Work-energy Relation Research Articles

Experiences of participation in patient's with infective endocarditis: a qualitative study

Abstract Funding Acknowledgements Type of funding sources: None. Background Infective Endocarditis (IE) is a life-threatening disease with increasing incidence worldwide. An important aspect in a patient’s course of illness is having a close and understanding caregiver. Receiving support from a partner or spouse has been found to be associated with increased survival and lower recurrence of heart diseases. Likewise, the caregiver may be able to experience positive emotions and personal growth by being an important part of the patient’s course of illness. Previous studies have explored patients’ and caregivers’ experiences with participation during the patient’s course of illness. To our knowledge, these perspectives have not yet been studied in patients with IE and their caregivers. Purpose The purpose of this study was to explore and elucidate patients with IE and their caregivers’ experiences with each other’s participation during the patient’s course of illness including hospitalization and recovery at home. Methodology The design was a holistic single-case study, where patients with IE and their caregivers were the target of interest. The empirical data was collected using qualitative, semi-structured dyadic interviews where the participants were interviewed in pairs. Theory-driven and data-driven coding was used as the analytical tools in the analysis of the data. Results The empirical data suggest that social support plays a significant role in the participants’ lives and course of illness, in which emotional support, physiological and practical assistance, as well as attitude transmission accounted for the greatest sources of impact. Important factors to the psychological well-being of participants were spending time with family members and maintaining a positive outlook on life. In light of theories of coping in social psychology, some participants reported using emotion-focused coping, problem-focused coping and protective buffering coping, whilst others did not use these. The majority of the caregivers reported that the course of illness did not have an impact on their working life and social relations, while some stated that it had a negative impact on their work, finances, mental and physical energy and social relations. An additional insight was given as the participants shared their thoughts on a need for psychological counseling and their experiences with compassionate healthcare professionals. Conclusion: The study concludes that the participation of patients with IE and their caregivers in the course of illness played an important and positive role in their lives. As such, it could be advised that healthcare professionals should focus more on how patients and their caregivers cope both individually and together in the course of illness. Understanding their perspectives could have implications on how healthcare professionals plan health measures to improve outcomes for both the patient and the caregiver.

University student understanding and reasoning on work–energy relations

An understanding the general principle of work and energy (GPWE) is essential to apply work and energy relations in general physics courses. In this paper, students’ reasoning about the GPWE is analysed in a social-constructivist theoretical framework of conceptual understanding and reasoning. We designed a questionnaire with open-ended questions to detect students’ difficulties with the concepts involved. The responses were analysed by defining explicative categories for student understanding. We have identified ‘intermediate frames’ for understanding GPWE. The ‘intermediate frames’ that students construct halfway between their prior knowledge and scientific understanding include reasoning, such as (a) considering superficial features and incorrectly analysing particular cases (b) not considering that the application of the GPWE is only valid in a previously chosen system.

Jarzynski on work and free energy relations: The case of variable volume

AbstractDerivations of the Jarzynski equality (JE) appear to be quite general, and applicable to any particle system, whether deterministic or stochastic, under equally general perturbations of an initial equilibrium state at given temperature T. At the same time, the definitions of the quantities appearing in the JE, in particular the work, have been questioned. Answers have been given, but a deeper understanding of the range of phenomena to which the JE applies is necessary, both conceptually and in order to interpret the experiments in which it is used. In fact, domains in which the JE is not applicable have been identified. To clarify the issue, we scrutinize the applicability of the JE to a Hamiltonian particle system in a variable volume. We find that, in this case, the standard interpretation of the terms appearing in the JE is not adequate.

The work-energy relation for particles on geodesics in the pp-wave spacetimes

A non-linear gravitational wave imparts gravitational acceleration to all particles that are hit by the wave. We evaluate this acceleration for particles in the pp-wave space-times, and integrate it numerically along the geodesic trajectories of the particles during the passage of a burst of gravitational wave. The time dependence of the wave is given by a Gaussian, so that the particles are free before and after the passage of the wave. The gravitational acceleration is understood from the point of view of a flat space-time, which is the initial and final gravitational field configuration. The integral of the acceleration along the geodesics is the analogue of the Newtonian concept of work per unit mass. Surprisingly, it yields almost exactly the variation of the non-relativistic kinetic energy per unit mass of the free particle. Therefore, the work-energy relation Δ K = Δ W of classical Newtonian physics also holds for a particle on geodesics in the pp-wave space-times, in a very good approximation, and explains why the final kinetic energy of the particle may be smaller or larger than the initial kinetic energy.

Analytic solution for planar indeterminate impact problems using an energy constraint

This work proposes an analytic method for resolving planar multi-point indeterminate impact problems for rigid-body systems. An event-based approach is used to detect impact events, and constraints consistent with the rigid-body assumption are used to resolve the indeterminacy associated with multi-point impact analysis. The work-energy relation is utilized to determine post-impact velocities based on an energetic coefficient of restitution to model energy dissipation, thereby yielding an energetically consistent set of post-impact velocities based on Stronge’s energetic coefficient of restitution for the treatment of rigid impacts. The effect of stick–slip transition is analyzed based on Coulomb friction. This paper also discusses the transition from impact to contact. This analysis is essential for considering the rocking block problem that is used as an example herein. The predictions of the model for the rocking block problem are compared to experimental results published in the literature. An example of a planar ball undergoing two-point impact is also presented.

Quasilocal energy exchange and the null cone

Energy is at best defined quasilocally in general relativity. Quasilocal energy definitions depend on the conditions one imposes on the boundary Hamiltonian, i.e., how a finite region of spacetime is "isolated". Here, we propose a method to define and investigate systems in terms of their matter plus gravitational energy content. We adopt a generic construction, that involves embedding of an arbitrary dimensional world sheet into an arbitrary dimensional spacetime, to a 2 + 2 picture. In our case, the closed 2-dimensional spacelike surface $\mathbb{S}$, that is orthogonal to the 2-dimensional timelike world sheet $\mathbb{T}$ at every point, encloses the system in question. The integrability conditions of $\mathbb{T}$ and $\mathbb{S}$ correspond to three null tetrad gauge conditions once we transform our notation to the one of the null cone observables. We interpret the Raychaudhuri equation of $\mathbb{T}$ as a work-energy relation for systems that are not in equilibrium with their surroundings. We achieve this by identifying the quasilocal charge densities corresponding to rotational and nonrotational degrees of freedom, in addition to a relative work density associated with tidal fields. We define the corresponding quasilocal charges that appear in our work-energy relation and which can potentially be exchanged with the surroundings. These charges and our tetrad conditions are invariant under type-III Lorentz transformations, i.e., the boosting of the observers in the directions orthogonal to $\mathbb{S}$. We apply our construction to a radiating Vaidya spacetime, a $C$-metric and the interior of a Lanczos-van Stockum dust metric. The delicate issues related to the axially symmetric stationary spacetimes and possible extensions to the Kerr geometry are also discussed.

Nonequilibrium work energy relation for non-Hamiltonian dynamics.

Recent years have witnessed major advances in our understanding of nonequilibrium processes. The Jarzynski equality, for example, provides a link between equilibrium free energy differences and finite-time nonequilibrium dynamics. We propose a generalization of this relation to non-Hamiltonian dynamics, relevant for active matter systems, continuous feedback, and computer simulation. Surprisingly, this relation allows us to calculate the free energy difference between the desired initial and final equilibrium states using arbitrary dynamics. As a practical matter, this dissociation between the dynamics and the initial and final states promises to facilitate a range of techniques for free energy estimation in a single universal expression.

Thermodynamics of relation-based systems with applications in econophysics, sociophysics, and music

A methodology was developed to analyze relation-based systems evolving in time by using the fundamental concepts of thermodynamics. The behavior of such systems can be tracked from the scattering matrix which is actually a network of directed vectors (or pathways) connecting subsequent values, which characterize an event, such as the index values in stock markets. A system behaves in a rigid (elastic) way to an external effect and resists permanent deformation, or it behaves in a viscous (or soft) way and deforms in an irreversible way. It was shown in the past that a formula derived using the slope of paths gives a measure about the extent of viscoelastic behavior of relation-based systems Gündüz (2009) [5] Gündüz and Gündüz (2010) [6]. In this research the ‘work’ associated with ‘elastic’ component, and ‘heat’ associated with ‘viscous’ component were discussed and elaborated. In a simple two subsequent pathway system in a scattering diagram the first vector represents ‘the cause’ and the second ‘the effect’. By using work and heat energy relations that involve force and also storage and loss modulus terms, respectively, one can calculate the energy involved in relation-based systems. The modulus values can be found from the parallel and vertical components of the second vector with respect to the first vector. Once work-like and heat-like terms were determined the internal energy is also easily found from their summation. The parallel and vertical components can also be used to calculate the magnitude of torque and torque energy in the system. Three cases, (i) the behavior of the NASDAQ-100 index, (ii) a social revolt, and (iii) the structure of a melody were analyzed for their ‘work-like’, ‘heat-like’, and ‘torque-like’ energies in the course of their evolution. NASDAQ-100 exhibits highly dissipative behavior, and its work terms are very small but heat terms are of large magnitude. Its internal energy highly fluctuates in time. In the social revolt studied work and heat terms are of comparable magnitude. The melody depicts highly organized structure, and usually has larger work terms than heat terms, but at some intervals heat terms burst out and attain very large magnitudes. Torque terms reach high values when the system is recovering from a minimum value.

Mechanism of Collapse of Tall Steel Moment-Frame Buildings under Earthquake Excitation

The mechanism of collapse of tall steel moment-frame buildings is explored through three-dimensional nonlinear analyses of two 18-story steel moment-frame buildings under earthquake excitation. Both fracture-susceptible and perfect-connection conditions are investigated. Classical energy-balance analysis shows that only long-period excitation imparts energy to tall buildings large enough to cause collapse. Under such long-period motion, the shear-beam analogy alludes to the existence of a characteristic mechanism of collapse or a few preferred mechanisms of collapse for these buildings. Numerical evidence from parametric analyses of the buildings under a suite of idealized sawtooth-like ground-motion time histories, with varying period (T), amplitude (peak ground velocity, PGV), and duration (number of cycles, N), is presented to support this hypothesis. Damage localizes to form a quasi-shear band over a few stories. When the band is destabilized, sidesway collapse is initiated, and gravity takes over. Only one to five collapse mechanisms occur out of a possible 153 mechanisms in either principal direction of the buildings considered. Where two or more preferred mechanisms do exist, they have significant story-overlap, typically separated by just 1 story. It is shown that a simple work-energy relation applied to all possible quasi-shear bands combined with plastic analysis principles can systematically identify all the preferred collapse mechanisms.

Non-uniqueness of the point of application of the buoyancy force

Even though the buoyancy force (also known as the Archimedes force) has always been an important topic of academic studies in physics, its point of application has not been explicitly identified yet. We present a quantitative approach to this problem based on the concept of the hydrostatic energy, considered here for a general shape of the cross-section of a floating body and for an arbitrary angle of heel. We show that the location of the point of application of the buoyancy force essentially depends (i) on the type of motion experienced by the floating body and (ii) on the definition of this point. In a rolling/pitching motion, considerations involving the rotational moment lead to a particular dynamical point of application of the buoyancy force, and for some simple shapes of the floating body this point coincides with the well-known metacentre. On the other hand, from the work–energy relation it follows that in the rolling/pitching motion the energetical point of application of this force is rigidly connected to the centre of buoyancy; in contrast, in a vertical translation this point is rigidly connected to the centre of gravity of the body. Finally, we consider the location of the characteristic points of the floating bodies for some particular shapes of immersed cross-sections. The paper is intended for higher education level physics teachers and students.

Geometrically Exact, Intrinsic Theory for Dynamics of Curved and Twisted Anisotropic Beams

A formulation is presented for the nonlinear dynamics of initially curved and twisted anisotropic beams. When the applied loads at the ends of, and distributed along, the beam are independent of the deformation, neither displacement nor rotation variables appear: an intrinsic formulation. Like well-known special cases of these equations governing nonlinear dynamics of rigid bodies and nonlinear statics of beams, the complete set of intrinsic equations has a maximum degree of nonlinearity equal to two. Advantages of such a formulation are demonstrated with a simple example. When the initial curvature and twist are constant along the beam, two space-time conservation laws are shown to exist, one being a work-energy relation and the other a generalized impulse-momentum relation. These laws can be used, for example, as benchmarks to check the accuracy of any proposed solution, including time-marching and finite element schemes. The structure of the intrinsic equations suggests parallel approaches to spatial and temporal discretization. A particularly simple spatial discretization scheme is presented for the special case of the nonlinear static behavior of end-loaded beams that, by virtue of the Kirchhoff analogy, leads to a time-marching scheme for the dynamics of a pivoted rigid body in a gravity field. This time-marching scheme conserves both the angular momentum about a vertical line passing through the pivot and total mechanical energy, whereas the analogous spatial discretization scheme for the nonlinear static behavior of end-loaded beams satisfies analogous integrals of deformation along the beam span. Remarkably, a straightforward generalization of these discretization schemes is shown to satisfy both space-time conservation laws for the nonlinear dynamics of beams when the applied loads are constant within a space-time element.

Statistical Simulation of Boxing Day Tsunami of The Indian Ocean and a Predictive Equation for Beach Run up Heights Based on Work-Energy Theorem

The tsunami similar to the one that has occurred in December 26, 2004 (Boxing Day Tsunami) in the Indian Ocean is simulated using the expression derived from Modified Weibull Distribution (for maximum wave height simulation) for extreme wave height predictions. The tuning coefficient plays a significant role in estimating the tsunami heights at various stages. It follows well defined mathematical laws at different stages. It is time dependent in the first three stages and depth dependent in the last two stages. The beach run-up heights estimated by the expression derived from the work-energy relation are comparable with observed values with reasonable accuracy.

The unreasonable effectiveness of equilibrium theory for interpreting nonequilibrium experiments

There has been much interest in applying the results of statistical mechanics to single molecule experiments. Recent work has highlighted nonequilibrium work-energy relations and fluctuation theorems that have an equilibriumlike (time independent) form. I give a simple heuristic example where an equilibrium result (the barometric law for colloidal particles in water) can be derived using the thermodynamically nonequilibrium behavior of a single colloidal particle falling through the water due to gravity. This description is possible because the particle, even while falling, is in mechanical equilibrium (the gravitational force equals the viscous drag force) at every instant. The results are generalized using Onsager’s thermodynamic action approach for stochastic processes to derive time independent equations that hold for thermodynamically nonequilibrium (and even nonstationary) systems. These relations offer great possibilities for the rapid determination of thermodynamic parameters from single molecule experiments.

Thermo-Electro-Mechanical Behavior of Ferroelectric Materials Part II: Introduction of Rate and Self-Heating Effects

A micro-electro-mechanical model of the behavior of piezoelectric ceramics including thermal, rate, and self-heating effects is presented and simulations are compared to experimental data. The rate dependent model is an extension of an earlier rate independent model. Results include analytical and numerical investigations of the behavior of piezoelectric ceramics. The model is based on physical mechanisms and includes elastic, dielectric, and piezoelectric anisotropy. Moreover, the model is based on an internal energy approach so that work-energy relations may be directly applied. Special consideration of potential physical mechanisms responsible for material behavior in the largely unexplored intermediate rate regime (50-1000 Hz) at high fields is given. Results from the model give insight into material behavior.

Thermo-Electro-Mechanical Behavior of Ferroelectric Materials Part I: A Computational Micromechanical Model Versus Experimental Results

A micro-electro-mechanical model of the behavior of piezoelectric ceramics including thermal effects is presented and compared to experimental data. Results include analytical and numerical investigations of the behavior of piezoelectric ceramics. The model is based on physical mechanisms and includes elastic, dielectric, and piezoelectric anisotropy. Moreover, the model is based on an internal energy approach so that work-energy relations may be directly applied. Results from the model give insight into material behavior.

The work-energy theorem: the effect of varying mass

This paper examines the work-energy theorem ofclassical physics and applies it to two situations withnon-constant mass. The first is that of a rocket burning fuel. The second is that of a proton in a particle acceleratorreaching relativistic speeds. The analysis leads to areformulation of the work-energy relation in terms of momentumand velocity rather than force and displacement. This allowsgraphical determinations of kinetic energy that are both simpleto make and clear even to beginning students. The use of graphical integration obviates the necessity of using calculusfor the non-constant mass situations. An unexpected result isthe invariance of this reformulation even for the relativistic case.

A Variational Formulation, a Work-Energy Relation and Damping Mechanisms of Active Constrained Layer Treatments

The purposes of this paper are to formulate active constrained layer (ACL) damping treatments through a variational approach, to study the work-energy relation of ACL, and to identify damping mechanisms of ACL treatments. Application of the extended Hamilton principle to ACL results in the equations of motion of ACL and the charge equation of electrostatics for the piezoelectric constraining layer. The work-energy equation together with the charge equation shows that the power dissipated through the active damping is the product of the electric field and the axial velocity of the piezoelectric constraining layer at the boundaries. This unique feature suggests that a self-sensing and actuating piezoelectric constraining layer may be an appropriate design in dissipating vibration energy without causing instability. To identify the damping mechanisms, a sensitivity analysis shows that the effectiveness of ACL damping primarily depends on the active and passive damping forces transmitted to the vibrating structure through the viscoelastic layer. The active damping force transmitted depends on the controller transfer function as well as a system parameter, termed active damping sensitivity factor, which depends entirely on the configuration of the passive constrained layer and the sensor. Finally, numerical results on ACL beams are obtained to illustrate the theoretical predictions above.

Near-minimum-time control of a flexible manipulator

Near-minimum-time control of flexible manipulators can be accomplished by designing a controller that tracks a reference maneuver. The control method presented here uses a near-minimum-time rigid-link reference maneuver to generate reference control torques and a Liapunov controller to make the flexible manipulator track the reference maneuver while reducing and eventually eliminating flexible motions. The near-minimumtime reference maneuver uses a smoothed bang-bang control plus a term to cancel the nonlinear dynamics of the rigid manipulator. The Liapunov function is a weighted sum of the energies of the elements of the flexible manipulator, and the control law is chosen to make the rate of change of the Liapunov function negative. The Liapunov function is bounded during a maneuver and decays asymptotically after the maneuver ends. RECISE control of a manipulator is an important aspect of robot performance. In the past, this has led to the design of very stiff links for manipulators, which also leads to very heavy links, large motors, and slow response. To avoid these problems, lighter and more flexible manipulators will require advanced control strategies. This work builds on results from the control of rigid robots1 and the control of flexible structures. Fujii and Ishijima2 developed a globally stable Liapunov controller to reorient a structure composed of a rigid hub and a flexible appendage. Junkins et al. 3 extended this control law to track a reference maneuver and showed that the Liapunov function is bounded during the maneuver and decays asymptotically to zero after the maneuver ends. Using a Gibbs phenomenon analysis, Baruh and Tadikonda4 have shown that using smoothed control torque profiles as in Ref. 3 reduces the excitation of the flexible modes during a maneuver. Experimental work in this area is also being done.5'6 In this work, we demonstrate that the control design procedure of Ref. 3 can be developed, using work-energy relations, and we extend it to a multibody case, using a planar two-link manipulator to demonstrate the procedure. A schematic diagram of the manipulator is shown in Fig. 1. The control law developed for the two-link manipulator allows the flexible motions to be stabilized without any finite-dimensional estimation of the flexible modes, thus avoiding any spillover problems.

An Instructive Example of the Sudden Approximation in Quantum Mechanics

Some features of the sudden approximation are examined and applied to the example of a particle in a suddenly expanded box. Among the points illustrated are the form of the work energy relation in quantum mechanics, the application of the energy-time uncertainty relation, some pitfalls in the use of theorems that apply only to Hermitian operators, and the periodic time-dependence of expectation values.

Heat, light and relativity

In this paper I argue that because we always observe nature through some spatial-temporal averaging operation we must interpret all observed statistical covariances of velocities and gradients as partial time derivatives. Systematic application of this result leads to a new interpretation of the radiation wave equation in whichc2 measures the statistical variance of velocity. The Galilean invariance ofc2 is then automatic. These results enable us to recast the Einstein-Minkowski space-time formalism within the framework of classical statistical mechanics. However, the Einstein work-energy relation and the constancy of the speed of light appear as equivalent approximations which become exact only in the adiabatic limit.