Diffusion over a saddle with a langevin equation

The diffusion problem over a saddle is studied using a multidimensional Langevin equation. An analytical solution is derived for a quadratic potential and the probability to pass over the barrier deduced. A very simple solution is given for the one-dimensional problem and a general scheme is shown for higher dimensions.     

Intermodulation in a microwave resonator with a high-temperature superconductor

Intermodulation, or the generation of a combination-frequency signal, is studied theoretically in the case where the nonlinearity is provided by a high-temperature superconductor placed in a microwave resonator. A general formula that relates the power of an intermodulation signal to the electromagnetic performance of the resonator, the physical parameters of the superconductor, and the intensity of pump waves is derived. A parameter that characterizes the nonlinearity is evaluated from data available from the literature. The potentialities of various resonators for the microwave characterization of the nonlinearities in high-temperature superconductors are assessed.     

Evolution of a Cosmological Model with Rotation with a Bianchi Type-Ix Metric

Russian Physics Journal - A cosmological model with expansion and rotation with a Bianchi Type-IX metric is constructed. The model describes the Friedmann stage of evolution of the Universe with...     

Bistability in a hyperchaotic system with a line equilibrium

A hyperchaotic system with an infinite line of equilibrium points is described. A criterion is proposed for quantifying the hyperchaos, and the position in the three-dimensional parameter space where the hyperchaos is largest is determined. In the vicinity of this point, different dynamics are observed including periodicity, quasi-periodicity, chaos, and hyperchaos. Under some conditions, the system has a unique bistable behavior, characterized by a symmetric pair of coexisting limit cycles that undergo period doubling, forming a symmetric pair of strange attractors that merge into a single symmetric chaotic attractor that then becomes hyperchaotic. The system was implemented as an electronic circuit whose behavior confirms the numerical predictions.     

Transition from a state with a certain momentum into a state with a certain parameter of spinless particle escape in the external field

A distribution function on the parameter of escape of particle B with the amplitude of process A → B in the external stationary field is investigated in this work. This distribution function is directly related to the form factor of the external-field source. By way of illustration consideration has been given to a hydrogen-like atom. It is shown that the distribution into the forward hemisphere comprises information on the spatial structure of an electron cloud, while the distribution into the backward hemisphere reproduces a spatial structure in the vicinity of a nucleus.     

Oscillator with a centrifugal barrier

We study the wave functions and energy levels of a one-dimensional oscillator with a centrifugal barrier of the form s(s+1)/x². It is shown that a barrier of this kind automatically implies the point potential A(s)(x)/x. It is also shown that two different sets of even states are physically admissible, but that only one of these sets transforms continuously into the set of states of harmonic oscillator when the centrifugal barrier is allowed to vanish and is preferable for this reason.Translated from Izvestiya Vysshkh Uchebnykh Zavedenii, Fizika, No. 5, pp. 35–39, May, 1987.The authors acknowledge useful discussions with B. M. Bolotovskii, B. A. Lysov, and O. A. Khrustalev.     

Band-rejection filter based on a Bragg fiber with a defect layer

<正>A novel band-rejection filter based on a Bragg fiber with a defect layer is proposed.A defect layer is introduced in the periodic high/low index layers in the cladding of the Bragg fiber,which results in large confinement loss for some resonant wavelengths inside the band gap range of the Bragg fiber.A segment of the Bragg fiber with a defect layer can be used as a band-rejection filter,whose characteristics are mainly determined by the structure of the Bragg fiber.The simulation results show that the bandwidth of such a band-rejection filter is dependent on the number of the periodic high/low index layers in both sides of the defect layer in the cladding of the Bragg fiber.     

Hadronic jets associated with a photon trigger

We consider, within Quantum Chromodynamics, the fragmentation function of a quark into a hadron and a photon. A simple analytic expression is given which is adequate for practical applications. A measurable quantity is proposed, which is independent of the hadronization process and tests the underlying dynamics.     

Dimers on a Simple-Quartic Net with a Vacancy

A seminal milestone in lattice statistics is the exact solution of the enumeration of dimers on a simple-quartic net obtained by Fisher, Kasteleyn, and Temperley (FKT) in 1961. An outstanding related and yet unsolved problem is the enumeration of dimers on a net with vacant sites. Here we consider this vacant-site problem with a single vacancy occurring at certain specific sites on the boundary of a simple-quartic net. First, using a bijection between dimer and spanning tree configurations due to Temperley, Kenyon, Propp, and Wilson, we establish that the dimer generating function is independent of the location of the vacancy, and deduce a closed-form expression for the generating function. We next carry out finite-size analyses of this solution as well as that of the FKT solution. Our analyses lead to a logarithmic correction term in the large-size expansion for the vacancy problem with free boundary conditions. A concrete example exhibiting this difference is given. We also find the central charge c=–2 in the language of conformal field theory for the vacancy problem, as versus the value c=1 when there is no vacancy.     

Charmonium spectrum with a generalized Fermi-Breit equation

A recently derived Fermi-Breit equation for a non-Coulombic vector interaction is used to construct a specific model for the charmonium spectrum. A scalar interaction term is also considered. Momentum-dependent terms, generated by the requirement of relativistic covariance, are included in the model.     

Microgeon with a Kerr metric

The structure of electromagnetic and gravitational fields near the singular ring of the Kerr metric is analyzed. An approximate joint solution of the system of Maxwell-Einstein equations is given for a metric with the parameters of an electron; this solution describes a microgeon, a model of an electron. A new interpretation of the two-sheet nature of the Kerr metric is given.     

Propagation characteristics of a circular waveguide filled with a chiroferrite medium

A chiroferrite is made from chiral objects immersed in a magnetically biased ferrite. A waveguide including a chiroferrite is anticipated to possess some novel features due to the presence of chirality in combination with anisotropy. In this paper, the propagation characteristics of a circular metal waveguide filled with a chiroferrite medium are investigated by an analytical procedure. The equations of relations between the transverse components and the longitudinal ones of electromagnetic fields in general chiroferrite waveguides are derived in a cylindrical coordinate system. The coupled wave equations for the longitudinal electric and magnetic fields are decoupled into two Helmholtz equations which are then solved analytically. The characteristic equation is formulated for the circular chiroferrite waveguide. Propagation constants varying with the structural and material parameters have been calculated for several lower chiral modes. A number of interesting features have been revealed by the numerical results.     

Interaction of a moving atom with a metal

A calculation of the energy losses and their fluctuations for a neutral or partially charged atom in motion in a solid is carried out.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 86–90, July, 1990.     

Triggering of a spark gap with a low-power laser

A spark gap is triggered by injection of electrons due to heating of the cathode with a single-mode Nd-YAG laser of relatively low power.     

Activated drift motion of a classical particle with a dynamical pinning effect

A one dimensional trap model for a thermally activated classical particle is introduced to simulate driven dynamics in presence of “ageing” effects. The depth of each trap increases with the time elapsed since the particle has fallen into it. The consequences of this dynamical pinning are studied, and velocity-force characteristics are numerically obtained. A special attention is paid to the situation where the particle is pulled with a spring to ensure a finite average velocity. In the low velocity regime, the presence of a broad distribution of trapping times leads to suppression of linear response, replaced by a threshold or by sublinear dynamics. A regime of strong fluctuations is obtained when the particle is driven at intermediate velocities. Received: 12 December 1997 / Accepted: 25 February 1998     

Discrete model of a dynamo with diffusion

A model of magnetic field generation by the turbulent motions of a highly conducting fluid is constructed. It is assumed that the field is generated in individual cells of space in a statistically independent manner. A coupling between the cells is realized by magnetic diffusion. The rates of growth of the field and its moments are calculated. The field distribution generated by this mechanism possesses an intermittent nature in both time and space.     

Emissivity of a multibeam electron gun with a glassy carbon field-emission cathode

A multibeam triode electron gun with a glassy carbon field-emission cathode that is intended for an O-type microwave amplifier is studied. The electric field strength and the current density at the microtips versus the distance to the center of a cell of the cathode–grid unit are calculated. Calculation data are compared with experimental results. It is shown that about 70% of the cathode current in each cell is accounted for by microtips arranged in a circumferential ring no wider than 20 μm. The field-emission current density inside the ring exceeds 40 A/cm², and the current per microtip equals 43.1 μA.     

Narrow-wavelength-spread spectral combining laser with a reflector for a double pass with a single grating

We proposed a novel wavelength-spread compression technique for spectral beam combining of a diode laser array. A reflector, which is parallel to the grating, is introduced to achieve a double pass with a single grating.This facilitated the reduction of the wavelength spread by half and doubled the number of combined elements in the gain range of the diode laser. We achieved a power of 26.1 W under continuous wave operation using a19 element single bar with a wavelength spread of 6.3 nm, which is nearly half of the original wavelength spread of 14.2 nm, demonstrating the double-compressed spectrum capability of this structure. The spectral beam combining efficiency was 63.7%. The grating efficiency and reflector reflectance were both over 95%; hence, the efficiency loss of the double-pass grating with a reflector is acceptable. In contrast to double-grating methods,the proposed method introduces a reflector that efficiently uses the single grating and shows significant potential for a more efficient spectral beam combining of diode laser arrays.     

Vortex solutions with a smooth core

A Yang-Mills field is used to smooth over the core of a vortex solution.     

Contact problem with wear for a foundation with a surface nonuniform coating

The plane contact problem with wear for an elastic foundation with a longitudinally nonuniform (surface nonuniform) coating and a rigid punch with a flat foundation has been solved for the first time. The case of linear wear is considered. The nonuniformity of the coating is described by a rapidly changing function. This strong nonuniformity arises when coatings are deposited using modern additive manufacturing technologies. The problem is reduced to the solution of an integral equation with two different integral operators: a compact self-adjoint positively defined operator with respect to the coordinate and the non-selfadjoint integral Volterra operator with respect to time. The solution is obtained in series using author’s projection method. The efficiency of the proposed approach for constructing a high-accuracy approximate solution to the problem (with only a few expansion terms retained) is demonstrated. A simple engineering formula for estimating the contact stresses under a punch for large values of times is proposed.