Sound waves in a liquid with polydisperse vapor–gas bubbles

A mathematical model is presented for the propagation of plane, spherical, and cylindrical sound waves in a liquid containing polydisperse vapor–gas bubbles with allowance for phase transitions. A system of integro-differential equations is constructed to describe perturbed motion of a two-phase mixture, and a dispersion relation is derived. An expression for equilibrium sound velocity is obtained for a gas–liquid or vapor–liquid mixture. The theoretical results agree well with the known experimental data. The dispersion curves obtained for the phase velocity and the attenuation coefficient in a mixture of water with vapor–gas bubbles are compared for various values of vapor concentration in the bubbles and various bubble distributions in size. The evolution of pressure pulses of plane and cylindrical waves is demonstrated for different values of the initial vapor concentration in bubbles. The calculated frequency dependence of the phase sound velocity in a mixture of water with vapor bubbles is compared with experimental data.     

Generalized Noether theorems in canonical formalism for field theories and their applications

A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained.     

A primitive-variable Riemann method for solution of the shallow water equations with wetting and drying

A Riemann flux that uses primitive variables rather than conserved variables is developed for the shallow water equations with nonuniform bathymetry. This primitive-variable flux is both conservative and well behaved at zero depth. The unstructured finite-volume discretization used is suitable for highly nonuniform grids that provide resolution of complex geometries and localized flow structures. A source-term discretization is derived for nonuniform bottom that balances the discrete flux integral both for still water and in dry regions. This primitive-variable formulation is uniformly valid in wet and dry regions with embedded wetting and drying fronts. A fully nonlinear implicit scheme and both nonlinear and time-linearized explicit schemes are developed for the time integration. The implicit scheme is solved by a parallel Newton-iterative algorithm with numerically computed flux Jacobians. A concise treatment of characteristic-variable boundary conditions with source terms is also given. Computed results obtained for the one-dimensional dam break on wet and dry beds and for normal-mode oscillations in a circular parabolic basin are in very close agreement with the analytical solutions. Other results for a forced breaking wave with friction interacting with a sloped bottom demonstrate a complex wave motion with wetting, drying and multiple interacting wave fronts. Finally, a highly nonuniform, coastline-conforming unstructured grid is used to demonstrate an unsteady simulation that models an artificial coastal flooding due to a forced wave entering the Gulf of Mexico.     

The formation of quantum images and their transformation and super-resolution reading

Images formed by light with suppressed photon fluctuations are interesting objects for studies with the aim of increasing their limiting information capacity and quality. This light in the sub-Poisson state can be prepared in a resonator filled with a medium with Kerr nonlinearity, in which self-phase modulation takes place. Spatially and temporally multimode light beams are studied and the production of spatial frequency spectra of suppressed photon fluctuations is described. The efficient operation regimes of the system are found. A particular schematic solution is described, which allows one to realize the potential possibilities laid in the formation of the squeezed states of light to a maximum degree during self-phase modulation in a resonator for the maximal suppression of amplitude quantum noises upon two-dimensional imaging. The efficiency of using light with suppressed quantum fluctuations for computer image processing is studied. An algorithm is described for interpreting measurements for increasing the resolution with respect to the geometrical resolution. A mathematical model that characterizes the measurement scheme is constructed and the problem of the image reconstruction is solved. The algorithm for the interpretation of images is verified. Conditions are found for the efficient application of sub-Poisson light for super-resolution imaging. It is found that the image should have a low contrast and be maximally transparent.     

Geometrical Form Factor Improvement for Receiving System of Infrared Lidar

Improvement of an infrared light detection and ranging (IR-lidar) system for a short range (0–1000 m) and with high resolution is studied to enhance a geometrical form factor. Theoretical modeling of Mie scattering echo signals agrees with the experimental results. Introduction of a lens in front of the detector is effective for increasing the geometrical form factor, and a significant improvement in the received signal intensity is achieved, especially for short-range measurements around 100 m. This is useful for the IR-lidar system with a detector diameter of less than 1 mm. In the theoretical model, a ray-tracing technique was applied and a transmitting laser beam with Gaussian profile was considered for better accuracy.     

Cross sections for the photodisintegration of a deuteron and neutron capture by a proton calculated for the case of nonlocal potential

The processes of deuteron photodisintegration by a gamma-quantum and the radiative capture of a neutron by a proton with the emission of a gamma-quantum are considered. Interaction between nucleons is described by a nonlocal potential of the Yamaguchi type but allowing for repulsion due to the nucleon cores. In contrast to other potentials, the Schroedinger equation is solved exactly for the proposed potential. The potential is more exactly defined in comparison with the previously obtained values for the parameters; information on this potential is important in solving certain fundamental problems in nuclear theory. The effective cross sections for photodisintegration of a deuteron and for radiative capture are computed. Calculations show that the proposed potential makes it possible to describe the photodisintegration processes quite accurately for intermediate (up to 20 MeV) energies. The cross section computed for radiative capture is in somewhat better agreement with experiment than is the same cross section determined for other potentials.     

AN ESTIMATOR-BASED SLIDING-MODE CONTROL FOR MANEUVERING A FLEXIBLE SPACECRAFT

An estimator-based sliding-mode controller (ESMC) is discussed for a linear stochastic system with a known disturbance and is utilized in a flexible spacecraft for the reduction of residual vibration while allowing natural deflection during operation. By converting the tracking problem into a regulator problem, the ESMC minimizes the expected value of the guadratic objective function composed of errors which always remain in the intersection of sliding hypersurfaces. For the numerical evaluation to take place in a flexible with a flexible spacecraft, a large slewing maneuver strategy is devised, with a tracking model for the nominal trajectory. A start-coast-stop strategy for an economical maneuver is employed in conjunction with the input shaping technique. The performance and efficacy of the proposed control scheme are illustrated with a comparison of different maneuvering strategies.     

Dielectric losses in heterogeneous systems

Analytic formulas are derived for the effective complex dielectric constant of a matrix system with Maxwell-Wagner losses. An approximate solution is given for a system of dielectrics with a single relaxation time. It is shown that this approximation is applicable to systems containing a semiconductor with blocking electrodes. The effect of spread in the dimensions of the semiconductor component on the frequency dependence of losses in a matrix system is discussed.     

A collapsing bubble in a fluid: a statistical mechanical approach

The first non-equilibrium statistical mechanical theory is presented for the mechanical and thermal behaviour of the collapse of a microsropically small bubble in a liquid. First the number density and temperature space-time profiles for the special case of weakly interacting particles, the perfect gas model, are obtained. This is then generalized to a model in which the motion of the molecules is characterized by a single finite diffusion constant. The results for the collapse of a small bubble in a typical fluid are compared with those recently obtained through computer simulation. The agreement with the simulation is remarkably good for the perfect gas model; very high temperatures, sufficient for sonoluminescence, appear in a simple and natural way. An unexpected conclusion is that the perfect gas model agrees better with computer simulation than the model characterized by a single bulk diffusion constant. This may be because the collapse of the bubble is controlled by the leading shell of the fluid where the fluid density is low.     

Wave-front reversal of multifrequency continuous emission by Bragg scattering from phase regular inhomogeneities

The possibility of wave-front reversal of continuous multifrequency emission with a wide line spectrum (in particular, emission of lasers operating on cascade vibrational-rotational transitions of diatomic molecules, e.g., HF or CO) is analyzed; the reversal is based on Bragg scattering from a spatial phase hologram that is recorded in a resonance-absorbing medium by emission with a frequency different from any of the reversed-signal frequencies. The mechanism of formation of a spatial phase hologram and the features of optical Bragg scattering on such structures are analyzed. It is shown that a scattered wave-front is complex conjugate to one of the waves recording the phase grating. An optical system for wave-front reversal is proposed and the Bragg scattering efficiency is estimated for a particular example. The analysis indicates that the proposed system does not exhibit frequency selectivity and is basically suitable for wave-front reversal of emission with a broad line spectrum. The main problem is to choose a medium with resonance absorption at the center of a multifrequency emission spectrum and with complete transparency for the reversed signal.     

On the sound field of a resilient disk in free space

Radiation characteristics are calculated for a circular planar sound source in free space with a uniform surface pressure distribution, which can be regarded as a freely suspended membrane with zero mass and stiffness. This idealized dipole source is shown to have closed form solutions for its far-field pressure response and radiation admittance. The latter is found to have a simple mathematical relationship with the radiation impedance of a rigid piston in an infinite baffle. Also, a single expansion is derived for the near-field pressure field, which degenerates to a closed form solution on the axis of symmetry. From the normal gradient of the surface pressure, the surface velocity is calculated. The near-field expression is then generalized to an arbitrary surface pressure distribution. It is shown how this can be used as a simplified solution for a rigid disk in free space or a more realistic sound source such as pre-tensioned membrane in free space with non-zero mass and a clamped rim.     

Quantum Nonlocality of Photon Pairs in Interference in a Mach-Zehnder Interferometer

Nonlocal character of entangled photon pairs generated in spontaneous parametric downconversion is demonstrated. One photon from a pair propagates through a Mach-Zehnder interferometer and is detected in coincidence-count measurement with its twin. Width of the coincidence-count interference pattern (measured for various values of path difference in the Mach-Zehnder interferometer) depends on spectral width of the twin as a result of entanglement of photons in a pair. The experimental setup is analyzed for a Gaussian spectral filter and a Fabry-Perot resonator. It is shown that nonlocal interference is much stronger for cw pumping in comparison with femtosecond pulsed pumping for values of parameters commonly used in spontaneous parametric downconversion experiments.     

A model for the operation of a laser-triggered vacuumlow-inductance switch

A new model for the operation of a laser-triggered vacuum switch utilizing a composite target pellet in the cathode is given along with supporting experimental results. It is shown that two separate mechanisms are responsible for the operation of the switch, namely, a thermal mechanism for the initial current flow and an ion regeneration mechanism for the current buildup. The current buildup is strongly dependent upon geometry, as is evident from the experiments with 3- and 1-mm apertures in the anode. The jitter time is primarily determined during current buildup and nearly independent of the laser energy. An ion regeneration mechanism is consistent with the experimental data for current buildup, and a thermal mechanism is consistent with the initial generation of current     

The magnetic susceptibilities of NO and OH

A non-isothermal kinetic equation for the distribution function of a sub-system weakly coupled to a bath is derived by modification of the analysis and assumptions of a previous paper [1]. The equation has the form of a generalized non-isothermal Fokker-Planck equation when it is linearized in thermodynamic gradients and only terms through second order in the coupling parameters are retained. Higher order terms in the coupling parameter do not diverge with time. The equation is compared with certain ‘exact’ model results of Ullersma and with the coherence time method. The equation is used to calculate a jump rate for diffusion of a harmonic particle weakly coupled to a lattice and it is found that the jump rate becomes independent of the mass of the particle for a heavy enough particle. The source of the discrepancy of this result with a similar calculation of Prigogine and Bak is indicated. The model of the jump rate is inappropriate for diffusion in a thermal gradient and more appropriate models of the jump are briefly considered. A brief comparison of the derivation of the kinetic equation with the Fano coherence time approximation is made and a difference is noted.     

Models of the Dynamics of Spatially Separated Broadband Electromagnetic Fields Interacting with Resonant Atoms

The Markov model of spontaneous emission of an atom localized in a spatial region with a broadband electromagnetic field with zero photon density is considered in the conditions of coupling of the electromagnetic field with the broadband field of a neighboring space. The evolution operator of the system and the kinetic equation for the atom are obtained. It is shown that the field coupling constant affects the rate of spontaneous emission of the atom, but is not manifested in the atomic frequency shift. The analytic expression for the radiative decay constant for the atom is found to be analogous in a certain sense to the expression for the decay constant for a singly excited localized ensemble of identical atoms in the conditions when the effect of stabilization of its excited state by the Stark interaction with the vacuum broadband electromagnetic field is manifested. The model is formulated based on quantum stochastic differential equations of the non- Wiener type and the generalized algebra of the Ito differential of quantum random processes.     

Dynamic response of circular plates in contact with a fluid subjected to general dynamic pressures on a fluid surface

This paper is concerned with a method for solving dynamic response problems of a circular plate in contact with a fluid whose surface is excited by general dynamic pressures. By utilizing the Fourier expansion and the Laplace transform methods, the expression for the dynamic response of displacement is obtained in a general form which is applicable to general dynamic pressures. As applications, numerical calculations have been carried out for three types of sinusoidal, trapezoidal and explosive pressures. The results obtained in a certain type of impact pressure are compared with the exact ones.     

Theory of frequency modulation spectroscopy of coherent dark resonances

The interaction of a three-level atom in the A configuration with a frequency-modulated (FM) field is analyzed theoretically for the first time. The two-frequency model for solving the problem of frequency modulation spectroscopy of coherent dark resonances is described and analyzed for a three-level A system. The effectiveness of the two-frequency model is demonstrated by comparing the results obtained using this model with the results of solving the exact problem of interaction of a A system with an FM field, which can be solved by the density matrix method. It is shown that the simple two-frequency model corresponds to the exact solution and is in qualitative agreement with experimental data.     

On the quark-antiquark potential at short distances

We investigate the static quark-antiquark potential up to distances of 8 lattice units for pure SU(2) gauge theory on lattices with anisotropic couplings. The action is the Wilson action with a coupling for time-like plaquettes which differs from those for space-like ones. Numerical simulations are performed in a large range of β The potential is obtained by fitting “cooled” Wilson loops with up to four exponential terms. An interpolation of the potentials by a sum of a perturbative term, a linear term and by lattice artifacts shows poor scaling in comparison with he isotropic case. If the coupling in the time-like region is reduced, the linear term is much smaller than in the isotropic case, and vice versa. Consequences for the bag picture for hadrons are discussed.     

Resonance oscillation damping of a scanning microscope probe by a near-surface viscous liquid layer

Viscous liquid layer motion between a probe with a tip shaped as a paraboloid of revolution and a surface is considered for semicontact-mode operation of a scanning probe microscope. The presence of a viscous liquid layer leads to energy dissipation and is one of the factors responsible for the decrease in the probe oscillation amplitude. The Reynolds equation for viscous liquid motion is used to obtain an analytic solution to the problem. The formula derived for the loss is compared with experimental data obtained for probes and layers with various curvature radii and viscosities.