Scale function vs Topological entropy

In the realm of topological automorphisms of totally disconnected locally compact groups, the scale function introduced by Willis in \cite{Willis} is compared with the topological entropy. We prove that the logarithm of the scale function is always dominated by the topological entropy and we provide examples showing that this inequality can be strict. Moreover, we give a condition equivalent to the equality between these two invariants. Various properties of the scale function, inspired by those of the topological entropy, are presented.Comment: 21 page

Benchmark Structures and Conformational Landscapes of Amino Acids in the Gas Phase: A Joint Venture of Machine Learning, Quantum Chemistry, and Rotational Spectroscopy

The accurate characterization of prototypical bricks of life can strongly benefit from the integration of high resolution spectroscopy and quantum mechanical computations. We have selected a number of representative amino acids (glycine, alanine, serine, cysteine, threonine, aspartic acid and asparagine) to validate a new computational setup rooted in quantum-chemical computations of increasing accuracy guided by machine learning tools. Together with low-lying energy minima, the barriers ruling their interconversion are evaluated in order to unravel possible fast relaxation paths. Vibrational and thermal effects are also included in order to estimate relative free energies at the temperature of interest in the experiment. The spectroscopic parameters of all the most stable conformers predicted by this computational strategy, which do not have low-energy relaxation paths available, closely match those of the species detected in microwave experiments. Together with their intrinsic interest, these accurate results represent ideal benchmarks for more approximate methods

Myeloid sarcoma of submandibular salivary gland

Objective: To report a rare case of a myeloid sarcoma of submandibular salivary gland. Methods: A 65-year-old woman with a history of successfully treated myelodysplastic syndrome, presenting with periodic painful swelling of her right submandibular area. Results: Physical evaluation, ultrasound and CT scan revealed the presence of a 3-cm mass contiguous to the submandibular salivary gland. A core needle biopsy confirmed the diagnosis of myeloid sarcoma. Bone marrow biopsy was still showing complete remission and the submandibular gland was the only extramedullary site involved. The patient was submitted to chemotherapy. Conclusion: Myeloid sarcoma is a rare extramedullary neoplasm. It can virtually involve any anatomic site, but it usually involves lymph nodes, paranasal sinuses, skin, soft tissue and periostium. Myeloid sarcomas of salivary glands are very rare and ENTs should be aware of this disease in order to include it in the differential diagnosis of a solitary neck mass

Fast exploration of potential energy surfaces with a joint venture of quantum chemistry, evolutionary algorithms and unsupervised learning

Contemporary molecular spectroscopy allows the study of flexible molecules, whose conformational behavior is ruled by flat potential energy surfaces (PESs) involving a large number of energy minima with comparable stability. Under such circumstances assignment and interpretation of the spectral signatures can strongly benefit from quantum chemical computations, which face, however, several difficulties. In particular, the mandatory characterization of all the relevant energy minima leads to a huge increase in the number of accurate quantum chemical computations (which may even hamper the feasibility of a study) and the intricate couplings among several soft degrees of freedom can defy simple heuristic approaches and chemical intuition. From this point of view, the exploration of flat PESs is akin to other optimization problems and can be tackled with suitable metaheuristics, which can drive QC computations by reducing the number of necessary calculations and providing effective routes to sample the most relevant regions of the PES. Unfortunately, in spite of the significant reduction of the number of QC calculations, a brute-force approach based on state-of-the-art methods remains infeasible. This problem can be solved effectively by multi-level strategies combining methods of different accuracy in the first PES exploration, refinement of the structures of the most important stationary points and computation of spectroscopic parameters. Building on previous experience, in this contribution we introduce new improvements in an evolutionary algorithm based method using curvilinear coordinates for both intra- and inter-molecular interactions. Two test cases will be analyzed in detail, namely aspartic acid in the gas-phase and the silver cation in aqueous solution. Comparison between fully a priori computed spectroscopic parameters and the experimental counterparts will provide an unbiased validation of the proposed strategy

Analytical relation between two chaos indicators: FLI and MEGNO

We report an intrinsic relation between the mean exponential growth factor of nearby orbits (MEGNO) and the fast Lyapunov indicator (FLI), two variational methods that have been widely applied to stability issues in astronomy. For both continuous-time and discrete-time systems, we arrive at an analytic formula that expresses the MEGNO in terms of the FLI and its time-average. This connection, unknown for more than 10 years, allows us to understand the differences and similarities in the performance of both indicators.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

Analytical relation between two chaos indicators: FLI and MEGNO

We report an intrinsic relation between the mean exponential growth factor of nearby orbits (MEGNO) and the fast Lyapunov indicator (FLI), two variational methods that have been widely applied to stability issues in astronomy. For both continuous-time and discrete-time systems, we arrive at an analytic formula that expresses the MEGNO in terms of the FLI and its time-average. This connection, unknown for more than 10 years, allows us to understand the differences and similarities in the performance of both indicators.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

Integration of Quantum Chemistry, Statistical Mechanics, and Artificial Intelligence for Computational Spectroscopy: The UV-Vis Spectrum of TEMPO Radical in Different Solvents

The ongoing integration of quantum chemistry, statistical mechanics, and artificial intelligence is paving the route toward more effective and accurate strategies for the investigation of the spectroscopic properties of medium-to-large size chromo-phores in condensed phases. In this context we are developing a novel workflow aimed at improving the generality, reliability, and ease of use of the available computational tools. In this paper we report our latest developments with specific reference to unsupervised atomistic simulations employing non periodic boundary conditions (NPBC) followed by clustering of the trajectories employing optimized feature spaces. Next accurate variational computations are performed for a representative point of each cluster, whereas intracluster fluctuations are taken into account by a cheap yet reliable perturbative approach. A number of methodological improvements have been introduced including, e.g., more realistic reaction field effects at the outer boundary of the simulation sphere, automatic definition of the feature space by continuous perception of solute-sol v e n t interactions, full account of polarization and charge transfer in the first solvation shell, and inclusion of vibronic contributions. After its validation, this new approach has been applied to the challenging case of solvatochromic effects on the UV-vis spectra of a prototypical nitroxide radical (TEMPO) in different solvents. The reliability, effectiveness, and robustness of the new platform is demonstrated by the remarkable agreement with experiment of the results obtained through an unsupervised approach characterized by a strongly reduced computational cost as compared to that of conventional quantum mechanics and molecular mechanics models without any accuracy reduction

Cryogenic Hydrogen Storage Tanks Exposed to Fires: a CFD study

Hydrogen is one of the most suitable candidates in replacing heavy hydrocarbons. Liquefaction of fuels is one of the most effective processes to increase their low density. This is critical especially in large-scale or mobile applications such as in the maritime or aeronautical fields. A potential loss of integrity of the cryogenic storage equipment might lead to severe consequences due to the properties of these substances (e.g. high flammability). For this reason, this critical event must be avoided. The aim of this study is to analyse the behaviour of the cryogenic vessel and its lading when it is exposed to a fire and understand how to prevent a catastrophic rupture of the tank during this accident scenario. A two-dimensional computational fluid dynamic (CFD) analysis is carried out on a cryogenic liquid hydrogen (LH2) vessel to investigate its thermal response when engulfed in a fire. The model accounts for the evaporation and condensation of the substance and can predict the tank pressurization rate and temperature distribution. It is assumed that the vessel is completely engulfed in the fire (worst-case scenario). The CFD model is validated with the outcomes of a small-scale fire test of an LH2 tank. Critical indications on the dynamic response of the cryogenic tank involved in a worst-case accident scenario are provided. Tank pressurisation and temperature distributions of the case study can be exploited to provide conservative estimations of the time to failure (TTF) of the vessel. These outcomes represent useful information to support the emergency response to this type of accident scenario and can aid the selection of appropriate and effective safety barriers to prevent the complete destruction of the tank

Stochastic approach to diffusion inside the chaotic layer of a resonance

We model chaotic diffusion in a symplectic four-dimensional (4D) map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus on the diffusion process in the action I of the FR, obtaining a seminumerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case, the numerically computed probability density function for the action I is well interpolated by the solution of a Fokker-Planck (FP) equation, whereas it presents a nonconstant time shift with respect to the concomitant FP solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in celestial mechanics and accelerator physics.Instituto de Astrofísica de La Plat

Chirikov and Nekhoroshev diffusion estimates : Bridging the two sides of the river

We present theoretical and numerical results pointing towards a strong connection between the estimates for the diffusion rate along simple resonances in multidimensional nonlinear Hamiltonian systems that can be obtained using the heuristic theory of Chirikov and a more formal one due to Nekhoroshev. We show that, despite a wide-spread impression, the two theories are complementary rather than antagonist. Indeed, although Chirikov’s 1979 review has thousands of citations, almost all of them refer to topics such as the resonance overlap criterion, fast diffusion, the Standard or Whisker Map, and not to the constructive theory providing a formula to measure diffusion along a single resonance. However, as will be demonstrated explicitly below, Chirikov’s formula provides values of the diffusion coefficient which are quite well comparable to the numerically computed ones, provided that it is implemented on the so-called optimal normal form derived as in the analytic part of Nekhoroshev’s theorem. On the other hand, Chirikov’s formula yields unrealistic values of the diffusion coefficient, in particular for very small values of the perturbation, when used in the original Hamiltonian instead of the optimal normal form. In the present paper, we take advantage of this complementarity in order to obtain accurate theoretical predictions for the local value of the diffusion coefficient along a resonance in a specific 3DoF nearly integrable Hamiltonian system. Besides, we compute numerically the diffusion coefficient and a full comparison of all estimates is made for ten values of the perturbation parameter, showing a very satisfactory agreement.Instituto de Astrofísica de La Plat