An analysis of decoupling procedures in generating thermal Green's functions of O([lambda]â ´) by the Zubarev equation of motion method

The Zubarev equation of motion method has been applied to an anharmonic crystal of O( ,,4). All possible decoupling schemes have been interpreted in order to determine finite temperature expressions for the one phonon Green's function (and self energy) to 0()\4) for a crystal in which every atom is on a site of inversion symmetry. In order to provide a check of these results, the Helmholtz free energy expressions derived from the self energy expressions, have been shown to agree in the high temperature limit with the results obtained from the diagrammatic method. Expressions for the correlation functions that are related to the mean square displacement have been derived to 0(1\4) in the high temperature limit.

Equation of Motion Governing the Dynamics of Vertically Collapsing Buildings

The present paper aims at contributing to a discussion, opened by several authors, on the proper equation of motion that governs the vertical collapse of buildings. The most striking and tragic example is that of the World Trade Center Twin Towers, in New York City, about 10 years ago. This is a very complex problem and, besides dynamics, the analysis involves several areas of knowledge in mechanics, such as structural engineering, materials sciences, and thermodynamics, among others. Therefore, the goal of this work is far from claiming to deal with the problem in its completeness, leaving aside discussions about the modeling of the resistive load to collapse, for example. However, the following analysis, restricted to the study of motion, shows that the problem in question holds great similarity to the classic falling-chain problem, very much addressed in a number of different versions as the pioneering one, by von Buquoy or the one by Cayley. Following previous works, a simple single-degree-of-freedom model was readdressed and conceptually discussed. The form of Lagrange's equation, which leads to a proper equation of motion for the collapsing building, is a general and extended dissipative form, which is proper for systems with mass varying explicitly with position. The additional dissipative generalized force term, which was present in the extended form of the Lagrange equation, was shown to be derivable from a Rayleigh-like energy function. DOI: 10.1061/(ASCE)EM.1943-7889.0000453. (C) 2012 American Society of Civil Engineers.

Analytische Ableitungen der Energie für den "Equation-of-Motion-Coupled-Cluster"-Ansatz zur Berechnung von Ionisationspotentialen

In der vorliegenden Arbeit wird die Theorie der analytischen zweiten Ableitungen für die EOMIP-CCSD-Methode formuliert sowie die durchgeführte Implementierung im Quantenchemieprogramm CFOUR beschrieben. Diese Ableitungen sind von Bedeutung bei der Bestimmung statischer Polarisierbarkeiten und harmonischer Schwingungsfrequenzen und in dieser Arbeit wird die Genauigkeit des EOMIP-CCSD-Ansatzes bei der Berechnung dieser Eigenschaften für verschiedene radikalische Systeme untersucht. Des Weiteren können mit Hilfe der ersten und zweiten Ableitungen vibronische Kopplungsparameter berechnet werden, welche zur Simulation von Molekülspektren in Kombination mit dem Köppel-Domcke-Cederbaum (KDC)-Modell - in der Arbeit am Beispiel des Formyloxyl (HCO2)-Radikals demonstriert - benötigt werden.rnrnDer konzeptionell einfache EOMIP-CC-Ansatz wurde gewählt, da hier die Wellenfunktion eines Radikalsystems ausgehend von einem stabilen geschlossenschaligen Zustand durch die Entfernung eines Elektrons gebildet wird und somit die Problematik der Symmetriebrechung umgangen werden kann. Im Rahmen der Implementierung wurden neue Programmteile zur Lösung der erforderlichen Gleichungen für die gestörten EOMIP-CC-Amplituden und die gestörten Lagrange-Multiplikatoren zeta zum Quantenchemieprogramm CFOUR hinzugefügt. Die unter Verwendung des Programms bestimmten Eigenschaften werden hinsichtlich ihrer Leistungsfähigkeit im Vergleich zu etablierten Methoden wie z.B. CCSD(T) untersucht. Bei der Berechnung von Polarisierbarkeiten und harmonischen Schwingungsfrequenzen liefert die EOMIP-CCSD-Theorie meist gute Resultate, welche nur wenig von den CCSD(T)-Ergebnissen abweichen. Einzig bei der Betrachtung von Radikalen, für die die entsprechenden Anionen nicht stabil sind (z.B. NH2⁻ und CH3⁻), liefert der EOMIP-CCSD-Ansatz aufgrund methodischer Nachteile keine aussagekräftige Beschreibung. rnrnDie Ableitungen der EOMIP-CCSD-Energie lassen sich auch zur Simulation vibronischer Kopplungen innerhalb des KDC-Modells einsetzen.rnZur Kopplung verschiedener radikalischer Zustände in einem solchen Modellpotential spielen vor allem die Ableitungen von Übergangsmatrixelementen eine wichtige Rolle. Diese sogenannten Kopplungskonstanten können in der EOMIP-CC-Theorie besonders leicht definiert und berechnet werden. Bei der Betrachtung des Photoelektronenspektrums von HCO2⁻ werden zwei Alternativen untersucht: Die vertikale Bestimmung an der Gleichgewichtsgeometrie des HCO2⁻-Anions und die Ermittlung adiabatischer Kraftkonstanten an den Gleichgewichtsgeometrien des Radikals. Lediglich das adiabatische Modell liefert bei Beschränkung auf harmonische Kraftkonstanten eine qualitativ sinnvolle Beschreibung des Spektrums. Erweitert man beide Modelle um kubische und quartische Kraftkonstanten, so nähern sich diese einander an und ermöglichen eine vollständige Zuordnung des gemessenen Spektrums innerhalb der ersten 1500 cm⁻¹. Die adiabatische Darstellung erreicht dabei nahezu quantitative Genauigkeit.

Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach

A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed. (c) 2007 American Institute of Physics.

Motion of a charged particle in superposed Heliotron and biconical cusp fields

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.

Evolution and propagation of density waves on galactic disk .1. General evolution equation of wavelet and discussion of its solution

This paper presents a general self-consistent theory of evolution and propagation of wavelets on the galactic disk. A simplified model for this theory, i. e. the thin transition-layer approximation is proposed.There are three types of solutions to the basic equation governing the evolution of wavelets on the disk: (ⅰ) normal propagating type; (ⅱ) swing type; (ⅲ) general evolving type. The results show that the first two types are applicable to a certain domain on the galactic disk and a certain region of the wave number of wavelets. The third is needed to join the other two types and to yield a coherent total picture of the wave motion. From the present theory, it can be seen that the well-known "swing theory" of the G-L sheet model holds only for a certain class of basic states of galaxies.

A non-contact measurement system for the range of motion of the hand

An accurate and standardised tool to measure the active range of motion (ROM) of the hand is essential to any progressive assessment scenario in hand therapy practice. Goniometers are widely used in clinical settings for measuring the ROM of the hand. However, such measurements have limitations with regard to inter-rater and intra-rater reliability and involve direct physical contact with the hand, possibly increasing the risk of transmitting infections. The system proposed in this paper is the first non-contact measurement system utilising Intel Perceptual Technology and a Senz3D Camera for measuring phalangeal joint angles. To enhance the accuracy of the system, we developed a new approach to achieve the total active movement without measuring three joint angles individually. An equation between the actual spacial position and measurement value of the proximal inter-phalangeal joint was established through the measurement values of the total active movement, so that its actual position can be inferred. Verified by computer simulations, experimental results demonstrated a significant improvement in the calculation of the total active movement and successfully recovered the actual position of the proximal inter-phalangeal joint angles. A trial that was conducted to examine the clinical applicability of the system involving 40 healthy subjects confirmed the practicability and consistency in the proposed system. The time efficiency conveyed a stronger argument for this system to replace the current practice of using goniometers.

SURFACE PERTURBATIONS OF A SHALLOW VISCOUS-FLUID HEATED FROM BELOW AND THE (2+1)-DIMENSIONAL BURGERS-EQUATION

The (2 + 1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfies the condition R not-equal 30. A solution to this equation is explicitly exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink.

Improved simultaneous computation of motion detection and optical flow for object tracking

Object tracking systems require accurate segmentation of the objects from the background for effective tracking. Motion segmentation or optical flow can be used to segment incoming images. Whilst optical flow allows multiple moving targets to be separated based on their individual velocities, optical flow techniques are prone to errors caused by changing lighting and occlusions, both common in a surveillance environment. Motion segmentation techniques are more robust to fluctuating lighting and occlusions, but don't provide information on the direction of the motion. In this paper we propose a combined motion segmentation/optical flow algorithm for use in object tracking. The proposed algorithm uses the motion segmentation results to inform the optical flow calculations and ensure that optical flow is only calculated in regions of motion, and improve the performance of the optical flow around the edge of moving objects. Optical flow is calculated at pixel resolution and tracking of flow vectors is employed to improve performance and detect discontinuities, which can indicate the location of overlaps between objects. The algorithm is evaluated by attempting to extract a moving target within the flow images, given expected horizontal and vertical movement (i.e. the algorithms intended use for object tracking). Results show that the proposed algorithm outperforms other widely used optical flow techniques for this surveillance application.

The silk road project : dance and embodiment in the age of motion capture

The Silk Road Project was a practice-based research project investigating the potential of motion capture technology to inform perceptions of embodiment in dance performance. The project created a multi-disciplinary collaborative performance event using dance performance and real-time motion capture at Deakin University’s Deakin Motion Lab. Several new technological advances in producing real-time motion capture performance were produced, along with a performance event that examined the aesthetic interplay between a dancer’s movement and the precise mappings of its trajectories created by motion capture and real-time motion graphic visualisations.

A radiological method to determine the accuracy of motion capture marker placement on palpable anatomical landmarks through a shoe

The accuracy of marker placement on palpable surface anatomical landmarks is an important consideration in biomechanics. Although marker placement reliability has been studied in some depth, it remains unclear whether or not the markers are accurately positioned over the intended landmark in order to define the static position and orientation of the segment. A novel method using commonly available X-ray imaging was developed to identify the accuracy of markers placed on the shoe surface by palpating landmarks through the shoe. An anterior–posterior and lateral–medial X-ray was taken on 24 participants with a newly developed marker set applied to both the skin and shoe. The vector magnitude of both skin- and shoe-mounted markers from the anatomical landmark was calculated, as well as the mean marker offset between skin- and shoe-mounted markers. The accuracy of placing markers on the shoe relative to the skin-mounted markers, accounting for shoe thickness, was less than 5mm for all markers studied. Further, when using the developed guidelines provided in this study, the method was deemed reliable (Intra-rater ICCs¼0.50–0.92). In conclusion, the method proposed here can reliably assess marker placement accuracy on the shoe surface relative to chosen anatomical landmarks beneath the skin.