Magnetization structure of a Bloch point singularity

Switching of magnetic vortex cores involves a topological transition characterized by the presence of a magnetization singularity, a point where the magnetization vanishes (Bloch point). We analytically derive the shape of the Bloch point that is an extremum of the free energy with exchange, dipolar and Landau terms. From a one parameter family of solutions, two types of singularities are distinguished, a radial one (hedgehog) corresponding to a local energy maximum, and a twisted one corresponding to a local energy minimum. Micromagnetic simulations show that the hedgehog magnetization naturally evolves to a twisted one if the size of the ferromagnet is much larger than the exchange length.     

The Kerr space-time near the ring singularity

We investigate the geometry of the Kerr space-time near the ring singularity. A systematic study of the mathematical and physical structure of this region reveals that the singularity in the Kerr space-time is naturally understood in terms of a subset of the immersion of the set defined byr=0 (in Boyer-Lindquist coordinates) in the Kerr space-time. It is well known that the Kerr space-time is not a differentiable manifold (due to the curvature singularity) or a topological manifold, but a well defined topological space with a structure that is manifested by the constrast in taking limits along the hypersurface atr=0 and the equatorial plane which approach singularity. We find that the ring singularity is either an edge or a self-intersection of the topological space depending on which extension of the metric throughr=0 is implemented. A major result of this analysis is the extrapolation to the general accelerating case of Carter's proof that the only nonspacelike geodesics which can reach the ring singularity are restricted to the equatorial plane. For finite magnitudes of proper acceleration, it is shown that only lightlike trajectories that asymptotically approach the null generator of the ring singularity can reach it from above or below the equatorial plane.     

The decay of an unstable equilibrium state near a “critical point”

We show that it is possible to understand the decay of an unstable equilibrium state on the basis of a simple “short-time approximation scheme”. The theory gives meaningful results also near the instability point in the space of parameters associated with the deterministic force acting on our system.     

A doubly-confocal unstable ring resonator

An unstable ring resonator made by two positive lenses having their two foci in common is discussed and studied. This laser yields quasi-travelling-wave operation with a very high ratio of the powers of the two opposite rotating waves (about 400), and is suitable for mode-locking or Q-switching.     

Focusators into a ring

Using numerical and analytical approaches, we have computed the optical elements (focusators) required for focusing laser light into a narrow ring, a wide ring and a set of rings. A numerical comparison of the various computational techniques is reported. Finally the operation of a fabricated rotor axicon to focus light into a ring is reported.     

Front propagation into an unstable state of reaction-transport systems

We studied the propagation of traveling fronts into an unstable state of the reaction-transport systems involving integral transport. By using a hyperbolic scaling procedure and singular perturbation techniques, we determined a Hamiltonian structure of reaction-transport equations. This structure allowed us to derive asymptotic formulas for the propagation rate of a reaction front. We showed that the macroscopic dynamics of the front are "nonuniversal" and depend on the choice of the underlying random walk model for the microscopic transport process.     

Shearograms of an optical phase singularity

Shearograms are known to represent phase gradients but when vortices are present in the optical field, these do not represent true phase gradients. Phase gradients of an optical phase singularity are presented. A lateral shear interferometer is used for obtaining shearograms of optical fields with vortices. A diffractive phase element is used to generate vortices. It is shown that shearograms can be used in the detection of optical vortices. Shearogram of speckle field is also presented.     

Sink flow deforms the interface between a viscous liquid and air into a tip singularity

In our experiment, an interface between a viscous liquid and air is deformed by a sink flow of constant flow rate to form a sharp tip. Using a microscope, the interface shape is recorded down to a tip size of 1 microm. The curvature at the tip is controlled by the distance h between the tip and the sink. As a critical distance h*is approached, the curvature diverges like 1/(h-h*)3and the tip becomes cone shaped. As the distance to the sink is decreased further, the opening angle of the cone vanishes like h2. No evidence for air entrainment was found, except when the tip was inside the orifice.     

Models of an open universe with a variable equation of state near a singularity

A new approach is discussed for reducing the problem of integration of the Einstein equations for a conformally flat model of an open universe to integration of Newton's equation for the one-dimensional motion of a plate of unit mass in a certain potential field. Exact solutions are obtained with an equation of state that depends on the point in the space—time continuum. Finite values of the metric, pressure, and energy density are obtained at the initial world point for a definite choice of potential in Newton's equation. It is shown that a smooth transition to the stage of the evolution of the universe is possible with the appropriate choice of potential and parameters.This work has been carried out under the auspices of the Astronomiya Joint Scientific-Technical Program.State University, Krasnoyarsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 51–55, July, 1994.     

Brane decay and an initial spacelike singularity

We present a novel string theory scenario where matter in a spacetime originates from a decaying brane at the origin of time. The decay could be considered as a big-bang-like event at X0=0. The closed string interpretation is a time-dependent spacetime with a semi-infinite time direction, with the initial energy of the brane converted into energy flux from the origin. The open string interpretation can be viewed as a string theoretic nonsingular initial condition.     

Scalar Green's functions in an Euclidean space with a conical-type line singularity

In an Euclidean space with a conical-type line singularity, we determine the Green's function for a charged massive scalar field interacting with a magnetic flux running through the line singularity. We give an integral expression of the Green's function and a local form in the neighbourhood of the point source, where it is the sum of the usual Green's function in Euclidean space and a regular term. As an application, we derive the vacuum energy-momentum tensor in the massless case for an arbitrary magnetic flux.Supported by a grant from CNPq (Brazilian government agency FA)     

Quantum evaporation of a naked singularity

We investigate here quantum effects in gravitational collapse of a scalar field model which classically leads to a naked singularity. We show that nonperturbative semiclassical modifications near the singularity, based on loop quantum gravity, give rise to a strong outward flux of energy. This leads to the dissolution of the collapsing cloud before the singularity can form. Quantum gravitational effects thus censor naked singularities by avoiding their formation. Further, quantum gravity induced mass flux has a distinct feature which may lead to a novel observable signature in astrophysical bursts.     

Complex singularity of a stokes wave

Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave propagating with the constant velocity. The increase in the scaled wave height H/λ from the linear limit H/λ = 0 to the critical value H _max/λ marks the transition from the limit of almost linear wave to a strongly nonlinear limiting Stokes wave. Here, H is the wave height and λ is the wavelength. We simulated fully nonlinear Euler equations, reformulated in terms of conformal variables, to find Stokes waves for different wave heights. Analyzing spectra of these solutions we found in conformal variables, at each Stokes wave height, the distance ν _c from the lowest singularity in the upper half-plane to the real line which corresponds to the fluid free surface. We also identified that this singularity is the square-root branch point. The limiting Stokes wave emerges as the singularity reaches the fluid surface. From the analysis of data for ν _c → 0 we suggest a new power law scaling ν _c ∝ (H _max ? H)^3/2 as well as new estimate H _max/λ ? 0.1410633.     

Single-slit diffraction of an optical beam with phase singularity

Single-slit diffraction of an optical beam carrying phase singularity is presented. Due to azimuthal phase dependence, the diffraction pattern of the singular beam differs from that of a plane wave. The fringes in the diffraction pattern of singular beam undergo continuous bending, while passing through the centre of the pattern and exhibit left to right or right to left shift, depending on the sign of the topological charge of singular beam. It is shown that diffraction of a singular beam through a slit can be used to determine magnitude and sign of its topological charge.     

A scalar polynomial singularity without an event horizon

It is shown that the solution of the field equations for a static spherically symmetric scalar field has a scalar polynomial singularity and no event horizon. The solution does not develop from nonsingular data on any Cauchy surface. The possible existence of a universal scalar field, the conformal diagram and geodesies of the solution, and the energy and momentum of the field present are discussed.     

Orbital classical solutions,non-perturbative phenomena and singularity at the zero coupling constant point

We try to extend previous arguments on orbital classical solutions in non-relativistic quantum mechanics to the $\text{1}\text{4}\text{λ|φ|}{}^4$ complex relativistic field theory. The single valuedness of the Green function in the semiclassical $\text{(}\text{h}\text{?}\text{→ 0)}$ limit leads to a Bohr-Sommerfeld quantization. A path integral formalism for the Green functions analogous to that in non-relativistic quantum mechanics is employed and a semiclassical approach which uses our classical solutions indicates non-perturbative effects. They reflect and $\text{e}{}^{\mathrm{<mtext>1</mtext><mtext>\lambda </mtext>}}$ singularity at the zero coupling constant point.     

带抗共振环的非稳腔对撞脉冲锁模Nd:YAP(Nd:YAL0_3)激光器

本文报道用Nd:YAP (Nd:YALO_3)激光介质在带抗共振环的平-凸非稳腔结构中,选用五甲川-1,2-二氯乙烷染料,实现对撞脉冲被动锁模,获得良好锁模脉冲波形的实验结果.在1Hz的重复频率下,锁模脉冲平均脉宽<10ps,输出脉冲系列平均能量80mJ,脉冲系列能量集中于中央的三个脉冲,锁模成功率100%.输出能量稳定性80±4mJ.     

On the behavior of an oscillator clock near the singularity of a gravitational field

In 1975 Møller tried to show that the general relativistic concept of standard time or proper time would lose its physical meaning in the vicinity of singularities of a gravitational field [1]. His treatment of a classical harmonic oscillator clock falling into a singularity is checked in the present paper and is found to be insufficient to prove the above statement. A relativistic clock model is given to ensure the reasonable physical meaning of proper time.