Hamilton-Jacobi formulation for singular systems with second-order Lagrangians

Recently, the Hamilton-Jacobi formulation for first-order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi formulation for singular systems with second-order Lagrangians and apply this new formulation to Podolsky electrodynamics, comparing with the results obtained through Dirac's method.

Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

Odd homoclinic orbits for a second order Hamiltonian system

The aim of this paper is to find an odd homoclinic orbit for a class of reversible Hamiltonian systems. The proof is variational and it employs a version of the concentration compactness principle of P. L. Lions in a lemma due to Struwe.

Variational second order flow estimation for PIV sequences

[EN] We present in this paper a variational approach to accurately estimate simultaneously the velocity field and its derivatives directly from PIV image sequences. Our method differs from other techniques that have been presented in the literature in the fact that the energy minimization used to estimate the particles motion depends on a second order Taylor development of the flow. In this way, we are not only able to compute the motion vector field, but we also obtain an accurate estimation of their derivatives. Hence, we avoid the use of numerical schemes to compute the derivatives from the estimated flow that usually yield to numerical amplification of the inherent uncertainty on the estimated flow. The performance of our approach is illustrated with the estimation of the motion vector field and the vorticity on both synthetic and real PIV datasets.

Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.

Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

The interface between morphology and action planning: a comparison of two species of New World monkeys

Recent research with several species of nonhuman primates suggests sophisticated motor-planning abilities observed in human adults may be ubiquitous among primates. However, there is considerable variability in the extent to which these abilities are expressed across primate species. In the present experiment, we explore whether the variability in the expression of anticipatory motor-planning abilities may be attributed to cognitive differences (such as tool use abilities) or whether they may be due to the consequences of morphological differences (such as being able to deploy a precision grasp). We compared two species of New World monkeys that differ in their tool use abilities and manual dexterity: squirrel monkeys, Saimiri sciureus (less dexterous with little evidence for tool use) and tufted capuchins, Sapajus apella (more dexterous and known tool users). The monkeys were presented with baited cups in an untrained food extraction task. Consistent with the morphological constraint hypothesis, squirrel monkeys frequently showed second-order motor planning by inverting their grasp when picking up an inverted cup, while capuchins frequently deployed canonical upright grasping postures. Findings suggest that the lack of ability for precision grasping may elicit more consistent second-order motor planning, as the squirrel monkeys (and other species that have shown a high rate of second-order planning) have fewer means of compensating for inefficient initial postures. Thus, the interface between morphology and motor planning likely represents an important factor for understanding both the ontogenetic and phylogenetic origins of sophisticated motor-planning abilities.

The Interface Between Morphology and Action Planning: a Comparison of Two Species of New World Monkeys

Recent research with several species of nonhuman primates suggests sophisticated motor-planning abilities observed in human adults may be ubiquitous among primates. However, there is considerable variability in the extent to which these abilities are expressed across primate species. In the present experiment, we explore whether the variability in the expression of anticipatory motor-planning abilities may be attributed to cognitive differences (such as tool use abilities) or whether they may be due to the consequences of morphological differences (such as being able to deploy a precision grasp). We compared two species of New World monkeys that differ in their tool use abilities and manual dexterity: squirrel monkeys, Saimiri sciureus (less dexterous with little evidence for tool use) and tufted capuchins, Sapajus apella (more dexterous and known tool users). The monkeys were presented with baited cups in an untrained food extraction task. Consistent with the morphological constraint hypothesis, squirrel monkeys frequently showed second-order motor planning by inverting their grasp when picking up an inverted cup, while capuchins frequently deployed canonical upright grasping postures. Findings suggest that the lack of ability for precision grasping may elicit more consistent second-order motor planning, as the squirrel monkeys (and other species that have shown a high rate of second-order planning) have fewer means of compensating for inefficient initial postures. Thus, the interface between morphology and motor planning likely represents an important factor for understanding both the ontogenetic and phylogenetic origins of sophisticated motor-planning abilities. (C) 2013 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Using the Natural Period of a Structure as an Indicator of the Significance of Second-Order Effects

This study investigates the feasibility of predicting the momentamplification in beam-column elements of steel moment-resisting frames using the structure's natural period. Unlike previous methods, which perform moment-amplification on a story-by-story basis, this study develops and tests two models that aim to predict a global amplification factor indicative of the largest relevant instance of local moment amplification in the structure. To thisend, a variety of two-dimensional frames is investigated using first and secondorder finite element analysis. The observed moment amplification is then compared with the predicted amplification based on the structure's natural period, which is calculated by first-order finite element analysis. As a benchmark, design moment amplification factors are calculated for each story using the story stiffness approach, and serve to demonstrate the relativeconservatism and accuracy of the proposed models with respect to current practice in design. The study finds that the observed moment amplification factors may vastly exceed expectations when internal member stresses are initially very small. Where the internal stresses are small relative to the member capacities, thesecases are inconsequential for design. To qualify the significance of the observed amplification factors, two parameters are used: the second-order moment normalized to the plastic moment capacity, and the combined flexural and axial stress interaction equations developed by AISC