Shell effects in the symmetric-modal fission of pre-actinide nuclei

Mass distributions of fragments in the low-energy fission of nuclei from ¹⁸⁷Ir to ²¹³At have been analysed. This analysis has shown that shell effects in symmetric-mode fragment mass yields from the fission of pre-actinide nuclei could be described if one assumes the existence of two strongly deformed neutron shells in the arising fragments with neutron numbers N₁ ≈ 52 and N₂ ≈ 68. A new method has been proposed for quantitatively describing the mass distributions of the symmetric fission mode for pre-actinides with A ≈ 180–220.     

On nonspecular “total internal reflection” of powerful electromagnetic waves

It is shown that the nonstable character of nonlinear interaction of a system of waves similar to that resulting from double stimulated Brillouin scattering is retained upon the oblique incidence of a powerful electromagnetic wave on a layer of supercritical plasma. In this case we have nonlinear back reflection from a layer of supercritical plasma. The threshold intensity of the pump wave is greater than that in the case of subcritical plasma for TE polarization waves but can markedly decrease for waves polarized in the incidence plane. Instability is possible only for a layer of finite thickness.Radiophysical Research Institute, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 298–303, March–April, 1995.     

A prototype 3D optically interconnected neural network

We report the implementation of a prototype three-dimensional (3D) optoelectronic neural network that combines free-space optical interconnects with silicon-VLSI-based optoelectronic circuits. The prototype system consists of a 16-node input, 4-neuron hidden, and a single-neuron output layer, where the denser input-to-hidden-layer connections are optical. The input layer uses PLZT light modulators to generate optical outputs which are distributed over an optoelectronic neural network chip through space-invariant holographic optical interconnects. Optical interconnections provide negligible fan-out delay and allow compact, purely on-chip electronic H-tree type fan-in structure. The small prototype system achieves a measured 8-bit electronic fan-in precision and a calculated maximum speed of 640 million interconnections per second. The system was tested using synaptic weights learned off system and was shown to distinguish any vertical line from any horizontal one in an image of 4×4 pixels. New, more efficient light detector and small-area analog synapse circuits and denser optoelectronic neuron layouts are proposed to scale up the system. A high-speed, feed-forward optoelectronic synapse implementation density of up to 10⁴/cm² seems feasible using new synapse design. A scaling analysis of the system shows that the optically interconnected neural network implementation can provide higher fan-in speed and lower power consumption characteristics than a purely electronic, crossbar-based neural network implementation     

Solution of the Problem of Convecitve Heat Exchange for A Two-Dimensional Body in A Low-Prandtl-Number Fluid Flow

It is shown that the exact solution of the problem of convective heat exchange in a low-Prandtl-number fluid flow (Pr ? 1) can be obtained for a two-dimensional body of arbitrary shape provided that the conformal mapping relating the body contour with a circle is known. By way of example, the Joukowsky airfoil is considered.     

On finite convolutions of singular distributions and a “singular analog” of the Jessen-Wintner theorem

We study the fractal properties of a convolution of two Cantor distributions. By using the method of characteristic functions, we establish sufficient conditions for the singularity of the convolution of an arbitrary finite number of distributions of random variables with independent s-adic digits. We disprove the hypothesis on the validity of a “singular analog” of the Jessen-Wintner theorem for anomalously fractal distributions. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1082–1088, August, 1998. The present work was partially supported by the International Soros Program of Educational Support in Exact Sciences (grant No. APU 061086).     

Homogeneous Stäckel-type systems

A class of Hamiltonian dynamic systems integrated by the variable separation method is considered. The integration for this class is the inversion of an Abel mapping on hyperelliptic curves. We prove that the derivative of the Abel mapping is the Stäckel matrix, which determines a diagonal Riemannian metric and curvilinear orthogonal coordinate systems in a flat space. Lax representations with the spectral parameter are constructed. The corresponding classicalr-matrices are dynamic. It is shown how the class of pointwise canonical transformations can be naturally generalized using the Abel integral reduction theory.     

Constructing a model transport equation for a massless bose gas and its analytic solution

A model kinetic equation is constructed for the transport of a massless Bose gas. This equation is applied to solve the boundary value problem for the transport of radiation in the half-space occupied by a dispersive medium that is in local thermal equilibrium with the radiation. It is shown that the difference in temperature between the dispersive medium and the incident radiation substantially depends on the character of the scattering properties of the particles in the medium. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 3, pp. 462–472, June, 1997.     

Ultralow-voltage boron-doped diamond field emitter vacuum diode

A boron-doped diamond field emitter diode with ultralow turn-on voltage and high emission current is reported. The diamond field emitter diode structure with a built-in cap was fabricated using molds and electrostatic bonding techniques. The emission current versus anode voltage of the capped diamond emitter diode with boron doping, sp² content, and vacuum thermal electric (VTE) treatment shows a very low turn-on voltage of 2 V. A high emission current of 1 μA at an anode voltage of less than 10 V can be obtained from a single diamond tip. The turn-on voltage is significantly lower than comparable silicon field emitters