Uniform Acceleration Research Articles

Directional dependence of the Unruh effect for spatially extended detectors

We analyse the response of a spatially extended direction-dependent local quantum system, a detector, moving on the Rindler trajectory of uniform linear acceleration in Minkowski spacetime, and coupled linearly to a quantum scalar field. We consider two spatial profiles: (i) a profile defined in the Fermi-Walker frame of an arbitrarily-accelerating trajectory, generalising the isotropic Lorentz-function profile introduced by Schlicht to include directional dependence; and (ii) a profile defined only for a Rindler trajectory, utilising the associated frame, and confined to a Rindler wedge, but again allowing arbitrary directional dependence. For (i), we find that the transition rate on a Rindler trajectory is non-thermal, and dependent on the direction, but thermality is restored in the low and high frequency regimes, with a direction-dependent temperature, and also in the regime of high acceleration compared with the detector's inverse size. For (ii), the transition rate is isotropic, and thermal in the usual Unruh temperature. We attribute the non-thermality and anisotropy found in (i) to the leaking of the Lorentz-function profile past the Rindler horizon.

Recent and future manifestations of a contingent global mean sea level acceleration

Abstract We analyzed globally averaged satellite altimetry mean sea level time series during 1993 – 2018 and their future manifestations for the following 25 years using a kinematic model, which consists of a trend, a contingent uniform acceleration, and a random error model. The analysis of variance results shows that the model explains 71.7% of the total variation in global mean sea level for which 70.6% is by the secular trend, and 1.07% is due to a contingent uniform acceleration. The remaining 28.3% unexplained variation is due to the random errors, which are dominated by a first order autoregressive process driven mostly by oceanic and atmospheric variations over time. These numbers indicate more bumps and jumps for the future manifestations of the global mean sea level anomalies as illustrated using a one-step ahead predictor in this study. Our findings suggest preponderant random errors are poised to further confound and negatively impact the certitude of published estimates of the uniform global sea level acceleration as well as its prediction under an increasingly warmer Earth.

Impulsively Started Horizontal Riga Plate Embedded in Unsteady Casson Fluid Flow with Rotation

This article is based on the impulsively started horizontal Riga plate in two dimensional unsteady Casson fluid flows with rotation. The plate starts abruptly from the rest relative to the rotating fluids moving with uniform acceleration in its plane. Numerical solutions are acquired by using explicit finite difference method and estimated results have been gained for various values of the Rotational parameter, modified Hartmann number, Prandtl number, Radiative parameter, Eckert number, Heat source parameter, Schmidt number, and the Soret number. Both the Compaq visual FORTRAN 6.6a and MATLAB R2015a tools have been used to find the numerical solutions and the graphical presentation. The Skin friction, Nusselt number and Sherwood number have been computed and the effects of some pertinent parameters on various distributions are discussed briefly and presented graphically.

The certitude of a global sea level acceleration during the satellite altimeter era

Abstract Recent studies reported a uniform global sea level acceleration during the satellite altimetry era (1993–2017) by analyzing globally averaged satellite altimetry measurements. Here, we discuss potential omission errors that were not thoroughly addressed in detecting and estimating the reported global sea level acceleration in these studies. Our analyses results demonstrate that the declared acceleration in recent studies can also be explained equally well by alternative kinematic models based on previously well-established multi-decadal global mean sea level variations of various origins, which suggests prudence before declaring the presence of an accelerating global mean sea level with confidence during the satellite altimetry era.

Radiative Processes of Two Accelerated Entangled Atoms Near Boundaries

By considering the interaction between a two-atom system and the vacuum massless scalar field in the viewpoint of an instantaneously inertial observer, we study the rates of transition of a uniformly accelerated two-atom system in the symmetric/antisymmetric entangled state near a reflecting boundary and in a cavity, respectively. We find that both the downward transition | ψ ± ⟩ → | g A g B ⟩ and the upward transition | ψ ± ⟩ → | e A e B ⟩ occur for the accelerated two-atom system, as in sharp contrast with the case of a static two-atom system, in which the upward transition can never happen. Similar to the rates of transition of atoms immersed in a thermal bath with the FDU temperature, both the downward transition rate and the upward transition rate are characterized by the Plank factor ( e 2 π ω 0 / a − 1 ) − 1 . This character of the transition rates is very different from the other radiative properties of the accelerated two-atom system, such as the resonance interatomic energy, for which the revisions of the effects of uniform acceleration are never characterized by such a factor. We show with analytical and numerical results that both the downward transition and the upward transition processes can be effectively manipulated by the atomic non-inertial motion and by the presence of boundaries. By comparing the upward transition rate with the downward transition rate, we discover that, when ω 0 ≫ a , with ω 0 and a being the energy space and the proper acceleration of the two-atom system, the disentanglement caused by the upward transition is negligible, while, if ω 0 ≪ a , the disentanglement caused by the upward transition becomes as important as that caused by the downward transition.

Tetrapartite entanglement features of W-Class state in uniform acceleration

Using the single-mode approximation, we first calculate entanglement measures such as negativity (1–3 and 1–1 tangles) and von Neumann entropy for a tetrapartite W-Class system in noninertial frame and then analyze the whole entanglement measures, the residual π4 and geometric Π4 average of tangles. Notice that the difference between π4 and Π4 is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer to four accelerated observers. The results show that there still exists entanglement for the complete system even when acceleration r tends to infinity. The degree of entanglement is disappeared for the 1–1 tangle case when the acceleration r > 0.472473. We reexamine the Unruh effect in noninertial frames. It is shown that the entanglement system in which only one qubit is accelerated is more robust than those entangled systems in which two or three or four qubits are accelerated. It is also found that the von Neumann entropy S of the total system always increases with the increasing accelerated observers, but the Sκξ and Sκζδ with two and three involved noninertial qubits first increases and then decreases with the acceleration parameter r, but they are equal to constants 1 and 0.811278 respectively for zero involved noninertial qubit.

Unruh acceleration radiation revisited

When ground-state atoms are accelerated and the field with which they interact is in its normal vacuum state, the atoms detect Unruh radiation. We show that atoms falling into a black hole emit acceleration radiation which, under appropriate initial conditions (Boulware vacuum), has an energy spectrum which looks much like Hawking radiation. This analysis also provides insight into the Einstein principle of equivalence between acceleration and gravity. The Unruh temperature can also be obtained by using the Kubo–Martin–Schwinger (KMS) periodicity of the two-point thermal correlation function, for a system undergoing uniform acceleration; as with much of the material in this paper, this known result is obtained with a twist.

Tripartite Entanglement Measures of Generalized GHZ State in Uniform Acceleration**Supported by the CONACYT of Mexico under Grant No 288856-CB-2016, and the 20190234-SIP-IPN of Mexico.

Using the single-mode approximation, we study entanglement measures including two independent quantities; i.e., negativity and von Neumann entropy for a tripartite generalized Greenberger–Horne–Zeilinger (GHZ) state in noninertial frames. Based on the calculated negativity, we study the whole entanglement measures named as the algebraic average π3-tangle and geometric average Π3-tangle. We find that the difference between them is very small or disappears with the increase of the number of accelerated qubits. The entanglement properties are discussed from one accelerated observer and others remaining stationary to all three accelerated observers. The results show that there will always exist entanglement, even if acceleration r arrives to infinity. The degree of entanglement for all 1–1 tangles are always equal to zero, but 1–2 tangles always decrease with the acceleration parameter r. We notice that the von Neumann entropy increases with the number of the accelerated observers and SκIζI (κ, ζ ∈ (A, B, C)) first increases and then decreases with the acceleration parameter r. This implies that the subsystem ρκIζI is first more disorder and then the disorder will be reduced as the acceleration parameter r increases. Moreover, it is found that the von Neumann entropies SABCI, SABICI and SAIBICI always decrease with the controllable angle θ, while the entropies of the bipartite subsystems S2−2non (two accelerated qubits), S2-1non (one accelerated qubit) and S2-0non (without accelerated qubit) first increase with the angle θ and then decrease with it.

Uniform risk vs. uniform hazard spectral acceleration for different soil types in Alborze seismic zone

Various methods have been proposed in the last decade to determine maximum credible earthquake for seismic structural design purpose. Uniform risk and uniform hazard approaches are the two ways to investigate the earthquake design spectral acceleration. The current study aims to draw a comparison between uniform risk spectra (URS) and uniform hazard spectra (UHS) at four locations with different soil types in Mazandaran (north of Iran). Since seismic hazard curves were not available for the region of interest, probabilistic seismic hazard analysis was performed at four stations by considering three attenuation relationships to account for local, regional and global effects of earthquakes. The UHS was determined at each station for the 2500-year return period. Furthermore, URS, which leads to one percent probability of collapse of a building in 50 years, was investigated by an iterative technique. It was found that a UHS leads to a greater ground shaking than URS at short periods at all soil conditions. The differences were more evident for a period range of about 0.3–0.4 s and for very strong and soft soil. To sum up, as ASCE 7–10 recommends, using uniform risk spectral acceleration is more confidential for designing short structures on all ground types. The current findings add to a growing body of literature on determination of maximum credible earthquake in seismic design of structures.

Entanglement property of the Werner state in accelerated frames

We study the entanglement property of a free Dirac field in a Werner state as seen by two relatively accelerated parties. We study the concurrence, negativity, mutual information and $$\pi $$ -tangle of the tripartite system. We show how these entanglement properties depend on both the free parameter F, which is a real parameter called fidelity, and the acceleration parameter r. The degree of entanglement is degraded by the Unruh effect, but we notice that the Werner state always remains entangled even in the acceleration limit, and thus, it can become a good candidate to quantum teleportation in uniform acceleration frame. We notice that the entropy $$S(\rho _{A\, \mathrm{I}\, \mathrm{II}})$$ decreases with the free parameter F, and also $$S(\rho _{A\, \mathrm{I}\, \mathrm{II}})$$ , $$S(\rho _{A})$$ and $$S(\rho _{\mathrm{I}\, \mathrm{II}})$$ are independent of the acceleration parameter r. The von Neumann entropy is not a good entanglement measure any more for this mixed state. We verify that the Werner state in a noninertial frame obeys the Coffman–Kundu–Wootters (CKW) monogamous inequality and find that two useful relations for the concurrence and negativity.

Exact and efficient calculation of the derivatives of Lagrange multipliers for molecular dynamics simulations of biological molecules and polymers

In the simulation of biological molecules and polymers, it is customary to impose constraints on the fastest degrees of freedom so as to freeze their motion and increase the time step. An evaluation of the corresponding constraint forces must be performed in an efficient manner, otherwise it would create a bottleneck in the calculations. If integrators of a higher order than two (for example, Gear predictor–corrector methods) are used to find the trajectories of atoms, the derivatives of the forces on the atoms with respect to the time—including the derivatives of constraint forces—also need to be calculated. In this letter, we present a method to perform the calculation of the constraint forces (i.e. of the Lagrange multipliers) as well as their time derivatives in an analytic, accurate and efficient manner. This method can be used together with integrators of a higher order than two, going beyond the simplification of uniform acceleration to perform calculations of enhanced accuracy for atomic paths, while keeping a low numerical complexity in the calculation of constraint forces.

Visualization of shockwave behavior in water and gelatin

Explosive welding is a popular method that is utilized to bond different types of metals. In particular, with the use of underwater explosive welding technique, the uniform acceleration of a thin plate over a very short flying distance is possible, which makes the technique suitable for the welding of thin plates onto a base plate to modify various properties of the surface of interest for protection against extreme environments. However, the use of water complicates the setup of the assembly, and therefore, in this study, we attempt to use other pressure-transmitting media, such as gelatin, which exhibits shockwave propagation similar to water. The similarity of shockwave propagation of the two materials is confirmed via optical observations utilizing a high-speed camera for two types of explosives. Thus, our findings confirm the viability of the use of gelatin as a pressure-transmitting medium for explosive welding.

Tetrapartite entanglement measures of GHZ state with uniform acceleration

Using the single-mode approximation, we calculate entanglement measures such as negativity (1 − 3, 1 − 1 and 2 − 2 tangles) and von Neumann entropy for a tetrapartite Greenberger–Horne–Zeilinger system in a non-inertial frame. We then analyze the whole entanglement measures, the residual π4 and geometric Π4 average of tangles. We find that the difference between them is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer and others remaining stationary to all four accelerated observers. The results presented here show that entanglement still exists for the complete system even when acceleration r tends to infinity. The degree of entanglement is always equal to zero for the 1 − 1 tangle case. We also study the negativity 2 − 2 tangle for completeness. We reexamine the existence of the Unruh effect in non-inertial frames. It is also found that the von Neumann entropy increases with the increasing accelerated observers, and and first increase and then decrease with the acceleration parameter r, e.g. at r = 0.599881 and at r = 0.676196. This implies that the subsystems and are at first more disordered and then the disorder is reduced with the increasing acceleration parameter r.

Heavy-Traffic Analysis Through Uniform Acceleration of Queues with Diminishing Populations

We consider a single-server queue that serves a finite population of [Formula: see text] customers that will enter the queue (require service) only once, also known as the [Formula: see text] queue. This paper presents a method for analyzing heavy-traffic behavior by using uniform acceleration, which simultaneously lets [Formula: see text] and the service rate grow large, while the initial resource utilization approaches one. A key feature of the model is that, as time progresses, more customers have joined the queue, and fewer customers can potentially join. This diminishing population gives rise to a class of reflected stochastic processes that vanish over time and hence do not have a stationary distribution. We establish that, when the arrival times are exponentially distributed, by suitably rescaling space and time, the queue-length process converges to a Brownian motion with a negative quadratic drift, a stochastic-process limit that captures the effect of the diminishing population. When the arrival times are generally distributed, our techniques provide information on the typical queue length and the first busy period.

Spontaneous excitation of an accelerated atom coupled with quantum fluctuations of spacetime

A direct consequence of quantization of gravity would be quantum gravitational vacuum fluctuations which induce quadrupole moments in gravitationally polarizable atoms. In this paper, we study the spontaneous excitation of a gravitationally polarizable atom with a uniform acceleration $a$ in interaction with a bath of fluctuating quantum gravitational fields in vacuum, and compare the result with that of a static one in a thermal bath of gravitons at the Unruh temperature. We find that, under the fluctuations of spacetime itself, transitions to higher-lying excited states from the ground state are possible for both the uniformly accelerated atom in vacuum and the static one in a thermal bath. The appearance of terms in the transition rates proportional to $a^4$ and $a^2$ indicates that the equivalence between uniform acceleration and thermal field is lost.

Gait Recognition of Acceleration Sensor for Smart Phone Based on Multiple Classifier Fusion

Gait, as a kind of biological feature, has a profound value in personnel identification. This paper analyzes gait characteristics based on acceleration sensors of smart phones and proposes a new gait recognition method. First, in view of the existing methods in the process of extraction of gait features, a large number of redundant calculations, cycle detection error, and the phase deviation issue during the week put forward the Shape Context (SC) and Linear Time Normalized (LTN) combining SCLTN calibration method of gait cycle sequence matching, to represent the whole extract typical gait cycle gait. In view of the existing extracted gait features are still some conventional features; the velocity change of relatively uniform acceleration and the change of acceleration per unit time are proposed as new features. Secondly, combining new features with traditional features to form a new feature is set for training alternative feature set, from which the training time and recognition effect of multiple classifiers are screened. Finally, a new multiclassifier fusion method, Multiple Scale Voting (MSV), is proposed to fuse the results of Multiple classifiers to obtain the final classification results. In order to verify the performance of the proposed method, gait data of 32 testers are collected. The final experimental results show that the new feature has good separability, and the recognition rate of fusion feature set after MSV algorithm is 98.42%.

Tetrapartite entanglement measures of W-class in noninertial frames**Project partially supported by the CONACYT, Mexico under the Grant No. 288856-CB-2016, partially by 20190234-SIP-IPN, Mexico, and partially by the program XXVIII Verano de la Investigación Científica 2018 supported by the Academia Mexicana de Ciencias.

We present the entanglement measures of a tetrapartite W-class entangled system in a noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied. Two cases are considered. First, when one qubit has uniform acceleration whilst the other three remain stationary. Second, when two qubits have nonuniform accelerations and the others stay inertial. The 1–1 tangle, 1–3 tangle, and whole entanglement measurements and , are studied and illustrated with graphics through their dependence on the acceleration parameter rd for the first case and rc and rd for the second case. It is found that the negativities (1–1 tangle and 1–3 tangle) and π-tangle decrease when the acceleration parameter rd or in the second case rc and rd increase, remaining a nonzero entanglement in the majority of the results. This means that the system will be always entangled except for special cases. It is shown that only the 1–1 tangle for the first case vanishes at infinite accelerations, but for the second case the 1–1 tangle disappears completely when . An analytical expression for the von Neumann information entropy of the system is found and we note that it increases with the acceleration parameter.

The Role of Vacuum Fluctuations and Symmetry in the Hydrogen Atom in Quantum Mechanics and Stochastic Electrodynamics

Stochastic Electrodynamics (SED) has had success modeling black body radiation, the harmonic oscillator, the Casimir effect, van der Waals forces, diamagnetism, and uniform acceleration of electrodynamic systems using the stochastic zero-point fluctuations of the electromagnetic field with classical mechanics. However the hydrogen atom, with its 1/r potential remains a critical challenge. Numerical calculations have shown that the SED field prevents the electron orbit from collapsing into the proton, but, eventually the atom becames ionized. We look at the issues of the H atom and SED from the perspective of symmetry of the quantum mechanical Hamiltonian, used to obtain the quantum mechanical results, and the Abraham-Lorentz equation, which is a force equation that includes the effects of radiation reaction, and is used to obtain the SED simulations. We contrast the physical computed effects of the quantized electromagnetic vacuum fluctuations with the role of the real stochastic electromagnetic field.

Intuitive physics of gravitational motion as shown by perceptual judgment and prediction-motion tasks

In Experiment 1, we explored participants' perceptual knowledge of vertical fall by presenting them with virtually simulated polystyrene or wooden spheres falling to the ground from about two meters high. Participants rated the perceived naturalness of the motion. Besides the implied mass of the sphere, we manipulated the motion pattern (i.e., uniform acceleration vs. uniform velocity), and the magnitude of acceleration or velocity. Results show that relatively low values of acceleration or velocity were judged as natural for the polystyrene sphere, whereas relatively high values of acceleration or velocity were judged as natural for the wooden sphere. In Experiment 2, the same stimuli of Experiment 1 were used, but the sphere disappeared behind an invisible occluder at some point of its trajectory. Participants were asked to predict the time-to-contact (TTC) of the sphere with the ground by pressing a key at the exact time of impact of the lower edge of the sphere with the floor of the room. Results show that the estimated TTC for the simulated wooden sphere was slightly but consistently smaller than the estimated TTC for the simulated polystyrene sphere. The influence of the implied mass on participants' responses might be the manifestation of two processes, namely an explicit ‘heavy-fast, light-slow’ heuristic, and/or an implicit, automatic association between mass and falling speed.

A New Geosynchronous SAR Constellation and its Signal Characteristics

The Geosynchronous Synthetic Aperture Radar (GEO SAR) has a long synthetic aperture time. The temporal decoherence and azimuth variance characteristics of echo are significant, that brings great challenges to signal to process. In order to reduce the synthetic aperture time and thus improve the observation flexibility and efficiency, this paper proposes a SAR system mounted on a special satellite in reverse equatorial geosynchronous orbit, so-called the reverse equatorial GEO SAR. The orbit is nearly circular and the orbital plane coincides with the equatorial plane. The satellite flies against the direction of the Earth's rotation. The relative velocity is accelerated twice and the synthetic aperture time is shorter. The satellite does not drift in latitude direction and drifts uniformly in longitude direction. The echo has azimuth invariance property. Meanwhile, the 24-hour continuous observation can be achieved for areas with a certain range of latitude by means of large squint technique and constellation design. As the GEO SAR has high orbit, large delay, large squint angle, and wide pulse width, the complex modulation effects are generated by continuous motion between the satellite and target during the imaging period. In this paper, the uniform acceleration curve motion is used to describe the motion of both satellite and target, and the linear approximation is used to describe the slant range change in the process of transmitting and receiving one pulse. Accordingly, an accurate signal model for the reverse equatorial GEO SAR is established, which provides a theoretical model for signal characteristics analysis and imaging algorithms development.