Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations

We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g.~as in finite element or NURBS surface representations. Our goal is to use this method to solve numerically tensor-valued partial differential equations (PDE) on surfaces. Previous methods use scalar potentials to numerically describe vector fields on surfaces, at the expense of requiring higher-order derivatives of the approximated fields and limited to simply connected surfaces, or represent tangential tensor fields as tensor fields in 3D subjected to constraints, thus increasing the essential number of degrees of freedom. In contrast, the LMP method uses an optimal number of degrees of freedom to represent a tensor, is general with regards to the topology of the surface, and does not increase the order of the PDEs governing the tensor fields. The main idea is to construct maps between the element parametrizations and a local Monge parametrization around each node. We test the LMP method by approximating in a least-squares sense different vector and tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply the LMP method to two physical models on surfaces, involving a tension-driven flow (vector-valued PDE) and nematic ordering (tensor-valued PDE). The LMP method thus solves the long-standing problem of the interpolation of tensors on general surfaces with an optimal number of degrees of freedom.Comment: 16 pages, 6 figure

Inverse cascades and resonant triads in rotating and stratified turbulence

Kraichnan’s seminal ideas on inverse cascades yielded new tools to study common phenomena in geophysical turbulent flows. In the atmosphere and the oceans, rotation and stratification result in a flow that can be approximated as two-dimensional at very large scales but which requires considering three-dimensional effects to fully describe turbulent transport processes and non-linear phenomena. Motions can thus be classified into two classes: fast modes consisting of inertia-gravity waves and slow quasi-geostrophic modes for which the Coriolis force and horizontal pressure gradients are close to balance. In this paper, we review previous results on the strength of the inverse cascade in rotating and stratified flows and then present new results on the effect of varying the strength of rotation and stratification (measured by the inverse Prandtl ratio N/f, of the Coriolis frequency to the Brunt-Väisäla frequency) on the amplitude of the waves and on the flow quasi-geostrophic behavior. We show that the inverse cascade is more efficient in the range of N/f for which resonant triads do not exist, /2≤N/f≤21/2≤N/f≤2. We then use the spatio-temporal spectrum to show that in this range slow modes dominate the dynamics, while the strength of the waves (and their relevance in the flow dynamics) is weaker.Fil: Oks, D.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Mininni, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Marino, R.. Universite Lyon 2; FranciaFil: Pouquet, A.. State University of Colorado Boulder; Estados Unido

Synchronous Context-Free Grammars and Optimal Linear Parsing Strategies

Synchronous Context-Free Grammars (SCFGs), also known as syntax-directed translation schemata, are unlike context-free grammars in that they do not have a binary normal form. In general, parsing with SCFGs takes space and time polynomial in the length of the input strings, but with the degree of the polynomial depending on the permutations of the SCFG rules. We consider linear parsing strategies, which add one nonterminal at a time. We show that for a given input permutation, the problems of finding the linear parsing strategy with the minimum space and time complexity are both NP-hard

Structure-Property Relationships at the Nano-Bio Interface: Engineering the Nanoparticle Surface for Immunomodulation

Each year, a variety of novel nanomaterials are being developed with the objective of treating different diseases. However, since nanomaterials are foreign to the human body, one of the principal factors that limit their use is the encounter with the first line of defense from the body: the immune system. If this interaction is not taken into account, an undesired recognition takes place and the efficiency of nanoparticle based therapies is dramatically reduced. As such, understanding the rules that govern this recognition is of prime importance in the field of nanomedicine. Following this line of thoughts (the driving force), the work described in this dissertation takes a systematic approach to understand and use the relationship between immunological responses and the chemical nature of the nanoparticle surface. We first explored the chemical rules of the immunological recognition, to then re-engineer our materials based on the acquired knowledge, setting a final goal in the development of new nanomaterials capable of modulating immune responses. Our findings demonstrated not only the vast potential of nanomaterials for their use in immunotherapies, but also the power of Chemistry in the development of these systems

Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy

Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations.Peer ReviewedPostprint (author’s final draft

A variational model of fracture for tearing brittle thin sheets

Tearing of brittle thin elastic sheets, possibly adhered to a substrate, involves a rich interplay between nonlinear elasticity, geometry, adhesion, and fracture mechanics. In addition to its intrinsic and practical interest, tearing of thin sheets has helped elucidate fundamental aspects of fracture mechanics including the mechanism of crack path selection. A wealth of experimental observations in different experimental setups is available, which has been often rationalized with insightful yet simplified theoretical models based on energetic considerations. In contrast, no computational method has addressed tearing in brittle thin elastic sheets. Here, motivated by the variational nature of simplified models that successfully explain crack paths in tearing sheets, we present a variational phase-field model of fracture coupled to a nonlinear Koiter thin shell model including stretching and bending. We show that this general yet straightforward approach is able to reproduce the observed phenomenology, including spiral or power-law crack paths in free standing films, or converging/diverging cracks in thin films adhered to negatively/positively curved surfaces, a scenario not amenable to simple models. Turning to more quantitative experiments on thin sheets adhered to planar surfaces, our simulations allow us to examine the boundaries of existing theories and suggest that homogeneous damage induced by moving folds is responsible for a systematic discrepancy between theory and experiments. Thus, our computational approach to tearing provides a new tool to understand these complex processes involving fracture, geometric nonlinearity and delamination, complementing experiments and simplified theories.Fil: Li, Bin. Universidad Politécnica de Catalunya; España. Sorbonne Université; Francia. Centre National de la Recherche Scientifique; FranciaFil: Millán, Raúl Daniel. Universidad Nacional de Cuyo. Facultad de Ciencias Aplicadas a la Industria; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Politécnica de Catalunya; EspañaFil: Torres Sánchez, Alejandro. Universidad Politécnica de Catalunya; EspañaFil: Roman, Benoît. Centre National de la Recherche Scientifique; Francia. Sorbonne Université; FranciaFil: Arroyo Balaguer, Marino. Universidad Politécnica de Catalunya; Españ

EFFECTS OF FATIGUE ON FORWARD, MAXIMUM VELOCITY IN ICE HOCKEY SKATING

The purpose of the study was to compare the skating mechanics of skilled and less skilled hockey skaters under fatigued and non-fatigued conditions. 14 subjects participated in the skating task. Each was video taped from two views on three occasions during a 380 m task. The first occasion was considered non-fatigued and the latter two fatigued conditions. The video was analysed via a three dimensional APAS. The independent variables were skill level and fatigue level. Several dependent variables reflecting skating mechanics were also measured. Statistical analysis indicated several changes accompanying fatigue. The variables affected included stride length, skating velocity, and range of motion and angular velocities in the lower limbs. It was concluded that fatigue does have significant detrimental affects on skaters at both skill levels prompting rapid redeployment during game situations

Charting molecular free-energy landscapes with an atlas of collective variables

Collective variables (CVs) are a fundamental tool to understand molecular flexibility, to compute free energy landscapes, and to enhance sampling in molecular dynamics simulations. However, identifying suitable CVs is challenging, and is increasingly addressed with systematic data-driven manifold learning techniques. Here, we provide a flexible framework to model molecular systems in terms of a collection of locally valid and partially overlapping CVs: an atlas of CVs. The specific motivation for such a framework is to enhance the applicability and robustness of CVs based on manifold learning methods, which fail in the presence of periodicities in the underlying conformational manifold. More generally, using an atlas of CVs rather than a single chart may help us better describe different regions of conformational space. We develop the statistical mechanics foundation for our multi-chart description and propose an algorithmic implementation. The resulting atlas of data-based CVs are then used to enhance sampling and compute free energy surfaces in two model systems, alanine dipeptide and ß-D-glucopyranose, whose conformational manifolds have toroidal and spherical topologies

Improved synthesis of phytanyl α-D-cellobiosyldiphosphate as substrate for α-D-mannosyltransferase

Polyisoprenyl-pyrophosphate-linked cellobiose is the natural acceptor of the α-1,3- mannosyltransferase AceA from Acetobacter xylinum, which transfers mannose from GDPmannose during the assembly of the heptasaccharide repeat unit of the exopolysaccharide acetan. Phytanyl α-D-cellobiosyldiphosphate 4 has been previously synthesized as an analogue acceptor by condensation of hepta-O-acetyl-α-D-cellobiosylphosphate 1 with phytanylphosphate 2, but the procedure was briefly described. We report here a modified detailed synthesis of 4. The complete NMR characterization of 4 is provided and also a selection of NMR signals of all the intermediate compounds which facilitate monitoring the synthesis.Fil: Barrios, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones en Hidratos de Carbono; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Orgánica; ArgentinaFil: Ielpi, Luis. Fundación Instituto Leloir; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; ArgentinaFil: Marino, Carla. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones en Hidratos de Carbono; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Química Orgánica; Argentin