Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

Bose-Einstein condensation and the glassy state

The distinction between a classical glass and a classical liquid is difficult, since both are disordered. The difference is in the fact that a glass is frozen while the liquid is not. In this Letter an equilibrium measure is suggested that distinguishes between a glass and a liquid. The choice of this measure is based on the idea that in a system which is not frozen symmetry under permutation of particles is physically relevant, because particles can be permuted by actual physical motion. This is not the case in a frozen system. In this Letter it is shown how to generalize naturally the quantum mechanical concept of Bose condensed fraction to classical systems in order to distinguish between the glass and the liquid. It is finite in the liquid and zero in the frozen state. The actual value of the condensed fraction in the liquid may serve also as a measure of the glassiness in the liquid.     

A Born scatterer in an acoustical waveguide

Scattering from a Born inhomogeneity in a homogeneous, acoustical waveguide is considered and results compared to the corresponding scattering in a homogeneous, unbounded medium. It is found that the Ewald sphere in the unbounded medium case is replaced by a Ewald "strip" in a waveguide, the strip consisting of many individual Ewald spheres embedded in a ball the radius of which is twice that of an individual sphere. The physics behind the Ewald strip is discussed along with the implications of waveguide Born data.     

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

The shape gradient of the least-squares objective functional in optimal shape design problems of radiative heat transfer

Optimal shape design problems of steady-state radiative heat transfer are considered. The optimal shape design problem (in the three-dimensional space) is formulated as an inverse one, i.e., in the form of an operator equation of the first kind with respect to a surface to be optimized. The operator equation is reduced to a minimization problem via a least-squares objective functional. The minimization problem has to be solved numerically. Gradient minimization methods need the gradient of a functional to be minimized. In this paper the shape gradient of the least-squares objective functional is derived with the help of the shape sensitivity analysis and adjoint problem method. In practice a surface to be optimized may be (or, most likely, is to be) given in a parametric form by a finite number of parameters. In this case the objective functional is, in fact, a function in a finite-dimensional space and the shape gradient becomes an ordinary gradient. The gradient of the objective functional, in the case that the surface to be optimized is given in a finite-parametric form, is derived from the shape gradient. A particular case, that a surface to be optimized is a “two-dimensional” polyhedral one, is considered. The technique, developed in the paper, is applied to a synthetic problem of designing a “two-dimensional” radiant enclosure.     

Relativity of quantum states in entanglement swapping

The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell test is performed. For an observer in the laboratory frame, a Bell violation is observed between the qubits with the swapped entanglement. In a moving frame, the order of the measurements is reversed, and a Bell violation is observed even though the particles are not entangled, directly or indirectly, or at any point in time. Although the measurement results are identical, the wavefunctions for the two frames are starkly different — one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that the maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both non-local and non-simultaneous aspects of entanglement.     

Gain calculation of a free-electron laser operating with a non-uniform ion-channel guide

Amplification of an electromagnetic wave by a free electron laser (FEL) with a helical wiggler and an ion channel with a periodically varying ion density is examined. The relativistic equation of motion for a single electron in the combined wiggler and the periodic ion-channel fields is solved and the classes of possible trajectories in this configuration are discussed. The gain equation for the FEL in the low-gain-per-pass limit is obtained by adding the effect of the periodic ion channel. Numerical calculation is employed to analyse the gain induced by the effects of the non-uniform ion density. The variation of gain with ion-channel density is demonstrated. It is shown that there is a gain enhancement for group I orbits in the presence of a non-uniform ion-channel but not in a uniform one. It is also shown that periodic ion-channel guiding is used to reach the maximum peak gain in a low ion-channel frequency (low ion density).     

Self-oscillations in a hybrid bistable optical device

The Van der Pol, Krylov-Bogoliubov method for self-oscillation calculations in nonlinear systems is applied to a piezoelectrically driven Fabry-Perot interferometer which is operated as a hybrid bistable optical device. It is shown that in cases where the time delay in the feedback signal cannot be ignored, or when a reactive element is inserted in the appropriate place in the electrical circuit, self-oscillation will result. Experiments in which a piezoelectric element serves as the basic component of a hybrid bistable device demonstrate that self-oscillation occurs with a frequency which is very near the piezoelement self-frequency.     

Acoustic streaming in a rotating fluid

Acoustic streaming theory is derived that is applicable to a fluid that is slow moving in a reference frame that rotates with a constant angular velocity omega. A simplified streaming equation is obtained for the special case in which the acoustic angular frequency omega is large relative to omega, and the change in fluid density due to rotation alone is negligible. For this special case it is shown that the "driving force" for the acoustic streaming is independent of omega. Thus, if no acoustic streaming is present in a fluid system that is stationary, then no steady-state acoustic streaming is predicted for a similar system that rotates with constant angular velocity. For a system in which acoustic streaming is present, the flow behavior depends on the relative magnitudes of the Coriolis forces and the viscous forces. If the Ekman number is large (that is, the viscous force dominates) then the predicted flow is identical to that which would exist in a stationary system. If, on the other hand, the Ekman number is small then the Coriolis force dominates and the component of flow in the direction of the axis of rotation can be much smaller in the rotating system than in a similar system at rest.     

The nature of oscillations of the crystallization front in a diluted binary melt during the initial transient process

The cause of oscillations of the crystallization rate of a binary melt that arise in the initial transient process and have been revealed earlier in numerical experiments is investigated theoretically. Within a simple time-dependent model of directed crystallization, the problem of impurity diffusion in the melt from which a crystal is drawn at constant rate is solved in a linear approximation. It is shown that, under certain conditions, the solution represents a superposition of two concentration waves, a traveling and a standing wave. The concept of a characteristic distance of directed crystallization of a binary melt is introduced. It is established that the nonmonotonic behavior of the crystallization rate during the initial transient process, in particular, its damped oscillations, is attributed to the accumulation of impurities in the melt that is excessive with respect to its distribution in the stationary regime. Impurities in the melt are accumulated excessively when the characteristic distance of directed crystallization starts to exceed the characteristic diffusion length of the impurity in the melt.     

The spectrometer for the GunLab experiment

The spectrometer for the GunLab experiment is described. This spectrometer incorporates a dipole magnet, a fluorescent screen, and a CCD camera and is designed to measure the momentum of electron beams in the range of 1–10 MeV/c with a resolution of 0.1%. If a transversely deflecting RF cavity is installed in front of the dipole magnet, one may investigate the longitudinal phase portrait of a beam. The spectrometer is distinctive in that a Hall sensor is placed in the magnetic field of the dipole magnet. This sensor allows one to accurately measure the magnetic field and, consequently, the momentum of an electron beam.     

Poisson brackets and the Feynman problem

A derivation of a pair of Maxwell equations which is based on the concept of a Poisson structure on a manifold is given. The idea is geometric in character, and is extended to a generalized algebra. The special case of the dynamics for a particle in a Yang-Mills field is obtained as a consequence of the generalized case.     

Velocity autocorrelations and viscosity renormalization in sheared granular flows

The decay of the velocity autocorrelation function in a sheared granular flow is analyzed in the limit where the wavelength of fluctuations is larger than the "conduction length," so that energy is a nonconserved variable. The decay of the velocity autocorrelation function is much faster than that in a fluid at equilibrium for which energy is a conserved variable. Specifically, the autocorrelation function in a sheared granular flow decays proportional to t-3 in 2D and t-9/2 in 3D, in contrast with the decay proportional to t-1 in 2D and t-3/2 in 3D for a fluid at equilibrium. The renormalization of the viscosity due to mode coupling is evaluated using this form of the decay of the autocorrelation function. It is found that the logarithmic divergence in the viscosity in 2D, and the divergence of the Burnett coefficients in 3D, which is characteristic of a fluid of elastic particles at equilibrium, is absent in a sheared granular flow.     

Trees at an Interface

A lattice tree at an interface between two solvents of different quality is examined as a model of a branched polymer at an interface. Existence of the free energy is shown, and the existence of critical lines in its phase diagram is proven. In particular, there is a line of first order transitions separating a positive phase from a negative phase (the tree being predominantly on either side of the interface in these phases), and a curve of localization–delocalization transitions which separate the delocalized positive and negative phases from a phase where the tree is localized at the interface. This model is generalized to a branched copolymer which is examined in a certain averaged quenched ensemble. Existence of a thermodynamic limit is shown for this model, and it is also shown that the model is self-averaging. Lastly, a model of branched polymers interacting with one another through a membrane is considered. The existence of a limiting free energy is shown, and it is demonstrated that if the interaction is strong enough, then the two branched polymers will adsorb on one another.     

Generalized Sasaki Projections and Riesz Ideals in Pseudoeffect Algebras

A noncommutative version of generalized Sasaki projections in pseudoeffect algebras is introduced. It is proved that an ideal in a pseudoeffect algebra is Riesz if and only if it is closed under the right and left Sasaki projections. In lattice ordered pseudoeffect algebras, it is shown that generalized Sasaki projections are one-element sets, and their explicit form is found. It is shown that if a supremum of a normal Riesz ideal in a lattice ordered pseudoeffect algebra exists, it is a central element. These results extend those obtained recently by Avallone and Vitolo for effect algebras.     

Fractal structure of the acoustic signal excited in a liquid by an unstable laser radiation

Thermooptical excitation of sound in a liquid by a laser radiation with a harmonically modulated intensity randomly distributed over the beam cross-section is considered. The processes are considered to be statistically homogeneous. It is assumed that the spatial spectrum of the intensity fluctuations in a laser beam is described by a power (fractal) law. It is demonstrated that the acoustic field in a liquid has a fractal structure.     

Moving load on a thick sandwich plate strip

This paper is concerned with the steady state response of a thick sandwich strip plate to a moving line load of constant magnitude. The problem is studied on the basis of a thick plate theory and the solution is obtained by applying the method of the complex Fourier transform. The effect on the plate response of increase of the core thickness is studied in detail. It is shown that a 20% increase in the total mass coming from an increase in core thickness is compensated by a 140% increase in the critical speed for which a resonance effect occurs in the system. This shows that the sandwich construction is effective in making the plate stable to lateral moving loads.     

On the fluctuation enhanced conductivity of a superconductor: The correct evaluation of the Maki graph

According to Maki, a particular diagram—the Maki graph—gives a contribution to the fluctuation enhanced conductivity of a superconductor which is infinite in the case of a thin film. It is shown that this result is spurious and that it is due to a breakdown of the standard Green function impurity technique. A new method is developed which is strictly based on the Boltzmann equation. It is shown that the temperature dependent contribution of the Maki graph to the conductivity is negligibly small in a dirty metal.     

A TB-Mode Accelerator

An accelerator is proposed in which a TE-mode wave is used to drive charged particles in contrast to the usual linear accelerators in which longitudinal electric fields or TM-mode waves are supposed to be utilized. The principle of the acceleration is based on the Vp × B acceleration of a dynamo force acceleration. That is, a charged particle trapped in a transverse wave feels a constant electric field (Faraday induction field) and subsequently is accelerated when an appropriate magnetic field is externally applied in the direction perpendicular to the wave propagation. A pair of dielectric plates is used to produce a slow TE mode. Discussions will be given on what the conditions of the particle trapping are and how to stabilize the particle orbit.     

Two-coordinate diffusion of optical beams by an acoustooptic Raman-Nath modulator based on a paratellurite crystal

Acoustooptic Raman-Nath diffraction by a standing acoustic wave in a paratellurite crystal is investigated. An acoustic line is made in the form of a polished cube and serves as a high-Q acoustic resonator. A slow shear wave is excited by a single piezoelectric transducer. Multiple lossless sound reflections lead to two-coordinate light diffusion. When the acoustic intensity introduced into the crystal is about 2 W/cm² at a sound frequency of 7 MHz, there appears a diffraction pattern in the form of a homogeneous light spot with a solid angle of about 0.5 sr. An explanation for the features of the acoustooptic interaction is given. It is shown that this type of diffraction is helpful in designing acoustooptic two-coordinate diffusers of light beams.