Nash Equilibria,Variational Inequalities,and Dynamical Systems

In this paper, we introduce some relationships between Nash equilibria, variational equilibria, and dynamical equilibria for noncooperative games.     

Screw dislocation in spherical particle

The elastic fields generated by a straight-line screw dislocation axially arranged in a spherical particle have been calculated and analyzed. Some features of the distribution of elastic fields in this case and in the case of a screw dislocation lying along the axis of a cylindrical whisker are similar. The elastic energies per unit dislocation length differ slightly in the two cases. This corroborates the validity of application of some of the results obtained for screw dislocations in elastic cylinders to the study of properties of screw dislocations in equiaxed particles.Authors are very indebted to dr. A. B. Lebedev for his kind support.     

Determination of the rate of nonradiative relaxation,processes on excitation of electronic states in YAG:Nd3+

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 2, pp. 229–233, February, 1991.     

Cyclotron resonance for electrons over helium in a resonator

The cyclotron resonance (CR) problem for electrons over a helium film occupying the lower part of a resonator is solved. This problem is shown to represent an example of the well-known problem on the behavior of a system of coupled oscillators. For such oscillators, the coupling constant is determined as a function of the problem parameters with its minimal value in zero magnetic field and its maximal value at resonance conditions, when the cyclotron frequency coincides with one of the resonator modes. The details of the CR absorption of microwave energy by the coupled system formed by 2D electrons and a resonator are calculated. The results are discussed in application to the known CR experiments with electrons over helium.     

Convergence of the method of partition of regions for second-order elliptic conjugation problems

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 8, pp. 1137–1141, August, 1989.     

Temperature distribution in the bright spot of the optical discharge in an optical fiber

2D simulation of the optical discharge propagation in an optical fiber is performed. In contrast to the previous works, the temperature dependences of the transfer coefficient are taken into account for the bright-spot plasma. The results are compared with the recently published measurements of the spatial distribution of the bright-spot radiation intensity. Good agreement is obtained for the discharge propagation velocity and the dependence of the bright-spot size on the laser power.     

Ionization of Hydrogen and Helium Atoms in Collisions with Relativistic Structural Heavy Ions

Based on the eikonal approximation, cross sections for single and double ionization of hydrogen and helium atoms in collisions with structural multiply charged heavy ions moving with relativistic velocities are calculated. In the present paper, the structural ions are taken to mean the ions with partially filled electronic shells. It is demonstrated that a consideration of the ion charge extension may noticeably change the corresponding cross sections compared to the cross sections for ionization by point ions having the same charges and energies.     

Analysis of Static Simulated Annealing Algorithms

Generalized hill climbing (GHC) algorithms provide a framework for modeling local search algorithms to address intractable discrete optimization problems. This paper introduces a measure for determining the expected number of iterations to visit a predetermined objective function level, given that an inferior objective function level has been reached in a finite number of iterations. A variation of simulated annealing (SA), termed static simulated annealing (S²A), is analyzed using this measure. S²A uses a fixed cooling schedule during the algorithm execution. Though S²A is probably nonconvergent, its finite-time performance can be assessed using the finite-time performance measure defined in this paper.     

STM/AFM studies of the evolution of morphology of electroplated Ni/W alloys

The surface morphology evolution of Ni/W alloys was studied, as a function of the alloy composition. Using the modified plating baths developed in our laboratory recently, electroplated Ni/W alloys with different W content, in the range of 7–67 atom percent (a/o), can be obtained. This was found to lead to different structures, ranging from polycrystalline fcc-Ni type structure to amorphous, followed by orthorhombic with increasing W content in the alloy. Powder XRD was studied to determine the crystal structures. Ex situ STM, AFM and SEM were used to study in detail the surface morphologies of the different alloys, and their evolution with increasing W content.

The important findings are that a mixture of two crystalline forms can give rise to an amorphous structure. Hillocks that are usually a characteristic of epitaxial growth can also exist in the amorphous alloys. Oriented scratches caused by stress can also be formed.

Up to 20 a/o of W is deposited in the alloys in crystalline form, with the fcc-Ni type structure. Between 20 and about 40 a/o an amorphous structure is observed, and above that an orthorhombic crystal structure is seen, which is characteristic of the NiW binary alloy. Careful choice of the composition of the plating bath allowed us to deposit an alloy containing 67 a/o W, which corresponds to the composition NiW₂.