A low-memory algorithm for finding short product representations in finite groups

We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-ρ approach. Given an element z and a sequence of elements S, our algorithm attempts to find a subsequence of S whose product in G is equal to z. For a random sequence S of length d log₂ n, where n = #G and d ≥ 2 is a constant, we find that its expected running time is O(?n log n){O(\sqrt{n}\,{\rm log}\,n)} group operations (we give a rigorous proof for d > 4), and it only needs to store O(1) group elements. We consider applications to class groups of imaginary quadratic fields, and to finding isogenies between elliptic curves over a finite field.     

Green synthesis and antioxidant activity of new PEGylated ferulic acids

PEGylation of ferulic acid is described through a green esterification process involving poly(ethylene glycol) (PEG) with three different average molecular weights (200, 400 and 1000 g/mol) as both reactive and solvent. Esterification with PEG400 and PEG1000 leads to original compounds soluble in all proportions in water. These new compounds display an antioxidant activity similar to that of ferulic acid.     

Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments

We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of countable infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency–energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers. PACS numbers: 05.45.Xt, 02.30.Hq     

Classification of periodic orbits of two-dimensional homogeneous granular crystals with no pre-compression

In the present study we classify the periodic orbits of a squarely packed, uncompressed and undamped, homogeneous granular crystal, assuming that all elastic granules oscillate with the same frequency (i.e., under condition of 1:1 resonance); this type of Hamiltonian periodic orbits have been labeled as nonlinear normal modes. To this end we formulate an auxiliary system which consists of a two-dimensional, vibro-impact lattice composed of non-uniform “effective particles” oscillating in an anti-phase fashion. The analysis is based on the idea of balancing linear momentum in both horizontal and vertical directions for separate, groups of particles, whereby each such a group is represented by the single effective particle of the auxiliary system. It is important to emphasize that the auxiliary model can be defined for general finite, squarely packed granular crystals composed of n rows and m columns. The auxiliary model is successful in predicting the total number of such periodic orbits, as well as the amplitude ratios for different periodic regimes including strongly localized ones. In fact this methodology enables one to systematically study the generation of mode localization in these strongly nonlinear, highly degenerate dynamical systems. Good correspondence between the results of the theoretical model and direct numerical simulations is observed. The results presented herein can be further extended to study the intrinsic dynamics of the more complex granular materials, such as heterogeneous two-dimensional and three-dimensional granular crystals and multi-layered structures.     

The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview

Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study.     

Generation of Accurate Finite Element Models of Nonlinear Systems – Application to an Aeroplane-Like Structure

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the other hand, updating nonlinear models is something the structural dynamicist prefers to avoid mainly because tools such as modal analysis are no longer available. The objective of the present study is to propose a two-step methodology for dealing with nonlinear systems. Its most appealing feature is that it decouples the estimation of the linear and nonlinear parameters. A numerical application consisting of an aeroplane-like structure is used to assess the efficiency of the procedure.     

Theoretical and Experimental Study of Multimodal Targeted Energy Transfer in a System of Coupled Oscillators

The purpose of this study is the theoretical and experimental investigation of targeted energy transfers from a two-degree-of-freedom primary structure to a nonlinear energy sink (NES). It is demonstrated that an NES can resonate with and extract energy from both modes of the primary structure. By facilitating these energy transfers, notably through excitation of appropriate periodic and quasi-periodic orbits, one can promote dissipation of a major portion of externally induced energy in the nonlinear attachment.     

In vivo feasibility study of ultrasound potentiated collagenase therapy of chronic total occlusions

Arterial chronic total occlusions (CTOs) pose considerable challenges for percutaneous interventions, due primarily to the presence of stiff proximal fibrous caps (PFCs) which act as a barrier to the penetration of guide wires. A new approach under development for improving the success rate of guide wire crossing in CTOs is to employ collagenase to degrade the mechanical integrity of the PFCs. This has been shown to be feasible in preclinical work and in a Phase 1 clinical trial. In a recent study we demonstrated using ex vivo experimental CTO specimens that ultrasound-stimulated microbubbles (USMBs) could potentiate the effects of collagenase and result in increased mechanical degradation of the PFCs of CTOs. Here we report the results of the first in vivo study examining the feasibility of this approach, which demonstrates that the force required to puncture through the PFCs of CTOs is reduced with combined USMB + collagenase treatments relative to collagenase only treatments. This approach has the potential to further improve the efficacy of the emerging technique of collagenase facilitation of percutaneous interventions for CTO.     

Optimized liquid chromatography-mass spectrometry approach for the isolation of minor stress biomarkers in plant extracts and their identification by capillary nuclear magnetic resonance

A LC-MS approach is presented for the isolation of minor key plant biomarkers, in view of their characterization by NMR at the microgram scale. Due to the complexity of plant extracts, the purification of metabolites present in low concentrations is critical. The strategy used relies on the optimization of the chromatographic analysis using ultra-performance liquid chromatography-time-of-flight mass spectrometry (UPLC-TOF-MS), thanks to modelling software. The optimized method is then transferred to semi-preparative LC conditions with MS detection. The approach is illustrated by the isolation of wound-induced jasmonate derivatives revealed by a metabolomic study in Arabidopsis thaliana leaves and their subsequent characterization by capillary NMR (CapNMR).