Support theorems on R-n and non-compact symmetric spaces

We consider convolution equations of the type f * T = g, where f, g is an element of L-P (R-n) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T, we show that f is compactly supported, provided g is. Similar results are proved for non-compact symmetric spaces as well. (C) 2010 Elsevier Inc. All rights reserved.

Velocity distribution for a dilute vibrated granular material

The velocity distribution for a vibrated granular material is determined in the dilute limit where the frequency of particle collisions with the vibrating surface is large compared to the frequency of binary collisions. The particle motion is driven by the source of energy due to particle collisions with the vibrating surface, and two dissipation mechanisms-inelastic collisions and air drag-are considered. In the latter case, a general form for the drag force is assumed. First, the distribution function for the vertical velocity for a single particle colliding with a vibrating surface is determined in the limit where the dissipation during a collision due to inelasticity or between successive collisions due to drag is small compared to the energy of a particle. In addition, two types of amplitude functions for the velocity of the surface, symmetric and asymmetric about zero velocity, are considered. In all cases, differential equations for the distribution of velocities at the vibrating surface are obtained using a flux balance condition in velocity space, and these are solved to determine the distribution function. It is found that the distribution function is a Gaussian distribution when the dissipation is due to inelastic collisions and the amplitude function is symmetric, and the mean square velocity scales as [[U-2](s)/(1 - e(2))], where [U-2](s) is the mean square velocity of the vibrating surface and e is the coefficient of restitution. The distribution function is very different from a Gaussian when the dissipation is due to air drag and the amplitude function is symmetric, and the mean square velocity scales as ([U-2](s)g/mu(m))(1/(m+2)) when the acceleration due to the fluid drag is -mu(m)u(y)\u(y)\(m-1), where g is the acceleration due to gravity. For an asymmetric amplitude function, the distribution function at the vibrating surface is found to be sharply peaked around [+/-2[U](s)/(1-e)] when the dissipation is due to inelastic collisions, and around +/-[(m +2)[U](s)g/mu(m)](1/(m+1)) when the dissipation is due to fluid drag, where [U](s) is the mean velocity of the surface. The distribution functions are compared with numerical simulations of a particle colliding with a vibrating surface, and excellent agreement is found with no adjustable parameters. The distribution function for a two-dimensional vibrated granular material that includes the first effect of binary collisions is determined for the system with dissipation due to inelastic collisions and the amplitude function for the velocity of the vibrating surface is symmetric in the limit delta(I)=(2nr)/(1 - e)much less than 1. Here, n is the number of particles per unit width and r is the particle radius. In this Limit, an asymptotic analysis is used about the Limit where there are no binary collisions. It is found that the distribution function has a power-law divergence proportional to \u(x)\((c delta l-1)) in the limit u(x)-->0, where u(x) is the horizontal velocity. The constant c and the moments of the distribution function are evaluated from the conservation equation in velocity space. It is found that the mean square velocity in the horizontal direction scales as O(delta(I)T), and the nontrivial third moments of the velocity distribution scale as O(delta(I)epsilon(I)T(3/2)) where epsilon(I) = (1 - e)(1/2). Here, T = [2[U2](s)/(1 - e)] is the mean square velocity of the particles.

On Uniform Approximate Solutions in Bending of Symmetric Laminated Plates

A layer-wise theory with the analysis of face ply independent of lamination is used in the bending of symmetric laminates with anisotropic plies. More realistic and practical edge conditions as in Kirchhoff's theory are considered. An iterative procedure based on point-wise equilibrium equations is adapted. The necessity of a solution of an auxiliary problem in the interior plies is explained and used in the generation of proper sequence of two dimensional problems. Displacements are expanded in terms of polynomials in thickness coordinate such that continuity of transverse stresses across interfaces is assured. Solution of a fourth order system of a supplementary problem in the face ply is necessary to ensure the continuity of in-plane displacements across interfaces and to rectify inadequacies of these polynomial expansions in the interior distribution of approximate solutions. Vertical deflection does not play any role in obtaining all six stress components and two in-plane displacements. In overcoming lacuna in Kirchhoff's theory, widely used first order shear deformation theory and other sixth and higher order theories based on energy principles at laminate level in smeared laminate theories and at ply level in layer-wise theories are not useful in the generation of a proper sequence of 2-D problems converging to 3-D problems. Relevance of present analysis is demonstrated through solutions in a simple text book problem of simply supported square plate under doubly sinusoidal load.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

Two Glass Transitions Associated to Different Dynamic Disorders in the Nematic Glassy State of a Non-Symmetric Liquid Crystal Dimer Dopped with gamma-Alumina Nanoparticles

In the present work, the nematic glassy state of the non-symmetric LC dimer -(4-cyanobiphenyl-4-yloxy)--(1-pyrenimine-benzylidene-4-oxy) undecane is studied by means of calorimetric and dielectric measurements. The most striking result of the work is the presence of two different glass transition temperatures: one due to the freezing of the flip-flop motions of the bulkier unit of the dimer and the other, at a lower temperature, related to the freezing of the flip-flop and precessional motions of the cyanobiphenyl unit. This result shows the fact that glass transition is the consequence of the freezing of one or more coupled dynamic disorders and not of the disordered phase itself. In order to avoid crystallization when the bulk sample is cooled down, the LC dimer has been confined via the dispersion of -alumina nanoparticles, in several concentrations.

Triclinic deformation and anisotropic strain relaxation of an InAs film on a GaAs(001) substrate measured by a series of symmetric double crystal X-ray diffraction

We presented a series of symmetric double crystal X-ray diffraction (DCXD) measurements, (0 0 4), (2 2 0) and (2 - 2 0) diffraction, to investigate the strain relaxation in an InAs film grown on a GaAs(0 0 1) substrate. The strain tensor and rotation tensor were calculated according to the DCXD results. It is found that the misfit strain is relaxed nearly completely and the strain relaxation caused a triclinic deformation in the epilayer. The lattice parameter along the [1 1 0] direction is a little longer than that along the [1 - 1 0] direction. Furthermore, a significant tilt, 0.2 degrees, towards the [1 1 0] direction while a very slight one: 0.002 degrees, towards [1 - 1 0] direction were discussed. This anisotropic strain relaxation is attributed to the asymmetric distribution of misfit dislocations, which is also indicated by the variation of the full-width at half-maximum (FWHM) of (0 0 4) diffraction along four azimuth angles. (C) 1998 Elsevier Science B.V. All rights reserved.

Hydroelastic dynamic characteristics of a slender axis-symmetric body

The slender axis-symmetric submarine body moving in the vertical plane is the object of our investigation. A coupling model is developed where displacements of a solid body as a Euler beam (consisting of rigid motions and elastic deformations) and fluid pressures are employed as basic independent variables, including the interaction between hydrodynamic forces and structure dynamic forces. Firstly the hydrodynamic forces, depending on and conversely influencing body motions, are taken into account as the governing equations. The expressions of fluid pressure are derived based on the potential theory. The characteristics of fluid pressure, including its components, distribution and effect on structure dynamics, are analyzed. Then the coupling model is solved numerically by means of a finite element method (FEM). This avoids the complicacy, combining CFD (fluid) and FEM (structure), of direct numerical simulation, and allows the body with a non-strict ideal shape so as to be more suitable for practical engineering. An illustrative example is given in which the hydroelastic dynamic characteristics, natural frequencies and modes of a submarine body are analyzed and compared with experimental results. Satisfactory agreement is observed and the model presented in this paper is shown to be valid.

Fusion dynamics of symmetric systems near barrier energies

Within the framework of the improved isospin-dependent quantum molecular dynamics (ImIQMD) model,he fusion dynamics of symmetric reaction systems are investigated systematically. Calculations show that the number of nucleon transfer in the neck region is appreciably dependent on the incident energies, but strongly on he reaction systems. A comparison of the neck dynamics is performed for the symmetric reactions 58Ni+58Niand 64Ni+64Ni at energies in the vicinity of the Coulomb barrier. An increase of the ratios of the neutron to proton in the neck region at initial collision stage is observed and obvious for the latter system, which reduces the fusion barrier of two colliding nuclei. The distribution of the dynamical fusion barriers and the fusion excitation functions are calculated and compared with the available experimental data.

Monte Carlo simulation on symmetric ABA/AB copolymer blends in confined thin films

The effects of blend composition on morphology, order-disorder transition (ODT), and chain conformation of symmetric ABA/AB copolymer blends confined between two neutral hard walls have been investigated by lattice Monte Carlo simulation. Only lamellar structure is observed in all the simulation morphologies under thermodynamic equilibrium state, which is supported by theoretical prediction. When the composition of AB diblock copolymer (phi) increases, both lamellar spacing and the corresponding ODT temperature increase, which can be attributed to the variation of conformation distribution of the diblock and the triblock copolymer chains. In addition, both diblock and triblock copolymer, chains with bridge conformation extend dramatically in the direction parallel to the surface when the system is in ordered state. Finally, the copolymer chain conformation depends strongly on both the blend composition and the incompatibility parameter chi N.

The formation of ordered nanoholes in binary, chemically similar, symmetric diblock copolymer blend films

Binary symmetric diblock copolymer blends, that is, low-molecular-weight poly(styrene-block-methyl methacrylate) (PS-b-PMMA) and high-molecular-weight poly(styrene-block-methacrylate) (PS-b-PMA), self-assemble on silicon substrates to form structures with highly ordered nanoholes in thin films. As a result of the chemically similar structure of the PMA and the PMMA block, the PMMA chain penetrates through the large PMA block that absorbs preferentially on the polar silicon substrate. This results in the formation of nanoholes in the PS continuous matrix.

Angular distribution for the elastic scattering of electrons from Ar+(3s^2 3p^5 ^2P) above the first inelastic threshold

The measured angular differential cross section (DCS) for the elastic scattering of electrons from Ar+(3s2 3p5 2P) at the collision energy of 16 eV is presented. By solving the Hartree-Fock equations, we calculate the corresponding theoretical DCS including the coupling between the orbital angular momenta and spin of the incident electron and those of the target ion and also relaxation effects. Since the collision energy is above one inelastic threshold for the transition 3s2 3p5 2P–3s 3p6 2S, we consider the effects on the DCS of inelastic absorption processes and elastic resonances. The measurements deviate significantly from the Rutherford cross section over the full angular range observed, especially in the region of a deep minimum centered at approximately 75°. Our theory and an uncoupled, unrelaxed method using a local, spherically symmetric potential by Manson [Phys. Rev. 182, 97 (1969)] both reproduce the overall shape of the measured DCS, although the coupled Hartree-Fock approach describes the depth of the minimum more accurately. The minimum is shallower in the present theory owing to our lower average value for the d-wave non-Coulomb phase shift s2, which is due to the high sensitivity of s2 to the different scattering potentials used in the two models. The present measurements and calculations therefore show the importance of including coupling and relaxation effects when accurately modeling electron-ion collisions. The phase shifts obtained by fitting to the measurements are compared with the values of Manson and the present method.

Theory of pixel lensing toward M31. II. The velocity anisotropy and flattening of the MACHO distribution

The POINT-AGAPE collaboration is currently searching for massive compact halo objects (MACHOs) toward the Andromeda galaxy (M31). The survey aims to exploit the high inclination of the M31 disk, which causes an asymmetry in the spatial distribution of M31 MACHOs. Here, we investigate the effects of halo velocity anisotropy and flattening on the asymmetry signal using simple halo models. For a spherically symmetric and isotropic halo, we find that the underlying pixel lensing rate in far-disk M31 MACHOs is more than 5 times the rate of near-disk events. We find that the asymmetry is further increased by about 30% if the MACHOs occupy radial orbits rather than tangential orbits, but it is substantially reduced if the MACHOs lie in a flattened halo. However, even for halos with a minor- to major-axis ratio of q = 0.3, the number of M31 MACHOs in the far side outnumber those in the near side by a factor of similar to2. There is also a distance asymmetry, in that the events on the far side are typically farther from the major axis. We show that, if this positional information is exploited in addition to number counts, then the number of candidate events required to confirm asymmetry for a range of flattened and anisotropic halo models is achievable, even with significant contamination by variable stars and foreground microlensing events. For pixel lensing surveys that probe a representative portion of the M31 disk, a sample of around 50 candidates is likely to be sufficient to detect asymmetry within spherical halos, even if half the sample is contaminated, or to detect asymmetry in halos as flat as q = 0.3, provided less than a third of the sample comprises contaminants. We also argue that, provided its mass-to-light ratio is less than 100, the recently observed stellar stream around M31 is not problematic for the detection of asymmetry.

Seismic Assessment of a Steel Braced Plan Mass Symmetric/Asymmetric Building Structure

This paper presents a seismic response investigation into a code designed concentrically braced frame structure that is subjected to but not designed for in-plan mass eccentricity. The structure has an accidental uneven distribution of mass in plan resulting in an increased torsional component of vibration. The level of inelasticity that key structural elements in plan mass asymmetric structures are subjected to is important when analysing their ability to sustain uneven seismic demands. In-plan mass asymmetry of moment resisting frame and shear wall type structures have received significant investigation, however, the plan asymmetric response of braced frame type structures is less well understood. A three-dimensional non-linear time history analysis (NLTHA) model is created to capture the torsional response of the plan mass asymmetric structure to quantify the additional ductility demand, interstorey drifts and floor rotations. Results show that the plan mass asymmetric structure performs well in terms of ductility demand, but poorly in terms of interstorey drifts and floor rotations when compared to the plan mass symmetric structure. New linear relationships are developed between the normalised ductility demand and normalised slenderness of the bracing on the sides of the plan mass symmetric/asymmetric structures that the mass is distributed towards and away from.

Méthodes de génération et de validation de champs de déformation pour la recombinaison de distribution de dose à l’aide d’images 4DCT dans le cadre d’une planification de traitement de cancers pulmonaires

Des efforts de recherche considérables ont été déployés afin d'améliorer les résultats de traitement de cancers pulmonaires. L'étude de la déformation de l'anatomie du patient causée par la ventilation pulmonaire est au coeur du processus de planification de traitement radio-oncologique. À l'aide d'images de tomodensitométrie quadridimensionnelles (4DCT), une simulation dosimétrique peut être calculée sur les 10 ensembles d'images du 4DCT. Une méthode doit être employée afin de recombiner la dose de radiation calculée sur les 10 anatomies représentant une phase du cycle respiratoire. L'utilisation de recalage déformable d'images (DIR), une méthode de traitement d'images numériques, génère neuf champs vectoriels de déformation permettant de rapporter neuf ensembles d'images sur un ensemble de référence correspondant habituellement à la phase d'expiration profonde du cycle respiratoire. L'objectif de ce projet est d'établir une méthode de génération de champs de déformation à l'aide de la DIR conjointement à une méthode de validation de leur précision. Pour y parvenir, une méthode de segmentation automatique basée sur la déformation surfacique de surface à été créée. Cet algorithme permet d'obtenir un champ de déformation surfacique qui décrit le mouvement de l'enveloppe pulmonaire. Une interpolation volumétrique est ensuite appliquée dans le volume pulmonaire afin d'approximer la déformation interne des poumons. Finalement, une représentation en graphe de la vascularisation interne du poumon a été développée afin de permettre la validation du champ de déformation. Chez 15 patients, une erreur de recouvrement volumique de 7.6 ± 2.5[%] / 6.8 ± 2.1[%] et une différence relative des volumes de 6.8 ± 2.4 [%] / 5.9 ± 1.9 [%] ont été calculées pour le poumon gauche et droit respectivement. Une distance symétrique moyenne 0.8 ± 0.2 [mm] / 0.8 ± 0.2 [mm], une distance symétrique moyenne quadratique de 1.2 ± 0.2 [mm] / 1.3 ± 0.3 [mm] et une distance symétrique maximale 7.7 ± 2.4 [mm] / 10.2 ± 5.2 [mm] ont aussi été calculées pour le poumon gauche et droit respectivement. Finalement, 320 ± 51 bifurcations ont été détectées dans le poumons droit d'un patient, soit 92 ± 10 et 228 ± 45 bifurcations dans la portion supérieure et inférieure respectivement. Nous avons été en mesure d'obtenir des champs de déformation nécessaires pour la recombinaison de dose lors de la planification de traitement radio-oncologique à l'aide de la méthode de déformation hiérarchique des surfaces. Nous avons été en mesure de détecter les bifurcations de la vascularisation pour la validation de ces champs de déformation.

Conditional symmetric instability in sting-jet storms

Sting jets are transient mesoscale jets of air that descend from the tip of the cloud head towards the top of the boundary layer in severe extratropical cyclones and can lead to damaging surface wind gusts. This recently identified jet is distinct from the well-documented jets associated with the cold and warm conveyor belts. One mechanism proposed for their development is the release of conditional symmetric instability (CSI). Here the spatial distribution and temporal evolution of several CSI diagnostics in four severe storms are analysed. A sting jet has been identified in three of these storms; for comparison, we also analysed one storm that did not have a sting jet, even though it hadmany of the apparent features of sting-jet storms. The sting-jet storms are distinct from the non-sting-jet storms by having much greater andmore extensive conditional instability (CI) and CSI. CSI is released by ascending air parcels in the cloud head in two of the sting-jet storms and by descending air parcels in the other sting-jet storm. By contrast, only weak CI to ascending air parcels is present at the cloud-head tip in the non-sting-jet storm. CSI released by descending air parcels, as diagnosed by decaying downdraught slantwise convective available potential energy (DSCAPE), is collocated with the sting jets in all three sting-jet storms and has a localisedmaximum in two of them. Consistent evolutions of saturated moist potential vorticity are found.We conclude that CSI release has a role in the generation of the sting jet, that the sting jet may be driven by the release of instability to both ascending and descending parcels, and that DSCAPE could be used as a discriminating diagnostic for the sting jet based on these four case-studies.