Statistics of non-linear stochastic dynamical systems under L\'evy noises by a convolution quadrature approach

This paper describes a novel numerical approach to find the statistics of the non-stationary response of scalar non-linear systems excited by L\'evy white noises. The proposed numerical procedure relies on the introduction of an integral transform of Wiener-Hopf type into the equation governing the characteristic function. Once this equation is rewritten as partial integro-differential equation, it is then solved by applying the method of convolution quadrature originally proposed by Lubich, here extended to deal with this particular integral transform. The proposed approach is relevant for two reasons: 1) Statistics of systems with several different drift terms can be handled in an efficient way, independently from the kind of white noise; 2) The particular form of Wiener-Hopf integral transform and its numerical evaluation, both introduced in this study, are generalizations of fractional integro-differential operators of potential type and Gr\"unwald-Letnikov fractional derivatives, respectively.Comment: 20 pages, 5 figure

Direct Observation of Localized Radial Oxygen Migration in Functioning Tantalum Oxide Memristors

Oxygen migration in tantalum oxide, a promising next-generation storage material, is studied using in-operando x-ray absorption spectromicroscopy and is used to microphysically describe accelerated evolution of conduction channel and device failure. The resulting ring-like patterns of oxygen concentration are modeled using thermophoretic forces and Fick diffusion, establishing the critical role of temperature-activated oxygen migration that has been under question lately.Comment: 7 pages, Advanced Materials (2016); updated abstrac

Resistive Switching Mechanisms on TaOx and SrRuO3 Thin-Film Surfaces Probed by Scanning Tunneling Microscopy

The local electronic properties of tantalum oxide (TaO[subscript x], 2 ≤ x ≤ 2.5) and strontium ruthenate (SrRuO[subscript 3]) thin-film surfaces were studied under the influence of electric fields induced by a scanning tunneling microscope (STM) tip. The switching between different redox states in both oxides is achieved without the need for physical electrical contact by controlling the magnitude and polarity of the applied voltage between the STM tip and the sample surface. We demonstrate for TaO[subscript x] films that two switching mechanisms operate. Reduced tantalum oxide shows resistive switching due to the formation of metallic Ta, but partial oxidation of the samples changes the switching mechanism to one mediated mainly by oxygen vacancies. For SrRuO[subscript 3], we found that the switching mechanism depends on the polarity of the applied voltage and involves formation, annihilation, and migration of oxygen vacancies. Although TaO[subscript x] and SrRuO[subscript 3] differ significantly in their electronic and structural properties, the resistive switching mechanisms could be elaborated based on STM measurements, proving the general capability of this method for studying resistive switching phenomena in different classes of transition metal oxides.National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Grant DMR-1419807

Efficient NiII2LnIII2 electrocyclization catalysts for the synthesis of trans-4,5-diaminocyclopent-2-enones from 2-furaldehyde and primary or secondary amines

A series of heterometallic coordination clusters (CCs) [NiII2LnIII2(L1)4Cl2(CH3CN)2] 2CH3CN [Ln = Y (1Y), Sm (1Sm), Eu (1Eu), Gd (1Gd), or Tb (1Tb)] were synthesized by the reaction of (E)-2-(2-hydroxy-3-methoxybenzylidene-amino)phenol) (H2L1) with NiCl2·6(H2O) and LnCl3·x(H2O) in the presence of Et3N at room temperature. These air-stable CCs can be obtained in very high yields from commercially available materials and are efficient catalysts for the room-temperature domino ring-opening electrocyclization synthesis of trans-4,5-diaminocyclopent-2-enones from 2-furaldehyde and primary or secondary amines under a non-inert atmosphere. Structural modification of the catalyst to achieve immobilization or photosensitivity is possible without deterioration in catalytic activity

Speed oscillations of a vehicle rolling on a wavy road

Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investigates the resulting travel speed oscillations of a quarter car model rolling in contact on a sinusoidal and stochastic road surface. The nonlinear equations of motion of the vehicle road system leads to ill-conditioned differential-algebraic equations. They are solved introducing polar coordinates into the sinusoidal road model. Numerical simulations show the Sommerfeld effect, in which the vehicle becomes stuck before the resonance speed, exhibiting limit cycles of oscillating acceleration and speed, which bifurcate from one-periodic limit cycle to one that is double periodic. Analytical approximations are derived by means of nonlinear Fourier expansions. Extensions to more realistic road models by means of noise perturbation show limit flows as bundles of nonperiodic trajectories with periodic side limits. Vehicles with higher degrees of freedom become stuck before the first speed resonance, as well as in between further resonance speeds with strong vertical vibrations and longitudinal speed oscillations. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated

Physical Activity and Exercise with Blood Flow Restriction as Medicine During the COVID-19 Pandemic and Beyond

During the COVID-19 pandemic, physical activity levels have decreased and sitting time has increased. This is a major concern as physical inactivity increases the risk for severe COVID-19 outcomes. Evidence also indicates that COVID-19 survivors can experience reduced physical function (i.e., ability to complete daily living activities) long after acute illness. Currently, there are no evidence-based guidelines for recovering physical function following COVID-19 infection. Exercise with blood flow restriction (BFR) presents a promising rehabilitation strategy as the benefits of traditional exercise can be achieved using lower intensities. However, several barriers such as cost, access to equipment, and lack of standardized methods limit its use. The goal of this research was to promote and facilitate the use of physical activity as a critical form of medicine during the COVID-19 pandemic and beyond. With study 1, I implemented a community-based program to provide free physical activity resources to the rural Upper Peninsula during the pandemic. Physical activity was promoted through a widespread media campaign and over 260 virtual home-based workouts were delivered to community members using several platforms (i.e., Zoom, Facebook Live, YouTube, TV, DVD). With study 2, I developed a working hypothesis and theoretical framework for using BFR to help restore physical function in those individuals infected with COVID-19. Specifically, I hypothesized that passive BFR modalities can mitigate losses of muscle mass and muscle strength that occur during acute infection and 2) exercise with BFR can serve as an effective alternative to traditional higher intensity exercise for regaining muscle mass, muscle strength, and aerobic capacity during convalescence. With study 3, I collected laboratory-based measures using Doppler ultrasound and anthropometric techniques in healthy adults (n=143) and applied linear regression methods to develop and validate a prediction equation for performing BFR without the need for specialized equipment. Finally, with study 4, I developed and usability tested a web-based application designed to serve as user support tool that aids physical therapists in implementing BFR. Collectively, my research addressed two major public health problems (COVID-19 and physical inactivity) and sought to enhance accessibility of physical activity and exercise with BFR during the pandemic and beyond