Probability of the occurrence of freak waves

The statistics of the occurrence of freak waves on a surface of an ideal heavy liquid is studied. The freak (rogue, extreme) waves arise in the course of evolution of a statistically homogeneous random Gaussian wave field. The mean steepness of initial data varies from small (μ² = 1.54 × 10⁻³) to moderate (μ² = 3.08 × 10⁻³) values. The frequency of the occurrence of extreme waves decreases with an increase in the spectral width of the initial distribution, but remains relatively high even for broad spectra (Δ _k /Δ ∼ 1).     

Electron-impact excitation of the S°, P°, and D° doublet levels of cobalt atoms

The excitation of transitions from the ² S ^∘, ² P ^∘, and ² D ^∘ levels of the cobalt atom is studied by the method of extended crossing beams. Seventy-six excitation cross sections are measured at an exciting electron energy of 50 eV. Nine optical excitation functions are recorded in the electron energy region of 0–200 eV. Possible channels of excitation of levels under study are discussed.     

The influence of surface roughness in X-ray resonant magnetic reflectivity experiments

We present simulations of X-ray resonant magnetic reflectivity (XRMR) spectra of the surface magnetic dead layer in La_1−x Sr _x MnO₃ (LSMO) films that take in account the effect of different forms of roughness that can be encountered experimentally. The results demonstrate a method to distinguish between surface (morphological) roughness, and two generic kinds of magnetic roughness at the buried interface between the surface dead layer and the fully magnetic bulk part of the film. We show that the XRMR technique can distinguish between different types of magnetic roughness at the dead layer/bulk interface only if the sample surface is nearly atomically flat (the morphological roughness is one unit cell or less). Furthermore, to distinguish between the two types of magnetic roughness, the simulations show that fitting of XRMR spectra out to very high incidence angles must be performed. In the specific case of LSMO films with a dead layer with average thickness of 4 unit cells, this corresponds to an incidence angle > 50^∘.     

Electromagnetic backscattering from freak waves in(1+1)-dimensional deep-water

To study the electromagnetic (EM) backscatter characteristics of freak waves at moderate incidence angles, we establish an EM backscattering model for freak waves in (1+1)-dimensional deep water. The nonlinear interaction between freak waves and Bragg short waves is considered to be the basic hydrodynamic spectra modulation mechanism in the model. Numerical results suggest that the EM backscattering intensities of freak waves are less than those from the background sea surface at moderate incidence angles. The normalised radar cross sections (NRCSs) from freak waves are highly polarisation dependent, even at low incidence angles, which is different from the situation for normal sea waves; moreover, the NRCS of freak waves is more polarisation dependent than the background sea surface. NRCS discrepancies between freak waves and the background sea surface with using horizontal transmitting horizomtal (HH) polarisation are larger than those with using vertical transmitting vertical (VV) polarisation, at moderate incident angles. NRCS discrepancies between freak waves and background sea surface decreases with the increase of incidence angle, in both HH and VV polarisation radars. As an application, in the synthetic-aperture radar (SAR) imaging of freak waves, we suggest that freak waves should have extremely low backscatter NRCSs for the freak wave facet with the strongest slope. Compared with the background sea surface, the freak waves should be darker in HH polarisation echo images than in VV echo images, in SAR images. Freak waves can be more easily detected from the background sea surface in HH polarisation images than in VV polarisation images. The possibility of detection of freak waves at low incidence angles is much higher than at high incidence angles.     

畸形波电磁散射特性分析及其特征识别标识的研究

针对弱非线性的Longuet-Higgins模型在模拟强非线性畸形波海面时所存在的问题,采用修正的相位调制法模拟一维畸形波时间、空间波面,该方法能够实现畸形波的定时定点生成,并且其波形既能保持目标谱的频谱结构,又能较大程度地满足波浪序列的统计特性.同时,基于改进的双尺度(TSM)法及时域有限差分法建立畸形波的电磁散射模型,经过相对平均偏差和均方根偏差误差分析后,基于TSM法研究分析了畸形波及其背景海面波的归一化雷达散射截面(NRCS)的计算结果.实验表明,合成孔径雷达成像中畸形波的NRCS比背景波要小,即畸形波的合成孔径雷达图像成像比背景波要灰暗,因此可以将NRCS作为畸形波的特征识别标识.通过分析研究不同极化方式、入射角、入射频率条件下畸形波与背景波面的电磁散射特性实验数据得出:当二者的NRCS差值大于-11.8 dB及以上时,即认为产生畸形波,这为实际的工程应用提供了参照标准.     

Phase transformation of nanostructured titanium dioxide thin films grown by sol–gel method

Nanostructured TiO₂ thin films were deposited on quartz glass at room temperature by sol–gel dip coating method. The effects of annealing temperature between 200^∘C to 1100^∘C were investigated on the structural, morphological, and optical properties of these films. The X-ray diffraction results showed that nanostructured TiO₂ thin film annealed at between 200^∘C to 600^∘C was amorphous transformed into the anatase phase at 700^∘C, and further into rutile phase at 1000^∘C. The crystallite size of TiO₂ thin films was increased with increasing annealing temperature. From atomic force microscopy images it was confirmed that the microstructure of annealed thin films changed from column to nubbly. Besides, surface roughness of the thin films increases from 1.82 to 5.20 nm, and at the same time, average grain size as well grows up from about 39 to 313 nm with increase of the annealing temperature. The transmittance of the thin films annealed at 1000 and 1100^∘C was reduced significantly in the wavelength range of about 300–700 nm due to the change of crystallite phase. Refractive index and optical high dielectric constant of the n-TiO₂ thin films were increased with increasing annealing temperature, and the film thickness and the optical band gap of nanostructured TiO₂ thin films were decreased.     

Ground state of an antiferromagnet with uniform antisymmetric exchange in a magnetic field

A system of two nonlinear differential equations for sublattice angles is proposed to describe the spin orientation distribution in a planar antiferromagnet with uniform antisymmetric exchange in a magnetic field. This system involves the initial symmetry of the problem and is reduced to a single delay differential equation. The solutions of this system are parameterized by the initial condition imposed on the angle of one sublattice at the hyperbolic singular point of the phase space. The numerical analysis of the stability boundary of soliton solutions demonstrates that the transition to the commensurate phase takes place outside the region where the stochastic solutions appear and is accompanied by the magnetization jump Δm ∼ 10⁻¹ m.     

Surfing and generation of cosmic rays in relativistic shock waves

We consider the problem of cosmic-ray generation through the surfing acceleration of charged particles in relativistic magnetosonic shock waves (the branch of fast magnetic sound) propagating in magnetized space plasmas. The dependence of the particle surfing acceleration efficiency on the angle θ _Bn between the normal to the shock front plane and the magnetic field vector in the plasma upstream of the shock is analyzed in detail. We show that for angles satisfying the condition χ = βΓ tan θ _Bn ⩾ 1, where β = U/c, Γ = (1 − β)^{2 −1/2}, U is the shock velocity, and c is the speed of light, the particles can theoretically be accelerated through surfing for an unlimited time and can gain an unlimited energy. For angles satisfying the condition χ < 1, the kinetic energy ℰ of the particles is limited by ℰ = 2mc ²χ²/(1 − χ²) (m is the particle rest mass). Our main conclusion is that the generation of cosmic rays through the surfing acceleration of particles in the front of a relativistic shock wave for Γ ≫ 1 is also efficient when the angle θ _Bn is very small, i.e., it differs significantly from a right angle. Estimates for the energies of particles accelerated through surfing in relativistic jets are provided.     

Optical surface <Emphasis Type="Italic">TM</Emphasis>-waves at the boundary of a nonlinear Kerr-type medium

Solutions for a nonlinear system of Maxwell’s equations and for a corresponding boundary problem describing the propagation of a surface TM-wave (p-polarization) along an interface with an optically nonlinear Kerr-type medium are presented. An analytical expression for the intensity of an integrated flux J₀ carried by such a wave along the interface between two media has been derived as a function of both the wave propagation constant ξ and the optical characteristics of the adjacent media. It is shown that flux intensities corresponding to the same values of the propagation constant ξ are much smaller for p-polarization than for s-polarization.     

Bound states of topological defects in parametrically excited capillary waves

Bound states of topological defects arising in a tetragonal lattice formed by two orthogonal standing parametrically excited capillary surface waves are investigated. Such bound states are shown to consist either of two topological charges of one sign (type 1) or of topological charges having opposite signs (type 2). It was found that bound states of type 1 move primarily along wave fronts, and type 2 bound states move at an angle of 45^○ to the wave fronts forming a tetragonal lattice. A system of four coupled Ginzburg–Landau equations is proposed to model bound states. Numerical modeling of this system gave solutions corresponding to type 1 bound states observed in experiment.     

Research of Gravitation in Flat Minkowski Space

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor φ, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the n-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order c ⁻².     

Cold collisions in strong laser fields: partial wave analysis of magnesium collisions

We have developed Monte Carlo wave function simulation schemes to study cold collisions between magnesium atoms in a strong red-detuned laser field. In order to address the strong-field problem, we extend the Monte Carlo wave function framework to include the partial wave structure of the three-dimensional system. The average heating rate due to radiative collisions is calculated with two different simulation schemes which are described in detail. We show that the results of the two methods agree and give estimates for the radiative collision heating rate for ²⁴Mg atoms in a magneto-optical trap based on the ¹S₀–¹P₁ atomic laser cooling transition.     

New parameterization of the trinucleon wave function and its application to the π <Superscript>3</Superscript>He scattering length

We present a new parameterization of the trinucleon wave function. As a novel feature a separable parameterization for the complete wave function is given. In this way any calculation that considers two-body currents only is largely simplified. To demonstrate this we calculate the π³He scattering length in chiral-perturbation theory. We find reasonable agreement with experimental values inferred from data on level shifts in pionic ³He bound states. The relevance of the π-triton system for an alternative determination of the πN scattering lengths is discussed. Received: 12 August 2002 / Accepted: 25 November 2002 / Published online: 25 February 2003 RID="a" ID="a"e-mail: c.hanhart@fz.juelich.de Communicated by V. Vento     

Application of CI expansion techniques to the computation of two-photon absorptivities

Summary We show how conventional linear expansion techniques for both electronic and vibrational wave functions can be used for the computation of matrix elements governing the two-photon absorption probability in molecules. In particular, the²Σ⁺ A←²∏X transition matrix elements of OH and the¹Σ _g ⁺ E,F←¹Σ _g ⁺ X of H₂are computed using 1) the sum over states in the Born-Oppenheimer approximation with inclusion of vibrational wave functions, 2) solution of perturbation theory equations by expansion in the CI basis at fixed nuclei, followed by a kind of vibrational averaging. The results are compared with experiment and discussed. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Hyper-Kähler metrics and a generalization of the Bogomolny equations

We generalize the Bogomolny equations to field equations on ^{3 n} and describe a twistor correspondence. We consider a general hyper-Kähler metric in dimension 4n with an action of the torusT ⁿ compatible with the hyper-Kähler structure. We prove that such a metric can be described in terms of theT ⁿ -solution of the field equations coming from the twistor space of the metric.     

A Simple Homemade Reaction Station for use in Parallel Solution-Phase Synthesis. Optimization of a Regioselective One-Step Deprotective o-formylation Reaction Mediated by the Vilsmeier-Haack Reagent POCl3⋅DMF

Summary We report herein the fabrication of a simple and price-affordable portable reaction station for use in parallel solution-phase synthesis. This homemade device uses currently available laboratory components and equipment. Specifically designed to fit standard magnetic hotplates/stirrers, it can simultaneously hold up to 24 heated and magnetically stirred glass reactors of both 10 and 50 mL capacities. Glass reactors are connected by flexible 16-gauge metal needles to a central gas manifold equipped with an inlet/outlet for vacuum and inert gases. Reaction temperatures can be optimally varied from −78 ^∘C to 150 ^∘C. Using a statistical screening DOE method, this parallel array reactor station has been successfully operated to optimize the one-step deprotective O-formylation of a sterically hindered bis-O-tert-butyldiphenylsilyl (O-TBDPS) aromatic diol. The latter transformation was mediated by the Vilsmeier-Haack reagent POCl₃⋅DMF using a range of Lewis acid and metal salt promoters, including their binary combinations.     

B→K transition form factor up to $\mathcal{O}(1/m^2_b)$ within the kT factorization approach

We apply the k_T factorization approach to deal with the B→K transition form factor F^B→K _+,0(q²) in the large recoil regions. The B-meson wave functions Ψ_B and Ψ̄_B that include the 3-particle Fock states’ contributions are adopted to give a consistent PQCD analysis of the form factor up to . It has been found that the two wave functions Ψ_B and Ψ̄_B can give sizable contributions to the form factor and should be kept for a better understanding of the B-meson decays. Next the contributions from different twist structures of the kaon wave function are discussed, including SU_f(3)-breaking effects. A sizable contribution from the twist-3 wave function Ψ_p is found, whose model dependence is discussed by taking two groups of parameters that are determined by different distribution amplitude moments obtained in the literature. It is also shown that F^B→K _+,0(0)=0.30±0.04 and [F^B→K _+,0(0)/F^B→π _+,0(0)]=1.13±0.02, which are more reasonable and consistent with the light-cone sum rule results in the large recoil regions. PACS  12.38.Aw; 12.38.Bx; 13.20.He; 14.40.Aq     

On the problem of constraints in minimally coupled relativistic wave equations for particles of unique mass

We study the problem of a possible change in the number of constraints in linear relativistic wave equations (-iβ _μ ∂ ^μ +m)ψ=0 for particles of unique mass, on introduction of minimal coupling to an external electromagnetic field. Complementing our earlier work in which we obtained conditions for non-loss of constraints in equations characterised by the minimalβ-algebraβ ₀ ⁵ =β ₀ ³ we derive here the conditions for such theories not to generate more constraints than in the free case. The results are illustrated by considering specific equations and a fallacy in certain conclusions of Kobayashi and Shamaly on this problem is pointed out.     

A laser accelerator

We show that a laser can efficiently accelerate charged particles if a magnetic field is introduced to improve the coupling between the particle and the wave. Solving the relativistic equations of motion for an electron in a uniform magnetic field and superposed, circularly polarized electromagnetic wave, we find that in energy-position phase space an electron traces out a curtate cycloid: it alternately gains and loses energy. If, however, the parameters are chosen so that the electron's oscillations in the two fields are resonant, it will continually accelerate or decelerate depending on its initial position within a wavelength of light. A laboratory accelerator operating under these resonant conditions appears attractive: in a magnetic field of 10⁵ Gauss, and the fields of a 5×10¹² W, 10 μm wavelength laser, an optimally positioned electron would accelerate to 700 MeV in only 10m. Supported by NASA Grant NSG-7490     

Analysis and optimization of propagation losses in LiNbO3 optical waveguides produced by swift heavy-ion irradiation

The propagation losses (PL) of lithium niobate optical planar waveguides fabricated by swift heavy-ion irradiation (SHI), an alternative to conventional ion implantation, have been investigated and optimized. For waveguide fabrication, congruently melting LiNbO₃ substrates were irradiated with F ions at 20 MeV or 30 MeV and fluences in the range 10¹³–10¹⁴ cm⁻². The influence of the temperature and time of post-irradiation annealing treatments has been systematically studied. Optimum propagation losses lower than 0.5 dB/cm have been obtained for both TE and TM modes, after a two-stage annealing treatment at 350 and 375^∘C. Possible loss mechanisms are discussed.