Abelian Extensions of the Group of Diffeomorphisms of a Torus

In this Letter we construct Abelian extensions of the group of diffecomorphisms of a torus. We consider the Jacobian map, which is a crossed homomorphism from the group of diffeomorphisms into a toroidal gauge group. A pull-back under this map of an invariant central 2-cocycle on a gauge group turns out to be an Abelian cocycle on the group of diffeomorphisms. In the case of a circle we get an interpretation of the Virasoro–Bott cocycle as a pull-back of the Heisenberg cocycle. We also give an Abelian generalization of the Virasoro–Bott cocycle to the case of a manifold with a volume form.     

Rayleigh mechanism of local elevation of energy in propagation of a shock wave in an active medium

A mechanism of action of a shock wave on an active medium, which leads to an additional energy release source, is considered. This source moves together with the shock wave front and depends on the magnitude and direction of the electric field applied to the plasma and on the current density in the plasma. The study is a continuation of an earlier publication devoted to the propagation of weak shock waves. Here, we consider shock waves of an arbitrary intensity with an arbitrary mechanism of formation of an additional energy contribution due to variation of the parameters of the medium as a result of passage of the shock wave. Special cases of this effect are the propagation of a shock wave in a plasma and detonation burning.     

Discrete dislocation simulation of nanoindentation: the influence of obstacles and a limited number of dislocation sources

Nanoindentation is simulated on the computer by means of a 2D discrete dislocation model under the conditions of a constrained geometry. First, an indentation test near a grain boundary is investigated by the arrangement of only one boundary and second, an indentation test into the center of the surface of a small grain (lamella) is mimicked by the arrangement of two boundaries. The effect of a limited number of dislocation sources is studied by the simulations of an indentation test in a plastically deformable film on an ideal elastic substrate and by such tests on an ideal elastic film on a plastically deformable substrate. The discrete nature of plasticity is shown to have a significant influence on the mechanical material behavior in all our investigations.     

A mathematical characterization of the physical structure of observers

It is proposed that the physical structure of an observer in quantum mechanics is constituted by a pattern of elementary localized switching events. A key preliminary step in giving mathematical expression to this proposal is the introduction of an equivalence relation on sequences of spacetime sets which relates a sequence to any other sequence to which it can be deformed without change of causal arrangement. This allows an individual observer to be associated with a finite structure. The identification of suitable switching events in the human brain is discussed. A definition is given for the sets of sequences of quantum states which such an observer could occupy. Finally, by providing an a priori probability for such sets, the definitions are incorporated into a complete mathematical framework for a many-worlds interpretation. At a less ambitious level, the paper can be read as an exploration of some of the technical and conceptual difficulties involved in constructing such a framework.     

Amplification of entangled states of squeezed light

Two amplification schemes are considered for entangled squeezed states of light, including an Einstein-Podolsky-Rosen entangled state of continuous variables (EPR pair): propagation in a nonlinear medium and reflection from a cavity. Both schemes make use of a parametric process that can be implemented in a periodic nonlinear medium. The existence of an integral of motion makes it possible to amplify an entangled state of light while preserving the initial entanglement. To analyze the cavity-based scheme, a master equation is derived for the density matrix of the field inside the cavity. The feasibility of amplification that preserves entanglement of an EPR pair is demonstrated for this scheme.     

Optics of oblique meridional and nonmeridional rays of a conicoid

Based on the exact expression for the angular eikonal of an axisymmetric conicoid (a surface formed by revolution of a second-order curve, or conic) the expressions for the Gaussian optics of oblique meridional rays are obtained, which differ from the well-known Gullstrand-Young invariants for a sphere by a set of independent arguments and contain explicitly the parameters of an optical system. The collinear properties of an optical surface with oblique meridional beams are studied. The theory of astigmatism is extended to the case of oblique nonmeridional rays, which makes it possible to construct and analyze in the first approximation the focal surfaces of an actual wide beam of rays. The theory is tested using the example of optimization of an aplanatic lens for the case of an off-axis point of an object. Based on the exact expression for the angular eikonal, definitions of integral aberrations are given. It is proposed to use the method developed in optimization of optical systems.     

Quotients of interval effect algebras

Nearly every orthostructure that has been proposed as a model for a logic of propositions affiliated with a physical system can be represented as an interval effect algebra; that is, as the partial algebra under addition of an interval from zero to an order unit in a partially ordered Abelian group. If the system is in a state that precludes certain elements of such an interval, an appropriate quotient interval algebra can be constructed by factoring out the order-convex subgroup generated by the precluded elements. In this paper we launch a study of the resulting quotient effect algebras.     

On the possibility of laboratory shock wave studies of the equation of state of a material at gigabar pressures with beams of laser-accelerated particles

The possibility of laboratory shock wave studies of the equation of state of a material with beams of laser-accelerated charged particles at pressures an order of magnitude higher than those reached in current experiments has been discussed. The possibility of the generation of a plane quasistationary shock wave with a pressure of several gigabars behind its front at the irradiation of a target by a laser beam with an energy of several kilojoules and an intensity of about 10¹⁷ W/cm², which is accompanied by the generation of fast electrons with an average energy of 20–50 keV, has been justified.     

Investigation of pressure characteristics of a perforated membrane in an oscillating liquid flow

Results of a parametric study of pressure characteristics of a perforated membrane in an oscillating liquid flow are reported. A diagram of an experimental facility for evaluation of the pressure produced by a perforated membrane in an oscillating flow is given.     

New mechanism of formation of virtual surface magnetic polaritons

By using an easy-axis antiferromagnetic material as an example, the conditions are found under the fulfillment of which, the quadratic magneto-optical interaction in an external dc electric field perpendicular to the easy axis gives rise to the formation of a new type of virtual surface magnetic TM polaritons at the interface both between an antiferromagnet and an ideal metal and between an antiferromagnet and vacuum.     

Anti-inertial lift in foams: a signature of the elasticity of complex fluids

To understand the mechanics of a complex fluid such as a foam we propose a model experiment (a bidimensional flow around an obstacle) for which an external sollicitation is applied, and a local response is measured, simultaneously. We observe that an asymmetric obstacle (cambered airfoil profile) experiences a downwards lift, opposite to the lift usually known (in a different context) in aerodynamics. Correlations of velocity, deformations, and pressure fields yield a clear explanation of this inverse lift, involving the elasticity of the foam. We argue that such an inverse lift is likely common to complex fluids with elasticity.     

Anomalous behavior of the coefficient of normal restitution in oblique impact

The coefficient of normal restitution in an oblique impact is theoretically studied. Using a two-dimensional lattice model for an elastic disk and an elastic wall, we demonstrate that the coefficient of normal restitution can exceed unity and has a peak against the incident angle in our simulation. We also explain this behavior based upon a phenomenological theory.     

Diffraction of sound by an elastic cylinder near the surface of an elastic halfspace

Diffraction of an acoustic wave by an elastic cylinder near the surface of an elastic halfspace is considered. The solution relies on a Helmholtz-type integral equation and uses the Green function of an elastic halfspace. The latter function is represented in the form of an integral over the Sommerfeld contour on the plane of a complex variable that has the meaning of the angle of the wave incidence on the halfspace boundary. An integral equation for the sound pressure distribution over the cylinder surface is derived. This equation is reduced to an infinite system of equations for the Fourier-series expansion coefficients of this distribution. The results obtained are valid for the diffraction of a cylindrical wave and a plane wave. They also describe the diffraction of a spherical wave when the transmitter and receiver are far from the cylinder and lie in one plane that is orthogonal to the cylinder axis.     

Dynamics of a circular array of liquid columns

We report on an experimental study of an array of liquid columns, hanging below an overflowing circular dish fed at a constant flow-rate. This one-dimensional pattern exhibits spatio-temporal chaos as well as a host of ordered dynamical regimes, depending on flow-rate, initial positions, number of columns, and liquid properties. In this paper, we present stability diagrams obtained with liquids of different properties and an extensive quantitative study of the ordered, predictable dynamical states. Some destabilization mechanisms of these regimes are also presented.     

Influence of the heat loss intensity on the characteristics of the filtration combustion of solid organic fuels

The effect of lateral heat loss on the characteristics of the filtration combustion of solid organic fuels is studied experimentally and theoretically. The results show that, for an reaction trailing, an increase in the heat loss intensity leads to a marked reduction in the combustion temperature and an increase in the temperature at which fuel pyrolysis is complete, with the yield of liquid pyrolysis products remaining practically unchanged. For a reaction leading, an increase in the heat transfer coefficient causes a reduction in the combustion temperature and the yield of liquid pyrolysis products.     

A theoretical study of the vibration and acoustics of ancient Chinese bells

In this paper, the acoustics of an ancient Chinese bell, which was made some 3000 years B.C., is studied theoretically. In ancient times, a set of the bells was used as a musical instrument. Unlike a western church bell and an ancient Indian bell, an ancient Chinese bell has two interesting acoustics. First, two tones can be heard separately as the bell is struck at two special points. The interval between the two pitches is always a minor or major third. Second, tones of the bell attenuate quickly, which is necessary for a musical instrument. So, an ancient Chinese bell is sometimes called a two-tone bell or a music bell. Although a three-dimensional model should be used to simulate the acoustics of the bell, a simplified model proposed in this paper does give some insight. Based on the lens-shaped cross section of an ancient Chinese bell, two tones of an ancient Chinese bell can be simulated by the vibration of a double-circular arch and the quick attenuation of tones can be simulated by acoustics of a cylinder with the lens-shaped cross section like a double-circular arch. Numerical results on the vibration and acoustics of the models are presented.     

Analysis of aberrations of an image formed by a system of noncentered optical surfaces

In the general case of an arbitrary arrangement of optical surfaces in space, it is proposed to take a straight line passing through the center of the entrance pupil perpendicularly to its plane as an assembly base. The coordinates of a point in the object plane and in the entrance pupil plane uniquely determine the position of the incident ray in the space. The wave aberration in the image of a point is represented by a power series of the general form as a function of these coordinates with terms of up to the fourth order. Aberrational analysis of individual components of this series is carried out. A particular case of decentering of an individual component in an axially symmetric optical system is considered. A new kind of aberration is shown to appear in this case.     

Deformation of Si under conditions of the combined influence of an electric current and a magnetic field

Changes in the physical and mechanical properties of single crystals of n- and p-type silicon are investigated under the combined influence of a constant electric current and a magnetic field and an electric current separately. There is a slight increase in the resistivity of Si as pressure is applied. Increased resistance to compressive deformation is observed under the combined influence of a magnetic field and an electric cur- rent during compression, while increased plasticity is seen under the sole influence of an electric current for p-Si samples. There is an opposite effect for samples of n-Si. Increased plasticity is observed under the combined influence of a magnetic field and an electric current during compression, while increased strength is seen under the sole influence of an electric current. Surface microstructures of deformed samples are studied. A possible physical explanation for the observed phenomena is proposed.     

Nanoscale displacement of the image of an atomic source of radiation

Light emitted by an atomic source of radiation appears to travel along a straight line （ray） from the location of the source to the observer in the far field. However, when the energy flow pattern of the radiation is resolved with an accuracy better than an optical wavelength, it turns out that the field lines are usually curved. We consider electric dipole radiation, a prime example of which is the radiation emitted by an atom during an electronic transition, and we show that the field lines of energy flow are in general curves. Near the location of the dipole, the field lines exhibit a vortex structure, and in the far field they approach a straight line. The spatial extension of the vortex in the optical near field is of nanoscale dimension. Due to the rotation of the field lines near the source, the asymptotic limit of a field line is not exactly in the radially outward direction and as a consequence, the image in the far field is slightly shifted. This sub-wavelength displacement of the image of the source should be amenable to experimental observation with contemporary nanoscale-precision techniques.