Vortex-bearing array of singular beams with very high orbital angular momentum

We consider theoretically and experimentally an array of singular beams whose axes lie on the surface of a hyperboloid of revolution. We show that such a singular array can carry a very high orbital angular momentum. Experimental results demonstrate a way of generating such singular arrays.     

Jumplike deformation of γ-irradiated polymethyl methacrylate

Nonuniformity of the microdeformation rate and the parameters of microdeformation jumps were studied in the creep regime for a polymethyl methacrylate irradiated by various dozes of the Co-60 γ radiation. The creep rate during compression of the polymethyl methacrylate was measured by an interferogram on 300-nm deformation increments. It is shown that the periods L of rate oscillations (jumps of deformation) on three scale levels are dependent on the irradiation doze and are also changed after prolonged exposure of samples in air. In the doze range 0 to 330 kGy, both a decrease and an increase in L are observed, which corresponds to the unstable kinetics of radiation chemical processes. The deformation jumps permit estimates of the radiation effect on various structural levels. It is concluded that the effect of radiation on coarser microstructural formations is the largest.

     

Experiments on the physics of charged particle beams at the VEPP-4M electron-positron collider

The VEPP-4M accelerator facility with a universal KEDR detector is designed to conduct experiments with colliding electron-positron beams. High-energy physics, nuclear physics, and studies using synchrotron radiation are the main directions of research with this facility. In addition, experiments on poorly explored issues in the physics of beams in the electron-positron storage ring and methodological studies to prepare an experiment aimed at testing corollaries of the CPT theorem for an electron and a positron are regularly conducted at the VEPP-4 facility. A number of works performed in recent years are described: studies to increase the accuracy of comparing the electron and positron spin precession frequencies by the resonant depolarization method; measurements of the count rate of Touschek electrons as a function of the beam energy in a wide range; comparison of the methods for measuring the beam energy spread; a study of the electron beam dynamics when a nonlinear betatron resonance is crossed.     

Initial conditions in quasi-classical field theory

We investigate the problem of divergences and renormalizations in the Hamiltonian formalism of quasiclassical field theory. This approach is known to involve divergences in the leading term of the expansion. Proposals have been made to eliminate the divergences by using nonequivalent representations of the canonical commutation relations at different moments of time. In this paper, we consider the Schrödinger equation with ultraviolet and infrared cutoffs. In order to remove the cutoffs, conditions are imposed on the initial state of the regularized theory in addition to the conditions imposed on the counterterms in the Hamiltonian. In the leading order of the quasi-classical expansion, we give the explicit form of these conditions, which is invariant under the evolution. This allows us to show that this approximation does not require the introduction of nonunitary evolution transformations.     

Approximation of exact and closed differential forms by finite ones

Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 2, pp. 49–65, March–April, 1992.