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Isogeometric approach applied to Boundary Element Methods is an emerging research area. In this context, the aim of the present contribution is that of investigating, from a numerical point of view, the Symmetric Galerkin Boundary Element Method (SGBEM) devoted to the solution of 2D boundary value problems for the Laplace equation, where the boundary and the unknowns on it are both represented by B-splines. We mainly compare this approach, which we call IGA-SGBEM, with a curvilinear SGBEM, which operates on any boundary given by explicit parametric representation and where the approximate solution is obtained using Lagrangian basis. Both techniques are further compared with a standard (conventional) SGBEM approach, where the boundary of the assigned problem is approximated by linear elements and the numerical solution is expressed in terms of Lagrangian basis. Several examples will be presented and discussed, underlying benefits and drawbacks of all the above-mentioned approaches.

In this paper we present a new class of cubature rules with the aim of accurately integrating weakly singular double integrals. In particular we focus on those integrals coming from the discretization of Boundary Integral Equations for 3D Laplace boundary value problems, using a collocation method within the Isogeometric Analysis paradigm. In such setting the regular part of the integrand can be defined as the product of a tensor product B-spline and a general function. The rules are derived by using first the spline quasi-interpolation approach to approximate such function and then the extension of a well known algorithm for spline product to the bivariate setting. In this way efficiency is ensured, since the locality of any spline quasi-interpolation scheme is combined with the capability of an ad--hoc treatment of the B-spline factor. The numerical integration is performed on the whole support of the B-spline factor by exploiting inter-element continuity of the integrands

This paper deals with the discrete counterpart of 2D elliptic model problems rewritten in terms of Boundary Integral Equations. The study is done within the framework of Isogeometric Analysis based on B-splines. In such a context, the problem of constructing appropriate, accurate and efficient quadrature rules for the Symmetric Galerkin Boundary Element Method is here investigated. The new integration schemes, together with row assembly and sum factorization, are used to build a more efficient strategy to derive the final linear system of equations. Key ingredients are weighted quadrature rules tailored for B--splines, that are constructed to be exact in the whole test space, also with respect to the singular kernel. Several simulations are presented and discussed, showing accurate evaluation of the involved integrals and outlining the superiority of the new approach in terms of computational cost and elapsed time with respect to the standard element-by-element assembly.

We report Ultraviolet Brillouin light scattering experimental data on v-SiO2 in an unexplored frequency region, performed with a newly available spectrometer up to exchanged wavevector q values of 0.075 nm^{-1}, as a function of temperature. The measured attenuation scales on visible data following a q^2 behavior and is temperature-dependent. Such temperature dependence is found in a good agreement with that measured at lower q, suggesting that its origin is mainly due to a dynamic attenuation mechanism. The comparison between the present data with those obtained by Inelastic X-ray Scattering suggests the existence of a cross-over to a different attenuation regimes., Comment: 4 pages, 3 figures

The high frequency collective dynamics of molten potassium has been investigated by inelastic x-ray scattering, disclosing an energy/momentum transfer region unreachable by previous neutron scattering experiments (INS). We find that a two-step relaxation scenario, similar to that found in other liquid metals, applies to liquid potassium. In particular, we show how the sound velocity determined by INS experiments, exceeding the hydrodynamic value by $\approx 30 %$, is the higher limit of a speed up, located in the momentum region $1

Features of the energy landscape sampled by supercooled liquids are numerically analyzed for several Lennard-Jones like model systems. The properties of quasisaddles (minima of the square gradient of potential energy W=|grad V|^2), are shown to have a direct relationship with the dynamical behavior, confirming that the quasisaddle order extrapolates to zero at the mode-coupling temperature T_MCT. The same result is obtained either analyzing all the minima of W or the saddles (absolute minima of W), supporting the conjectured similarity between quasisaddles and saddles, as far as the temperature dependence of the properties influencing the slow dynamics is concerned. We find evidence of universality in the shape of the landscape: plots for different systems superimpose into master curves, once energies and temperatures are scaled by T_MCT. This allows to establish a quantitative relationship between T_MCT and potential energy barriers for LJ-like systems, and suggests a possible generalization to different model liquids., Comment: 8 pages, 5 figures

The potential energy landscape in the Kob-Andersen Lennard-Jones binary mixture model has been studied carefully from liquid down to the supercooled regime, from T =2 down to T =0.46. One thousand of independent configurations along the time evolution have been examined at each investigated temperature. From the starting configuration we searched the nearest saddle (or quasi-saddle) and minimum of the potential energy. The vibrational densities of states for the starting and the two derived configurations have been evaluated. Besides the number of negative eigenvalues of saddle, other quantities show some signature of the approaching of the dynamical arrest temperature., Comment: 15 pages, 8 figures, to be published on Journal of Physics: Cond. Matt

The density response of supercooled glycerol to an impulsive stimulated thermal grating (q=0.63 micron^-1) has been studied in the temperature range (T=200-340 K) where the structure rearrangement (alpha-relaxation) and thermal diffusion occur on the same time scale. A strong interaction between the two modes occurs giving rise to a dip in the T-dependence of the apparent thermal conductivity and a flattening of the apparent alpha-relaxation time upon cooling. A non-equilibrium thermodynamic (NET) model for the long time response of relaxing fluids has been developed. The model is capable to reproduce the experimental data and to explain the observed phenomenology., Comment: to be published in PRE Rapid Commun

The depolarized light scattering spectra of the glass forming liquid ortho-terphenyl have been calculated in the low frequency region using molecular dynamics simulation. Realistic system's configurations are produced by using a recent flexible molecular model and combined with two limiting polarizability schemes, both of them using the dipole-induced-dipole contributions at first and second order. The calculated Raman spectral shape are in good agreement with the experimental results in a large temperature range. The analysis of the different contributions to the Raman spectra emphasizes that the orientational and the collision-induced (translational) terms lie on the same time-scale and are of comparable intensity. Moreover, the cross terms are always found to be an important contribution to the scattering intensity., Comment: RevTeX4, 7 pages, 8 eps figures

The dynamics of the fragile glass-forming o-ter-phenyl is investigated by time-resolved transient grating experiment with an heterodyne detection technique in a wide temperature range. We investigated the dynamics processes of this glass-former over more then 6 decades in time with an excellent signal/noise. Acoustic, structural and thermal relaxations have been clearly identify and measured in a time-frequency window not covered by previous spectroscopic investigations. A detailed comparison with the density response function, calculated on the basis of generalized hydrodynamics model, has been worked out.

The results of a Transient Grating experiment in a supercooled molecular liquid of anisotropic molecules and its theoretical interpretation are presented. These results show the existence of two distinct dynamical contributions in the response function of this experiment, density and orientation dynamics. These dynamics can be experimentally disentangled by varying the polarisation of the probe and diffracted beams and they have been identified and measured in a Heterodyne Detected experiment performed on m-toluidine. The results of the theory show a good qualitative agreement with the measurements at all temperatures., Comment: PDF format, 14 pages including 4 figures, accepted for publication in EPL. minor modifications

Using a realistic flexible molecule model of the fragile glass former orthoterphenyl, we calculate via molecular dynamics simulation the collective dynamic structure factor, recently measured in this system by Inelastic X-ray Scattering. The comparison of the simulated and measured dynamic structure factor, and the study of its properties in an extended momentum, frequency and temperature range allows: i) to conclude that the utilized molecular model gives rise to a dynamic structure factor in agreement with the experimental data, for those thermodynamic states and momentum values where the latter are available; ii) to confirm the existence of a slope discontinuity on the T-dependence of the sound velocity that, at finite Q, takes place at a temperature T_x higher than the calorimetric glass transition temperature T_g; iii) to find that the values of T_x is Q-dependent and that its vanishing Q limit is consistent with T_g. The latter finding is interpreted within the framework of the current description of the dynamics of supercooled liquids in terms of exploration of the potential energy landscape., Comment: RevTex, 9 pages, 10 eps figures

We present a molecular dynamics study of the collective dynamics of a flexible model for the fragile glass-former orthoterphenyl [ S. Mossa, R. Di leonardo, G. Ruocco, and M. Sampoli, Phys. Rev. E 62, 612 (2000)]. We study the behavior of the coherent scattering functions, considering the density fluctuations of both molecular and phenyl rings centers of mass; moreover we directly simulate the neutron scattering spectra taking into account both the contributions due to the carbon and hydrogens atoms. We compare our results with the main predictions of the Mode Coupling Theory and with the available coherent neutron scattering experimental data., Comment: 13 pages, 15 eps figures

A relaxation process, with the associated phenomenology of sound attenuation and sound velocity dispersion, is found in a simulated harmonic Lennard-Jones glass. We propose to identify this process with the so called microscopic (or instantaneous) relaxation process observed in real glasses and supercooled liquids. A model based on the memory function approach accounts for the observation, and allows to relate to each others: 1) the characteristic time and strength of this process, 2) the low frequency limit of the dynamic structure factor of the glass, and 3) the high frequency sound attenuation coefficient, with its observed quadratic dependence on the momentum transfer., Comment: 11 pages, 3 figures

We present a realistic model of the fragile glass former orthoterphenyl and the results of extensive molecular dynamics simulations in which we investigated its basic static and dynamic properties. In this model the internal molecular interactions between the three rigid phenyl rings are described by a set of force constants, including harmonic and anharmonic terms; the interactions among different molecules are described by Lennard-Jones site-site potentials. Self-diffusion properties are discussed in detail together with the temperature and momentum dependencies of the self-intermediate scattering function. The simulation data are compared with existing experimental results and with the main predictions of the Mode Coupling Theory., Comment: 20 pages and 28 postscript figures

New Raman and incoherent neutron scattering data at various temperatures and molecular dynamic simulations in amorphous silica, are compared to obtain the Raman coupling coefficient $C(\omega)$ and, in particular, its low frequency limit. This study indicates that in the $\omega \to 0$ limit $C(\omega)$ extrapolates to a non vanishing value, giving important indications on the characteristics of the vibrational modes in disordered materials; in particular our results indicate that even in the limit of very long wavelength the local disorder implies non-regular local atomic displacements., Comment: Revtex, 4 ps figures

New temperature dependent inelastic x-ray (IXS) and Raman (RS) scattering data are compared to each other and with existing inelastic neutron scattering data in vitreous silica (v-SiO_2), in the 300 - 1775 K region. The IXS data show collective propagating excitations up to Q=3.5 nm^-1. The temperature behaviour of the excitations at Q=1.6 nm^-1 matches that of the boson peak found in INS and RS. This supports the acoustic origin of the excess of vibrational states giving rise to the boson peak in this glass., Comment: 10 pages and 4 figures

We propose an explanation for the quadratic dependence on the momentum $Q$, of the broadening of the acoustic excitation peak recently found in the study of the dynamic structure factor of many real and simulated glasses. We ascribe the observed $Q^2$ law to the spatial fluctuations of the local wavelength of the collective vibrational modes, in turn produced by the dishomegeneity of the inter-particle elastic constants. This explanation is analitically shown to hold for 1-dimensional disordered chains and satisfatorily numerically tested in both 1 and 3 dimensions., Comment: 4 pages, RevTeX, 5 postscript figures

We report a molecular dynamics simulation study of the sound waves in vitreous silica in the mesoscopic exchanged momentum range. The calculated dynamical structure factors are in quantitative agreement with recent experimental inelastic neutron and x-ray scattering data. The analysis of the longitudinal and transverse current spectra allows to discriminate between opposite interpretations of the existing experimental data in favour of the propagating nature of the high frequency sound waves., Comment: 4 pages, Revtex, 4 ps figures; to be published in Phys. Rev. Lett., February 1988