Phase diagram of 2D array of mesoscopic granules

A lattice boson model is used to study ordering phenomena in regular 2D array of superconductive mesoscopic granules, Josephson junctions or pores filled with a superfluid helium. Phase diagram of the system, when quantum fluctuations of both the phase and local superfluid density are essential, is analyzed both analytically and by quantum Monte Carlo technique. For the system of strongly interacting bosons it is found that as the boson density $n_0$ is increased the boundary of ordered superconducting state shifts to {\it lower temperatures} and at $n_0 > 8$ approaches its limiting position corresponding to negligible relative fluctuations of moduli of the order parameter (as in an array of "macroscopic" granules). In the region of weak quantum fluctuations of phases mesoscopic phenomena manifest themselves up to $n_0 \sim 10$. The mean field theory and functional integral $1/n_0$ - expansion results are shown to agree with that of quantum Monte Carlo calculations of the boson Hubbard model and its quasiclassical limit, the quantum XY model.Comment: 7 pages, 5 Postscript figure

New model for system of mesoscopic Josephson contacts

Quantum fluctuations of the phases of the order parameter in 2D arrays of mesoscopic Josephson junctions and their effect on the destruction of superconductivity in the system are investigated by means of a quantum-cosine model that is free of the incorrect application of the phase operator. The proposed model employs trigonometric phase operators and makes it possible to study arrays of small superconducting granules, pores filled with superfluid helium, or Josephson junctions in which the average number of particles $n_0$ (effective bosons, He atoms, and so on) is small, and the standard approach employing the phase operator and the particle number operator as conjugate ones is inapplicable. There is a large difference in the phase diagrams between arrays of macroscopic and mesoscopic objects for $n_0 < 5$ and $U<J$ ($U$ is the characteristic interaction energy of the particle per granule and $J$ is the Josephson coupling constant). Reentrant superconductivity phenomena are discussed.Comment: 4 pages, 3 Postscript figure

Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number $n_0$ of the sites in the system leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on $n_0$. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in $n_0$ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum Path-Integral Monte Carlo calculations.Comment: 12 pages, 8 Postscript figure

A New High Energy Photon Tagger for the H1 - Detector at HERA

The H1 detector at HERA has been upgraded by the addition of a new electromagnetic calorimeter. This is installed in the HERA tunnel close to the electron beam line at a position 8m from the interaction point in the electron beam direction. The new calorimeter extends the acceptance for tagged photoproduction events to the high y range, 0.85 < y < 0.95, and thus significantly improves the capability of H1 to study high energy gamma-p processes. The calorimeter design, performance and first results obtained during the 1996-1999 HERA running are described.Comment: 17 pages, 16 figure

Tagging High Energy Photons in the H1 Detector at HERA

Measures taken to extend the acceptance of the H1 detector at HERA for photoproduction events are described. These will enable the measurement of electrons scattered in events in the high y range 0.85 < y < 0.95 in the 1998 and 1999 HERA run period. The improvement is achieved by the installation of an electromagnetic calorimeter, the ET8, in the HERA tunnel close to the electron beam line 8 m downstream of the H1 interaction point in the electron direction. The ET8 will allow the study of tagged gamma p interactions at centre-of-mass energies significantly higher than those previously attainable. The calorimeter design and expected performance are discussed, as are results obtained using a prototype placed as close as possible to the position of the ET8 during the 1996 and 1997 HERA running.Comment: 13 pages, 13 figure

Representations of (2,n)(2,n)-semigroups by multiplace functions

We describe the representations of $(2,n)$-semigroups, i.e. groupoids with $n$ binary associative operations, by partial $n$-place functions and prove that any such representation is a union of some family of representations induced by Schein's determining pairs.Comment: 17 page

Origin of volatiles emitted by Plinian mafic eruptions of the Chikurachki volcano, Kurile arc, Russia : trace element, boron and sulphur isotope constraints

Author Posting. © The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Chemical Geology 478 (2018): 131-147, doi:10.1016/j.chemgeo.2017.10.009.Chikurachki is a 1816-m high stratovolcano on Paramushir Island, Kurile arc, Russia, which has repeatedly produced highly explosive eruptions of mafic composition. The present work is aimed at constraining the origin of volatile components (CO2, H2O, F, S, and Cl), along with B and S isotopic compositions in a series of phenocryst-hosted melt inclusions and groundmass glasses from basaltic andesite pyroclasts of the 1853, 1986, and prehistoric Plinian eruptions of the volcano. The ranges of volatile concentrations in melt inclusions (47–1580 μg/g CO2, 0.4–4.2 wt% H2O, 399–633 μg/g F, 619–3402 μg/g S and 805–1240 μg/g Cl) imply a sudden pressure release from ~ 460 through ~ 35 MPa that corresponds to ~ 1.2–16-km-depth range of magma ascent upon decompression. We conclude that rapid ascent of the volatile-rich basaltic magmas from ~ 16-km initial depth accompanied by near-surface bubble nucleation and growth, and subsequent magma fragmentation appear to be a primary reason for the Plinian character of the Chikurachki eruptions. Significant negative correlations of S with K, Zr, Nb, Ba, La, Ce, Pr (R = − 0.8 to − 0.9), no clear relationships of S with H2O, CO2 and Cl, but strong positive correlations of S/K2O with H2O/K2O, Cl/K2O and F/K2O preclude magma degassing to be the only process affecting volatile concentrations dissolved in the melt. The δ34S values of the studied inclusion and groundmass glasses range from − 1.6 to + 12.3‰, decrease with decreasing S, show significant positive correlations with H2O/K2O, Cl/K2O and F/Zr, and negative correlations with a number of incompatible trace elements. Neither open- nor close-system magma degassing can account for the observed range of δ34S. The δ11B values of the melt inclusions range from − 7.0 to + 2.4‰ with 13–23 μg/g B. The relationships of δ11B with B/K2O and B/Nb are inconsistent with magma contamination at shallow crustal depths. Linear character of 1/S vs. δ34S relationship suggests two-component mixing. The possible mixing end-members could be the magmas having similar major and trace element compositions, but strongly contrasting volatile contents and S isotopes. Based on the behaviour of fluid-mobile vs. fluid-immobile incompatible trace elements, we conclude that the subduction component likely represents a mixture of subduction sediment-derived melt with up to 60% of slab-derived fluid. Admixture of ~ 1–8% of the inferred subduction component to the depleted mantle wedge source is required to account for the compositional range of the Chikurachki melt inclusions, and ~ 0.4–10% to constrain the composition of Kurile arc mafic magmas.This work was benefited from the NENIMF financial support of AAG during his training as a SIMS research specialist, the NSF grant EAR 0911093 to AAG, and partially from the Russian Science Foundation grant #16-17-10145 to VSK and MEZ

Stochastic Turing patterns in the Brusselator model

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross diffusive terms, often neglected in the heuristic derivation of reaction diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.Comment: modified version submitted to Phys Rev. E. 5. 3 Figures (5 panels) adde

Representations of Menger (2,n)(2,n)-semigroups by multiplace functions

Investigation of partial multiplace functions by algebraic methods plays an important role in modern mathematics were we consider various operations on sets of functions, which are naturally defined. The basic operation for $n$-place functions is an $(n+1)$-ary superposition $[ ]$, but there are some other naturally defined operations, which are also worth of consideration. In this paper we consider binary Mann's compositions \op{1},...,\op{n} for partial $n$-place functions, which have many important applications for the study of binary and $n$-ary operations. We present methods of representations of such algebras by $n$-place functions and find an abstract characterization of the set of $n$-place functions closed with respect to the set-theoretic inclusion

Innovations as a tool for providing cyber security and increasing the efficiency of banking system

Objective: to research innovative technologies as a means of protecting important information; to reveal the relationship between information security and improving the performance of banks.Methods: the problem of banks’ counteraction to cyberattacks was researched with systematic approach and a method of statistical analysis.Results: under the development of information and communication technologies, the problem of theft, modification, and forgery of information has acquired the greatest importance. Cyberattacks threaten the loss of personal data and can affect both the functioning of financial and commercial organizations, and the economy of the state as a whole. In this article, cyber threats are viewed as a priority problem of banks under widespread digitalization. The main trends in the field of cyber risks are identified; the dynamics of cyber attacks is studied. The activities carried out in Russia to prevent cybercrime are considered. The main reasons for cyber threats in the banking sector are systematized, including the human factor. Conclusions are made that in order to prevent cyberthreats it is necessary to introduce banking innovations based, among other things, on the positive foreign experience of applying the process-oriented approach, BigData technologies, blockchain, and biometric identification of customers.Scientific novelty: a set of measures was developed to introduce banking innovations and reduce cyber threats, including the development of cyber insurance.Practical significance: the proposed recommendations can be used in the practical activities of government agencies and banking professionals when making decisions in the field of cybersecurity