Radial Nodes Research Articles

Wave functions ofSU(3)pure gauge glueballs on the lattice

The Bethe-Salpeter wave functions of $SU(3)$ pure gauge glueballs are revisited in this study. The ground and the first excited states of scalar and tensor glueballs are identified unambiguously by using the variational method on the basis of large operator sets. We calculate their wave functions in the Coulomb gauge and use two lattices with different lattice spacings to check the discretization artifacts. For ground states, the radial wave functions are approximately Gaussian and the size of the tensor is twice as large as that of the scalar. For the first excited states, the radial nodes are clearly observed for both the scalar and the tensor glueballs, such that they can be interpreted as the first radial excitations. These observations may shed light on the theoretical understanding of the inner structure of glueballs.

On the Shape of Core Overshooting in Stellar Model Computations, and Asteroseismic Tests

Slowly pulsating B stars (SPB) and $\gamma$ Dor stars pulsate in high-order gravity (g-) modes. The frequencies of g-modes are sensitive to the detailed structure and evolution history of stars having convective cores. Receding convective cores in OB-type stars leave behind a chemically inhomogenous $\nabla_\mu>0$ radiative zone. Once a g-mode has radial nodes near the boundaries of these layers, the mode gets trapped and its period deviates from asymptotic period spacing. Careful study of such trapped modes allows constraining the extent of such layers by fitting individual pulsation frequencies. We employ 19 consecuitve dipole g-modes of a very rich Kepler SPB pulsator, KIC 10526294, to demonstrate the power of mode trapping in B-stars in studying the thermal and chemical stratification in the overshooting layer.

Ellipsoid Reticulated Shell of Parametric Design and Analysis of Mechanical Characteristics

By using the parametric design language APDL, developed ellipsoidal reticulated shell parametric macros, only enter the long axis S1, short axis S2, high vector F, scale factor t, ring symmetric region shares Kn, radial nodes turns Nx, to generate the desired lattice shell; comparative analysis of 30 kinds of scheme through two types of single-shell ellipsoid reticulated shell with different rise span ratio force, studied its stress characteristics, providing a theoretical reference for designing and engineering ellipsoid reticulated shell application.

RBF-network based sparse signal recovery algorithm for compressed sensing reconstruction

The approach of applying a cascaded network consisting of radial basis function nodes and least square error minimization block to Compressed Sensing for recovery of sparse signals is analyzed in this paper to improve the computation time and convergence of an existing ANN based recovery algorithm. The proposed radial basis function—least square error projection cascade network for sparse signal Recovery (RASR) utilizes the smoothed L0 norm optimization, L2 least square error projection and feedback network model to improve the signal recovery performance over the existing CSIANN algorithm. The use of ANN architecture in the recovery algorithm gives a marginal reduction in computational time compared to an existing L0 relaxation based algorithm SL0. The simulation results and experimental evaluation of the algorithm performance are presented here.

The Temperature Field Research for Large LNG Cryogenic Storage Tank Wall

According to the structural characteristic of LNG cryogenic storage tank concrete prestressed wall and heat transfer theory, the paper obtain the calculation formula of the temperature field distribution, emphasis studying the heat flux distribution along the radial and axial and node temperature distribution of the section nodes for a 160,000 m3 capacity LNG cryogenic tank by ABAQUS. The paper also establish a set of method which is suitable for the temperature field analysis, proof the feasibility of finite element analysis technique in the analysis of the LNG cryogenic storage tank, and have a certain reference for the prestressed concrete walls and insulation layer design of the large LNG storage tank.

Square Pyramid Partial Double Layer of Schwedler Spherical Reticulated Shell Parametric Design and Mechanical Analysis

Using ANSYS software comes with parametric design language APDL, developed a square pyramid partial double layer of Schwedler spherical reticulated shell parametric design macro program; achieved this kind of spherical shell parametric modeling with the given shell span S, vector high F, the thickness (height) of the pyramid, ring copies of the symmetric region Kn and radial nodes laps Nx. Analyzed the static performance of the spherical reticulated shell under different structural parameters, studied the displacement of the structure and the distribution of the stress change with macroscopic geometric parameter change rule. Analysis results of eight kinds of conditions showed that the square pyramid partial double layer of Schwedler spherical reticulated shell has good mechanical performance. The result of the analysis provides a theoretical basis for the relevant engineering design.

On optimization based extreme learning machine in primal for regression and classification by functional iterative method

In this paper, the recently proposed extreme learning machine in the aspect of optimization method by Huang et al. (Neurocomputing, 74: 155–163, 2010) has been considered in its primal form whose solution is obtained by solving an absolute value equation problem by a simple, functional iterative algorithm. It has been proved under sufficient conditions that the algorithm converges linearly. The pseudo codes of the algorithm for regression and classification are given and they can be easily implemented in MATLAB. Experiments were performed on a number of real-world datasets using additive and radial basis function hidden nodes. Similar or better generalization performance of the proposed method in comparison to support vector machine (SVM), extreme learning machine (ELM), optimally pruned extreme learning machine (OP-ELM) and optimization based extreme learning machine (OB-ELM) methods with faster learning speed than SVM and OB-ELM demonstrates its effectiveness and usefulness.

AXISYMMETRIC TOROIDAL MODES OF GENERAL RELATIVISTIC MAGNETIZED NEUTRON STAR MODELS

We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength $B_{{\rm{S}}}\sim10^{16}$ G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd parity, but no toroidal modes of even parity are found. The frequencies of the toroidal modes form distinct mode sequences and the frequency in a given mode sequence gradually decreases as the number of radial nodes of the eigenfunction increases. From the frequency spectra computed for neutron stars of different masses, we find that the frequency is almost exactly proportional to $B_{{\rm{S}}}$ and is well represented by a linear function of $R/M$ for a given $B_{{\rm{S}}}$, where $M$ and $R$ are the mass and radius of the star. The toroidal mode frequencies for $B_{{\rm{S}}}\sim 10^{15}$ G are in the frequency range of the quasi-periodic oscillations (QPOs) detected in the soft-gamma-ray repeaters, but we find that the toroidal normal modes cannot explain all the detected QPO frequencies.

Orthogonal incremental extreme learning machine for regression and multiclass classification

Single-hidden-layer feedforward networks with randomly generated additive or radial basis function hidden nodes have been theoretically proved that they can approximate any continuous function. Meanwhile, an incremental algorithm referred to as incremental extreme learning machine (I-ELM) was proposed which outperforms many popular learning algorithms. However, I-ELM may produce redundant nodes which increase the network architecture complexity and reduce the convergence rate of I-ELM. Moreover, the output weight vector obtained by I-ELM is not the least squares solution of equation Hβ = T. In order to settle these problems, this paper proposes an orthogonal incremental extreme learning machine (OI-ELM) and gives the rigorous proofs in theory. OI-ELM avoids redundant nodes and obtains the least squares solution of equation Hβ = T through incorporating the Gram---Schmidt orthogonalization method into I-ELM. Simulation results on nonlinear dynamic system identification and some benchmark real-world problems verify that OI-ELM learns much faster and obtains much more compact neural networks than ELM, I-ELM, convex I-ELM and enhanced I-ELM while keeping competitive performance.

Parametric Design of Six Typical Semi-Outdoor Reticulated Domes

According to the rules of six typical spherical reticulated shell nodes, the modeling method and the design macro program is developed for the nodes and the bars of six typical semi-outdoor spherical reticulated shell structures by using the ANSYS parametric design language APDL, so as to achieve the parametric design of six typical semi-outdoor spherical reticulated shells. The modeling design examples indicate that it's convenient to achieve the parametric modeling and design of semi-outdoor shell with given span S, rise high F, number of hoop symmetry areas kn, radial node cycles of whole structure nx and the upper removed laps ns, which provides big convenience for the force analysis and the optimization scheme comparison of semi-outdoor spherical lattice shells with varied types and geometric parameters.

Particle on a Boron Disk: Ring Currents and Disk Aromaticity in B202–

The B20(2-) cluster is predicted to exhibit a planar sheet-like structure with a circular circumference. Orbital plots and energy correlations demonstrate the close correspondence between the electronic structure of B20(2-) and the Bessel functions describing the waves of a quantum mechanical particle confined to a disk. The π-band of B20(2-), and its B19(-) congener, contains 12 π-electrons, forming a (1σ)(2)(1π)(4)(1δ)(4)(2σ)(2) configuration, which corresponds to a "disk aromaticity" electron count. The analogy not only applies to the π-band, but also extends to the 50 valence σ-electrons. The occupied σ-orbitals are assigned on the basis of radial and angular nodes of the scalar disk waves. The magnetic response of the cluster was examined by Nucleus Independent Chemical Shift (NICS) values and current density calculations based on the ipsocentric model. B20(2-) is found to exhibit a remarkable inner paratropic current in the σ-channel and an outer diatropic current in the π-channel. The orbital excitations responsible for the antiaromaticity in σ and the disk-aromaticity in π are identified.

Coupling a small torsional oscillator to large optical angular momentum

We propose a new configuration for realizing torsional optomechanics: an optically trapped windmill-shaped dielectric interacting with Laguerre–Gaussian cavity modes containing both angular and radial nodes. In contrast to existing schemes, our method can couple mechanical oscillators smaller than the optical beam waist to the in-principle unlimited orbital angular momentum that can be carried by a single photon, and thus generate substantial optomechanical interactions. Combining the advantages of small mass, large coupling, and low clamping losses, our work conceptually opens the way for the observation of quantum effects in torsional optomechanics. 10.1080/09500340.2013.778341-SUP0001 Supplementary data

Ab initio calculation of double ionization of atoms

The Solov’ev-Vinitsky method was used to perform an ab initio calculation of the triple-differential cross section for the double single-photon photoionization of helium for the case of equal emitted-electron energies. A Gaussian width γ describing angular electron-electron correlations at the total electron energy E taking values in range between 0.1 and 100 eV was obtained for this cross section. The results agree with available experimental data, but they raise a doubt as to whether the well-known Wannier law γ ∝ E1/4 is applicable at experimentally accessible energies. The Gaussian width γ was investigated as a function of the total emitted-electron energy for targets that have a strongly asymmetric configuration of the initial state—specifically, a negative atomic-hydrogen ion H− and heliumin the 1s2s1S and 1s3s1S excited states. It was found that this function, γ(E), had a maximum at low energies. It was also shown that, at low energies, the dependence of the double-differential cross section on the angle between the emitted-electron momenta for the targets indicated above differed substantially from the Gaussian dependence, featuring maxima whose number was equal to the number of radial nodes in the initial state. This opens new possibilities for a qualitative analysis of the electron structure of targets.

Role of resonance-enhanced multiphoton excitation in high-harmonic generation of N2: A time-dependent density-functional-theory study

A minimum at $\ensuremath{\sim}$39 eV is observed in the high-harmonic-generation spectra of N${}_{2}$ for several laser intensities and frequencies. This minimum appears to be invariant for different molecular orientations. We reproduce this minimum for a set of laser parameters and orientations in time-dependent density-functional-theory calculations, which also render orientation-dependent maxima at 23--26 eV. Photon energies of these maxima overlap with ionization potentials of excited states observed in photoelectron spectra. Time profile analysis shows that these maxima are caused by resonance-enhanced multiphoton excitation. We propose a four-step mechanism, in which an additional excitation step is added to the well-accepted three-step model. Excitation to a linear combination of Rydberg states ${c}_{4}^{\ensuremath{'}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ and ${c}_{3}\phantom{\rule{0.16em}{0ex}}{{}^{1}\ensuremath{\Pi}}_{u}$ gives rise to an orientation-invariant minimum analogous to the ``Cooper minimum'' in argon. When the molecular axis is parallel to the polarization direction of the field, a radial node goes through the atomic centers, and hence the Cooper-like minimum coincides with the minimum predicted by a modified two-center interference model that considers the de-excitation of the ion and symmetry of the Rydberg orbital.

In-Plane and Transverse Eigenmodes of High-Speed Rotating Composite Disks

We apply Hamilton's principle and model the coupled in-plane and transverse vibrations of high-speed spinning disks, which are fiber-reinforced circumferentially. We search for eigenmodes in the linear regime using a collocation scheme, and compare the mode shapes of composite and isotropic disks. As the azimuthal wavenumber varies, the radial nodes of in-plane waves are remarkably displaced in isotropic disks while they resist such displacements in composite disks. The reverse of this phenomenon happens for transversal waves and the radial nodes move toward the outer disk edge as the azimuthal wavenumber is increased in composite disks. This result is in accordance with the predictions of Nowinski's theory, and therefore, it is independent of the magnitude of the spinning velocity and the mode frequency. Although there are notable differences between the form of governing equations derived from Hamilton's principle and Nowinski's theory, transverse eigenmodes differ a little in the two approaches. We argue that the application of orthotropic composites as the core material of the next generation of hard disk drives, together with an angular velocity controller, can enhance the data access rate.

A development of the HEXNEM nodal expansion method

In this paper a development of the HEXNEM nodal expansion methods is presented, together with a program implementation and results from comparisons with benchmark problem solutions. The new development consists in the introduction of tangentially weighted exponential basis functions and continuity and boundary conditions for the tangential moments of the partial current in a way similar to that employed in some methods of the AFEN family. This is aimed at a better accounting for the flux variation along the radial node faces which for the large WWER-1000 assemblies can be a significant source of error. The test problem results presented in the paper indicate that an improved accuracy for WWER-1000 is achieved as compared with the HEXNEM2 method.

On the “simple check” of electrocapillarity

Contrary to some recent publications, the trivial definition of the surface charge density q = Q/A does not give any information about the charge Q and area A. Therefore this definition cannot be used as a “simple check,” rejecting results of electrochemical experiments where the values Q and A are the independent variables. Experimental confirmation and practical applications can be the two self-contained checks for the equations of solid-state electrocapillarity. Along with thermodynamics, the kinetic aspect is important here since the charge and area can oscillate in the large frequency range. Cycling the surface charge gives the three different contributions to the alternating surface tension of solids, corresponding to the double layer charging, reversible chemisorption, and discrete transitions closed within the rigid surface layer. The derivative of the charge density with respect to elastic deformation represents chemisorption and can be decreased to negligibly small value at the point of zero charge by increasing the frequency. On the base of the solid-state electrocapillarity, the dependence between the adsorption energy and elastic deformation was measured for the first time. It was thus found that stretching reinforces the bonding of hydrogen to the platinum surface. Acting inside the rigid surface monolayer, the alternating surface tension of solids is an independent tool in solving some complex problems of electrochemistry and solid-state physics. Two consecutive transitions are discovered on platinum instead of two coexistent hydrogen states which earlier were associated with two waves of the charging current. There are three consecutive hydrogen states separated along the potential axis by transitions from one state to another. Similar surface transitions are observed also on iridium, rhodium, and palladium. The number of transitions coincides with the number of finite radial nodes of the wave functions formed by d-electrons of these metals.

Dual reciprocity hybrid radial boundary node method for Winkler and Pasternak foundation thin plate

An efficient dual reciprocity hybrid radial boundary node method is developed for the analysis of Winkler and Pasternak foundation thin plate, in which a hybrid displacement variational principle, radial point interpolation method (RPIM) and dual reciprocity method (DRM) are combined. Firstly, the hybrid displacement variational principle is developed, in which the domain variables are interpolated by two groups of symmetric fundamental solutions, while the boundary variables are interpolated by RPIM instead of the traditional moving least square, and the shape function obtained by RPIM satisfies the delta function property, so boundary conditions can be applied directly. Besides, DRM is exploited to evaluate the particular solutions of inhomogeneous terms, which can be used to transform the domain integrals arising from the inhomogeneous term into equivalent boundary integrals. Finally, some additional equations based on the DRM theory are proposed to overcome the problem that the boundary integral equations are not enough to solve all variables. This method has the advantages of both no element mesh of meshless method and dimensionality reduction of boundary element method. Numerical examples of Winkler and Pasternak foundation plates are given to illustrate that the present method is effective, accurate and it can be further expanded into practical engineering.

Postavulsion channel evolution: Niger Delta continental slope

Channel avulsion is fundamental in defining submarine fan morphology yet, as a process, is poorly understood. The postavulsion evolution of five channel-levee systems, documented from both the shallow subsurface and the sea floor, is marked in the early stages by relatively wide axial channel belts containing sinuous channel elements. The axial channel belt in each system narrowed through time in association with levee aggradation, which resulted in increased channel confinement. Of the five systems studied, four avulsed from a radial avulsion node at the mouth of the basin feeder-channel complex, which is the entry point to the basin. Only one avulsion occurred at an avulsion node downflow of the mouth of the feeder-channel complex. The degree of channel instability in three of the four systems before an avulsion event was increased by channel-floor aggradation caused by the backfilling of channel-confined turbidity current deposits. Channel-floor aggradation reduced the confinement relief of the systems, thereby increasing the probability of avulsion during an outsized flow event. The backfilled deposits in the channel belts display relatively high seismic-reflection amplitudes inferred to be coarser grained (more sand rich) than their surroundings, that is, out-of-channel deposits. Overbank cyclic steps are exceptionally well preserved on subsurface levees, and their potential function in promoting an avulsion event is discussed. The actual process of avulsion is caused by the flow itself instead of a reduction in confinement relief, and although outsized flows are the likely trigger, depending on the degree of this relief in the channel, multiple small flows could also be responsible for levee breaching, resulting in avulsion. The process of channel-system evolution resulting in avulsion can be applied to other subsurface data where compensating high-amplitude channel belts are recognized. In the context of hydrocarbon exploration, investigating up depositional dip to identify avulsion nodes increases the chance of locating sand-rich deposits, especially where multiple channels converge on one point.

Exact Vibration Solutions of Nonhomogeneous Circular, Annular and Sector Membranes

AbstractIn this paper, exact vibration frequencies of circular, annular and sector membranes with a radial power law density are presented for the first time. It is found that in general, the sequence of modes may not correspond to increasing az-imuthal mode number n. The normalized frequency increases with the absolute value of the power index |ν|. For a circular membrane, the fundamental frequency occurs at n = 0 where n is the number of nodal diameters. For an annular membrane, the frequency increases with respect to the inner radius b. When b is close to one, the width 1 – b is the dominant factor and the differences in frequencies are small. For a sector membrane, n – 1 is the number of internal radial nodes and the fundamental frequency occurs at n = 1. Increased opening angle β increases the frequency.