flow direction is also observed in the smectic phase. The transition in the nematic phase on cooling has previously been ascribed to an aligning-nonaligning or tumbling transition. At high flow rates there is evidence for tumbling around an average alignment of layers along the flow direction. At lower flow rates this orientation is more clearly defined. The layer alignment is ascribed to surface-induced ordering propagating into the bulk of the capillary, an observation supported by the parallel alignment of layers observed for a static sample at low temperatures in the nematic phase.

Efficient on the fly calculation of time correlation functions in computer simulations

Time correlation functions yield profound information about the dynamics of a physical system and hence are frequently calculated in computer simulations. For systems whose dynamics span a wide range of time, currently used methods require significant computer time and memory. In this paper, we discuss the multiple-tau correlator method for the efficient calculation of accurate time correlation functions on the fly during computer simulations. The multiple-tau correlator is efficacious in terms of computational requirements and can be tuned to the desired level of accuracy. Further, we derive estimates for the error arising from the use of the multiple-tau correlator and extend it for use in the calculation of mean-square particle displacements and dynamic structure factors. The method described here, in hardware implementation, is routinely used in light scattering experiments but has not yet found widespread use in computer simulations.