Computer simulations are nowadays a rmly established third pillar of modern natural sciences, complementing experimentation and paper-and-pencil theoret- ical studies. Simulations, experiments in silico, prove indispensable in diverse areas of research in physics and other natural sciences. This volume collects papers based on presentations delivered at the Sec- ond International Conference on Computer Simulations in Physics and beyond (CSP2017), which took place October 9-12, 2017 in Moscow. The Conference, which continues a biannual tradition started by an innaugural conference in 2015, took place on campus of A.N. Tikhonov Moscow Institute of Electronics and Mathematics, was jointly organized by the National Research University Higher School of Economics, the Landau Insitute for Theoretical Physics and Science Center in Chernogolovka. As the name implies, the Conference is a multidisciplinary meeting, with a focus on computational physics and related subjects. Indeed, methods of computational physics prove useful in a broad spectrum of research in multiple branches of natural sciences, and this volume provides a sample. We hope that this volume will interest a wide range of readers, and we are already looking forward for the next conference in this biannual series.

This book highlights selected topics of standard and modern theory of accretion onto black holes and magnetized neutron stars. The structure of stationary standard discs and non-stationary viscous processes in accretion discs are discussed to the highest degree of accuracy analytic theory can provide, including relativistic effects in flat and warped discs around black holes. A special chapter is dedicated to a new theory of subsonic settling accretion onto a rotating magnetized neutron star. The book also describes supercritical accretion in quasars and its manifestation in lensing events. Several chapters cover the underlying physics of viscosity in astrophysical discs with some important aspects of turbulent viscosity generation. The book is aimed at specialists as well as graduate students interested in the field of theoretical astrophysics.

The present book gathers chapters from colleagues of A. Ezersky from Russia, especially those from Nizhny Novgorod Institute of Applied Physics of the Russian Academy of Science and from France, with whom he has been collaborating on experimental and theoretical developments. The book is subdivided into two parts. Part I contains eight chapters related to nonlinear water waves and Part II addresses in five chapters, patterns dynamics in nonequilibrium media. The contributions of Alexander B. Ezersky were valuable from both the experimental and the theoretical points of view. We thank all the authors for their contributions and the Springer Editor for having kindly accepted the edition of this book in memory of our colleague and friend, Prof. Alexander Borisovich Ezersky.

The materials of The International Scientific – Practical Conference is presented below.

The Conference reflects the modern state of innovation in education, science, industry and social-economic sphere, from the standpoint of introducing new information technologies.

It is interesting for a wide range of researchers, teachers, graduate students and professionals in the field of innovation and information technologies.

These notes have appeared as a result of a one-term course in superfluidity and superconductivity given by the author to fourth-year undergraduate students and first-year graduate students of the Department of Physics, Moscow State University of Education. The goal was not to give a detailed picture of these two macroscopic quantum phenomena with an extensive coverage of the experimental background and all the modern developments, but rather to show how the knowledge of undergraduate quantum mechanics and statistical physics could be used to discuss the basic concepts and simple problems, and draw parallels between superconductivity and superfluidity.

Superconductivity and superfluidity are two phenomena where quantum mechanics, typically constrained to the microscopic realm, shows itself on the macroscopic level. Conceptually and mathematically, these phenomena are related very closely, and some results obtained for one can, with a few modifications, be immediately carried over to the other. However, the student of these notes should be aware of important differences between superconductivity and superfluidity that stem mainly from two facts: (1) electrons in a superconductor carry a charge, therefore one has to take into account interaction with electromagnetic radiation; (2) electrons move in a lattice, therefore phonons play a role not only a mediators of attractive interaction between pairs of electrons, but also as scatterers of charge carriers.

Although these are notes on superfluidity and superconductivity, and there are a few cross-references, the two subjects can be studied independently with, perhaps, a little extra work by the student to fill in the gaps resulting from such study. The material of Chapter 1 introduces the method of second quantisation that is commonly used to discuss systems with many interacting particles. It is then applied in Chaper 2 to treat the uniform weakly interacting Bose gas within the approach by N. Bogoliubov, and in Chapter 4 to formulate the theory of the uniform superconducting state put forth by J. Bardeen, L. Cooper and R. Schrieffer. Chapter 3 presents the theory proposed independently by E. Gross and L. Pitaevskii of a non-uniform weakly interacting Bose gas, with a discussion of vortices, rotation of the condensate, and the Bogoliubov equations. In Chapter 5 we discuss the Ginzburd-Landau theory of a non-uniform superconductor near the critical temperature and apply it to a few simple problems such as the surface energy of the boundary between a normal metal and a superconductor, critical current and critical magnetic field, and vortices.

In this paper we present the studies of an ultrametric mathematical model for protein operation and give them physical interpretations that extend the conventional view of ensymatic activity regulation. The model is based on a representation of a multidimentional rugged energy landscapes by a hierarchy of nested basins of local minima and an approximation of protein dynamics with an ultrametric random walk. In contrast to an ordinary random walk, the ultrametric random walk is more suitable for describing of multiscale conformational dynamics and it is consistent with the kinetic features of ligand binding. Using our ultrametric model we show different ways to regulate enzymatic activity.

Superconducting properties of metallic nanowires can be entirely different from those of bulk superconductors because of the dominating role played by thermal and quantum fluctuations of the order parameter. For superconducting channels with diameters below ∼ 50 nm fluctuations of the phase of the complex order parameter - the phase slippage  -  lead to non-zero resistance below the critical temperature.  Fluctuations of the modulus of the complex order parameter broaden the gap edge of the quasiparticle energy spectrum and modify the density of states. In extreme case of very narrow channels imbedded in high-impedance environment  (which fix the charge and, hence, enable strong fluctuations of the quantum-conjugated variable, the phase) the superconductor can be driven to insulating state  – the Coulomb blockade. We review recent experimental activities in the field demonstrating rather unusual phenomena.

The materials of The International Scientific – Practical Conference is presented below. The Conference reflects the modern state of innovation in education, science, industry and social-economic sphere, from the standpoint of introducing new information technologies.

It is interesting for a wide range of researchers, teachers, graduate students and professionals in the field of innovation and information technologies.

The textbook is meant for students continuing to study English (levels B1-B2 according to the European Framework) and majoring in science. The exercises and tasks are aimed at developing speaking, writing and reading skills on the basis of authentic texts on the achievements of scientists rewarded the Nobel Prize in the years 2000-2014

Adequate assessment of individual functional motor potentials is important for developing appropriate rehabilitation strategies in ischemic stroke [1]. Microstructural changes in corticospinal tract (CST) and corpus callosum (CC) were repeatedly correlated to post-stroke outcome [2, 3]. However, relationship between them and functional recovery remains unclear. Here we investigated relationship between integrity of CST and CC assessed with diffusion tensor imaging (DTI) and brain functional state assessed with navigated transcranial magnetic stimulation (nTMS) in chronic ischemic supratentorial stroke.

In this volume we have collected papers based on the presentations given at the International Conference on Computer Simulations in Physics and beyond (CSP2015), held in Moscow, September 6-10, 2015. We hope that this volume will be helpful and scientifically interesting for readers.

The Conference was organized for the first time with the common efforts of the Moscow Institute for Electronics and Mathematics (MIEM) of the National Research University Higher School of Economics, the Landau Institute for Theoretical Physics, and the Science Center in Chernogolovka. The name of the Conference emphasizes the multidisciplinary nature of computational physics. Its methods are applied to the broad range of current research in science and society. The choice of venue was motivated by the multidisciplinary character of the MIEM. It is a former independent university, which has recently become the part of the National Research University Higher School of Economics.

The development of terahertz imaging instruments for security systems is on the cutting edge of terahertz technology. We are developing a THz imaging system based on a superconducting integrated receiver (SIR). An SIR is a new type of heterodyne receiver based on an SIS mixer integrated with a flux-flow oscillator (FFO) and a harmonic mixer which is used for phase-locking the FFO. Employing an SIR in an imaging system means building an entirely new instrument with many advantages compared to traditional systems. In this project we propose a prototype THz imaging system using an 1 pixel SIR and 2D scanner. At a local oscillator frequency of 500 GHz the best noise equivalent temperature difference (NETD) of the SIR is 10 mK at an integration time of 1 s and a detection bandwidth of 4 GHz. The scanner consists of two rotating flat mirrors placed in front of the antenna consisting of a spherical primary reflector and an aspherical secondary reflector. The diameter of the primary reflector is 0.3 m. The operating frequency of the imaging system is 600 GHz, the frame rate is 0.1 FPS, the scanning area is 0.5 × 0.5 m2, the image resolution is 50 × 50 pixels, the distance from an object to the scanner was 3 m. We have obtained THz images with a spatial resolution of 8 mm and a NETD of less than 2 K.

IVEC was originally created in 2000 by merging the U.S. Power Tubes Conferences and the European Space Agency TWTA Workshops. Now a fully international conference, IVEC is held every other year in the U.S., and in Europe and Asia alternately every fourth year. After the successful and enjoyable meeting in Paris, France in May, IVEC 2014 will return to its beautiful U.S. location in the city of Monterey.

These proceedings have been written in an attempt to communicate the major purpose of the NATO Advanced ResearchWorkshop (ARW), 2013, that is, to bring to light the possibilities of performance, based on the actual level, of the everpromising THz (terahertz) technology, a kind of Araba Fenice, not yet known tomost technical operators, especially its appeal in security applications. To achieve this, the ARWhas invited highly experienced scientists with expertise in THz science and technology and its application areas. We begin with the consideration that the risk of mass murder due to terroristic attacks is on the rise, thus posing a threat for security in the civil and military world. To counter this problem, we look at one of the most appealing, newly emerging, technologies that is based on the THz detection of explosives and other forms of threats. However, operational difficulties (both for THz sensors and sources), especially regarding size, complexity of use, overall cost, and the need of very low temperatures for sensors, strongly limit the application of this technology. To find solutions to these and related issues, we invited expert scientists to present review papers on the most advanced sensors and sources based on THz technology, especially for security system applications. The ARW has been conferred the major task of describing the most advanced technologies, in terms of identifying their operational strengths and weaknesses, forecasting the best technological solutions to overcome the actual operational limits, and suggesting to the NATO SPS (Science for Peace and Security) Division the most reliable ways to proceed for future developments. To achieve a broad evaluation of the above aspects, a questionnaire on various key points with regard to the actual performance and possible future developments in the field of THz science, technology, and applications has been discussed.

Overview This book concisely presents the latest trends in the physics of superconductivity and superfluidity and magnetismin novel systems, as well as the problem of BCS-BEC crossover in ultracold quantum gases and high-Tc superconductors. It further illuminates the intensive exchange of ideas between these closely related fields of condensed matter physics over the last 30 years of their dynamic development. The content is based on the author’s original findings obtained at the Kapitza Institute, as well as advanced lecture courses he held at the Moscow Engineering Physical Institute, Amsterdam University, Loughborough University and LPTMS Orsay between 1994 and 2011. In addition to the findings of his group, the author discusses the most recent concepts in these fields, obtained both in Russia and in the West. The book consists of 16 chapters which are divided into four parts. The first part describes recent developments in superfluid hydrodynamics of quantum fluids and solids, including the fashionable subject of possible supersolidity in quantum crystals of 4He, while the second describes BCS-BEC crossover in quantum Fermi-Bose gases and mixtures, as well as in the underdoped states of cuprates. The third part is devoted to non-phonon mechanisms of superconductivity in unconventional (anomalous) superconductors, including some important aspects of the theory of high-Tc superconductivity. |The last part considers the anomalous normal state of novel superconductive materials and materials with colossal magnetoresistance (CMR). The book offers a valuable guide for senior-level undergraduate students and graduate students, postdoctoral and other researchers specializing in solid-state and low-temperature physics.

IVEC 2013 is intended to be a forum of information and discussion between the various players in the field of vacuum electronics: device users, manufacturers and operators, government/institutions, academics, and students. Submissions from all groups are encouraged. IVEC 2013 will provide the right place for the exchange of scientific and technical information and will foster collaboration and cooperation in the vacuum electronics domain both at European and worldwide level.

Formation of carbon nanoparticles is an important type of complex non-equilibrium processes that require precise atomistic theoretical understanding. In this work, we consider the process of ultrafast cooling of pure carbon gas that results in nucleation of an onion-like fullerene. The model is based on molecular dynamics simulation with the interaction between carbon atoms described via a reactive ReaxFF model. We study the consecutive stages of fullerene-like nanoparticle formation and identify the corresponding temperature ranges. Analysis of hybridization and graphitization reveals the underlying microscopic mechanisms connected with rearrangements of dihedral angles and density changes.

The transmission and the circular transmission are investigated for a ring of quantum dots (in a benzene-type configuration) connected to external leads in the meta-configuration. A computational method utilizing the tight-binding approximation to the Schrödinger equation is used to solve for the transmission probabilities as a function of the electron energy and external magnetic flux. The flux dependence is incorporated into the model using a standard procedure involving the Aharonov–Bohm effect. The positions of the transmission zeros and poles in the complex energy plane, and their possible interference with or even complete cancellation of each other, are shown to correlate with the amplitude and structure of the circular transmission resonances. Large-amplitude resonances of the circular transmission are found to occur when two poles of the transmission are separated along the imaginary axis. These resonances demonstrate a high degree of flux sensitivity at specific energy values and flux ranges. A small change in flux causes the orientation of the resonance poles in the complex energy plane to rotate parallel to the real energy axis, resulting in a concurrent decrease in the circular transmission amplitude. The flux-dependent interference between the transmission poles and zeros in the complex energy plane leads to a decrease of the circular transmission resonance amplitudes. The circular transmission and its corresponding current–voltage characteristic provide more information related to the external flux than can be obtained from the normal transmission alone.

Magneto-fermionic condensate under study is a Bose-Einstein condensate of cyclotron spin-flip magnetoexcitons in a quantum Hall insulator. This condensate features unique properties such as millisecond range lifetime and hundreds of micrometers of propagation length. In this study, utilizing the photo-induced resonant reflection technique, we measured the exciton escape time. Finally, we estimated the exciton condensate propagation velocity as 25 m/s, which is much higher than a single particle propagation velocity. We also proposed a mechanism of exciton condensation.

An attractive two-dimensional semiconductor with tunable direct bandgap and high carrier mobility, black phosphorus (BP) is used in batteries, solar cells, photocatalysis, plasmonics and optoelectronics. BP is sensitive to ambient conditions, with oxygen playing a critical role in structure degradation. Our simulations show that BP oxidation slows down charge recombination. This is unexpected, since typically charges are trapped and lost on defects. First, BP has no ionic character. It interacts with oxygen and water weakly, experiencing little perturbation to electronic structure. Second, phosphorus supports different oxidation states and binds extraneous atoms avoiding deep defect levels. Third, soft BP structure can accommodate foreign species without disrupting periodic geometry. Finally, BP phonon scattering on defects shortens quantum coherence and suppresses recombination. Thus, oxidation can be regarded as production of a self-protective layer that improves BP properties. These BP features should be common to other mono-elemental 2D materials, stimulating energy and electronics applications.

We propose a method of measuring low concentrations of fluorescent molecules located in a small volume of a liquid solvent (about 5 μl) based on the Ebbesen effect of the extraordinary transmission (EOT) of light through a state-of-the-art plasmonic crystal formed by a nanohole array perforated in the ultra-high-quality Ag film. In the method, the EOT effect is realized at the fluorescence wavelength of the detected molecules with a low transmission of light at the absorption wavelength. This approach enables the realization of high level sensor sensitivity approaching a sensitivity level of single molecules counting sensors, owing to the suppression of the sensor substrate’s inevitable parasitic luminescence. The proposed method was successfully demonstrated by detection an ultra-low concentration of Cy-5 fluorescent markers in a dimethyl sulfoxide solution corresponding to less than 1000 molecules in the sensor detection volume.

The issue of a recurrence of the modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation which appears from nowhere (i.e., is infinitesimal initially) and generates a rogue wave which then disappears with no trace. If so, this wave solution would be a breather solution of the primitive hydrodynamic equations. It is shown with the help of the fully nonlinear numerical simulation that when a rogue wave occurs from a uniform Stokes wave train, it excites other waves which have different lengths, what prevents the complete recurrence and, eventually, results in a quasi-periodic breathing of the wave envelope. Meanwhile the discovered effects are rather small in magnitude, and the period of the modulation breathing may be thousands of the dominant wave periods. Thus, the obtained solution may be called a quasi-breather of the Euler equations.

We report results of a spectral and timing analysis of the X-ray pulsar XTE J1829-098 using data obtained with the NuSTAR observatory during an outburst in 2018 August. A strong absorption feature was detected at the energy of Ecyc ≃ 15 keV in the source spectrum. This feature was interpreted as a cyclotron resonance scattering line corresponding to the magnetic field strength of the neutron star surface B ≃ 1.7 × 10^{12} G. The pulse phase-resolved spectroscopy shows that the cyclotron line is significantly detected at all phases of the pulse and its energy and other parameters are variable over the pulse period. The timing analysis of the source emission revealed strong pulsations with a period of P = 7.84480(2) s. The pulsed fraction is changed with the energy, including its local increase in the vicinity of the cyclotron line. Using the archival data of the RXTE observatory the presence of the cyclotron line in the spectrum of XTE J1829-098 was independently confirmed and tentative hint for the possible anticorrelation of the line energy with the source flux was revealed.

We report a discovery of low-frequency quasi-periodic oscillation at 0.3-0.7 Hz in the power spectra of the accreting black hole GRS 1739-278 in the hard-intermediate state during its 2014 outburst based on the NuSTAR and Swift/XRT data. The QPO frequency strongly evolved with the source flux during the NuSTAR observation. The source spectrum became softer with rising QPO frequency and simultaneous increasing of the power-law index and decreasing of the cut-off energy. In the power spectrum, a prominent harmonic is clearly seen together with the main QPO peak. The fluxes in the soft and the hard X-ray bands are coherent, however, the coherence drops for the energy bands separated by larger gaps. The phase lags are generally positive (hard) in the 0.1-3 Hz frequency range, and negative below 0.1 Hz. The accretion disc inner radius estimated with the relativistic reflection spectral model appears to be Rin < 7.3Rg. In the framework of the relativistic precession model, in order to satisfy the constraints from the observed QPO frequency and the accretion disc truncation radius, a massive black hole with MBH ≈ 100 M⊙ is required.

Thin superconducting films are usually regarded as type-II superconductors even when they are made of a type-I materials. The reason is a strong influence of the stray magnetic fields outside the superconductive sample. While very thin films indeed reach this limit, there is a sufficiently large interval of film thicknesses in which the magnetic properties cannot be classified as either of the two conventional superconductivity types. We demonstrate that in this interval superconducting condensate and magnetic field reveal exotic spatial profiles that are very sensitive to system parameters, in particular, the temperature and applied field. Magnetic properties of such systems can be attributed to a special regime of intertype superconductivity. Its physical origin lies in the removal of infinite degeneracy of the superconducting state at the critical Bogomolnyi point. Here we demonstrate that qualitative characteristics of obtained condensate-field structures and the way they change with the temperature and applied field are independent of the choice of the in-plane boundary conditions for the order parameter and magnetic field.

We study a model of a spatial evolutionary game, based on the Prisoner's dilemma for two regular arrangements of players, on a square lattice and on a triangular lattice. We analyze steady state distributions of players which evolve from irregular, random initial configurations. We find significant differences between the square and triangular lattice, and we characterize the geometric structures which emerge on the triangular lattice.

We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found that a finite step of the random walk produces a bias in the hitting probability and this bias vanishes in the limit of an infinitesimal step. Therefore, it is important to know how a change in the step size of the random walk influences the performance of simulations. We propose an algorithm with the most effective procedure for the step-length-change protocol.

We report the observation of a current-phase relation dominated by the second Josephson harmonic in superconductor-ferromagnet-superconductor junctions. The exotic current-phase relation is realized in the vicinity of a temperature-controlled 0-to-π junction transition, at which the first Josephson harmonic vanishes. Direct current-phase relation measurements, as well as Josephson interferometry, non-vanishing supercurrent and half-integer Shapiro steps at the 0-π transition selfconsistently point to an intrinsic second harmonic term, making it possible to rule out common alternative origins of half-periodic behavior. While surprising for diffusive multimode junctions, the large second harmonic is in agreement with theory predictions for thin ferromagnetic interlayers.

We study the peculiarities in current-phase relations (CPR) of the SIsFS junction in the region of 0 to p transition. These CPR consist of two independent branches corresponding to 0− and p− states of the contact. We have found that depending on the transparency of the SIs tunnel barrier the decrease of the s-layer thickness leads to transformation of the CPR shape going in the two possible ways: either one of the branches exists only in discrete intervals of the phase difference j or both branches are sinusoidal but differ in the magnitude of their critical currents. We demonstrate that the difference can be as large as 10% under maintaining superconductivity in the s layer. An applicability of these phenomena for memory and logic application is discussed.

We consider a quasi-one-dimensional model of a two-component Fermi gas at zero temperature on one, two and three-leg attractive-U Hubbard ladders. We construct the grand canonical phase diagram of a two-component spin-polarized gas. We find that the structure of the phase diagram of the attractive-U Hubbard model for two and three leg ladders significantly differs q from the structure of the phase diagram of a single chain. We argue that the single chain model is a special case, and that multichain ladders display qualitative features of the 1D-to-3D crossover, observed in experiments with trapped ultracold gases.

We review recent advances in the analysis of the Wang--Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random walk in the energy space biased with the Wang-Landau probability. Properties of the TMES can explain some features of the Wang-Landau algorithm, for example, the flatness of the histogram. We show that the Wang--Landau probability with the true DOS generates a Markov process in the energy space and the inverse spectral gap of the TMES can estimate the mixing time of this Markov process. We argue that an efficient implementation of the Wang-Landau algorithm consists of two simulation stages: the original Wang-Landau procedure for the first stage and a 1/t modification for the second stage. The mixing time determines the characteristic time for convergence to the true DOS in the second simulation stage. The parameter of the convergence of the estimated DOS to the true DOS is the difference of the largest TMES eigenvalue from unity. The characteristic time of the first stage is the tunneling time, i.e., the time needed for the system to visit all energy levels.

We propose a superconducting spin-triplet valve of a new type. This spin valve consists of a bilayer that involves a superconductor and an itinerant magnetic material, with the magnet showing an intrinsic non-collinear magnetic order characterized by a wave vector Q that may be aligned in a few equivalent preferred directions under control of a weak external magnetic field. Re-orienting the direction of Q allows one to controllably modify long-range spin-triplet superconducting correlations in the magnetic material, leading to spin-valve switching behavior. This new type of superconducting spin valve may be used as a magnetic memory element for cryogenic nanoelectronics. It has the following advantages in comparison with superconducting spin valves proposed earlier: (i) it contains only one magnetic layer, which may be more easily fabricated and controlled; (ii) its ground states are separated by a potential barrier, which solves the “half-select” problem of the addressed switch of such memory elements.

We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients insure the possibility of the odd-frequency pairing: 1) the topological surface states, 2) the induced pair potential, and 3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac cone in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.

In recent paper of Falkovich and Levitov it was shown, that geometry of separatrixes for viscous electronic flow in graphene is sensitive to boundary conditions. Here we discover theis relation in details. Also we propose, how boundary conditions could be probed experimentally, using weak magnetic field and observed features of separatrixes.

We study Josephson junctions with weak links consisting of two parallel disordered arms with magnetic properties -- ferromagnetic, half-metallic or normal with magnetic impurities. In the case of long links, the Josephson effect is dominated by mesoscopic fluctuations. In this regime, the system realises a $\varphi_0$ junction with sample-dependent $\varphi_0$ and critical current. Cooper pair splitting between the two arms plays a major role and leads to $2\Phi_0$ periodicity of the current as a function of flux between the arms. We calculate the current and its flux and polarization dependence for the three types of magnetic links.

The topic of superconductivity in strongly disordered materials has attracted a significant attention. In particular vivid debates are related to the subject of intrinsic spatial inhomogeneity responsible for non-BCS relation between the superconducting gap and the pairing potential. Here we report experimental study of electron transport properties of narrow NbN nanowires with effective cross sections of the order of the debated inhomogeneity scales. We find that conventional models based on phase slip concept provide reasonable fits for the shape of the R(T) transition curve. Temperature dependence of the critical current follows the text-book Ginzburg-Landau prediction for quasi-one-dimensional superconducting channel Ic~(1-T/Tc)3/2. Hence, one may conclude that the intrinsic electronic inhomogeneity either does not exist in our structures, or, if exist, does not affect their resistive state properties.

Dynamics of solitons is considered in an extended nonlinear Schrödinger equation, including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term (scattering on damping low-frequency waves, third-order dispersion (TOD) and inhomogeneity of the spatial second-order dispersion (SOD). It is shown that wave-number downshift by the pseudo-SRS may be compensated by upshift provided by spatially increasing SOD with taking into account TOD. The equilibrium state is stable for positive parameter of TOD and unstable for negative one. The analytical solutions are verified by comparison with numerical results

The neutrino dispersion in the magnetized medium was analyzed as a function of the neutrino spin and mass. It was shown that in a super-strong magnetic field plasma contribution to the neutrino energy greatly exceeds the analogous correction in the field-free case.

We investigate the eigenvalue density in ensembles of large sparse Bernoulli random matrices. Analyzing in detail the spectral density of ensembles of linear subgraphs, we discuss its ultrametric nature and show that near the spectrum boundary, the tails of the spectral density exhibit a Lifshitz singularity typical for Anderson localization. We pay attention to an intriguing connection of the spectral density to the Dedekind $\eta$-function. We conjecture that ultrametricity emerges in rare-event statistics and is inherit to generic complex sparse systems.

In order to determine the concept of space interpretation in several multiverse hypotheses, this article analyzes a number of them, which arises from some theories of modern physics. The interpretation of space in the history of philosophy and science and their interrelation with modern physical notions are presented. The research is based on the cognitive interpretation method of the contents of formalistic mathematics and physics theories, the method of comparative analysis (analysis of philosophical texts), the hermeneutical method, and the phenomenological method (analysis of representations). The author shows how the context of modern physics multiverse hypotheses contributes to new connotations in the perception of space. The research draws some conclusions about the present status of the philosophical perception of space.

Weyl semimetal is a three-dimensional material with a conical spectrum near an even number of point nodes, where two bands touch each other. Here we study spectral properties of surface electron states in such a system. We show that the density of surface states possesses a logarithmic singularity for the energy to 0. It decreases linearly at the intermediate energy of surface electron states and approaches zero. This universal behavior is a hallmark of the topological order that offers a new wide range of applications.