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.

Darcy`s law and the differential equation of motion

This note addresses the relation between the differential equation of motion and Darcy`s law. It is shown that, in different flow conditions, three versions of Darcy`s law can be rigorously derived from the equation of motion.

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.

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.

Proper motions of thermally emitting isolated neutron stars measured with Chandra

The remarkable astrometric capabilities of the Chandra Observatory offer the possibility to measure proper motions of X-ray sources with an unprecedented accuracy in this wavelength range. We recently completed a proper motion survey of three of the seven thermally emitting radio-quiet isolated neutron stars (INSs) discovered in the ROSAT all-sky survey. These INSs (RXJ0420.0-5022, RXJ0806.4-4123 and RXJ1308.6+2127) either lack an optical counterpart or have one so faint that ground based or space born optical observations push the current possibilities of the instrumentation to the limit. Pairs of ACIS observations were acquired 3 to 5 years apart to measure the displacement of the sources on the X-ray sky using as a reference the background of extragalactic or remote Galactic X-ray sources. We derive 2 sigma upper limits of 123 mas yr(-1) and 86 mas yr(-1) on the proper motion of RXJ0420.0-5022 and RXJ0806.4-4123, respectively. RXJ1308.6+2127 exhibits a very significant displacement (similar to 9 sigma) yielding mu = 220 +/- 25 mas yr(-1), the second fastest measured among all ROSAT-discovered INSs. The source is probably moving away rapidly from the Galactic plane at a speed which precludes any significant accretion of matter from the interstellar medium. Its transverse velocity of similar to 740 (d/700 pc) km s(-1) might be the largest of all ROSAT INSs and its corresponding spatial velocity lies among the fastest recorded for neutron stars. RXJ1308.6+2127 is thus a middle-aged (age similar to 1 My) high velocity cooling neutron star. We investigate its possible origin in nearby OB associations or from a field OB star. In most cases, the flight time from birth place appears significantly shorter than the characteristic age derived from spin down rate. Overall, the distribution in transverse velocity of the ROSAT INSs is not statistically different from that of normal radio pulsars.

Motion of a classical charged particle

The Lorentz-Dirac equation is not an unavoidable consequence of solely linear and angular momenta conservation for a point charge. It also requires an additional assumption concerning the elementary character of the charge. We here use a less restrictive elementarity assumption for a spinless charge and derive a system of conservation equations that are not properly the equation of motion because, as it contains an extra scalar variable, the future evolution of the charge is not determined. We show that a supplementary constitutive relation can be added so that the motion is determined and free from the troubles that are customary in the Lorentz-Dirac equation, i.e., preacceleration and runaways.

de Sitter geodesics: reappraising the notion of motion

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

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.

Perceptual learning of motion discrimination by mental imagery.

Perceptual learning can occur when stimuli are only imagined, i.e., without proper stimulus presentation. For example, perceptual learning improved bisection discrimination when only the two outer lines of the bisection stimulus were presented and the central line had to be imagined. Performance improved also with other static stimuli. In non-learning imagery experiments, imagining static stimuli is different from imagining motion stimuli. We hypothesized that those differences also affect imagery perceptual learning. Here, we show that imagery training also improves motion direction discrimination. Learning occurs when no stimulus at all is presented during training, whereas no learning occurs when only noise is presented. The interference between noise and mental imagery possibly hinders learning. For static bisection stimuli, the pattern is just the opposite. Learning occurs when presented with the two outer lines of the bisection stimulus, i.e., with only a part of the visual stimulus, while no learning occurs when no stimulus at all is presented.

Modern Computational Chemistry Methods for Prediction of Ground- and Excited-State Properties in Open-Shell Systems

The main goal of the research presented in this work is to provide some important insights about computational modeling of open-shell species. Such projects are: the investigation of the size-extensivity error in Equation-of-Motion Coupled Cluster methods, the analysis of the Long-Range corrected scheme in predicting UV-Vis spectra of Cu(II) complexes with the 4-imidazole acetate and its ethylated derivative, and the exploration of the importance of choosing a proper basis set for the description of systems such as the lithium monoxide anion. The most significant findings of this research are: (i) The contribution of the left operator to the size-extensivity error of the CR-EOMCC(2,3) approach, (ii) The cause of d-d shifts when varying the range-separation parameter and the amount of the exact exchange arising from the imbalanced treatment of localized vs. delocalized orbitals via the "tuned" CAM-B3LYP* functional, (iii) The proper acidity trend of the first-row hydrides and their lithiated analogs that may be reversed if the basis sets are not correctly selected.

Pain Intensity And Cervical Range Of Motion In Women With Myofascial Pain Treated With Acupuncture And Electroacupuncture: A Double-blinded, Randomized Clinical Trial.

Acupuncture stimulates points on the body, influencing the perception of myofascial pain or altering physiologic functions. The aim was to evaluate the effect of electroacupuncture (EAC) and acupuncture (AC) for myofascial pain of the upper trapezius and cervical range of motion, using SHAM acupuncture as control. Sixty women presenting at least one trigger point at the upper trapezius and local or referred pain for more than six months were randomized into EAC, AC, and SHAM groups. Eight sessions were scheduled and a follow-up was conducted after 28 days. The Visual Analog Scale assessed the intensity of local and general pain. A fleximeter assessed cervical movements. Data were analyzed using paired t or Wilcoxon's tests, ANOVA or Friedman or Kruskal-Wallis tests and Pearson's correlation (α=0.05). There was reduction in general pain in the EAC and AC groups after eight sessions (P<0.001). A significant decrease in pain intensity occurred for the right trapezius in all groups and for the left trapezius in the EAC and AC groups. Intergroup comparisons showed improvement in general pain in the EAC and AC groups and in local pain intensity in the EAC group (P<0.05), which showed an increase in left rotation (P=0.049). The AC group showed increases in inclination (P=0.005) sustained until follow-up and rotation to the right (P=0.032). EAC and AC were effective in reducing the pain intensity compared with SHAM. EAC was better than AC for local pain relief. These treatments can assist in increasing cervical range of motion, albeit subtly.

Análise do desempenho muscular do quadríceps e dos isquiotibiais em função da série temporal e da amplitude de movimento de atletas amadoras de futsal feminino = : Analysis of muscle performance of the quadriceps and hamstrings as a function of the times series and range of motion of amateurfemale futsal athletes

Universidade Estadual de Campinas . Faculdade de Educação Física

Equation of state for the magnetic-color-flavor-locked phase and its implications for compact star models

Using the solutions of the gap equations of the magnetic-color-flavor-locked (MCFL) phase of paired quark matter in a magnetic field, and taking into consideration the separation between the longitudinal and transverse pressures due to the field-induced breaking of the spatial rotational symmetry, the equation of state of the MCFL phase is self-consistently determined. This result is then used to investigate the possibility of absolute stability, which turns out to require a field-dependent ""bag constant"" to hold. That is, only if the bag constant varies with the magnetic field, there exists a window in the magnetic field vs bag constant plane for absolute stability of strange matter. Implications for stellar models of magnetized (self-bound) strange stars and hybrid (MCFL core) stars are calculated and discussed.

Dynamic polarizability, Cauchy moments, and the optical absorption spectrum of liquid water: A sequential molecular dynamics/quantum mechanical approach

The dynamic polarizability and optical absorption spectrum of liquid water in the 6-15 eV energy range are investigated by a sequential molecular dynamics (MD)/quantum mechanical approach. The MD simulations are based on a polarizable model for liquid water. Calculation of electronic properties relies on time-dependent density functional and equation-of-motion coupled-cluster theories. Results for the dynamic polarizability, Cauchy moments, S(-2), S(-4), S(-6), and dielectric properties of liquid water are reported. The theoretical predictions for the optical absorption spectrum of liquid water are in good agreement with experimental information.

Inertia in two simple problems of soil hydrodynamics

In the present paper the dynamic solutions of two non-steady seepage problems are discussed. It is shown that the acceleration term in the equation of motion is important for a correct qualitative description of the flow.