"Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits to perform spectroscopic calculations of high dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra

Semiclassical "Divide-and-Conquer" Method for Spectroscopic Calculations of High Dimensional Molecular Systems

A new semiclassical "divide-and-conquer" method is presented with the aim of demonstrating that quantum dynamics simulations of high dimensional molecular systems are doable. The method is first tested by calculating the quantum vibrational power spectra of water, methane, and benzene - three molecules of increasing dimensionality for which benchmark quantum results are available - and then applied to C60, a system characterized by 174 vibrational degrees of freedom. Results show that the approach can accurately account for quantum anharmonicities, purely quantum features like overtones, and the removal of degeneracy when the molecular symmetry is broken

How to Measure the Unobservable: A Panel Technique for the Analysis of TFP Convergence

This paper proposes a fixed-effect panel methodology that enables us to simultaneously take into account both TFP convergence and the traditional neoclassical-type of convergence. We analyse a sample of Italian regions between 1963 and 1993 and find strong evidence that both mechanisms were at work during the process of aggregate regional convergence observed in Italy up to the mid-seventies. Finally, we find that our TFP estimates are highly positively correlated with standard human capital measures, where the latter is not statistically significant in growth regressions. This evidence confirms one of the hypotheses of the Nelson and Phelps approach, namely that human capital is the main determinant of technological catch-up. Our results are robust to the use of different estimation procedures such as simple LSDV, Kiviet-corrected LSDV, and GMM à la Arellano and Bond.TFP, Panel data, Regional convergence

TFP convergence across European regions: a comparative spatial dynamics analysis

This paper proposes a fixed-effect panel methodology that enables us to simultaneously take into account both TFP and traditional neoclassical convergence. We analyse a sample of 199 regions in EU15 (plus Norway and Switzerland) between 1985 and 2006 and find the absence of an overall process of TFP convergence as we observe that TFP dispersion is virtually constant across the two sub-periods. This result is proved robust to the use of different estimation procedures such as simple LSDV, spatially corrected LSDV, Kiviet-corrected LSDV, and GMM à la Arellano and Bond. However, we also show that this absence of a strong process of global TFP convergence hides interesting dynamic patterns across regions. These patterns are revealed by the use of recent exploratory spatial data techniques that enable us to obtain a complete picture of the complex EU cross-regions dynamics. We find that, between 1985 and 2006, there has been numerous regional miracles and disasters in terms of TFP performance and that polarization patterns have significantly changed along time. Overall, results seem to suggest that a few TFP leaders are emerging and are distancing themselves from the rest, while the cluster of low TFP regions is increasing

Topological two-body bound states in the interacting Haldane model

We study the topological properties of the two-body bound states in an interacting Haldane model as a function of interparticle interactions. In particular, we identify topological phases where the two-body edge states have either the same or the opposite chirality as compared to single-particle edge states. We highlight that in the moderately interacting regime, which is relevant for the experimental realization with ultracold atoms, the topological transition is affected by the internal structure of the bound state, and the phase boundaries are consequently deformed

The Importance of the Pre-exponential Factor in Semiclassical Molecular Dynamics

This paper deals with the critical issue of approximating the pre-exponential factor in semiclassical molecular dynamics. The pre-exponential factor is important because it accounts for the quantum contribution to the semiclassical propagator of the classical Feynman path fluctuations. Pre-exponential factor approximations are necessary when chaotic or complex systems are simulated. We introduced pre-exponential factor approximations based either on analytical considerations or numerical regularization. The approximations are tested for power spectrum calculations of more and more chaotic model systems and on several molecules, for which exact quantum mechanical values are available. The results show that the pre-exponential factor approximations introduced are accurate enough to be safely employed for semiclassical simulations of complex systems

Turbulent heat transfer in spacer-filled channels: Experimental and computational study and selection of turbulence models

Heat transfer in spacer-filled channels of the kind used in Membrane Distillation was studied in the Reynolds number range 100–2000, encompassing both steady laminar and early-turbulent flow conditions. Experimental data, including distributions of the local heat transfer coefficient h, were obtained by Liquid Crystal Thermography and Digital Image Processing. Alternative turbulence models, both of first order (k-ε, RNG k-ε, k-ω, BSL k-ω, SST k-ω) and of second order (LRR RS, SSG RS, ω RS, BSL RS), were tested for their ability to predict measured distributions and mean values of h. The best agreement with the experimental results was provided by first-order ω-based models able to resolve the viscous/conductive sublayer, while all other models, and particularly ε-based models using wall functions, yielded disappointing predictions