Uniform Acceleration Research Articles

Slip flow along an impulsively started cylinder

This paper reports on the time-dependent axisymmetric flow of a viscous, incompressible fluid along a moving circular cylinder having infinite extent. A mathematical account is given to unsteady motion, in which the governing non-dimensional equations are obtained in the presence of a velocity-slip boundary condition near the cylinder wall. In the case where the cylinder is started impulsively from rest in (initially) still air, the Bingham number is obtained by means of Laplace transform techniques with particular emphasis regarding the cylinder in motion with uniform velocity and acceleration. The effects of the momentum slip length parameter on the shear stress are determined and presented.

Maxwell speed distribution and analogue Hawking–Unruh temperature in an ontological model of a Harmonic oscillator ground state

Within an ontological (hidden variable) model of quantum fluctuation, one can discuss the actual properties of a system regardless (independent) of measurement. Here we apply an ontological model proposed earlier to investigate a Harmonic oscillator in the quantum mechanical ground state. We first show that the actual speed of the oscillator fluctuates randomly following the Maxwell–Boltzmann distribution. On the other hand, the actual energy obeys a broad Gamma distribution with an average 3ħω/2, where ω is the classical angular frequency, so that one may conclude that the outcome of a single energy measurement reveals the average of the actual energy. The distribution of actual speed (energy) thus formally resembles the distribution of speed (energy) of an ideal gas in thermal equilibrium of temperature Tg=ħω/2. We shall then argue that Tg can be written in a form analogous to the Hawking temperature for a Schwarzschild black hole in which the average distance of the oscillator from the origin plays the analogous role of the radius of the black hole event horizon. It can also be written in a form analogous to the Unruh temperature experienced by a body moving with a uniform acceleration. In the analogy, the oscillator suffers an effective acceleration which balances the attractive force of the trapping Harmonic potential, thus keeps its average position away from the origin.

A Design of Mechanical Frequency Converter Linear and Non-linear Spring Combination for Energy Harvesting

In this study, the improvement of energy harvesting from wideband vibration with random change by using a combination of linear and nonlinear spring system is investigated. The system consists of curved beam spring for non-linear buckling, which supports the linear mass-spring resonator. Applying shock acceleration generates a snap through action to the buckling spring. From the FEM analysis, we showed that the snap through acceleration from the buckling action has no relationship with the applied shock amplitude and duration. We use this uniform acceleration as an impulse shock source for the linear resonator. It is easy to obtain the maximum shock response from the uniform snap through acceleration by using a shock response spectrum (SRS) analysis method. At first we investigated the relationship between the snap-through behaviour and an initial curved deflection. Then a time response result for non-linear springs with snap through and minimum force that makes a buckling behaviour were obtained by FEM analysis. By obtaining the optimum SRS frequency for linear resonator, we decided its resonant frequency with the MATLAB simulator.

Simplified Linear Static Analysis for Base-Isolated Buildings with Friction Pendulum Systems

Several methods of analysis used for the design of base-isolated buildings are proposed in many structural specifications. According to different structural codes, limited conditions of equivalent linearization of the friction pendulum system (FPS) and application scopes of simplified linear static analysis (LSA) are introduced. LSA of a reinforced concrete frame building isolated by FPS is performed and compared with fast nonlinear time-history analysis (FNA) to evaluate the suitability of the simplified method. Based on a specific spectrum used in the new Italian code, seven spectrum-compatible earthquake ground motions are selected and scaled as seismic input. To perform both linear and nonlinear analyses systematically, a program is specially developed by MATLAB in combination with a commercial software. Base displacement, story shear force, and energy dissipation are selected as response indicators. The results reveal that, as a substitute for the exact nonlinear analysis method in the preliminary design of base-isolated buildings, the LSA method yields conservative estimates in base displacement and total input energy. However, because of the uniform acceleration profile assumed over the structural height, the story shear forces are significantly underestimated by LSA.

Applicability of Frozen-Viscosity Models of Unsteady Wall Shear Stress

AbstractThe validity of assumed frozen-viscosity conditions underpinning an important class of theoretical models of unsteady wall shear stress in transient flows in pipes and channels is assessed using detailed computational fluid dynamics (CFD) simulations. The need for approximate one-dimensional (1D){x,t} models of the wall stress is unavoidable in analyses of transient flows in extensive pipe networks because it would be economically impracticable to use higher order methods of analysis. However, the bases of the various models have never been established rigorously. It is shown herein that a commonly used approach developed by the first authors is flawed in the case of smooth-wall flows although it is more plausible for rough-wall flows. The assessment process is undertaken for a particular, but important, unsteady flow case, namely, a uniform acceleration from an initially steady turbulent flow. First, detailed predictions from a validated CFD method are used to derive baseline solutions with which...

Particle detectors and the zero mode of a quantum field

We study the impact of the zero-mode of a quantum field on the evolution of a particle detector. For a massless scalar field in a periodic cavity, we show that the impact of the zero mode on the Unruh-DeWitt detector and its derivative-coupling generalisation is necessarily nonvanishing but can be made negligible in some limits, including those commonly occurring in non-relativistic quantum optics. For the derivative-coupling detector this can be accomplished by just tuning the zero mode's initial state, but the standard Unruh-DeWitt detector requires a more subtle and careful tuning. Applications include an inertial detector with arbitrary velocity, where we demonstrate the regularity of the ultrarelativistic limit, and a detector with uniform acceleration.

Research of the Belt Conveyor Starting Acceleration Based on AMESim

Based on AMESim, by the analysis of the Conveyor Belt four discrete model, Select and built the Kelvin-Voigt model which is simple and applicable, by comparative analysis of drawing on four commonly used to start the acceleration (uniform acceleration, triangle acceleration, trapezoidal acceleration and the Harrison), Select the Harrison speed as the starting acceleration and Using AMESim to establish the starting model of acceleration.

Laboratory Studies on Acoustic Emission Characteristics to Coal Dynamic Response under Variable Accelerative Load

To simulate the fracture of the coal under impact load, uniaxial pressure test of coal which retrieved from KongZhuang coal mine-DaTun coal and electricity Company of China coal group was done in the manner of strain control which rest with a function of uniform variable acceleration. Through researches on the stress-strain relationships and acoustic emission characteristics, the relationship between ring count rate and time series was founded, and the process before failure of coal was divided into four stages: low-level ringing count rate, higher level, highest level and peaceful period. Through the comparison and analysis, it is founded that acoustic emission characteristics in the stage of higher level of ringing count rate can be regarded as a basis for the prediction of coal fracture. According to three obvious rise stages of acoustic emission signal in the process before failure of coal, growth factor of climbing speed is introduced and the values are calculated between 2 to 4, and it is conferred that the value of is proportional to compressive strength of coal and loading rate. It is of great significance for the prediction of coal fracture by acoustic emission characteristics in the stage of new cracks.

A review on Lamb's atmospheric oscillations using initial value problem approach

Waves at a surface of discontinuity in the atmosphere were analysed in 1910 by Lamb, who derived, using normal mode approach, an analytical dispersion relation for a discrete mode (surface mode). Lamb examined the case of waves propagated along a horizontal plane where the equilibrium temperature is discontinuous. For simplicity, the upper and the lower regions are considered incompressible. The oscillations are treated in the ideal (dissipationless) limit and the uniform gravitational acceleration is taken to be co-aligned with the prevailing temperature gradient. In this work, in order to show how the modes appear in the response of a surface discontinuity to an initial perturbation, we consider the initial value problem (IPV). The main difference from the standard analysis is that solutions to the linearized equations of motion which satisfy general conditions are obtained in terms of Fourier-Laplace transform of the hydrodynamics variables. These transforms can be inverted explicitly to express the fluid variables as integrals of Green's functions multiplied by initial data. In addition to discrete mode (surface mode), sets of continuum modes due to branch cuts in the complex plane, not treated explicitly in the literature, appears.

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

Magneto-Hydrodynamic (MHD) flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

Effects of a uniform acceleration on atom–field interactions

We review some quantum electrodynamical effects related to the uniform acceleration of atoms in vacuum. After discussing the energy level shifts of a uniformly accelerated atom in vacuum, we investigate the atom–wall Casimir–Polder force for accelerated atoms, and the van der Waals/Casimir–Polder interaction between two accelerated atoms. The possibility of detecting the Unruh effect through these phenomena is also discussed in detail.

Improved Adaptive α-β Filtering Algorithm

To predict dynamic targets by using tracking gains, an improved adaptive α-β filtering algorithm is presented. First, we introduce the pseudo acceleration to build generalized model for uniform linear and acceleration motions. Then, the tracking gains based on tracking index are adaptively determined. Simulation results demonstrate that the proposed filtering algorithm can track both maneuvering and non-maneuvering targets with good performance.

Sight Distance Standards Based on Observational Data Risk Evaluation of Passing

The paper presents an application of a reliability analysis for evaluating the risk associated with passing sight distance (PSD) standards in terms of the expected probability of noncompliance. Calculation of PSD is required to determine where drivers can safely execute passing maneuvers. Traditional PSD standards are based on deterministic, theoretical models, which are calibrated with conservative percentile values for uncertain design inputs to account for uncertainty. The PSD standards do not provide information about the risk of deviation from them. Reliability analysis is a technique that is based on limit state design and that accounts for the propagation of variability from input random parameters to the design outputs. A total of 1,098 passing maneuvers were observed on several two-lane highways in Spain; two data collection methodologies were used: external observations and an instrumented vehicle. The most significant factors affecting PSD were impeding-vehicle speed, passing-vehicle acceleration, and headways between impeding and passing vehicles. A uniform acceleration model described the passing-vehicle trajectory. The characterized input parameters and the passing model were used to perform a reliability analysis. The results showed the probability of noncompliance in different scenarios, defined as the proportion of cases in which the required PSD would exceed the available sight distance. American and Spanish PSD standards were evaluated. Geometric design standards presented a probability of noncompliance of about 0.15, whereas some marking standards had a probability of noncompliance exceeding 0.85. These standards may be associated with higher risk levels if they are followed by drivers. As well, PSD risk levels were not consistent for different design speeds, since they underestimated operating speed at some locations.

Nonlinear Static Pushover Analysis for Shear Wall Structures in SAP2000 Program

To study the nonlinear mechanical characteristics of reinforced concrete shear wall structures under rare earthquakes, a single reinforced concrete shear wall model is established in SAP2000 program, which is simulated by nonlinear multi-layer shell element. Nonlinear static pushover analysis of the model is presented by uniform acceleration lateral load pattern and inverted triangle lateral load pattern. The relationship curve between base shear and top displacement of shear wall, and the stress distribution diagrams of the concrete layer and rebar layer are obtained. It may be concluded that, the yielding of rebar layer and the cracking of the concrete layer may be observed by stress distribution diagrams. SAP2000 program is feasible to nonlinear simulation of shear wall structures.

Self-interaction in the Bopp–Podolsky electrodynamics: Can the observable mass of a charged particle depend on its acceleration?

In this paper we obtain the expression for the self-force in the model with the Lagrangian containing additional terms, quadratic in Maxwell tensor derivatives (so-called Bopp–Podolsky electrodynamics). Features of this force are analyzed for various limiting cases. When a charged particle moves along straight line with a uniform acceleration, an explicit formula is found. In the framework of the considered model, an observable renormalized particle mass is shown to depend on its acceleration. This dependence allows, in principle, to extract experimentally a value of the particle bare mass.

Transient free convection flow past an accelerated vertical cylinder in a rotating fluid

The flow of a viscous incompressible fluid past an accelerated vertical circular cylinder in a rotating fluid is analyzed in this study. The cylinder starts impulsively from rest with uniform acceleration in its own plane relative to the rotating fluid. The closed form solutions of the governing boundary layer equations in non-dimensional form are obtained in terms of Bessel functions and modified Bessel functions by Laplace transform technique. Numerical values of the axial velocity, transverse velocity and temperature profiles are obtained for various physical parameters and presented in graphs. Skin friction and Nusselt number are also discussed graphically.

Unruh effect under non-equilibrium conditions: oscillatory motion of an Unruh-DeWitt detector

The Unruh effect refers to the thermal fluctuations a detector experiences while undergoing linear motion with uniform acceleration in a Minkowski vacuum. This thermality can be demonstrated by tracing the vacuum state of the field over the modes beyond the accelerated detector's event horizon. However, the event horizon is well-defined only if the detector moves with eternal uniform linear acceleration. This idealized condition cannot be fulfilled in realistic situations when the motion unavoidably involves periods of non-uniform acceleration. Many experimental proposals to test the Unruh effect are of this nature. Often circular or oscillatory motion, which lacks an obvious geometric description, is considered in such proposals. The proper perspective for theoretically going beyond, or experimentally testing, the Unruh-Hawking effect in these more general conditions has to be offered by concepts and techniques in non-equilibrium quantum field theory. In this paper we provide a detailed analysis of how an Unruh-DeWitt detector undergoing oscillatory motion responds to the fluctuations of a quantum field. Numerical results for the late-time temperatures of the oscillating detector are presented. We comment on the digressions of these results from what one would obtain from a naive application of Unruh's result.

Site specific response analysis for performance based design earthquake characteristics

During strong earthquakes, seismic waves travelling towards the ground surface alter the engineering characteristics of the soil layers and consequently the characteristics of travelling seismic waves also change with respect to their frequency and amplitude contents. In assessing the site-specific design earthquake characteristics in seismically active zones for performance levels of Collapse Prevention, Life Safety, and Immediate Occupancy that may correspond to 72, 475 and 2475 year return period earthquakes, detailed site characterization and site response analyses may be required. This process may be conducted in two consecutive statistically independent stages. The first stage involves the seismic hazard study to assess the design earthquake characteristics on rock outcrop for selected exceedance levels and the second stage involves detailed site characterization and site response analyses to estimate design earthquake characteristics on the ground surface. The uncertainties arising from the source characteristics need to be taken into account by using a representative number of strong motion acceleration records for site response analyses recorded in locations that are compatible with the seismic hazard with respect to fault mechanism, earthquake magnitude, and source distance. In addition, the strong motion acceleration records should be compatible with respect to peak acceleration and acceleration response spectra levels estimated by the probabilistic or deterministic seismic hazard study. One approach is to use the uniform acceleration hazard spectra and another option is to adopt conditional mean spectrum on rock outcrop estimated in the first stage from the earthquake hazard study for scaling input motions for site response analysis. It was observed that the scaling methodology adopted may play an important role in the calculated earthquake characteristics on the ground surface. A semi empirical procedure was proposed to determine the site specific design earthquake characteristics on the ground surface. A parametric study was conducted to demonstrate the applicability of the proposed methodology based on one dimensional site response analyses using Shake91 and DeepSoil site response codes to evaluate design earthquake characteristics on the ground surface.

Localized projective measurement of a quantum field in non-inertial frames

We propose a projective operator formalism that is well-suited to study the correlations of quantum fields in non-inertial frames and curved spacetimes. We generalize a Glauber model of detection of a single localized field mode to allow for making measurements in an arbitrary reference frame. We show that the model correctly reproduces the Unruh temperature formula of a single accelerated detector, and use it to extract vacuum entanglement by a pair of counter-accelerating detectors. This latter example is a proof of principle that this approach will be appropriate to further studies on the nature of entanglement in curved spacetimes and, in general, to model experimentally feasible scenarios in quantum field theory in non-inertial frames. Finally, as further confirmation of the validity of our approach, we introduce an explicit perturbative matter–radiation interaction model and show that under uniform acceleration it reproduces both the generalized Glauber model and the projective measurement results in the weak coupling regime.

Holographic EPR pairs, wormholes and radiation

As evidence for the ER=EPR conjecture, it has recently been observed that the string that is holographically dual to an entangled quark-antiquark pair separating with (asymptotically) uniform acceleration has a wormhole on its worldsheet. We point out that a two-sided horizon and a wormhole actually appear for much more generic quark-antiquark trajectories, which is consistent with the fact that the members of an EPR pair need not be permanently out of causal contact. The feature that determines whether the causal structure of the string worldsheet is trivial or not turns out to be the emission of gluonic radiation by the dual quark and antiquark. In the strongly-coupled gauge theory, it is only when radiation is emitted that one obtains an unambiguous separation of the pair into entangled subsystems, and this is what is reflected on the gravity side by the existence of the worldsheet horizon.