Particle line shape after γ-ray emission in flight

Line shapes broadened by theγ-ray emission are described in the coordinate frame, in which a quantization axis is chosen to be the direction of the center of mass scattering angle of a decaying nucleus. In this coordinate frame the line shapes can be described only by diagonal density matrix elements for finite values of kinematic factork. The method of this analysis has been applied to the single and mutual excitations of the first 2⁺ state of¹²C in the¹²C+¹²C inelastic scattering.     

Rydberg transition dipole matrix elements from sum frequency generation spectra

A new method for determination of relative dipole matrix elements for transitions between excited states is presented, using sum frequency generation spectroscopy. The method is based on measuring the frequency spacing of related extrema in the dispersion like shapes within the SFG-spectrum, caused by interference between resonant and nonresonant parts in the third order polarizability. It is applied to CdI with the generated frequency in the range of the principal series 5s¹S₀ → np¹P₁, n = 12–28. Values of the products μ_6snpμ_{np5 s} are presented obeying the n^1-3 law.     

A New Highly Sensitive 1H-14N Nuclear-Quandrupole Double-Resonance Technique

A new highly sensitive ¹H-¹⁴N nuclear-quadrupole double-resonance technique using magnetic field cycling is presented. It is based on a resonant proton-nitrogen coupling at ν_H = ν₀ and on the excitations of the two other ¹⁴N NQR transitions by a two-frequency irradiation or by a train of frequency sweeps. The sensitivity and resolution of the new technique are estimated. Some typical examples of its application are presented.     

A FAST TIME-DOMAIN INTEGRATION METHOD FOR COMPUTING NON-STATIONARY RESPONSE HISTORIES OF LINEAR OSCILLATORS WITH DISCRETE-TIME RANDOM FORCING

A new approach is presented for computing displacement histories of single linear oscillators with arbitrarily light damping and general forcing—of particular use for efficient Monte Carlo simulation of modal systems with ultra-light damping and very broadband non-Gaussian excitation. Solution methods are initially presented within a state transition context, to show limitations of FFT solutions, and to establish, for long-run non-stationary stochastic analysis via fast Laplace, the need for appropriate zero-padding, high cut-off frequency, and fixed-step sampling. Truncation errors arising in single-transition time-domain convolution are then examined via the Euler-Maclaurin summation formula. Errors are shown to be minimum when transition intervals are chosen as integer multiples of the damped natural period, precisely where the O (Δτ²Δf′) error can be evaluated, and the velocity transition equation can be dispensed with. The paper shows that an optimum O (Δτ⁴Δf?) integration scheme can be used for fast time-domain convolution in a two-stage algorithm. First, phased-pairs of accurate displacements are efficiently predicted at selected transition times. These are then used as boundary conditions in adaptive Chebychev polynomial solution giving continuous displacement histories for selected cycles—this considerably reduces the number of multiplications and integrations normally required. Two-stage integration turns out to be at least 100 times faster than explicit short-transition time-domain solution, and for general applications, at least as fast as the Laplace/IFFT approach. But for non-stationary probability density estimation, involving far-future history prediction the speed advantage over fast Laplace can be enormous.     

Free vibration of skew Mindlin plates by p-version of F.E.M.

Accurate natural frequencies and mode shapes of skew plates with and without cutouts are determined by p-version finite element method using integrals of Legendre polynomials for p=1-14. The hierarchical plate element is formulated based on Mindlin's plate theory including rotatory inertia effects and based on a skew co-ordinate system. Non-dimensional frequency parameter and mode shapes are presented for a range of skew angle (β), aspect ratio (a/b), thickness-width ratio (h/b), cutout dimensions and different boundary conditions. The results were verified by comparison with those available in the open literature.     

Explicit time-domain approaches based on numerical Green’s functions computed by finite differences – The ExGA family

The present paper describes a new family of time stepping methods to integrate dynamic equations of motion. The scalar wave equation is considered here; however, the method can be applied to time-domain analyses of other hyperbolic (e.g., elastodynamics) or parabolic (e.g., transient diffusion) problems. The algorithms presented require the knowledge of the Green’s function of mechanical systems in nodal coordinates. The finite difference method is used here to compute numerically the problem Green’s function; however, any other numerical method can be employed, e.g., finite elements, finite volumes, etc. The Green’s matrix and its time derivative are computed explicitly through the range [0, Δt] with either the fourth-order Runge–Kutta algorithm or the central difference scheme. In order to improve the stability of the algorithm based on central differences, an additional matrix called step response is also calculated. The new methods become more stable and accurate when a sub-stepping procedure is adopted to obtain the Green’s and step response matrices and their time derivatives at the end of the time step. Three numerical examples are presented to illustrate the high precision of the present approach.     

Laser spectroscopy in the island of inversion

An overview of the studies by collinear laser spectroscopy in the island of inversion is presented with emphasis on the β-detection method. The spin and magnetic-moment measurements of ³¹Mg and ³³Mg are described in detail. Comparison with the spherical and deformed shell models provides evidence for prolate shapes and indicates the ground-state parities. The results are considered in the context of other experimental studies in the region. The potential of the β-detection technique for studying rms charge radii is highlighted.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Microscopic form factor for DWBA analysis of light-ion induced three-nucleon transfer reactions

A modified zero-range distorted-wave Born approximation calculation was performed for the (p, α) reactions. The form factor is calculated by a first method, which is an extension of the Bayman and Kallio method to extract the relative l = 0 part of two-nucleon shell-model wave functions. The method includes some of the range effects so that one can predict the absolute magnitudes of the cross sections. A second method in finite range involves the ³He cluster expansion of the α-particle where the known (³He, α) transfer normalization may be used to estimate the absolute cross sections. The ¹¹⁸Sn(p, α)¹¹⁵In reactions are analyzed using the hole-vibration coupling model for ¹¹⁵In. The shapes of the experimental cross sections and the analyzing powers can be fitted by the calculations but the magnitudes of the cross sections are predicted to be too small.     

Optical soliton perturbation for Gerdjikov–Ivanov equation via two analytical techniques

This paper employs two integration procedures to obtain soliton solutions to the perturbed Gerdjikov–Ivanov equation. They are G′/G²–expansion method and the sine–cosine method. Bright, dark and singular solitons are revealed along with a few of the combo–soliton solutions. The existence criteria of these solitons are also given.     

Incorporating the Havriliak–Negami dielectric model in the FD-TD method

We derive and analyze an efficient algorithm to incorporate the anomalously dispersive Havriliak–Negami dielectric model of induced polarization in the Finite-difference time-domain (FD-TD) method. Our algorithm implements this dielectric model, which in the time-domain involves fractional derivatives and fractional differential operators, with a preset error over the desired computational time interval [0,T_comp] and correctly takes into account the singularity at t = 0⁺ of the corresponding time-domain dielectric susceptibility. The overall algorithm is shown to be second-order accurate in space and time, and to obey the standard FD-TD stability condition. Numerical experiments confirm our analysis.     

Error analysis and correction for Lattice Boltzmann simulated flow conductance in capillaries of different shapes and alignments

We study the relative error in conductance calculations, for simulated flow of a single component single phase fluid through a capillary in three dimensions, by the Lattice Boltzmann (LB) method with bounce-back boundary conditions. The relative error with respect to analytical results for capillary cross-sections of circular, triangular and square shapes are calculated as a function of the cross-section diameter, a, and for different alignment of the cross-section relative to the underlying lattice grid. It is shown, when the shapes are not aligned perfectly to the lattice, that the relative error decreases systematically with the size, a, as ～1/a when a is evaluated by mapping the computed cross-sectional area, in terms of the enclosed number of grid points, to the respective geometrical shapes concerned. For perfectly aligned geometries, viz. the square capillary aligned to the LB lattice grid or rotated with its side along the diagonal of the LB grid, the relative error decreases as ～1/a². A simple method is suggested to locate the boundary wall depending on its orientation relative to the grid, such that the exact conductance of the new shape matches the LB computed conductance.     

Search for a SM Higgs boson in dilepton plus missing transverse energy final state with the D??detector at {\sqrt s}{=}{1.96}?TeV

A search is presented for the Standard Model (SM) Higgs boson optimized in the decay channel H??W ^?+? W ^??, where both W bosons decay leptonically. The final state considered contains dileptons and missing transverse energy from the neutrinos. A multivariate analysis is used to suppress the background. No significant excess above the SM background has been observed and limits set on the Higgs boson production cross-section ? the branching ratio for m _H?= 115?C200?GeV are computed. Results using 8.1?fb^?1 of data are presented.     

Time-domain numerical computation of noise reduction by diffraction and finite impedance of barriers

A new time-domain numerical method is presented for the estimation of noise reduction by the diffraction and finite impedance of barriers. High order finite difference schemes conventionally used for computational aeroacoustics, and time-domain impedance boundary conditions are utilized for the development of the time-domain method. Compared with other methods, this method can be applied more easily to the problems related to nonlinear noise propagation such as impulsive noise and broadband noise. Linearized Euler equations in Cartesian co-ordinates are considered and solved numerically. Straight and T-shaped barriers with and without surface admittance are calculated. In order to assess the accuracy of this time-domain method, comparison with the results of SYSNOISE software (Ver. 5.3) are made. There are very good agreements between the results of the present time-domain numerical method and the boundary element method of the SYSNOISE software.     

Influencing the satellite transitions of half-integer quadrupolar nuclei for the enhancement of magic angle spinning spectra

Double frequency sweeps can induce spin transitions in a set of satellites of a half-integer quadrupolar nucleus by simultaneously passing through resonance for a satellite pair. It is shown that by transferring population from the outer spin levels to the inner |1/2 and |−1/2 levels an increased intensity for central transition spectra is obtained. Although Magic Angle Spinning in principle interferes with this process, and the adiabaticity of the passages is different for every crystallite in a powder, enhanced spectra with undistorted line shapes are obtained for I=3/2 (²³Na) and 5/2 (²⁷Al) spins experiencing quadrupolar interactions with ω_Q in the range 0.1–3 MHz. Even at spinning speeds up to 30 kHz significant enhancements are obtained. An analysis of the combined effects of double frequency sweeps (DFS) and MAS indeed shows strongly different effects for different crystallites in powder ranging from no gain at all to the theoretical maximum gain of 2I. As the effects are randomly distributed over all orientations on a sphere this is averaged over the whole line shape. Therefore, undistorted powder patterns are obtained enhanced by the average gain over the individual crystallites. Saturation of the satellite transitions, which can only be achieved if spin–spin relaxation is sufficiently strong, leads to identical results. Optimization of the sweeps should be toward an optimal effect on the population transfer to the central levels and chosen short with respect to spin–lattice relaxation times.     

Failsafe flux limiting and constrained data projections for equations of gas dynamics

A new approach to flux limiting for systems of conservation laws is presented. The Galerkin finite element discretization/L² projection is equipped with a failsafe mechanism that prevents the birth and growth of spurious local extrema. Within the framework of a synchronized flux-corrected transport (FCT) algorithm, the velocity and pressure fields are constrained using node-by-node transformations from the conservative to the primitive variables. An additional correction step is included to ensure that all the quantities of interest (density, velocity, pressure) are bounded by the physically admissible low-order values. The result is a conservative and bounded scheme with low numerical diffusion. The new failsafe FCT limiter is integrated into a high-resolution finite element scheme for the Euler equations of gas dynamics. Also, bounded L² projection operators for conservative interpolation/initialization are designed. The performance of the proposed limiting strategy and the need for a posteriori control of flux-corrected solutions are illustrated by numerical examples.     

Hot nuclei — Effective shapes and entrance channel effect

The γ-decay of the Giant Dipole Resonance in hot rotating compound nuclei has provided valuable information on the nuclear structure at finite temperature. A number of experimental results showing that the nuclear shapes change with temperature and angular momentum are here reviewed. In particular we concentrate on the temperature interval from 1 to 2 MeV, rotational frequencies from 0.2 to 1.5 MeV and on nuclei in the mass regionsA≈160–170 andA≈110, characterized by the prolate-oblate and spherical-oblate phase transitions, respectively. The possibility to study the shapes involved in the compound nucleus formation is also discussed. For this purpose long formation times are required and the nucleus¹⁷⁰W formed with the reaction⁶⁰Ni+¹¹⁰Pd, here studied, seems to be a good candidate. The gamma and particle decays were compared to those of the reaction⁴⁸Ti+¹²²Te. The comparison shows that in average the energy of the α-particles is larger for the more symmetric reaction, consistent with longer formation times and larger deformations in the pre-equilibrium stage.     

Development of a new damper to reduce resonant vibrations in lightweight steel joist floors

Floor vibrations annoying to humans often occur in lightweight constructions. A number of methods to solve the problem of resonant vibrations are reported in the literature. Tuned mass damper, semi-active tuned vibration absorber and active control system are all examples of existing methods. A new method has been tested in laboratory environment on a prefabricated floor containing a resilient ceiling with a size up to 6.8×4.8 m². The method takes advantage of small pieces of visco-elastic material connected between the ceiling joists and the primary beams. A finite element model is used to calculate the correct amount of visco-elastic material. The new damper is especially effective in damping mode shapes where the ceiling oscillates out of phase relative to the floor but shows improvements for other mode shapes as well.     

Some general properties of the exact acoustic fields in horns and baffles

The propagation of the fundamental, longitudinal acoustic mode in a duct of variable cross-section is considered, and the “Webster” wave equations for the sound pressure and velocity are used to establish some general properties of the exact acoustic fields. The equipartition of kinetic and compression energies is shown (section 2.1) to hold at all stations only for (i) a duct of constant cross-section and (ii) an exponential horn; these are the two cases for which the wave equations for the acoustic velocity and pressure coincide. It is proved (section 2.3) that there are only five duct shapes, forming two dual families, which have constant cut-off frequency(ies): namely, (I) the exponential duct, which is self-dual, and is the only shape with constant (and coincident) cut-offs both for the velocity and pressure; (II) the catenoidal horns, of cross-section S～cosh², sinh², which, with their duals (III) the inverse catenoidal ducts S～sech², csch², have one constant cut-off frequency, respectively, for the acoustic pressure and velocity. The existence of at least one constant cut-off frequency implies that the corresponding wave equation can be transformed into one with constant coefficients, and thus the acoustic fields calculated exactly in terms of elementary (exponential, circular and hyperbolic) functions; this property also applies to the imaginary transformations of the above shapes, viz., the sinusoidal S～sin² and inverse sinusoidal S～csc² ducts, that have no cut-off frequency, i.e., are acoustically “transparent”. It is shown that elementary exact solutions of the Webster equation exist only (section 3.1) for these seven shapes: namely, the exponential, catenoidal, sinusoidal and inverse ducts; it is implied that for all other duct shapes the exact acoustic fields involve special functions, in infinite or finite terms, e.g., Bessel and Hermite functions respectively for power-law and Gaussian horns. Examples of the method of analysis are given by calculating, in elementary form, the exact acoustic fields in inverse catenoidal ducts, for all cases of (a) propagating waves above, (b) non-oscillating modes below and (c) transition fields at the cut-off frequency. The inverse catenoidal ducts consist of (A) the horn of cross-section S～sech², ressembling the “soliton” of non-linear water wave fame, and (B) the baffle of cross-section S～csch², which also matches two exponentially converging ducts, but has infinite, instead of finite, flare at the origin. The geometrical and acoustic properties of these ducts are illustrated by sets of six plots, in Figure 1(a) for the sech-horn and in Figure 1(b) for the csch-baffle; the exact acoustic fields are described by amplitude and phase decompositions of the sound velocity and pressure, plotted as functions of position along the duct, for four frequencies ranging from the cut-off condition to the ray limit (or W.K.B.J. approximation).     

Two-loop background field calculations for arbitrary background fields

The ultraviolet divergences of two-loop vacuum graphs in the presence of an arbitrary background field are determined for four-dimensional φ⁴ and gauge theories on flat space. Dimensional regularisation is employed and the heat kernel is used to analyse the short-distance singularities in the products of propagators, in the presence of the background field, that occur for two-loop graphs. The single and double poles in ? = 4 ? d are determined in a concise fashion, giving known results for the β function. A procedure for determining the remaining finite parts in terms of explicit convergent integrals in four dimensions is described.