Symmetry Operators for the Fokker-Plank-Kolmogorov Equation with Nonlocal Quadratic Nonlinearity

The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker-Plank-Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

WHAT ARE SOCIOLOGISTS DOING IN THE 21ST CENTURY: LOOKING AT THE ISA CONGRESS IN TORONTO AND BEYOND

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Topological transitions in superconductor nanomembranes under a strong transport current

The topological defects, vortices in bulk superconductors (SCs) and phase slips in low-dimensional SCs are known to lead to the occurrence of a finite resistance. We report on a topological transition between the both types of topological defects under a strong transport current in an open SC nanotube with a submicron-scale inhomogeneity of the normal-to-the-surface component of the applied magnetic field. When the magnetic field is orthogonal to the axis of the nanotube, which carries the transport current in the azimuthal direction, the phase-slip regime is characterized by the vortex/antivortex lifetime ∼ 10−14 s versus the vortex lifetime ∼ 10−11 s for vortex chains in the half-tubes, and the induced voltage shows a pulse as a function of the magnetic field. The topological transition between the vortex-chain and phase-slip regimes determines the magnetic-field–voltage and current–voltage characteristics of curved SC nanomembranes to pursue high-performance applications in advanced electronics and quantum computing

Topological transitions in ac/dc-driven superconductor nanotubes

Extending of nanostructures into the third dimension has become a major research avenue in condensed-matter physics, because of geometry- and topology-induced phenomena. In this regard, superconductor 3D nanoarchitectures feature magnetic field inhomogeneity, non-trivial topology of Meissner currents and complex dynamics of topological defects. Here, we investigate theoretically topological transitions in the dynamics of vortices and slips of the phase of the order parameter in open superconductor nanotubes under a modulated transport current. Relying upon the time-dependent Ginzburg–Landau equation, we reveal two distinct voltage regimes when (i) a dominant part of the tube is in either the normal or superconducting state and (ii) a complex interplay between vortices, phase-slip regions and screening currents determines a rich FFT voltage spectrum. Our findings unveil novel dynamical states in superconductor open nanotubes, such as paraxial and azimuthal phase-slip regions, their branching and coexistence with vortices, and allow for control of these states by superimposed dc and ac current stimuli

Quadrupole lens with the controlled sextupole component

In the paper the quadrupole lens with a controlled sextupole component is considered. The results of magnetic field modeling for various modes of operations of a lens are shown. The required field is realized with the help of the special pole shape and by the additional excitation windings. The lens described is supposed to be used in the compact cyclic accelerators, sources of synchrotron and X-ray radiation

ARE SOCIOLOGISTS READY FOR ‘ARTIFICIAL SOCIALITY’? CURRENT ISSUES AND FUTURE PROSPECTS FOR STUDYING ARTIFICIAL INTELLIGENCE IN THE SOCIAL SCIENCES

Current sociology doesn’t have a settled view on what to do with a phenomenon that in the literature has been titled as “artificial intelligence” (AI). Sociological textbooks, handbooks, encyclopedias, and sociology classes’ syllabi typically either don’t have entries about AI at all or talk about it haphazardly with a stress on AI’s social effects and without discerning the underlying logic that moves the prodigy on. This paper is an invitation to a professional conversation about what and how social sciences can/should study “artificial intelligence”. It is based on a discussion of the preliminary results of an on-going three-year research project that has been launched at the ISA Congress in Toronto. The paper examines AI in relation with ‘artificial sociality’. It argues that research on AI-based technologies is flourishing mainly outside established disciplinary boundaries. Thus, social sciences have to look for new theoretical and methodological frameworks to approach AI and ‘artificial sociality’

Focusing of transition radiation and diffraction radiation from concave targets

In the article the transition radiation from a relativistic charge crossing a finite radius paraboloid target with taking into account the pre-wave zone effect is considered. It is shown that in this case the radiation cone narrowing occurs in contrast with the transition radiation from the flat target if the detector is situated at the distance, which is smaller than the focus distance (the focusing effect) from the target. At the charged particle passage through the central hole in a paraboloid target the diffraction radiation focusing (DR) occurs too. The focusing of coherent DR for the non-invasive measuring of the electron bunch length is proposed.Comment: 11 pages, 10 figures; Talk presented at the RC2005, Frascati, Ital

Symmetry Operators for the Fokker-Plank-Kolmogorov Equation with Nonlocal Quadratic Nonlinearity

The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker-Plank-Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented