Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws.

Live volumetric (4D) visualization and guidance of in vivo human ophthalmic surgery with intraoperative optical coherence tomography.

Minimally-invasive microsurgery has resulted in improved outcomes for patients. However, operating through a microscope limits depth perception and fixes the visual perspective, which result in a steep learning curve to achieve microsurgical proficiency. We introduce a surgical imaging system employing four-dimensional (live volumetric imaging through time) microscope-integrated optical coherence tomography (4D MIOCT) capable of imaging at up to 10 volumes per second to visualize human microsurgery. A custom stereoscopic heads-up display provides real-time interactive volumetric feedback to the surgeon. We report that 4D MIOCT enhanced suturing accuracy and control of instrument positioning in mock surgical trials involving 17 ophthalmic surgeons. Additionally, 4D MIOCT imaging was performed in 48 human eye surgeries and was demonstrated to successfully visualize the pathology of interest in concordance with preoperative diagnosis in 93% of retinal surgeries and the surgical site of interest in 100% of anterior segment surgeries. In vivo 4D MIOCT imaging revealed sub-surface pathologic structures and instrument-induced lesions that were invisible through the operating microscope during standard surgical maneuvers. In select cases, 4D MIOCT guidance was necessary to resolve such lesions and prevent post-operative complications. Our novel surgical visualization platform achieves surgeon-interactive 4D visualization of live surgery which could expand the surgeon's capabilities.

Undergrowth removal in Salgesch: Soil volumetric water content and temperature time series, hourly time resolution, 2010-2015

In the Salgesch forest in the Canton of Valais in Switzerland, the understory has been removed to test whether effects on pine tree vitality. The data set published here compromises 120 time series of 60 soil temperature and 60 volumetric water content (VWC) sensors (EC-TM and 5-TM) (Decagon Devices, WA, USA) at three soil depth levels (5, 30, 60 cm) employed in the direct vicinity of six control trees and six trees with the undergrowth removed. At the levels 5 and 60 cm, three replications were made whereas 4 replications were made at level 30 cm. Six loggers recorded hourly data since 2010 with 18% gaps or 11% when not considering winter months December, January and February. The figure attached to this repository shows the average VWC and temperature of all measurements within the same depth and treatment specific setting aggregated in a defined time interval and period. In addition to that, the standard deviations are plotted as transparent polygons. In case of insufficient values for calculating standard deviations, the setting specific mean standard deviation of the considered time period are inserted.

Effect of web holes on web crippling strength of cold-formed steel channel sections under end-one-flange loading condition - Part II: Parametric study and proposed design equations

A parametric study of cold-formed steel sections with web openings subjected to web crippling under end-one-flange (EOF) loading condition is undertaken, using finite element analysis, to investigate the effects of web holes and cross-section sizes. The holes are located either centred above the bearing plates or with a horizontal clear distance to the near edge of the bearing plates. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the depth of the web, the ratio of the length of bearing plates to the flat depth of the web and the location of the holes as defined by the distance of the hole from the edge of the bearing plate divided by the flat depth of web. In this study, design recommendations in the form of web crippling strength reduction factor equations are proposed, which are conservative when compared with the experimental and finite element results.

Projected equations of motion approach to hybrid quantum/classical dynamics in dielectric-metal composites

We introduce a hybrid method for dielectric-metal composites that describes the dynamics of the metallic system classically whilst retaining a quantum description of the dielectric. The time-dependent dipole moment of the classical system is mimicked by the introduction of projected equations of motion (PEOM) and the coupling between the two systems is achieved through an effective dipole-dipole interaction. To benchmark this method, we model a test system (semiconducting quantum dot-metal nanoparticle hybrid). We begin by examining the energy absorption rate, showing agreement between the PEOM method and the analytical rotating wave approximation (RWA) solution. We then investigate population inversion and show that the PEOM method provides an accurate model for the interaction under ultrashort pulse excitation where the traditional RWA breaks down.

Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in modern power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Northern Ireland.

Population inversion between the sup(3)Hsub(4) and the sup(3)Fsub(4) excited states of Tmsup(3+) investigated by means of numerical solutions of the rate equations system in Tmsup(3+)-doped and Tmsup(3+), Hosup(3+)-codoped fluoride glasses

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Energy transfer rates and population inversion of sup(4)Isub(11/2) excited state of Ersup(3+) investigated by means of numerical solutions of the rate equations system in Er:LiYFsub(4) crystal

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Model order reduction for parameterized nonlinear evolution equations

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016

Balancing related model order reduction applied to linear controlled evolution equations with Lévy Noise

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016

Fractional and time-scales differential equations

Resumo indisponível.

On (p, q) − equations with concave terms

We consider a (p, q)− equation (1 < q < p, p ≥ 2) with a parametric concave term and a (p − 1)− linear perturbation. We show that the problem have five nontrivial smooth solutions: four of constant sign and the fifth nodal. When q = 2 (i.e., (p, 2) equation) we show that the problem has six nontrivial smooth solutions, but we do not specify the sign of the sixth solution. Our approach uses variational methods, together with truncation and comparison techniques and Morse theory.