Orientational and induced contributions to the depolarized Rayleigh spectra of liquid and supercooled ortho-terphenyl

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 figure

Molecular dynamics simulation study of the high frequency sound waves in the fragile glass former ortho-terphenyl

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 figure

General features of the energy landscape in Lennard-Jones like model liquids

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 figure

Optimization of Corner Blending Curves

The blending or filleting of sharp corners is a common requirement in geometric design applications — motivated by aesthetic, ergonomic, kinematic, or mechanical stress considerations. Corner blending curves are usually required to exhibit a specified order of geometric continuity with the segments they connect, and to satisfy specific constraints on their curvature profiles and the extremum deviation from the original corner. The free parameters of polynomial corner curves of degree ≤6 and continuity up to G3 are exploited to solve a convex optimization problem, that minimizes a weighted sum of dimensionless measures of the mid-point curvature, maximum deviation, and the uniformity of parametric speed. It is found that large mid-point curvature weights result in undesirable bimodal curvature profiles, but emphasizing the parametric speed uniformity typically yields good corner shapes (since the curvature is strongly dependent upon parametric speed variation). A constrained optimization problem, wherein a particular value of the corner curve deviation is specified, is also addressed. Finally, the shape of Pythagorean-hodograph corner curves is compared with that of the optimized “ordinary” polynomial corner curves

Adaptive refinement in advection–diffusion problems by anomaly detection: A numerical study

We consider advection–diffusion–reaction problems, where the advective or the reactive term is dominating with respect to the diffusive term. The solutions of these problems are character-ized by the so-called layers, which represent localized regions where the gradients of the solutions are rather large or are subjected to abrupt changes. In order to improve the accuracy of the computed solution, it is fundamental to locally increase the number of degrees of freedom by limiting the computational costs. Thus, adaptive refinement, by a posteriori error estimators, is employed. The error estimators are then processed by an anomaly detection algorithm in order to identify those regions of the computational domain that should be marked and, hence, refined. The anomaly detection task is performed in an unsupervised fashion and the proposed strategy is tested on typical benchmarks. The present work shows a numerical study that highlights promising results obtained by bridging together standard techniques, i.e., the error estimators, and approaches typical of machine learning and artificial intelligence, such as the anomaly detection task

Isogeometric Analysis in advection-diffusion problems: tension splines approximation

We present a novel approach, within the new paradigm of isogeometric analysis introduced by Hughes et al., to deal with advection dominated advection-diffusion problems. The key ingredient is the use of Galerkin approximating spaces of functions with high smoothness, as in IgA based on classical B-splines, but particularly well suited to describe sharp layers involving very strong gradients

Relaxation processes in harmonic glasses?

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 figure

Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints

In the construction and analysis of a planar Pythagorean–hodograph (PH) quintic curve r(t), t∈[0,1] using the complex representation, it is convenient to invoke a translation/rotation/scaling transformation so r(t) is in canonical form with r(0)=0, r(1)=1 and possesses just two complex degrees of freedom. By choosing two of the five control–polygon legs of a quintic PH curve as these free complex parameters, the remaining three control–polygon legs can be expressed in terms of them and the roots of a quadratic or quartic equation. Consequently, depending on the chosen two control–polygon legs, there exist either two or four distinct quintic PH curves that are consistent with them. A comprehensive analysis of all possible pairs of chosen control polygon legs is developed, and examples are provided to illustrate this control–polygon paradigm for the construction of planar quintic PH curves