A Multiparameter, Numerical Stability Analysis of a Standing Cantilever Conveying Fluid

In this paper, we numerically examine the stability of a standing cantilever conveying fluid in a multiparameter space. Based on nonlinear beam theory, our mathematical model turns out to be replete with exciting behavior, some of which was totally unexpected and novel, and some of which confirm our intuition as well as the work of others. The numerical bifurcation results obtained from applying the Library of Continuation Algorithms (LOCA) reveal a plethora of one, two, and higher codimension bifurcations. For a vertical or standing cantilever beam, bifurcations to buckled solutions (via symmetry breaking) and oscillating solutions are detected as a function of gravity and the fluid-structure interaction. The unfolding of these results as a function of the orientation of the beam compared to gravity is also revealed

Dissipation-Induced Heteroclinic Orbits in Tippe Tops

This paper demonstrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top are determined by a complex version of the equations for a simple harmonic oscillator: the modified Maxwell–Bloch equations. A standard linear analysis reveals that the modified Maxwell–Bloch equations describe the spectral instability of the noninverted state and Lyapunov stability of the inverted state. Standard nonlinear analysis based on the energy momentum method gives necessary and sufficient conditions for the existence of a dissipation-induced connecting orbit between these relative equilibria

Tippe Top Inversion as a Dissipation-Induced Instability

By treating tippe top inversion as a dissipation-induced instability, we explain tippe top inversion through a system we call the modified Maxwell--Bloch equations. We revisit previous work done on this problem and follow Or's mathematical model [SIAM J. Appl. Math., 54 (1994), pp. 597--609]. A linear analysis of the equations of motion reveals that the only equilibrium points correspond to the inverted and noninverted states of the tippe top and that the modified Maxwell--Bloch equations describe the linear/spectral stability of these equilibria. We supply explicit criteria for the spectral stability of these states. A nonlinear global analysis based on energetics yields explicit criteria for the existence of a heteroclinic connection between the noninverted and inverted states of the tippe top. This criteria for the existence of a heteroclinic connection turns out to agree with the criteria for spectral stability of the inverted and noninverted states. Throughout the work we support the analysis with numerical evidence and include simulations to illustrate the nonlinear dynamics of the tippe top

The Quaternions with an application to Rigid Body Dynamics

William Rowan Hamilton invented the quaternions in 1843, in his effort to construct hypercomplex numbers, or higher dimensional generalizations of the complex numbers. Failing to construct a generalization in three dimensions (involving triplets) in such a way that division would be possible, he considered systems with four complex units and arrived at the quaternions. He realized that, just as multiplication by i is a rotation by 90o in the complex plane, each one of his complex units could also be associated with a rotation in space. Vectors were introduced by Hamilton for the first time as pure quaternions and Vector Calculus was at first developed as part of this theory. Maxwell\\u27s Electromagnetism was first written using quaternions.\u2

Multiple necking pattern in nonlinear elastic bars subjected to dynamic stretching: the role of defects and inertia

In this paper we explore the inception and development of multiple necks in incompressible nonlinear elastic bars subjected to dynamic stretching. The goal is to elucidate the role played by a spatial-localized defect of the strain rate field in the necking pattern that emerges in the bars at large strains. For that task, we have used two different approaches: (1) finite element simulations and (2) linear stability analyses. The finite element simulations have revealed that, while the defect of the strain rate field speeds up the development of the necking pattern in the late stages of the localization process, the characteristic (average) neck spacing is largely independent of the defect within a wide range of defect amplitudes. The numerical results have been rationalized with the linear stability analyses, which enabled to explain the average spacing characterizing the necking pattern at high strain rates. Moreover, the numerical calculations have also shown that, due to inertia effects, the core of the localization process occurs during the post-uniform deformation regime of the bar, at strains larger than the one based on the Considère criterion. This phenomenon of neck retardation is shown to have a meaningful influence on the necking pattern.AVR and JARM are indebted to the Ministerio de Economía y Competitividad de España (Projects EUIN2015-62556 and DPI2014- 57989-P ) for the financial support which permitted to conduct part of this work. AM and JARM acknowledge the support by the French State through the program Investment in the future operated by the National Research Agency (ANR) and referenced by ANR-11-LABX- 0 0 08-01 (LabEx DAMAS). The research leading to these results has received funding from the European Union’s Horizon2020 Programme (Excellent Sci- ence, Marie Sklodowska-Curie Actions) under REA grant agreement 675602 (Project OUTCOME)

Advanced computer techniques for inverse modeling of electric current in cardiac tissue

For many years, ECG`s and vector cardiograms have been the tools of choice for non-invasive diagnosis of cardiac conduction problems, such as found in reentrant tachycardia or Wolff-Parkinson-White (WPW) syndrome. Through skillful analysis of these skin-surface measurements of cardiac generated electric currents, a physician can deduce the general location of heart conduction irregularities. Using a combination of high-fidelity geometry modeling, advanced mathematical algorithms and massively parallel computing, Sandia`s approach would provide much more accurate information and thus allow the physician to pinpoint the source of an arrhythmia or abnormal conduction pathway

Characterization of the Precision Laser Beam Welding Process for the MC4368A Neutron Generator

The design of experiments (DOEx) approach was used to characterize the Precision Laser Beam Welding Process with respect to four processing factors: Angle of Attack, Volts, Pulse Length, and Focus. The experiment was performed with Lap Joints, Nickel-Wire Joints, and Kovar-Wire Joints. The laser welding process and these types of welds are used in the manufacture of MC4368A Neutron Generators. For each weld type an individual optimal condition and operating window was identified. The widths of the operating windows that were identified by experimentation indicate that the laser weld process is very robust. This is highly desirable because it means that the quality of the resulting welds is not sensitive to the exact values of the processing factors within the operating windows. Statistical process control techniques can be used to ensure that the processing factors stay well within the operating window

Diffusion tensor imaging in orthostatic tremor: a tract‐based spatial statistics study

[Abstract] Objective The pathogenesis of orthostatic tremor (OT) is unknown. We investigated OT‐related white matter changes and their correlations with scores from a neuropsychological testing battery. Methods Diffusion tensor imaging measures were compared between 14 OT patients and 14 age‐ and education‐matched healthy controls, using whole‐brain tract‐based spatial statistics analysis. Correlations between altered diffusion metrics and cognitive performance in OT group were assessed. Results In all cognitive domains (attention, executive function, visuospatial ability, verbal memory, visual memory, and language), OT patients’ cognitive performance was significantly worse than that of healthy controls. OT patients demonstrated altered diffusivity metrics not only in the posterior lobe of the cerebellum (left cerebellar lobule VI) and in its efferent cerebellar fibers (left superior cerebellar peduncle), but also in medial lemniscus bilaterally (pontine tegmentum), anterior limb of the internal capsule bilaterally, right posterior limb of the internal capsule, left anterior corona radiata, right insula, and the splenium of corpus callosum. No relationship was found between diffusion measures and disease duration in OT patients. Diffusion white matter changes, mainly those located in right anterior limb of the internal capsule, were correlated with poor performance on tests of executive function, visuospatial ability, verbal memory, and visual memory in OT patients. Interpretation White matter changes were preferentially located in the cerebellum, its efferent pathways, as well as in the pontine tegmentum and key components of the frontal–thalamic–cerebellar circuit. Further work needs to be done to understand the evolution of these white matter changes and their functional consequences.National Institutes of Health; R01 NS39422National Institutes of Health; R01 NS094607National Institutes of Health; R01 NS085136National Institutes of Health; R01 NS073872National Institutes of Health; R01 NS088257European Commission. Grant Number: ICT‐2011‐287739Ministerio de Ecnomía y Competitividad; RTC‐2015‐3967‐1Spanish Health Research Agency; FIS PI12/01602Spanish Health Research Agency; FIS PI16/00451Ministerio de Ecnomía y Competitividad; DPI‐2015‐68664‐C4‐1‐

Diffusion tensor imaging in orthostatic tremor: a tract-based spatial statistics study.

Objective: The pathogenesis of orthostatic tremor (OT) is unknown. We investigated OT-related white matter changes and their correlations with scores from a neuropsychological testing battery. Methods: Diffusion tensor imaging measures were compared between 14 OT patients and 14 age- and educationmatched healthy controls, using whole-brain tract-based spatial statistics analysis. Correlations between altered diffusion metrics and cognitive performance in OT group were assessed. Results: In all cognitive domains (attention, executive function, visuospatial ability, verbal memory, visual memory, and language), OT patients’ cognitive performance was significantly worse than that of healthy controls. OT patients demonstrated altered diffusivity metrics not only in the posterior lobe of the cerebellum (left cerebellar lobule VI) and in its efferent cerebellar fibers (left superior cerebellar peduncle), but also in medial lemniscus bilaterally (pontine tegmentum), anterior limb of the internal capsule bilaterally, right posterior limb of the internal capsule, left anterior corona radiata, right insula, and the splenium of corpus callosum. No relationship was found between diffusion measures and disease duration in OT patients. Diffusion white matter changes, mainly those located in right anterior limb of the internal capsule, were correlated with poor performance on tests of executive function, visuospatial ability, verbal memory, and visual memory in OT patients. Interpretation: White matter changes were preferentially located in the cerebellum, its efferent pathways, as well as in the pontine tegmentum and key components of the frontal–thalamic–cerebellar circuit. Further work needs to be done to understand the evolution of these white matter changes and their functional consequences.post-print404 K

Components determining the slowness of information processing in parkinson’s disease.

Introduction Bradyphrenia is a key cognitive feature in Parkinson's disease (PD). There is no consensus on whether information processing speed is impaired or not beyond motor performance. Objective This study aims to explore which perceptual, motor, or cognitive components of information processing are involved in the slowdown affecting cognitive performance. Methods The study included 48 patients with PD (age: 63, 3 ± 8, 18; HY I-III; UPDRS 15,46 ± 7,76) and 53 healthy controls (age: 60,09 ± 12,83). Five reaction time (RT) tasks were administered to all participants. The average RT in each of the tasks and the percentage of correct answers were measured. Patients with PD were in "ON state" at the time of the evaluation. Perceptual, motor, and cognitive components were isolated by means of a series of ANCOVAs. Results As expected, the motor component was slowed down in patients with PD. Moreover, while patients with PD showed slower RT than controls in all tasks, differences between groups did not exponentially increase with the increasing task complexity. ANCOVA analyses also revealed that the perceptual and sustained alert component resulted to be slowed down, with no differences being found in any of the remaining isolated cognitive components (i.e., response strategy-inhibition, decisional, visual search, or interference control). Conclusions The results revealed that slowness of information processing in PD was mainly associated with an impaired processing speed of the motor and perceptual-alertness components analyzed. The results may help designing new neurorehabilitation strategies, focusing on the improvement of perceptual and alertness mechanisms.post-print534 K