Uniform Acceleration Research Articles

Entanglement measures of W-state in noninertial frames

In this work we present the entanglement measures of a tripartite W-State entangled system in noninertial frame through the coordinate transformation between Minkowski and Rindler. Two cases are considered, i.e., when one qubit goes in a uniform acceleration a and the others remain stationary and when two qubits undergo in a uniform acceleration and while the other is stationary. The analytical negativities for one-tangle, two-tangle and π-tangle in total are not written out explicitly except for some special cases due to complicated expressions, but we illustrate them in graphics and study their dependencies on the acceleration parameters rb and rc. We find that the negativities of the one-tangle, two-tangle and π-tangle decrease with the acceleration parameters except for the constant NAB=NBA. The negativity NCI(AB) and the πCI decrease faster than NA(BCI) and πA(πB). The negativities NACI (NB(ACI))and NBICI decrease faster than those NAB and NABI, respectively. It is interesting to see there exist turning points for the negativity NA(BICI) at the coordinate position (rb,rc) with rb=rc, which implies that the NA(BICI) has minimum value when Bob and Charlie are on the same position and the degree of the entanglement of the subsystem ρA(BICI) becomes smallest. The von Neumann entropy of tripartite system densities ρABCI and ρABICI are obtained analytically. We notice that they all increase with the acceleration parameters rb and rc.

Relativistic motion of an Airy wave packet in a lattice potential

We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its velocity, and so the acceleration cannot continue indefinitely. Instead, we show that the wavepacket's motion is described by relativistic equations of motion, which surprisingly, arise naturally from evolution under the standard non-relativistic Schr\"odinger equation. The presence of the lattice potential allows the wavepacket's motion to be controlled by means of Floquet engineering. In particular, in the deep relativistic limit when the wavepacket's motion is photon-like, this form of control allows it to mimic both standard and negative refraction. Airy wavepackets held in lattice potentials can thus be used as powerful and flexible simulators of relativistic quantum systems.

Some further comments on special relativity and dark energy

In this note, we provide some new derivations and further elaboration on a recent proposal by the author Hill (Zeitschrift fur angewandte Mathematik und Physik 69: 133–145, 2018. https://doi.org/10.1007/s00033-018-1028-4) regarding the formal origins of dark energy. Using the framework of special relativity and validation through Lorentz invariance, Hill (2018) develops the usual relations of special relativity, but makes a distinction between particle energy \(e = mc^2\) and the actual work done by the particle \( \mathscr {E}\), and adopts the perspective that both the momentum vector \({\mathbf{p} = m\mathbf{u}}\) and the intrinsic particle energy e itself contribute to the work done \( \mathscr {E}\). The alternative formulation provides an extension of Newton’s second law that is properly invariant under the Lorentz group and yields new expressions for the work done involving the \(\log \) function. The \(\log \) terms can generate extremely large energies and may represent the first formal indication of the origin of dark energy. The new approach suggests that large energies might be generated for slowly moving systems and that dark energy might arise in consequence of conventional mechanical theory neglecting both the de Broglie wave energy and the work done in the direction of time. In these notes, a number of alternative derivations and connections relating to Hill (2018) are presented that were not made explicit in Hill (2018), including new derivations from the wave equation, a generalised approach and relating the solutions of Hill (2018) to a known result for uniform acceleration and to Hubble’s law for receding galaxies.

Acoustic response of a lean premixed flame propagating upward in a tube

An analysis is carried out of the response of a curved flame front rising in a vertical tube to acoustic perturbations of frequency small compared to the ratio of the speed of sound to the radius of the tube. The gas around the flame front, whose characteristic size is the radius of the tube, is then subjected to a oscillatory, nearly uniform acceleration that adds to the acceleration of gravity. As in the better studied case of a downward propagating flame, the response of the flame front to this oscillatory acceleration leads to fluctuations of the front area and the global thermal expansion of the gas, which may inject energy into the acoustic field and thus induce a thermoacoustic instability of the flame plus tube system. Acoustic temperature perturbations associated to adiabatic compression and expansion of the gas are assumed to be much smaller that the Frank–Kamenetskii temperature of the flame and are left out. The transfer function relating thermal expansion fluctuations to infinitesimal acoustic velocity perturbations is computed as a function of the frequency for conditions typical of a very lean flame in the standard flammability tube. The response of the flame front to finite amplitude acoustic perturbations has been also analyzed. At frequencies small compared to the inverse of the residence time of the gas around the flame front, the response is quasi-stationary until the oscillatory acceleration overcomes the acceleration of gravity during a part of the cycle sufficiently long for the front to develop wrinkles and eventually break down under a net upward acceleration. At higher frequencies, the curvature of the front decreases when the amplitude of the acoustic perturbation increases. A secondary instability of the oscillating flame that develops over many oscillation cycles and leads to breakdown appears at a certain value of the amplitude of the perturbation. The onset of this instability seems to be related to the oscillatory motion of the tube wall relative to the flame tip, which induces a flow that carries upwards a part of the front and causes negative velocities of the tip relative to the far fresh gas. This instability features period doubling in a certain range of frequencies.

Emanating Jets As Shaped by Surface Tension Forces.

We show that emanating jets can be regarded as growing liquid towers, which are shaped by the twofold action of surface tension: first the emanated fluid is being accelerated back by surface tension force, herewith creating the boundary conditions to solve the shape of the liquid tower as a solution of an equation mathematically related to the hydrostatic Young−Laplace equation, known to give solutions for the shape of pending and sessile droplets, and wherein the only relevant forces are gravity g and surface tension γ. We explain that for an emanating jet under specific constraints all mass parts with density ρ will experience a uniform time dependent acceleration a(t). An asymptotic solution is subsequently numerically derived by making the corresponding Young−Laplace type equation dimensionless and by dividing all lengths by a generalized time dependent capillary length λc(t) = . The time dependent surface tension γ(t) can be derived by measuring both time dependent acceleration a(t) and time dependent capillary length λc(t). Jetting experiments with water and coffee show that the dynamic surface tension behavior according to the emanating jet method and with the well-known maximum bubble pressure method are the same, herewith verifying the proposed model.

Radar maneuvering target detection based on two steps scaling and fractional Fourier transform

• The problems of quadratic range migration and Doppler frequency migration for the maneuvering target are addressed. • A method based on TSS-FrFT is proposed to achieve the coherent integration and it has superior detection performance and low computational complexity. • The acceleration matched filter is presented to remove the DFRC caused by the sudden change of targets acceleration. This paper considers the detection problem of radar maneuvering target with the range migration (RM) and Doppler frequency migration (DFM) and proposes an coherent integration method based on two steps scaling and fractional Fourier transform, i.e., TSS-FrFT. To be specific, this method corrects the quadratic RM (QRM) and DFM based on FrFT and a scaling processing of the rotation angle firstly. Then, it eliminates the coupling between the range frequency variable and FrFT domain (FrFD) variable via a second scaling processing. In the end, the coherent integration is achieved by the inverse Fourier transform (IFT) with respect to the range frequency variable. Compared with the existing methods, the proposed TSS-FrFT method has superior detection performance and low computational complexity. Moreover, considering the sudden change of the target acceleration within the coherent integration interval, this paper also presents an acceleration matched filter (AMF) to remove the Doppler frequency rate change (DFRC) caused by this acceleration change. Computer simulation results are also given to demonstrate the effectiveness of the proposed method from different aspects, i.e., computational complexity, coherent integration for a single target and multiple targets and detection performance for a uniform acceleration and non-uniform accelerations.

Comparison of measurement systems for free fall tests and calculations of the coefficient of restitution

The following article presents an overview of two measurement techniques for determining the coefficient of restitution (CoR) of multiple impacts of granules on a rigid plate. Experiments were performed with two different kinds of granules, which were dropped freely on an impact plate starting from a defined height. The impacts were recorded by an acoustic sensor as well as with a high-speed camera. The evaluation of the measured data shows slight differences between the CoRs arising from the two measurement techniques, which can be explained by the difference in accuracy between the two techniques. Furthermore, the influence of drag on the impacts is derived, and the necessity of a precise calculation method is discussed. Finally, a thorough description and a summary of the advantages and disadvantages of the measuring techniques and the calculation methods are given and it is shown when it is possible to estimate the CoR by uniform acceleration and when it is necessary to calculate the CoR considering the drag on the granule.

An Inverse Synthetic Aperture Ladar Imaging Algorithm of Maneuvering Target Based on Integral Cubic Phase Function-Fractional Fourier Transform

When imaging maneuvering targets with inverse synthetic aperture ladar (ISAL), dispersion and Doppler frequency time-variation exist in the range and cross-range echo signal, respectively. To solve this problem, an ISAL imaging algorithm based on integral cubic phase function-fractional Fourier transform (ICPF-FRFT) is proposed in this paper. The accurate ISAL echo signal model is established for a space maneuvering target that quickly approximates the uniform acceleration motion. On this basis, the chirp rate of the echo signal is quickly estimated by using the ICPF algorithm, which uses the non-uniform fast Fourier transform (NUFFT) method for fast calculations. At the best rotation angle, the range compression is realized by FRFT and the range dispersion is eliminated. After motion compensation, separation imaging of strong and weak scattering points is realized by using ICPF-FRFT and CLEAN technique and the azimuth defocusing problem is solved. The effectiveness of the proposed method is verified by a simulation experiment of an aircraft scattering point model and real data.

Einstein’s equations from the stretched future light cone

We define the stretched future light cone, a timelike hypersurface composed of the worldlines of radially accelerating observers with constant and uniform proper acceleration. By attributing temperature and entropy to this hypersurface, we derive Einstein's equations from the Clausius relation. Moreover, we show that the gravitational equations of motion for a broad class of diffeomorphism-invariant theories of gravity can be obtained from thermodynamics on the stretched future light cone, provided the Bekenstein-Hawking entropy is replaced by the Wald entropy.

Light emission by accelerated electric, toroidal, and anapole dipolar sources

Emission of electromagnetic radiation by accelerated particles with electric, toroidal and anapole dipole moments is analyzed. It is shown that ellipticity of the emitted light can be used to differentiate between electric and toroidal dipole sources, and that anapoles, elementary neutral non-radiating configurations, which consist of electric and toroidal dipoles, can emit light under uniform acceleration. The existence of non-radiating configurations in electrodynamics implies that it is impossible to fully determine the internal makeup of the emitter given only the distribution of the emitted light. Here we demonstrate that there is a loop-hole in this `inverse source problem'. Our results imply that there may be a whole range of new phenomena to be discovered by studying the electromagnetic response of matter under acceleration.

Fine-grained uncertainty relations under relativistic motion

Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this letter, we explore this uncertainty relation in a relativistic regime. For an observer undergoing a uniform acceleration who is immersed in an Unruh thermal bath, we show that the uncertainty bound is dependent on the acceleration parameter and the choice of Unruh modes. We find that the measurements in mutually unbiased bases, sharing the same uncertainty bound in the inertial frame, could be distinguished from each other for a noninertial observer. In an alternative scenario, for the observer restricted in a single rigid cavity, we show that the uncertainty bound exhibits a periodic evolution with respect to the duration of acceleration. With properly chosen cavity parameters, the uncertainty bounds could be protected. Moreover, we find that the uncertainty bound can be degraded for specific quantum measurements to violate the bound exhibited in the nonrelativistic limit, which can be attributed to the entanglement generation between cavity modes during a particular epoch. Several implications of our results are discussed.

Resonance Dipole–Dipole Interaction between Two Accelerated Atoms in the Presence of a Reflecting Plane Boundary

We study the resonant dipole–dipole interaction energy between two non-inertial identical atoms, one excited and the other in the ground state, prepared in a correlated Bell-type state, and interacting with the scalar field or the electromagnetic field nearby a perfectly reflecting plate. We suppose the two atoms move with the same uniform acceleration, parallel to the plane boundary, and that their separation is constant during the motion. By separating the contributions of radiation reaction field and vacuum fluctuations to the resonance energy shift of the two-atom system, we show that Unruh thermal fluctuations do not affect the resonance interaction, which is exclusively related to the radiation reaction field. However, non-thermal effects of acceleration in the radiation-reaction contribution, beyond the Unruh acceleration–temperature equivalence, affect the resonance interaction energy. By considering specific geometric configurations of the two-atom system relative to the plate, we show that the presence of the mirror significantly modifies the resonance interaction energy between the two accelerated atoms. In particular, we find that new and different features appear with respect to the case of atoms in the free-space, related to the presence of the boundary and to the peculiar structure of the quantum electromagnetic field vacuum in the locally inertial frame. Our results suggest the possibility to exploit the resonance interaction between accelerated atoms as a probe for detecting the elusive effects of atomic acceleration on radiative processes.

Discrete element analysis of particles flow in convex arc section of large corrugated sidewall belt conveyor

Convex arcs plays a key role in a large corrugated sidewall belt conveyor, which determines the large-capacity, high belt speed can smooth transportation, do not throw material. In order to study the convex arc section of corrugated sidewall belt conveyor conveying the material properties of the particle stream dynamics and logistics particle effects on the conveyor belt to the discrete element theory, by using a nonlinear Hertz Mindlin model built with corrugated sidewall belt conveyor discrete element model machine. The movement of materials with different speed is simulated; The average pressure and the maximum pressure of the base belt and the transverse plate of the corrugated sidewall conveyor belt under different conveyor belt speed were tested, and the average conveyor belt speed of rolling friction coefficient under three different particles were tested; Uniform acceleration of movement of the material flow when turning. Simulation results show that: With the increase of belt speed, the average pressure of corrugated sidewall conveyor increases nonlinearly, and gradually increases with the increase of velocity. The average velocity of the particle unit has nothing to do with the rolling friction coefficient.

A numerical investigation of two-degree-of-freedom VIV of a circular cylinder using the modified turbulence model

To simulate the fluctuating lift and resistance of the cylinder in vortex-induced vibration (VIV) accurately, the shear-stress transport (SST) turbulence model is modified in this paper. Then the correctness of the modified model is verified in the flow around a circular cylinder. After that, the numerical simulation of vortex-induced vibration of a cylinder with two degrees of freedom is carried out by using the embedded program of OpenFoam under three different initial conditions which are uniform acceleration, uniform deceleration and uniform velocity respectively. After the comparison and analyses of the vibration amplitude, frequency, fluid force, motion locus and vortex shedding, we find that there are some differences in the results obtained under three initial conditions. By contrast, the results of uniform acceleration condition are more accurate. Besides, the hysteresis mechanism can be analysed on the basis of the vortex shedding characteristics of uniform acceleration and deceleration. In general, the initial condition has a great influence on the numerical simulation of the vortex-induced vibration, and the validity of the modified turbulence model is further verified in the simulation.

The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 1. The principal flow

The free surface and flow field structure generated by the uniform acceleration (with dimensionless acceleration $\unicode[STIX]{x1D70E}$) of a rigid plate, inclined at an angle $\unicode[STIX]{x1D6FC}\in (0,\unicode[STIX]{x03C0}/2)$ to the exterior horizontal, as it advances ($\unicode[STIX]{x1D70E}>0$) or retreats ($\unicode[STIX]{x1D70E}<0$) from an initially stationary and horizontal strip of inviscid incompressible fluid under gravity, are studied in the small-time limit via the method of matched asymptotic expansions. This work generalises the case of a uniformly accelerating plate advancing into a fluid as studied by Needham et al. (Q. J. Mech. Appl. Maths, vol. 61 (4), 2008, pp. 581–614). Particular attention is paid to the innermost asymptotic regions encompassing the initial interaction between the plate and the free surface. We find that the structure of the solution to the governing initial boundary value problem is characterised in terms of the parameters $\unicode[STIX]{x1D6FC}$ and $\unicode[STIX]{x1D707}$ (where $\unicode[STIX]{x1D707}=1+\unicode[STIX]{x1D70E}\tan \unicode[STIX]{x1D6FC}$), with a bifurcation in structure as $\unicode[STIX]{x1D707}$ changes sign. This bifurcation in structure leads us to question the well-posedness and stability of the governing initial boundary value problem with respect to small perturbations in initial data in the innermost asymptotic regions, the discussion of which will be presented in the companion paper Gallagher et al. (J. Fluid Mech. vol. 841, 2018, pp. 146–166). In particular, when $(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D707})\in (0,\unicode[STIX]{x03C0}/2)\times \mathbb{R}^{+}$, the free surface close to the initial contact point remains monotone, and encompasses a swelling jet when $(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D707})\in (0,\unicode[STIX]{x03C0}/2)\times [1,\infty )$ or a collapsing jet when $(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D707})\in (0,\unicode[STIX]{x03C0}/2)\times (0,1)$. However, when $(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D707})\in (0,\unicode[STIX]{x03C0}/2)\times \mathbb{R}^{-}$, the collapsing jet develops a more complex structure, with the free surface close to the initial contact point now developing a finite number of local oscillations, with near resonance type behaviour occurring close to a countable set of critical plate angles $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D6FC}_{n}^{\ast }\in (0,\unicode[STIX]{x03C0}/2)$ ($n=1,2,\ldots$).

High quality ion acceleration through the interaction of two matched counterpropagating transversely polarized Gaussian lasers with a flat foil target

In order to generate high quality ion beams through a relatively uniform radiation pressure acceleration (RPA) of a common flat foil, a new scheme is proposed to overcome the curve of the target while being radiated by a single transversely Gaussian laser. In this scheme, two matched counterpropagating transversely Gaussian laser pulses, a main pulse and an auxiliary pulse, impinge on the foil target at the meantime. It is found that in the two-dimensional (2D) particle-in-cell (PIC) simulation, by the restraint of the auxiliary laser, the curve of the foil can be effectively suppressed. As a result, a high quality monoenergetic ion beam is generated through an efficient RPA of the foil target. For example, two counterpropagating transversely circularly polarized Gaussian lasers with normalized amplitudes ${a}_{1}=120$ and ${a}_{2}=30$, respectively, impinge on the foil target at the meantime, a 1.3 GeV monoenergetic proton beam with high collimation is obtained finally. Furthermore, the effects on the ions acceleration with different parameters of the auxiliary laser are also investigated.

Propagating stress-pulses and wiggling transition revealed in string dynamics

Understanding string dynamics yields insights into the intricate dynamic behaviors of various filamentary thin structures in nature and industry covering multiple length scales. In this work, we investigate the planar dynamics of a flexible string where one end is free and the other end is subject to transverse and longitudinal motions. Under transverse harmonic motion, we reveal the propagating pulse structure in the stress profile over the string, and analyze its role in bringing the system into a chaotic state. For a string where one end is under longitudinal uniform acceleration, we identify the wiggling transition, derive the analytical wiggling solution from the string equations, and present the phase diagram.

Research and Demonstration of the Refraction Problems

The introduction of function extremum promotes the development of calculus, which is the prerequisite and important condition for the development and development of many mathematical ideas. Except for extreme problems in social life or science and technology, the issue of cost in economic issues, the shortest distance in mathematics problem can be solved by the function extreme value thought. However, because the extreme value problem is not well described, learners cannot easily observe and learn. This paper takes the uniform speed and uniform acceleration and descent in the descent model as an example. In the uniform acceleration, the dichotomy is introduced to solve the function extremum problem. Through MATLAB simulation, the position of the steepest descent point is found intuitively and relevant conclusions are obtained. It is hoped that the research process of the problem can be helpful to the study of refractive problems, and it is hoped that the visually intuitive simulation results can enable learners to understand the descent model more objectively.

Thomas Precession by Uniform Acceleration and Gravity

Based on well known photometric rules for the number of galaxies as function of the distance in Mpc we model the so called "Great Wall" which is visible on the Cosmicflows-2 catalog. The gravitational field is evaluated at the light of the shell theorem and a finite value for the gravitational field is numerically derived.

Design of third-order uniform acceleration and deceleration trajectory based on Simulink StateFlow

In order to improve the movement accuracy of the robot, let the movement of the robot trajectory smoother, we design a third-order uniform acceleration / deceleration trajectory based on the Jerk value. Through the establishment of the mathematical model of the trajectory, combined with the logic control algorithm, constituted the core of the trajectory control. Finally, the StateFlow toolbox in Simulink as the carrier. Using the state module in StateFlow combined with the logic control conversion module, the third-order uniform acceleration and deceleration trajectory design is realized.