High-Sensitivity Fast Neutron Detector KNK-2-8M

The design of the fast neutron detector KNK-2-8M is outlined. The results of he detector study in the pulse counting mode with pulses from ²³⁸U nuclei fission in the radiator of the neutron-sensitive section and in the current mode with separation of functional section currents are presented. The possibilities of determination of the effective number of ²³⁸U nuclei in the radiator of the neutron-sensitive section are considered. The diagnostic capabilities of the detector in the counting mode are demonstrated, as exemplified by the analysis of reference data on characteristics of neutron fields in the BR-1 reactor hall. The diagnostic capabilities of the detector in the current mode are demonstrated, as exemplified by the results of measurements of ²³⁸U fission intensity in the power startup of the BR-K1 reactor in the fission pulse generation mode with delayed neutrons and the detector placed in the reactor cavity in conditions of large-scale variation of the reactor radiation fields.     

High-sensitivity fast neutron detector KNK-2-7M

The construction of the fast neutron detector KNK-2-7M is briefly described. The results of the study of the detector in the pulse-counting mode are given for the fissions of ²³⁷Np nuclei in the radiator of the neutron-sensitive section and in the current mode with the separation of sectional currents of functional sections. The possibilities of determining the effective number of ²³⁷Np nuclei in the radiator of the neutronsensitive section are considered. The diagnostic possibilities of the detector in the counting mode are shown by example of the analysis of the reference data from the neutron-field characteristics in the working hall of the BR-K1 reactor. The diagnostic possibilities of the detector in the current operating mode are shown by example of the results of measuring the ²³⁷Np-fission intensity in the BR-K1 reactor power start-ups implemented in the mode of fission-pulse generation on delayed neutrons at the detector arrangement inside the reactor core cavity under conditions of a wide variation of the reactor radiation field.     

Normalized split-spectrum: a detection approach

We consider in this paper the problem of automatic detection of ultrasonic echo pulses in a grain noise background. We start by assuming a reference model for grain noise: multivariate correlated Gaussian model having, in general, different variances under every hypothesis. We show that, even for this simple model, there is not practical optimum solution, except if the variances are equal under every hypothesis and the echo pulse satisfies a spectral constraint. Then we consider split-spectrum (SS) suboptimum solutions. Firstly, SS algorithms are formulated following an algebraic approach which is appropriate in an automatic detection framework. Popular minimization and polarity thresholding algorithms are considered under this framework. Then a new detector called normalized SS (NSS) is proposed. The underlying idea is to actually exploit the tuning frequency sensitivity (i.e., variability of the output magnitudes from one SS channel to another), making this measurement independent of the absolute magnitudes. Different experiments with simulated and real data show evidences of the interest of the new method in an automatic detection framework. Derivations of the formulas for fitting the probability of false alarm in every detector are included in the paper.     

Consistent empirical physical formula construction for recoil energy distribution in HPGe detectors by using artificial neural networks

The gamma-ray tracking technique is a highly efficient detection method in experimental nuclear structure physics. On the basis of this method, two gamma-ray tracking arrays, AGATA in Europe and GRETA in the USA, are currently being tested. The interactions of neutrons in these detectors lead to an unwanted background in the gamma-ray spectra. Thus, the interaction points of neutrons in these detectors have to be determined in the gamma-ray tracking process in order to improve photo-peak efficiencies and peak-to-total ratios of the gamma-ray peaks. In this paper, the recoil energy distributions of germanium nuclei due to inelastic scatterings of 1–5 MeV neutrons were first obtained by simulation experiments. Secondly, as a novel approach, for these highly nonlinear detector responses of recoiling germanium nuclei, consistent empirical physical formulas (EPFs) were constructed by appropriate feedforward neural networks (LFNNs). The LFNN-EPFs are of explicit mathematical functional form. Therefore, the LFNN-EPFs can be used to derive further physical functions which could be potentially relevant for the determination of neutron interactions in gamma-ray tracking process.     

Brueckner theory and Jastrow approach for finite nuclei

The results of Jastrow variational calculations and of Brueckner theory in lowest order (Brueckner-Hartree-Fock) are compared. The comparison is made for the calculations of ground state properties like binding energy and charge-radius of light and medium weight, closed shell nuclei (⁴He, ¹⁶O, ⁴⁰Ca). For the nucleon-nucleon interaction rather simple forces are used (Brink-Boeker potential B1, Afnan-Tang potential S3). For all cases considered it turns out that the results of the two different methods are in fairly good agreement, with the binding energy calculated in the Brueckner-Hartree-Fock approximation being always slightly below the corresponding upper bounds calculated in the Jastrow variational approach. This good agreement between the two methods indicates, that for light and medium weight nuclei the Jastrow variational approach and the Brueck-ner-Hartree-Fock approximation can be considered as reasonable approximations to a complete solution of the many-body problem.     

Aberration correction for time-domain ultrasound diffraction tomography

Extensions of a time-domain diffraction tomography method, which reconstructs spatially dependent sound speed variations from far-field time-domain acoustic scattering measurements, are presented and analyzed. The resulting reconstructions are quantitative images with applications including ultrasonic mammography, and can also be considered candidate solutions to the time-domain inverse scattering problem. Here, the linearized time-domain inverse scattering problem is shown to have no general solution for finite signal bandwidth. However, an approximate solution to the linearized problem is constructed using a simple delay-and-sum method analogous to "gold standard" ultrasonic beamforming. The form of this solution suggests that the full nonlinear inverse scattering problem can be approximated by applying appropriate angle- and space-dependent time shifts to the time-domain scattering data; this analogy leads to a general approach to aberration correction. Two related methods for aberration correction are presented: one in which delays are computed from estimates of the medium using an efficient straight-ray approximation, and one in which delays are applied directly to a time-dependent linearized reconstruction. Numerical results indicate that these correction methods achieve substantial quality improvements for imaging of large scatterers. The parametric range of applicability for the time-domain diffraction tomography method is increased by about a factor of 2 by aberration correction.     

Solving the inverse transport problem in intergalactic space and determining the energy spectrum and composition of extragalactic sources of ultrahigh-energy particles

The propagation of ultrahigh-energy nuclei in an expanding Universe filled with background electromagnetic radiation is considered. A numerical method for solving the inverse problem for the equation of cosmic-ray transport is developed that allows the spectrum of sources to be determined from the cosmic-ray spectrum observed near the Earth. The spectra of injected protons and nuclei in extragalactic sources are found by assuming that they are functions of the magnetic rigidity of particles. The data from observations obtained in the Auger experiment are used.     

Statistical analysis of rare events—synthesis of the element 114

Rare events pose a problem: is an observed chain of radioactive decays that of the background, or are they genetically linked? The paper suggests an approach for the problem solution, based on formalization of the background concept. This approach is an inevitable alternative to other methods, which require the a priori information about the linked decays, in a situation when such information is absent, but, instead, the background information is available, e.g., from the calibration measurements. The method is illustrated by the analysis of data registered in the experiment on the synthesis of the element 114 as one of practically important examples of the analysis of rare events.     

Dynamic polarization of 6,7Li nuclei in the elastic scattering of α particles

The elastic scattering of α particles on weakly bound ^6,7Li cluster nuclei is considered with allowance for their dynamic polarization within the three-particle model. The considered states of the αd and αt continuums are projected on a finite basis of stationary wave packets, which allows the total three-body problem to be reduced to a matrix problem. The results from calculating α + ^6,7Li-elastic scattering differential cross sections are considered as illustration of the three-particle approach and is compared to the results of other authors.     

Determination of the asymmetry parameter of EFG tensor from moments of NQR nutation spectra in powders

A novel approach to determination of the asymmetry parameter of the EFG tensor from zero-field nutation NQR spectra of the spinI = 3/2 nuclei in powder samples is reported. The proposed theoretical treatment uses lineshape analysis of the nutation NQR spectra by the method of line moments. The analytical formulas for the lineshape of the powder nutation spectrum are given. It is shown that the asymmetry parameter can be determined from the second moment 〈ω²〉 and the frequency of only one singularity ω₂ of the nutation spectrum. It is also shown that the asymmetry parameter can be determined from the second and fourth spectrum moments alone. The method is successfully demonstrated for the simulated nutation NQR spectra of the spinI = 3/2 nuclei in powder samples.     

Development of a new approach to simulate a particle track under electrochemical etching in polymeric detectors

A numerical approach based on image processing was developed to simulate a particle track in a typical polymeric detector, e.g., polycarbonate, under electrochemical etching. The physical parameters such as applied voltage, detector thickness, track length, the radii of curvature at the tip of track, and the incidence angle of the particle were considered, and then the boundary condition of the problem was defined. A numerical method was developed to solve Laplace equation, and then the distribution of the applied voltage was obtained through the polymer volume. Subsequently, the electric field strengths in the detector elements were computed. In each step of the computation, an image processing technique was applied to convert the computed values to grayscale images. The results showed that a numerical solution to Laplace equation is dedicatedly an attractive approach to provide us the accurate values of electric field strength through the polymeric detector volume as well as the track area. According to the results, for a particular condition of the detector thickness equal to 445 μm, track length of 21 μm, the radii of 2.5 μm at track tip, the incidence angle of 90°, and the applied voltage of 2080 V, after computing Laplace equation for an extremely high population of 4000 × 4000 elements of detector, the average field strength at the tip of track was computed equal to 0.31 MV cm⁻¹ which is in the range of dielectric strength for polymers. The results by our computation confirm Smythe’s model for estimating the ECE-tracks.     

On three particle stripping reactions

The formalism for the coupled-channel analysis of stripping reactions of complex nuclear projectiles by nuclei is presented. The general adiabatic approximation is developed. The indirect transitions that are considered are those which arise via intermediate rotational excitations of the target and product nuclei, i.e. the adiabatic approximation for rotational bands is used. At the same time the generalized DWBA procedure is considered for the intrinsic states. Also the antisymmetrization problem is solved. A new method for the calculation of the matrix elements of the (α,n) stripping reaction with finite range effective forces is developed. The method is based on an expansion of the radial functions which describe the relative motion in terms of harmonic oscillator wave functions multiplied by a Gauss one. Effective forces of Gauss type are assumed between the outgoing neutron and each captured nucleon     

Low-frequency linear vibrations of single-walled carbon nanotubes: Analytical and numerical models

Low-frequency vibrations of single-walled carbon nanotubes with various boundary conditions are considered in the framework of the Sanders–Koiter thin shell theory. Two methods of analysis are proposed. The first approach is based on the Rayleigh–Ritz method, a double series expansion in terms of Chebyshev polynomials and harmonic functions is considered for the displacement fields; free and clamped edges are analysed. This approach is partially numerical. The second approach is based on the same thin shell theory, but the goal is to obtain an analytical solution useful for future developments in nonlinear fields; the Sanders–Koiter equations are strongly simplified neglecting in-plane circumferential normal strains and tangential shear strains. The model is fully validated by means of comparisons with experiments, molecular dynamics data and finite element analyses obtained from the literature. Several types of nanotubes are considered in detail by varying aspect ratio, chirality and boundary conditions. The analyses are carried out for a wide range of frequency spectrum. The strength and weakness of the proposed approaches are shown; in particular, the model shows great accuracy even though it requires minimal computational effort.     

An Electrostatics Approach to the Determination of Extremal Measures

One of the most important aspects of the minimal energy (or induced equilibrium) problem in the presence of an external field – sometimes referred to as the Gauss variation problem – is the determination of the support of its solution (the so-called extremal measure associated with the field). A simple electrostatic interpretation is presented here, which is apparently new and anyway suggests a novel, rather systematic approach to the solution. By way of illustration, the classical results for Jacobi, Laguerre and Freud weights are explicitly recovered by this alternative method.     

On long-wave sound scattering by a Rankine vortex: Non-resonant and resonant cases

The well-known two-dimensional problem of sound scattering by a Rankine vortex at small Mach number M is considered. Despite its long history, the solutions obtained by many authors still are not free from serious objections. The common approach to the problem consists in the transformation of governing equations to the d’Alembert equation with right-hand part. It was recently shown [I.V. Belyaev, V.F. Kopiev, On the problem formulation of sound scattering by cylindrical vortex, Acoustical Physics 54(5) (2008) 603-614] that due to the slow decay of the mean velocity field at infinity the convective equation with nonuniform coefficients instead of the d’Alembert equation should be considered, and the incident wave should be excited by a point source placed at a large but finite distance from the vortex instead of specifying an incident plane wave (which is not a solution of the governing equations).Here we use the new formulation of Belyaev and Kopiev to obtain the correct solution for the problem of non-resonant sound scattering, to second order in Mach number M. The partial harmonic expansion approach and the method of matched asymptotic expansions are employed. The scattered field in the region far outside the vortex is determined as the solution of the convective wave equation, and van Dyke's matching principle is used to match the fields inside and outside the vortical region. Finally, resonant scattering is also considered; an O(M²) result is found that unifies earlier solutions in the literature. These problems are considered for the first time.     

Green׳s function method for piezoelectric energy harvesting beams

The development of validated mathematical models for piezoelectric harvesters is important as it provides predictive capabilities of their performance and insight to their coupled electromechanical behavior. Advanced solutions to these models allows for more realistic parameters to be considered. In this paper, we present a Fourier Transform–Green?s Function (FTGF) solution approach to the distributed parameter coupled electromechanical equations for a piezoelectric beam excited by an arbitrary external transverse force. This method, as opposed to modal analysis, allows for frequency-dependent material properties and damping coefficients to be considered. The special case of a harmonic base excitation is considered and closed-form expressions for the frequency response functions of the voltage generated by piezoelectric layer, relative tip displacement and local bending strain are obtained. Finally, the FTGF solution to these frequency response functions is compared with the modal analysis solution along with experimental data for validation.     

Reconstruction of the potential of an intermolecular interaction on the basis of the virial coefficients

Some formulations of the problem of reconstructing the potential of the two-body interaction from the temperature dependence of the second virial coefficient are considered. For three-parameter potential models (Morse and Kihara) the formalism of the Fisher matrix is used to calculate the coefficients of the amplification of the errors in the determination of each of the parameters. For the general case of the nonparametric approach a scheme of formal linearization of the problem is given and conditions for unique solution of it found. The example of the reconstruction of the potential of Maxwellian molecules is given. Some new possibilities are noted for the unique reconstruction on the basis of the temperature dependences of the transport coefficients.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 30–33, June, 1980.     

Modeling of Raman-Scattering Signals in Biological Tissues by Direct and Two-Step Approaches

A search for an effective method of modelling of the Raman-spectroscopy problem in turbid (scattering) media has been performed taking into account the corresponding parameters of the detector and sample volume. A solution of the radiative-transfer equation by Monte-Carlo method underlies the proposed model. Two fundamental approaches to numerical modeling of Raman scattering are considered: the direct transport problem of Rayleigh and Raman photons at each point of the medium and the two-step model, in which a photon flux in the medium is calculated in the first stage, followed by generation of the corresponding number of Raman photons at each point.     

Spectrum-modulation method for measuring the amplitude and phase characteristics of time-varying optical signals and transfer functions

The solution of the phase problem in optics, as applied to the determination of the amplitude and phase characteristics of optical signals varying in time and of the transfer functions of media transmitting the signals, is considered. The solution of this problem is based on using the spectrum-modulation method. In particular, the possibility of studying ultrashort processes is considered. The analysis was performed by probing the medium with an optical signal of an arbitrary structure. To obtain the information required, we used a four-channel optical arrangement with a spectral instrument, which records the intensity distributions directly for the signal under study after it passed through the medium; for the signal that was preliminary modulated in the specific manner and then passed through the medium; for the signal that was additionally modulated after passing through the medium; and for the signal that was additionally modulated both before and after passing through the medium. Each of these modulations should provide, to some extent, visualization of the phase information. Two variants of analysis were considered. In the first variant, the influence of the medium to be analyzed on the radiation considered is represented as modulation of the latter in time. The second variant is associated with studying the medium, whose influence on the signal brings about time-redistribution of the radiation and is described by a convolution operation.     

A note on transverse vibrations of a rectangular plate with a free,rectangular, corner cut-out

An approximate solution to the title problem is presented, obtained by using the Rayleigh-Ritz method. The analysis is presented for the case of simply supported and clamped plates. For the case of a rigidly clamped plate results are presented of numerical experiments on minimizing the calculated value of the fundamental frequency coefficient by using Schmidt's approach. An experimental investigation is described on a clamped square plate with a free square, corner cut-out, which has led to the conclusion that the fundamental frequency coeficient remains practically invariant with respect to size when compared with the frequency coefficient of the fully clamped plate. A similar conclusion is arrived at by means of the mathematical model. The problem under consideration is important from a practical viewpoint since cut-outs of the type considered here are quite common in engineering practice.