ALBERT

Description: We present experimental results obtained under normal gravity on the dynamics of solid particles in periodic oscillatory thermocapillary-driven flows in a non-isothermal liquid bridge made of decane. Inertial particles of different densities and in the size range approximately 0.75 − 75 μ m are able to form stable coherent structures (particle accumulation structures, or PASs). Two image processing techniques were developed and successfully applied to compute time required for an ensemble of particles to form a structure. It is shown that the formation time grows with the decrease of the Stokes number. The observations indicate the probable irrelevance of the memory term for these experiments. Two types of PAS were observed—single (SL-I) and double-loop (SL-II)—which sometimes co-existed. Only large or very dense particles may form an SL-II type structure. A number of novel features of the system were perceived. In some cases, intermittently stable structures emerged (their dynamics is characterized by alternating time intervals during which a structure exists and is destroyed). Whereas in most experiments we observed a conventional symmetric and centered PAS, there were cases when a long-term stable asymmetric structure appeared. Experiments wherein two different types of PAS-forming particles were used simultaneously revealed the destructive role of collisions between the particles on formation of structures.

Description: In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.

Description: This paper deals with the stability and bifurcation analysis of a general form of equation D α x ( t ) = g ( x ( t ) , x ( t − τ ) ) involving the derivative of order α ∈ (0, 1] and a constant delay τ  ≥ 0. The stability of equilibrium points is presented in terms of the stability regions and critical surfaces. We provide a necessary condition to exist chaos in the system also. A wide range of delay differential equations involving a constant delay can be analyzed using the results proposed in this paper. The illustrative examples are provided to explain the theory.

Description: In this paper, we propose a new consensus model in which the interactions among agents stochastically switch between attraction and repulsion. Such a positive-and-negative mechanism is described by the white-noise-based coupling. Analytic criteria for the consensus and non-consensus in terms of the eigenvalues of the noise intensity matrix are derived, which provide a better understanding of the constructive roles of random interactions. Specifically, we discover a positive role of noise coupling that noise can accelerate the emergence of consensus. We find that the converging speed of the multi-agent network depends on the square of the second smallest eigenvalue of its graph Laplacian. The influence of network topologies on the consensus time is also investigated.

Description: After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function E α , β ( z ) ,   z ∈ ℂ ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89 , 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on E α , β ( z ). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β . Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of E α , β ( z ), certainly opening new doors to modeling with two-parameter derivatives.

Description: The total electrostatic energy of systems of identical particles of equal charge is studied in configurations bounded in space, but divergent in the number of charges. This approach shall guide us to unveil a non-linear, functional form specifying the divergent nature of system energy. We consider fractals to be physical entities, with charges located in their vertices or nodes. This description is interesting since features, such as the corresponding fractal dimension, can characterize the total energy E N . Finally, at local length scales, we describe how energy diverges at charge accumulation points in the fractal, that is, almost everywhere by definition.

Description: The Kuramoto–Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.

Description: Basin of attraction of a stable equilibrium point is an effective concept for stability analysis in deterministic systems; however, it does not contain information on the external perturbations that may affect it. Here we introduce the concept of stochastic basin of attraction (SBA) by incorporating a suitable probabilistic notion of basin. We define criteria for the size of the SBA based on the escape probability, which is one of the deterministic quantities that carry dynamical information and can be used to quantify dynamical behavior of the corresponding stochastic basin of attraction. SBA is an efficient tool to describe the metastable phenomena complementing the known exit time, escape probability, or relaxation time. Moreover, the geometric structure of SBA gives additional insight into the system's dynamical behavior, which is important for theoretical and practical reasons. This concept can be used not only in models with small noise intensity but also with noise whose amplitude is proportional or in general is a function of an order parameter. As an application of our main results, we analyze a three potential well system perturbed by two types of noise: Brownian motion and non-Gaussian α -stable Lévy motion. Our main conclusions are that the thermal fluctuations stabilize the metastable system with an asymmetric three-well potential but have the opposite effect for a symmetric one. For Lévy noise with larger jumps and lower jump frequencies ( α = 0.5 ) metastability is enhanced for both symmetric and asymmetric potentials.

Description: We introduce mixing with piecewise isometries (PWIs) on a hemispherical shell, which mimics features of mixing by cutting and shuffling in spherical shells half-filled with granular media. For each PWI, there is an inherent structure on the hemispherical shell known as the exceptional set E , and a particular subset of E , E + , provides insight into how the structure affects mixing. Computer simulations of PWIs are used to visualize mixing and approximations of E + to demonstrate their connection. While initial conditions of unmixed materials add a layer of complexity, the inherent structure of E + defines fundamental aspects of mixing by cutting and shuffling.

Description: We studied the optical absorption and luminescence of agate (SiO 2 ), topaz (Al 2 [SiO 4 ](F,OH) 2 ), beryl (Be 3 Al 2 Si 6 O 18 ), and prehnite (Ca 2 Al(AlSi 3 O 10 )(OH) 2 ) doped with different concentrations of transition metal ions and exposed to fast neutron irradiation. The exchange interaction between the impurity ions and the defects arising under neutron irradiation causes additional absorption as well as bands' broadening in the crystals. These experimental results allow us to suggest the method for obtaining new radiation-defect induced jewellery colors of minerals due to neutron irradiation.

Description: We analyzed carefully the experimental kinetics of the low-temperature diffusion-controlled F, H center recombination in a series of irradiated alkali halides and extracted the migration energies and pre-exponential parameters for the hole H centers. The migration energy for the complementary electronic F centers in NaCl was obtained from the colloid formation kinetics observed above room temperature. The obtained parameters were compared with data available from the literature.

Description: The effect of low-temperature uniaxial deformation on the self-trapping-limited mean free path of excitons in a KI–Tl crystal was revealed from x-ray luminescence spectra. The analysis of the dependence of the intensity ratio of the Tl-center emission (2.85 eV) and the luminescence of self-trapped excitons (π-component; 3.3 eV) on the extent of low-temperature deformation showed that in the KI–Tl crystal (3 × 10 −3 mol. %) the self-trapping-limited mean free path of excitons is comparable with the distance between Tl atoms (20–27) a under a deformation ε = 2%. As the compression increases to ε ≥ 2%–5%, the mean free path drops to (27-5.35) a . The results of modeling based on the continuum approximation showed that with increasing temperature and the degree of low-temperature deformation the height of the potential barrier for the exciton self-trapping drops, which is consistent with the reduction of the mean free path of excitons in the KI–Tl crystal.

Description: Free volume and pore size distribution size in functional micro and macro-micro-modified Cu 0.4 Co 0.4 Ni 0.4 Mn 1.8 O 4 ceramics are characterized by positron annihilation lifetime spectroscopy in comparison with Hg-porosimetry and scanning electron microscopy technique. Positron annihilation results are interpreted in terms of model implication positron trapping and ortho-positronium decaying. It is shown that free volume of positron traps are the same type for macro and micro modified Cu 0.4 Co 0.4 Ni 0.4 Mn 1.8 O 4 ceramics. Classic Tao-Eldrup model in spherical approximation is used to calculation of the size of nanopores smaller than 2 nm using the ortho-positronium lifetime.

Description: In order to predict optical properties of insulating materials under intensive laser excitation, we generalized methods of quantum electrodynamics, allowing us to simulate excitation of electrons and holes, interacting with each other and acoustic phonons. The prototypical model considers a two-band dielectric material characterized by the dispersion relations for electron and hole states. We developed a universal description of excited electrons, holes and acoustic phonons within joint quantum kinetics formalism. Illustrative solutions for the quasiparticle birth-annihilation operators, applicable at short laser pulses at 0 K, are obtained by the transition from the macroscopic description to the quantum field formalism.

Description: Monoclinic antiferromagnetic NiWO 4 was studied by far-infrared (30–600 cm −1 ) absorption spectroscopy in the temperature range of 5–300 K using the synchrotron radiation from SOLEIL source. Two isomorphous CoWO 4 and ZnWO 4 tungstates were investigated for comparison. The phonon contributions in the far-infrared range of tungstates were interpreted using the first-principles spin-polarized linear combination of atomic orbital calculations. No contributions from magnetic excitations were found in NiWO 4 and CoWO 4 below their Neel temperatures down to 5 K.

Description: The creation spectrum of stable F centres (being part of F-H pairs of Frenkel defects) by synchrotron radiation of 7–40 eV has been measured for highly pure NaCl single crystals at 12 K using a highly sensitive luminescent method. It is shown that the efficiency of F centre creation in a closely packed NaCl is low at the decay of anion or cation excitons (7.8–8.4 and 33.4 eV, respectively) or at the recombination of relaxed conduction electrons and valence holes. Only the recombination of nonrelaxed (hot) electrons with holes provides the energy exceeding threshold value E FD , which is sufficient for the creation of Frenkel defects at low temperature.

Description: An unambiguous attribution of the absorption spectra to definite paramagnetic centres identified by the EPR techniques in the most cases is problematic. This problem may be solved by applying of a direct measurement techniques—the EPR detected via the magnetic circular dichroism, or briefly MCD–EPR. The present survey reports on the advantages and disadvantages applying the MCD–EPR techniques to simple and complex paramagnetic centres in crystals as well as glasses and glass-ceramics.

Description: Luminescence properties of SiO 2 in different structural states are compared. Similar comparison is made for GeO 2 . Rutile and α-quartz structures as well as glassy state of these materials are considered. Main results are that for α-quartz crystals the luminescence of self-trapped exciton is the general phenomenon that is absent in the crystal with rutile structure. In rutile structured SiO 2 (stishovite) and GeO 2 (argutite) the main luminescence is due to a host material defect existing in as-received (as-grown) samples. The defect luminescence possesses specific two bands, one of which has a slow decay (for SiO 2 in the blue and for GeO 2 , in green range) and another, a fast ultraviolet (UV) band (4.75 eV in SiO 2 and at 3 eV in GeO 2 ). In silica and germania glasses, the luminescence of self-trapped exciton coexists with defect luminescence. The latter also contains two bands: one in the visible range and another in the UV range. The defect luminescence of glasses was studied in details during last 60–70 years and is ascribed to oxygen deficient defects. Analogous defect luminescence in the corresponding pure nonirradiated crystals with α-quartz structure is absent. Only irradiation of a α-quartz crystal by energetic electron beam, γ-rays and neutrons provides defect luminescence analogous to glasses and crystals with rutile structure. Therefore, in glassy state the structure containing tetrahedron motifs is responsible for existence of self-trapped excitons and defects in octahedral motifs are responsible for oxygen deficient defects.

Description: The ground state properties of cubic scandium trifluoride (ScF 3 ) perovskite were studied using first-principles calculations. The electronic structure of ScF 3 was determined by linear combination of atomic orbital (LCAO) and plane wave projector augmented-wave (PAW) methods using modified hybrid exchange-correlation functionals within the density functional theory (DFT). The comprehensive comparison of the results obtained by two methods is presented. Both methods allowed us to reproduce the lattice constant found experimentally in ScF 3 at low temperatures and to predict its electronic structure in good agreement with known experimental valence-band photoelectron and F 1 s x-ray absorption spectra.

Description: Photoluminescence and excitation spectra of microcrystalline and nanocrystalline nickel tungstate (NiWO 4 ) were measured using UV-VUV synchrotron radiation source. The origin of the bands is interpreted using comparative analysis with isostructural ZnWO 4 tungstate and based on the results of recent first-principles band structure calculations. The influence of the local atomic structure relaxation and of Ni 2+ intra-ion d–d transitions on the photoluminescence band intensity are discussed.

Description: In this paper a novel method for synthesis of LaInO 3 :Er 3+ is reported and upconversion luminescence properties of the synthesized material at different temperatures (9–300 K) are studied. The samples were prepared by co-precipitation and subsequent heat treatment of lanthanum, indium and erbium hydroxides. It is shown that the excitation at 980 nm leads to a strong green upconversion luminescence in the material. At the concentrations above 0.1 mol. % of Er 3+ the energy transfer upconversion mechanism of the luminescence becomes evident. Further increase of Er 3+ content in the material leads to higher red-to-green upconversion luminescence intensity ratio. The mechanisms responsible for the observed variation are discussed.

Description: Possible proximity effects in gases of cold, multiply charged atoms are discussed. Here we deal with rarefied gases with densities n d of multiply charged ( Z ≫ 1) atoms at low temperatures in the well-known Thomas-Fermi (TF) approximation, which can be used to evaluate the statistical properties of single atoms. In order to retain the advantages of the TF formalism, which is successful for symmetric problems, the external boundary conditions accounting for the finiteness of the density of atoms (donors), n d ≠ 0, are also symmetrized (using a spherical Wigner-Seitz cell) and formulated in a standard way that conserves the total charge within the cell. The model shows that at zero temperature in a rarefied gas of multiply charged atoms there is an effective long-range interaction E proxi ( n d ), the sign of which depends on the properties of the outer shells of individual atoms. The long-range character of the interaction E proxi is evaluated by comparing it with the properties of the well-known London dispersive attraction E Lond ( n d ) 〈 0, which is regarded as a long-range interaction in gases. For the noble gases argon, krypton, and xenon E proxi 〉0 and for the alkali and alkaline-earth elements E proxi 〈 0. At finite temperatures, TF statistics manifests a new, anomalously large proximity effect, which reflects the tendency of electrons localized at Coulomb centers to escape into the continuum spectrum. The properties of thermal decay are interesting in themselves as they determine the important phenomenon of dissociation of neutral complexes into charged fragments. This phenomenon appears consistently in the TF theory through the temperature dependence of the different versions of E proxi . The anomaly in the thermal proximity effect shows up in the following way: for T ≠ 0 there is no equilibrium solution of TS statistics for single multiply charged atoms in a vacuum when the effect is present. Instability is suppressed in a Wigner-Seitz model under the assumption that there are no electron fluxes through the outer boundary R 3 ∝ n −1 d of a Wigner-Seitz cell. E proxi corresponds to the definition of the correlation energy in a gas of interacting particles. This review is written so as to enable comparison of the results of the TF formalism with the standard assumptions of the correlation theory for classical plasmas. The classic example from work on weak solutions (including charged solutions)—the use of semi-impermeable membranes for studies of osmotic pressure—is highly appropriate for problems involving E proxi . Here we are speaking of one or more sharp boundaries formed by the ionic component of a many-particle problem. These may be a metal-vacuum boundary in a standard Casimir cell in a study of the vacuum properties in the 2 l gap between conducting media of different kinds or different layered systems (quantum wells) in semiconductors, etc. As the mobile part of the equilibrium near a sharp boundary, electrons can (should) escape beyond the confines of the ion core into a gap 2 l with a probability that depends, among other factors, on the properties of E proxi for the electron cloud inside the conducting walls of the Casimir cell (quantum well). The analog of the Casimir sandwich in semiconductors is the widely used multilayer heterostructures referred to as quantum wells of width 2 l with sides made of suitable doped materials, which ensure statistical equilibrium exchange of electrons between the layers of the multilayer structure. The thermal component of the proximity effects in semiconducting quantum wells provides an idea of many features of the dissociation process in doped semiconductors. In particular, a positive E proxi 〉 0 (relative to the bottom of the conduction band) indicates that TF donors with a finite density n d ≠ 0 form a degenerate, semiconducting state in the semiconductor. At zero temperature, there is a finite density of free carriers which increases with a power-law dependence on T .

Description: In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.

Description: The relation between the Fisher information and Rényi dimensions is established: the Fisher information can be expressed as a linear combination of the first and second derivatives of the Rényi dimensions with respect to the Rényi parameter β . The Rényi parameter β is the parameter of the Fisher information. A thermodynamical description based on the Fisher information with β being the inverse temperature is introduced for chaotic systems. The link between the Fisher information and the heat capacity is emphasized, and the Fisher heat capacity is introduced.

Description: A Riesz difference is defined by the use of the Riemann–Liouville differences on time scales. Then the definition is considered for discrete fractional modelling. A lattice fractional equation method is proposed among which the space variable is defined on discrete domains. Finite memory effects are introduced into the lattice system and the numerical formulae are given. Adomian decomposition method is adopted to solve the fractional partial difference equations numerically.

Description: We present a universal characterization scheme for chimera states applicable to both numerical and experimental data sets. The scheme is based on two correlation measures that enable a meaningful definition of chimera states as well as their classification into three categories: stationary , turbulent , and breathing . In addition, these categories can be further subdivided according to the time-stationarity of these two measures. We demonstrate that this approach is both consistent with previously recognized chimera states and enables us to classify states as chimeras which have not been categorized as such before. Furthermore, the scheme allows for a qualitative and quantitative comparison of experimental chimeras with chimeras obtained through numerical simulations.

Description: A large parameter mismatch can induce amplitude death in two instantaneously coupled oscillators. Alternatively, a time delay in the coupling can induce amplitude death in two identical oscillators. We unify the mechanism of quenching of oscillation in coupled oscillators, either by a large parameter mismatch or a delay coupling, by a common lag scenario that is, surprisingly, different from the conventional lag synchronization. We present numerical as well as experimental evidence of this unknown kind of lag scenario when the lag increases with coupling and at a critically large value at a critical coupling strength, amplitude death emerges in two largely mismatched oscillators. This is analogous to amplitude death in identical systems with increasingly large coupling delay. In support, we use examples of the Chua oscillator and the Bonhoeffer-van der Pol system. Furthermore, we confirm this lag scenario during the onset of amplitude death in identical Stuart-Landau system under various instantaneous coupling forms, repulsive, conjugate, and a type of nonlinear coupling.

Description: Nonlinear oscillations lie at the heart of numerous complex systems. Impulsive forcing arises naturally in many scenarios, and we endeavour to study nonlinear oscillators subject to such forcing. We model these kicked oscillatory systems as a piecewise smooth dynamical system, whereby their dynamics can be investigated. We investigate the problem of pattern formation in a turbulent combustion system and apply this formalism with the aim of explaining the observed dynamics. We identify that the transition of this system from low amplitude chaotic oscillations to large amplitude periodic oscillations is the result of a discontinuity induced bifurcation. Further, we provide an explanation for the occurrence of intermittent oscillations in the system.

Description: Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.

Description: This paper addresses the need to deal with and control public opinion and rumors. Existing strategies to control public opinion include degree, random, and adaptive bridge control strategies. In this paper, we use the HK model to present a public opinion control strategy based on public authority (PA). This means utilizing the influence of expert or high authority individuals whose opinions we control to obtain the optimum effect in the shortest time possible and thus reach a consensus of public opinion. Public authority (PA) is only influenced by individuals' attributes (age, economic status, and education level) and not their degree distribution; hence, in this paper, we assume that PA complies with two types of public authority distribution (normal and power-law). According to the proposed control strategy, our experiment is based on random, degree, and public authority control strategies in three different social networks (small-world, scale-free, and random) and we compare and analyze the strategies in terms of convergence time ( T ), final number of controlled agents ( C ), and comprehensive efficiency ( E ). We find that different network topologies and the distribution of the PA in the network can influence the final controlling effect. While the effect of PA strategy differs in different network topology structures, all structures achieve comprehensive efficiency with any kind of public authority distribution in any network. Our findings are consistent with several current sociological phenomena and show that in the process of public opinion/rumor control, considerable attention should be paid to high authority individuals.

Description: Cells in the brain's Suprachiasmatic Nucleus (SCN) are known to regulate circadian rhythms in mammals. We model synchronization of SCN cells using the forced Kuramoto model, which consists of a large population of coupled phase oscillators (modeling individual SCN cells) with heterogeneous intrinsic frequencies and external periodic forcing. Here, the periodic forcing models diurnally varying external inputs such as sunrise, sunset, and alarm clocks. We reduce the dimensionality of the system using the ansatz of Ott and Antonsen and then study the effect of a sudden change of clock phase to simulate cross-time-zone travel. We estimate model parameters from previous biological experiments. By examining the phase space dynamics of the model, we study the mechanism leading to the difference typically experienced in the severity of jet-lag resulting from eastward and westward travel.

Description: The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications ranging from the power grid to cardiac excitation. Here, we study the control of network-coupled limit cycle oscillators, extending the previous work that focused on phase oscillators. Based on stabilizing a target fixed point, our method aims to attain complete frequency synchronization, i.e., consensus, by applying control to as few oscillators as possible. We develop two types of controls. The first type directs oscillators towards larger amplitudes, while the second does not. We present numerical examples of both control types and comment on the potential failures of the method.

Description: The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

Description: We construct a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model that is minimal, in the sense that the vector field has the least number of linearity zones, in order to reproduce all the dynamics present in the original HR model with classical parameter values. This includes square-wave bursting and also special trajectories called canards, which possess long repelling segments and organise the transitions between stable bursting patterns with n and n  + 1 spikes, also referred to as spike-adding canard explosions. We propose a first approximation of the smooth HR model, using a continuous PWL system, and show that its fast subsystem cannot possess a homoclinic bifurcation, which is necessary to obtain proper square-wave bursting. We then relax the assumption of continuity of the vector field across all zones, and we show that we can obtain a homoclinic bifurcation in the fast subsystem. We use the recently developed canard theory for PWL systems in order to reproduce the spike-adding canard explosion feature of the HR model as studied, e.g., in Desroches et al. , Chaos 23 (4), 046106 (2013).

Description: This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.

Description: We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential , i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable , while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.

Description: Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7 , 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuous change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.

Description: This paper generalizes the stability test method via integral estimation for integer-order neutral time-delay systems to neutral fractional-delay systems. The key step in stability test is the calculation of the number of unstable characteristic roots that is described by a definite integral over an interval from zero to a sufficient large upper limit. Algorithms for correctly estimating the upper limits of the integral are given in two concise ways, parameter dependent or independent. A special feature of the proposed method is that it judges the stability of fractional-delay systems simply by using rough integral estimation. Meanwhile, the paper shows that for some neutral fractional-delay systems, the stability is extremely sensitive to the change of time delays. Examples are given for demonstrating the proposed method as well as the delay sensitivity.

Description: The radiation properties and the electronic structure of hybrid composites based on suspension polystyrene (PS) and nanocrystals of BaZrO 3 (BZO) ( d 〈 50 nm) have been studied using luminescent spectroscopy and x-ray analysis. A strong cathodoluminescence (CL) in BZO-nanocrystals is observed in temperature range 80–293 K. It is modified in BZO-PS composites: both the low- and a high-energy bands (near 4 eV) appear, together with a significant reduction in the CL intensity. A decrease of the lattice parameter a for BZO phase in the composite and the modification of CL spectra indicate for changes in the nanocrystalline structure induced by the polymer.

Description: Fresh and aged melt-grown or gas-phase grown CdI 2 crystals are studied by means of low-temperature photoluminescence spectroscopy. Noticeable transformations of emission spectra are observed after long-term aging. The formation of nanostructures containing cadmium oxide and cadmium hydroxide as well as the changes in local surrounding of iodine atoms and the possible growth of polytypic modifications of CdI 2 are taken into account when considering the diversity of optical spectra.

Description: This paper focuses on impulsive synchronization of fractional Takagi-Sugeno (T-S) fuzzy complex networks. A novel comparison principle is built for the fractional impulsive system. Then a synchronization criterion is established for the fractional T-S fuzzy complex networks by utilizing the comparison principle. The method is also illustrated by applying the fractional T-S fuzzy Rössler's complex networks.

Description: In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system.

Description: Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.

Description: Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them—a phenomenon termed “generalized synchronization.” Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.

Description: Analytical calculations of the potential barrier hindering rotation of the hydrogen molecules in the molecular field of neighboring molecules are performed for molecular solid hydrogen. The calculations are made for the four-sublattice Pca 2 1 lattice which minimizes the electrostatic energy of classical quadrupoles on an hcp lattice.

Description: The model describing the effect of anharmonicity on the spin-crossover properties of Fe(II) complex is proposed. It is shown that anharmonicity can be one of the important factors controlling the magnetic transitions of the low-spin high-spin type.

Description: We report Raman light scattering in the phase separated superconducting single crystal Rb 0.77 Fe 1.61 Se 2 with T c = 32 K over a wide temperature region 3–500 K. The observed phonon lines from the majority vacancy ordered Rb 2 Fe 4 Se 5 (245) antiferromagnetic phase with T N = 525 K demonstrate modest anomalies in the frequency, intensity and halfwidth at the superconductive phase transition. We identify phonon lines from the minority compressed Rb δ Fe 2 Se 2 (122) conductive phase. The superconducting gap with d x 2 − y 2 symmetry has been detected in our spectra. In the range 0–600 cm −1 we observe a weak but highly polarized B 1 g -type background which becomes well-structured upon cooling. A possible magnetic or multiorbital origin of this background is discussed. We argue that the phase separation in M 0.8+ x Fe 1 . 6+y Se 2 is of pure magnetic origin. It occurs below the Néel temperature when the magnetic moment of iron reaches a critical value. We state that there is a spacer between the majority 245 and minority 122 phases. Using ab initio spin-polarized band structure calculations we demonstrate that the compressed vacancy ordered Rb 2 Fe 4 Se 5 phase can be conductive and therefore may serve as a protective interface spacer between the purely metallic Rb δ Fe 2 Se 2 phase and the insulating Rb 2 Fe 4 Se 5 phase providing percolative Josephson-junction like superconductivity all throughout of Rb 0.8+ x Fe 1.6+ y Se 2 . Our lattice dynamics calculations show significant differences in the phonon spectra of the conductive and insulating Rb 2 Fe 4 Se 5 phases.

Description: The relative elongation ε of samples of high purity (99.9999 mol. % with respect to nonhydrogenic impurities) parahydrogen ( p -H 2 , ∼0.2% o -H 2 ) with different amounts of the stable hydrogen isotope deuterium is measured as a function of applied stress σ at temperatures of 1.8–4.2 K. The samples were subjected to uniaxial tension by stepwise loading. The ratio [D]/[H] of the number [D] of deuterium atoms to the number [H] of p -H 2 hydrogen atoms ranged from 0.0055 ± 0.0005 at. % up to 0.07 at. %. For deuterium enriched p- H 2 , the easy slip dislocation stage vanished from the σ(ε) curves and there was a significant reduction in the total relative elongation of the samples, as well as a substantial increase in the hardening coefficient d σ/ d ε. Deformation of samples of p- H 2 with deuterium contents higher than the natural amount produces an unusual change in their shape owing to the appearance of a rotational component of the low-temperature plastic mass transfer.

Description: Raman spectrum of single-crystal SmFe 3 (BO 3 ) 4 was studied in the frequency range from 3 to 1500 cm −1 at temperatures 10–300 K. All the A 1 and E phonon modes predicted by the group theory for a given symmetry of the crystal were observed. The magnitudes of splitting between the LO and TO components of polar E phonons were determined. It was found that under the transition to a magnetically ordered phase, the behavior of the intensity of the line corresponding to the A 1 vibrational mode is anomalous. It was shown that at low temperatures the spectrum of two-magnon excitations has a complex shape and is observed with both nondiagonal and diagonal components of the scattering tensor. This complex shape reflects the features in the density of states of the magnetic branches. An estimate of the magnon energy E m at the Brillouin zone boundary gave ∼47 cm −1 . The structure of the ground multiplet 6 H 5/2 of a Sm +3 ion in paramagnetic and antiferromagnetic states as well as the effect of the magnetic phase transition on it were studied. Electron-phonon interaction for the electronic excitation at 225 cm −1 was revealed.

Description: Two series of nanosized cobalt spinel ferrites CoFe 2 O 4 are synthesized from metal salts using high-energy ball milling with the addition of NaCl as a growth agent (series CFO-NaCl), and without (CFO Series). The particle properties are characterized using atomic force microscopy, as well as magnetic and calorimetric measurements. It is shown that the average sizes of the nanoparticles were ∼5.6 and ∼10.3 nm for CFO and CFO-NaCl series, respectively. We performed magnetostatic measurements and determined the parameters that are required to analyze the magnetic state and remagnetization processes of the nanoparticles. It is shown that the blocking temperature is ≈160 K for CFO samples and ≈300 K for the CFO-NaCl series. It was concluded that at 293 K the CFO series particles exhibit a superparamagnetic state, whereas the CFO-NaCl series are in the blocked state. The specific loss power that is scattered by the synthesized nanoparticle ensembles placed in an alternating magnetic field, is measured experimentally and theoretically assessed. The nature of the processes that determine the thermal characteristics of the nanoparticles is analyzed.

Description: Amplification of acoustic in-plane phonons due to an external temperature gradient (∇ T ) in single-layer graphene (SLG) was studied theoretically. The threshold temperature gradient ( ∇ T ) 0 g and the threshold voltage ( V T ) 0 g in SLG were evaluated. For T = 77   K , the calculated value for ( ∇ T ) 0 g = 746.8     K / cm and ( V T ) 0 g = 6.6   mV . The calculation was done in the hypersound regime. Further, the dependence of the normalized amplification ( Γ / Γ 0 ) on the frequency ω q and ∇ T / T were evaluated numerically and presented graphically. The calculated threshold temperature gradient ( V T ) 0 g for SLG was higher than that obtained for homogeneous semiconductors ( n -InSb) ( ∇ T ) 0 hom ≈ 10 3   K / cm , superlattices ( ∇ T ) 0 S L ≈ 384   K / cm , and cylindrical quantum wire ( ∇ T ) 0 c q w ≈ 10 2   K / cm . This makes SLG a much better material for thermoelectric phonon amplification.

Description: We found that the coupled system of Josephson junctions under external electromagnetic radiation demonstrates a cascade of parametric instabilities. These instabilities appear along the IV characteristics within bias current intervals corresponding to Shapiro step subharmonics and lead to charging in the superconducting layers. The amplitudes of the charge oscillations increase with increasing external radiation power. We demonstrate the existence of longitudinal plasma waves at the corresponding bias current values. An essential advantage of the parametric instabilities in the case of subharmonics is the lower amplitude of radiation that is needed for the creation of the longitudinal plasma wave. This fact gives a unique possibility to create and control longitudinal plasma waves in layered superconductors. We propose a novel experiment for studying parametric instabilities and the charging of superconducting layers based on the simultaneous variation of the bias current and radiation amplitude.

Description: The Coulombic effect on the stability range of the photo-excited electron gas on liquid helium is shown to favor formation of domains of different densities. Domains appear to eliminate or greatly reduce regions with negative conductivity. An analysis of the density domain structure allows explaining remarkable observations reported recently for the photo-excited electron gas.

Description: We present thoroughly analyzed experimental results that demonstrate the anomalous manifestation of the exciton self-trapping effect, which is already well-known in bulk crystals, in ordered molecular nanoclusters called J -aggregates. Weakly-coupled one-dimensional (1D) molecular chains are the main structural feature of J -aggregates, wherein the electron excitations are manifested as 1D Frenkel excitons. According to the continuum theory of Rashba-Toyozawa, J -aggregates can have only self-trapped excitons, because 1D excitons must adhere to barrier-free self-trapping at any exciton-phonon coupling constant g = ε LR /2β, wherein ε LR is the lattice relaxation energy, and 2β is the half-width of the exciton band. In contrast, very often only the luminescence of free, mobile excitons would manifest in experiments involving J -aggregates. Using the Urbach rule in order to analyze the low-frequency region of the low-temperature exciton absorption spectra has shown that J -aggregates can have both a weak ( g 〈 1) and a strong ( g 〉 1) exciton-phonon coupling. Moreover, it is experimentally demonstrated that under certain conditions, the J -aggregate excited state can have both free and self-trapped excitons, i.e., we establish the existence of a self-trapping barrier for 1D Frenkel excitons. We demonstrate and analyze the reasons behind the anomalous existence of both free and self-trapped excitons in J -aggregates, and demonstrate how exciton-self trapping efficiency can be managed in J -aggregates by varying the values of g , which is fundamentally impossible in bulk crystals. We discuss how the exciton-self trapping phenomenon can be used as an alternate interpretation of the wide band emission of some J -aggregates, which has thus far been explained by the strongly localized exciton model.

Description: We present results of theoretical and experimental studies of the electronic structure and magnetic properties of RFe 4 Al 8 , RMn 4 Al 8 , and RCr 4 Al 8 compounds with nonmagnetic elements R = Sc, Y, La, and Lu. The electron spectrum and field induced magnetic moment, as well as their dependences on the unit cell volume, are calculated for the paramagnetic phase of the RT 4 Al 8 systems. The calculations are supplemented by measurements of the magnetic susceptibility of representative RT 4 Al 8 compounds as a function of temperature and hydrostatic pressure.

Description: Negative magnetoresistance of InSb whiskers with different impurity concentrations 4.4 × 10 16 –7.16 × 10 17 cm −3 was studied in longitudinal magnetic field 0–14 T in the temperature range 4.2–77 K. The negative magnetoresistance reaches about 50% for InSb whiskers with impurity concentration in the vicinity to the metal–insulator transition. The negative magnetoresistance decreases to 35 and 25% for crystals with Sn concentration from the metal and dielectric side of the transition. The longitudinal magnetoresistance twice crosses the axis of the magnetic field induction for the lightly doped crystals. The behavior of the negative magnetoresistance could be explained by the existence of classical size effect, in particular boundary scattering in the subsurface whisker layer.

Description: The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its stable manifold intersects a non-differentiable point of its unstable manifold (or vice-versa). This is a codimension-one bifurcation analogous to a homoclinic tangency of a smooth map, referred to here as a homoclinic corner. This paper presents an unfolding of generic homoclinic corners for saddle fixed points of planar piecewise-smooth continuous maps. It is shown that a sequence of border-collision bifurcations limits to a homoclinic corner and that all nearby periodic solutions are unstable.

Description: In this study, we investigate the role of the mesoscopic structural properties of a scale-free social network on the contagion spreading. We focus on both the exponent of power-law community size distribution function ( β ) and the mixing parameter ( μ ). Findings show that increasing β reduces the rate of epidemic spreading. On the other hand, increasing μ increases the rate of epidemic spreading. Two innovating parameters, Temperature and cos   θ , are introduced here to analyze these effects.

Description: Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag–synchronous states, and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.

Description: We consider the effects of several forms of delays on the existence and stability of travelling waves in non-locally coupled networks of Kuramoto-type phase oscillators and theta neurons. By passing to the continuum limit and using the Ott/Antonsen ansatz, we derive evolution equations for a spatially dependent order parameter. For phase oscillator networks, the travelling waves take the form of uniformly twisted waves, and these can often be characterised analytically. For networks of theta neurons, the waves are studied numerically.

Description: In this paper, transverse vibrations of an electrostatically actuated thin flexible cantilever perturbed by low-speed air flow are studied using both experiments and numerical modeling. In the experiments, the dynamic characteristics of the cantilever are studied by supplying a DC voltage with an AC component for electrostatic forcing and a constant uniform air flow around the cantilever system for aerodynamic forcing. A range of control parameters leading to stable vibrations are established using a dimensionless operating parameter that is the ratio of the induced and the free stream velocities. Numerical results are validated with experimental data. Assuming the amplitude of vibrations are small, then a non-linear dynamic Euler-Bernoulli beam equation with viscous damping and gravitational effects is used to model the equation of motion. Aerodynamic forcing is modelled as a temporally sinusoidal and uniform force acting perpendicular to the beam length. The forcing amplitude is found to be proportional to the square of the air flow velocity. Numerical results strongly agree with the experiments predicting accurate vibration amplitude, displacement frequency, and quasi-periodic displacement of the cantilever tip.

Description: We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized synchrony alignment function that encodes the interplay between the network structure and the oscillators' natural frequencies and serves as an objective measure for the network's degree of synchronization. Using the generalized synchrony alignment function, we show that a network's synchronization properties can be systematically optimized. This framework also allows us to study the properties of synchrony-optimized networks, and in particular, investigate the role of directed network properties such as nodal in- and out-degrees. For instance, we find that in optimally rewired networks, the heterogeneity of the in-degree distribution roughly matches the heterogeneity of the natural frequency distribution, but no such relationship emerges for out-degrees. We also observe that a network's synchronization properties are promoted by a strong correlation between the nodal in-degrees and the natural frequencies of oscillators, whereas the relationship between the nodal out-degrees and the natural frequencies has comparatively little effect. This result is supported by our theory, which indicates that synchronization is promoted by a strong alignment of the natural frequencies with the left singular vectors corresponding to the largest singular values of the Laplacian matrix.

Description: We investigate synchronization in complex networks of noisy phase oscillators. We find that, while too weak a coupling is not sufficient for the whole system to synchronize, too strong a coupling induces a nontrivial type of phase slip among oscillators, resulting in synchronization failure. Thus, an intermediate coupling range for synchronization exists, which becomes narrower when the network is more heterogeneous. Analyses of two noisy oscillators reveal that nontrivial phase slip is a generic phenomenon when noise is present and coupling is strong. Therefore, the low synchronizability of heterogeneous networks can be understood as a result of the difference in effective coupling strength among oscillators with different degrees; oscillators with high degrees tend to undergo phase slip while those with low degrees have weak coupling strengths that are insufficient for synchronization.

Description: We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking, we find localized spatiotemporal patterns that we call “frequency spirals.” These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as two-armed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase vortex. Unlike the stationary phase vortices seen in magnetic spin systems, or the rotating spiral waves seen in reaction-diffusion systems, frequency spirals librate: the phases of the oscillators surrounding the central vortex move forward and then backward, executing a periodic motion with zero winding number. We construct the simplest frequency spiral and characterize its properties using analytical and numerical methods. Simulations show that frequency spirals in large lattices behave much like this simple prototype.

Description: A “chimera state” is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic opto-electronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.

Description: The existence of localized spin excitations and spin deviations along the site in a one-dimensional antiferromagnet with Dzyaloshinski-Moriya (D-M) interaction has been studied using quasiclassical approximation. By introducing the Holstein-Primakoff bosonic representation of spin operators, the coherent state ansatz, and the time dependent variational principle, a discrete set of coupled nonlinear partial differential equations governing the dynamics is derived. Employing the multiple-scale method, one, two and three solitary wave solutions are constructed and depicted graphically.

Description: We survey general results relating patterns of synchrony to network topology, applying the formalism of coupled cell systems. We also discuss patterns of phase-locking for periodic states, where cells have identical waveforms but regularly spaced phases. We focus on rigid patterns, which are not changed by small perturbations of the differential equation. Symmetry is one mechanism that creates patterns of synchrony and phase-locking. In general networks, there is another: balanced colorings of the cells. A symmetric network may have anomalous patterns of synchrony and phase-locking that are not consequences of symmetry. We introduce basic notions on coupled cell networks and their associated systems of admissible differential equations. Periodic states also possess spatio-temporal symmetries, leading to phase relations; these are classified by the H / K theorem and its analog for general networks. Systematic general methods for computing the stability of synchronous states exist for symmetric networks, but stability in general networks requires methods adapted to special classes of model equations.

Description: A hybrid multi-agent systems model integrating the advantages of both metric interaction and topological interaction rules, called the metric-topological model, is developed. This model describes planar motions of mobile agents, where each agent can interact with all the agents within a circle of a constant radius, and can furthermore interact with some distant agents to reach a pre-assigned number of neighbors, if needed. Some sufficient conditions imposed only on system parameters and agent initial states are presented, which ensure achieving synchronization of the whole group of agents. It reveals the intrinsic relationships among the interaction range, the speed, the initial heading, and the density of the group. Moreover, robustness against variations of interaction range, density, and speed are investigated by comparing the motion patterns and performances of the hybrid metric-topological interaction model with the conventional metric-only and topological-only interaction models. Practically in all cases, the hybrid metric-topological interaction model has the best performance in the sense of achieving highest frequency of synchronization, fastest convergent rate, and smallest heading difference.

Description: Exploring the dynamical behaviors of high water cut and low velocity oil-water flows remains a contemporary and challenging problem of significant importance. This challenge stimulates us to design a high-speed cycle motivation conductance sensor to capture spatial local flow information. We systematically carry out experiments and acquire the multi-channel measurements from different oil-water flow patterns. Then we develop a novel multivariate weighted recurrence network for uncovering the flow behaviors from multi-channel measurements. In particular, we exploit graph energy and weighted clustering coefficient in combination with multivariate time-frequency analysis to characterize the derived complex networks. The results indicate that the network measures are very sensitive to the flow transitions and allow uncovering local dynamical behaviors associated with water cut and flow velocity. These properties render our method particularly useful for quantitatively characterizing dynamical behaviors governing the transition and evolution of different oil-water flow patterns.

Description: We discuss the influence of small phase lags on the synchronization transitions in the Kuramoto model for a large inhomogeneous population of globally coupled phase oscillators. Without a phase lag, all unimodal distributions of the natural frequencies give rise to a classical synchronization scenario, where above the onset of synchrony at the Kuramoto threshold, there is an increasing synchrony for increasing coupling strength. We show that already for arbitrarily small phase lags, there are certain unimodal distributions of natural frequencies such that for increasing coupling strength synchrony may decrease and even complete incoherence may regain stability. Moreover, our example allows a qualitative understanding of the mechanism for such non-universal synchronization transitions.

Description: Some chaotic attractors produced by three-dimensional dynamical systems without any singular point have now been identified, but explaining how they are structured in the state space remains an open question. We here want to explain—in the particular case of the Wei system—such a structure, using one-dimensional sets obtained by vanishing two of the three derivatives of the flow. The neighborhoods of these sets are made of points which are characterized by the eigenvalues of a 2 × 2 matrix describing the stability of flow in a subspace transverse to it. We will show that the attractor is spiralling and twisted in the neighborhood of one-dimensional sets where points are characterized by a pair of complex conjugated eigenvalues. We then show that such one-dimensional sets are also useful in explaining the structure of attractors produced by systems with singular points, by considering the case of the Lorenz system.

Description: Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or “ghost,” rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding of ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.

Description: Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamic-pituitary-adrenal (HPA) axis were systematically investigated. Conditions under which qualitative transitions between dynamic states occur are determined by independently varying the rate constants of all reactions that constitute the model. Bifurcation types were further characterized using continuation algorithms and scale factor methods. Regions of bistability and transitions through supercritical Andronov-Hopf and saddle loop bifurcations were identified. Dynamic state analysis predicts that the HPA axis operates under basal (healthy) physiological conditions close to an Andronov-Hopf bifurcation. Dynamic properties of the stress-control axis have not been characterized experimentally, but modelling suggests that the proximity to a supercritical Andronov-Hopf bifurcation can give the HPA axis both, flexibility to respond to external stimuli and adjust to new conditions and stability, i.e., the capacity to return to the original dynamic state afterwards, which is essential for maintaining homeostasis. The analysis presented here reflects the properties of a low-dimensional model that succinctly describes neurochemical transformations underlying the HPA axis. However, the model accounts correctly for a number of experimentally observed properties of the stress-response axis. We therefore regard that the presented analysis is meaningful, showing how in silico investigations can be used to guide the experimentalists in understanding how the HPA axis activity changes under chronic disease and/or specific pharmacological manipulations.

Description: In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developed approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.

Description: This paper focuses on the study of the stochastic Van der Pol vibro-impact system with fractional derivative damping under Gaussian white noise excitation. The equations of the original system are simplified by non-smooth transformation. For the simplified equation, the stochastic averaging approach is applied to solve it. Then, the fractional derivative damping term is facilitated by a numerical scheme, therewith the fourth-order Runge-Kutta method is used to obtain the numerical results. And the numerical simulation results fit the analytical solutions. Therefore, the proposed analytical means to study this system are proved to be feasible. In this context, the effects on the response stationary probability density functions (PDFs) caused by noise excitation, restitution condition, and fractional derivative damping are considered, in addition the stochastic P-bifurcation is also explored in this paper through varying the value of the coefficient of fractional derivative damping and the restitution coefficient. These system parameters not only influence the response PDFs of this system but also can cause the stochastic P-bifurcation.

Description: Fractal analysis (FA) should be able to yield reliable and fast results for high-resolution digital images to be applicable in fields that require immediate outcomes. Triggered by an efficient implementation of FA for binary images, we present three new approaches for fractal dimension ( D ) estimation of images that utilize image pyramids, namely, the pyramid triangular prism, the pyramid gradient, and the pyramid differences method (PTPM, PGM, PDM). We evaluated the performance of the three new and five standard techniques when applied to images with sizes up to 8192 × 8192 pixels. By using artificial fractal images created by three different generator models as ground truth, we determined the scale ranges with minimum deviations between estimation and theory. All pyramidal methods (PM) resulted in reasonable D values for images of all generator models. Especially, for images with sizes ≥ 1024 × 1024 pixels, the PMs are superior to the investigated standard approaches in terms of accuracy and computation time. A measure for the possibility to differentiate images with different intrinsic D values did show not only that the PMs are well suited for all investigated image sizes, and preferable to standard methods especially for larger images, but also that results of standard D estimation techniques are strongly influenced by the image size. Fastest results were obtained with the PDM and PGM, followed by the PTPM. In terms of absolute D values best performing standard methods were magnitudes slower than the PMs. Concluding, the new PMs yield high quality results in short computation times and are therefore eligible methods for fast FA of high-resolution images.

Description: The use of reverse time chaos allows the realization of hardware chaotic systems that can operate at speeds equivalent to existing state of the art while requiring significantly less complex circuitry. Matched filter decoding is possible for the reverse time system since it exhibits a closed form solution formed partially by a linear basis pulse. Coefficients have been calculated and are used to realize the matched filter digitally as a finite impulse response filter. Numerical simulations confirm that this correctly implements a matched filter that can be used for detection of the chaotic signal. In addition, the direct form of the filter has been implemented in hardware description language and demonstrates performance in agreement with numerical results.

Description: The spatial distributions of system's frequencies have significant influences on the critical coupling strengths for amplitude death (AD) in coupled oscillators. We find that the left and right critical coupling strengths for AD have quite different relations to the increasing spatial period m of the frequency distribution in coupled oscillators. The left one has a negative linear relationship with m in log-log axis for small initial frequency mismatches while remains constant for large initial frequency mismatches. The right one is in quadratic function relation with spatial period m of the frequency distribution in log-log axis. There is an optimal spatial period m 0 of frequency distribution with which the coupled system has a minimal critical strength to transit from an AD regime to reviving oscillation. Moreover, the optimal spatial period m 0 of the frequency distribution is found to be related to the system size N . Numerical examples are explored to reveal the inner regimes of effects of the spatial frequency distribution on AD.

Description: We propose a systematic methodology for creating 2 N +  1-scroll chaotic attractors from a simple three-dimensional system, which is named as the translation chaotic system. It satisfies the condition a 12 a 21  =  0, while the Chua system satisfies a 12 a 21  〉  0. In this paper, we also propose a successful (an effective) design and an analytical approach for constructing 2 N +  1-scrolls, the translation transformation principle. Also, the dynamics properties of the system are studied in detail. MATLAB simulation results show very sophisticated dynamical behaviors and unique chaotic behaviors of the system. It provides a new approach for 2 N +  1-scroll attractors. Finally, to explore the potential use in technological applications, a novel block circuit diagram is also designed for the hardware implementation of 1 -, 3 - , 5 - , and 7 - scroll attractors via switching the switches. Translation chaotic system has the merit of convenience and high sensitivity to initial values, emerging potentials in future engineering chaos design.

Description: Electrocardiogram (ECG) data from patients with a variety of heart conditions are studied using ordinal pattern partition networks. The ordinal pattern partition networks are formed from the ECG time series by symbolizing the data into ordinal patterns. The ordinal patterns form the nodes of the network and edges are defined through the time ordering of the ordinal patterns in the symbolized time series. A network measure, called the mean degree, is computed from each time series-generated network. In addition, the entropy and number of non-occurring ordinal patterns (NFP) is computed for each series. The distribution of mean degrees, entropies, and NFPs for each heart condition studied is compared. A statistically significant difference between healthy patients and several groups of unhealthy patients with varying heart conditions is found for the distributions of the mean degrees, unlike for any of the distributions of the entropies or NFPs.

Description: This paper proposes an epilepsy detection and closed-loop control strategy based on Particle Swarm Optimization (PSO) algorithm. The proposed strategy can effectively suppress the epileptic spikes in neural mass models, where the epileptiform spikes are recognized as the biomarkers of transitions from the normal (interictal) activity to the seizure (ictal) activity. In addition, the PSO algorithm shows capabilities of accurate estimation for the time evolution of key model parameters and practical detection for all the epileptic spikes. The estimation effects of unmeasurable parameters are improved significantly compared with unscented Kalman filter. When the estimated excitatory-inhibitory ratio exceeds a threshold value, the epileptiform spikes can be inhibited immediately by adopting the proportion-integration controller. Besides, numerical simulations are carried out to illustrate the effectiveness of the proposed method as well as the potential value for the model-based early seizure detection and closed-loop control treatment design.

Description: We construct spatiotemporal localized envelope solutions of a (3 + 1)-dimensional nonlinear Schrödinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely, constant, linear, Gaussian, hyperbolic, logarithm, and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely, breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3 + 1)-dimensional nonlinear Schrödinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields.

Description: The mechanical and electrical properties, and information processing capabilities of microtubules are the permanent subject of interest for carrying out experiments in vitro and in silico , as well as for theoretical attempts to elucidate the underlying processes. In this paper, we developed a new model of the mechano–electrical waves elicited in the rows of very flexible C–terminal tails which decorate the outer surface of each microtubule. The fact that C–terminal tails play very diverse roles in many cellular functions, such as recruitment of motor proteins and microtubule–associated proteins, motivated us to consider their collective dynamics as the source of localized waves aimed for communication between microtubule and associated proteins. Our approach is based on the ferroelectric liquid crystal model and it leads to the effective asymmetric double-well potential which brings about the conditions for the appearance of kink–waves conducted by intrinsic electric fields embedded in microtubules. These kinks can serve as the signals for control and regulation of intracellular traffic along microtubules performed by processive motions of motor proteins, primarly from kinesin and dynein families. On the other hand, they can be precursors for initiation of dynamical instability of microtubules by recruiting the proper proteins responsible for the depolymerization process.

Description: We introduce an approach to identify elliptic transport barriers in three-dimensional, time-aperiodic flows. Obtained as Lagrangian Coherent Structures (LCSs), the barriers are tubular non-filamenting surfaces that form and bound coherent material vortices. This extends a previous theory of elliptic LCSs as uniformly stretching material surfaces from two-dimensional to three-dimensional flows. Specifically, we obtain explicit expressions for the normals of pointwise (near-) uniformly stretching material surfaces over a finite time interval. We use this approach to visualize elliptic LCSs in steady and time-aperiodic ABC-type flows.

Description: We examine the use of recurrence networks in studying non-linear deterministic dynamical systems. Specifically, we focus on the case of k -nearest neighbour networks, which have already been shown to contain meaningful (and more importantly, easily accessible) information about dynamics. Superfamily phenomena have previously been identified, although a complete explanation for its appearance was not provided. Local dimension of the attractor is presented as one possible determinant, discussing the ability of specific motifs to be embedded in various dimensions. In turn, the Lyapunov spectrum provides the link between attractor dimension and dynamics required. We also prove invertibility of k -nearest neighbour networks. A new metric is provided, under which the k -nearest neighbour and ϵ -recurrence construction methods produce identical networks. Hence, the already established ϵ -recurrence inversion algorithm applies equally to the k -nearest neighbour case, and inversion is proved. The change in metric necessarily distorts the shape of the reconstructed attractor, although topology is conserved.

Description: Anomalously strong change of ferromagnetic ordering parameters upon a small variation of aluminum content was revealed in low-temperature experimental studies of electrical resistivity and galvanomagnetic properties of iron-vanadium-aluminum magnetic alloys with the compositions near the stoichiometric Fe 2 VAl. By comparing the temperature and magnetic field dependences of the electrical resistivity and Hall effect in Fe 2.1 V 0.91 Al 0.99 and Fe 2.05 V 0.91 Al 1.04 alloys, it was shown that a small increase of aluminum content leads to doubling of the Curie temperature and a sharp change in the temperature dependences of the magnetoresistance and saturation of the spontaneous magnetization.

Description: Specific heat C M ( T ) of polycrystalline Dy 0.6 Y 0.4 Rh 4 B 4 and Dy 0.6 Y 0.4 Rh 3.85 Ru 0.15 B 4 was studied in the temperature range of 0.5–9 K and magnetic fields 0–10 kOe for the first time. It was found that the λ-anomaly in the specific heat exists at T c ≈ 6 K for Dy 0.6 Y 0.4 Rh 4 B 4 and at T c ≈ 6.6 K for Dy 0.6 Y 0.4 Rh 3.85 Ru 0.15 B 4. It is suppressed in a magnetic field and shifted to lower temperatures. Partial substitution of Rh by Ru enhances superconductivity, presumably, due to stronger inner magnetism of the dysprosium sublattice in Dy 0.6 Y 0.4 Rh 4 B 4 as compared with Dy 0.6 Y 0.4 Rh 3.85 Ru 0.15 B 4 . Furthermore, it was observed that the molar heat capacity C M ( T ) of Dy 0.6 Y 0.4 Rh 3.85 Ru 0.15 B 4 increases with decreasing temperature for T 〈 4 K. In Dy 0.6 Y 0.4 Rh 4 B 4 , an increase in C M ( T ) with decreasing temperature is accompanied by the appearance of a maximum at T max = 1.5 K, which might be a manifestation of the magnetic phase transition in the dysprosium subsystem at this temperature.

Description: The thermoluminescence spectra of impurity-helium condensates (IHC) submerged in superfluid helium have been observed for the first time. Thermoluminescence of impurity-helium condensates submerged in superfluid helium is explained by neutralization reactions occurring in impurity nanoclusters. Optical spectra of excited products of neutralization reactions between nitrogen cations and thermoactivated electrons were rather different from the spectra observed at higher temperatures, when the luminescence due to nitrogen atom recombination dominates. New results on current detection during the IHC destruction are presented. Two different mechanisms of nanocluster charging are proposed to describe the phenomena observed during preparation and warm-up of IHC samples in bulk superfluid helium, and destruction of IHC samples out of liquid helium.

Description: X-ray diffractometry is used to study samples of type PM-A group B polyimide (Kapton H) subjected to uniaxial tension at room temperature and cooling to liquid nitrogen and helium temperatures. An asymmetry in the halo of the diffraction pattern from the amorphous sample is observed as a result of deformation and cooling of the samples. Deformation and cooling are found to have different effects on the intensity distribution. Thus, deformation produces “stretched” regions, while cooling produces “compressed” regions. An analysis of the diffraction patterns shows that uniaxial tension leads to partial ordering of the polyimide molecules in a sample along the direction of the applied load. The observed changes in the structure during cooling of films may indicate that mutual ordering of some of the molecules relative to one another is taking place.

Description: Integrated phosphorescence spectra of meta-bromobenzophenone crystals were measured in the temperature range from 1.6 to 297 K. The spectra were found to contain two series of monomeric bands associated with the stretching mode of the C=O carbonyl at all temperatures. Above 70 K in the red spectral region, a broad structureless band of unknown nature was observed, the center of gravity of which was shifted to red with increasing temperature. The above phenomena and others anomalies can be due to the structural properties of both the molecule and the crystal.

Description: The energy spectrum of a quasi-two-dimensional electron gas in an in-plane magnetic field is studied using the perturbation theory and quasiclassical approach in the presence of the Rashba and Dresselhaus spin-orbit coupling. The existence of the intersection of energy sublevels in electron spectrum is demonstrated. The reciprocal mass tensor of electrons is analyzed. The heat capacity of the degenerate electron gas is examined, and its relations with the key features of the spectrum are shown.

Description: We discuss and analyze the dependence spectra of the transmission coefficient T on the quasiparticle energy E of one variety of graphene-based Fibonacci superlattices (SL). The SL is built from armchair graphene nanoribbons (GNR), and the quasi-periodicity is produced by metal-like (MGNR) and semiconductor (SCGNR) ribbons, placed along the lattice growth axis in accordance with the Fibonacci sequence, which are used as individual SL elements. It is shown that the difference in the values of quantized transverse quasi-momentum of electrons in MGNR and SCGNR is enough to form an effective quasi-periodic modulation in the examined structure (no additional factors required), and the optimal nanoribbon width range for this purpose is determined. We also analyzed the dependence of the spectral properties of the test structure on the geometric parameters of the superlattice, and the external electrostatic potential. We paid particular attention to the fact that each Fibonacci generation had a Dirac superlattice band gap. The results of the study can be useful in the determination of optimal parameters for graphene-based nanoelectronic devices.

Description: Quasistable laminar flow of He II at a temperature of 140 mK is studied experimentally. The liquid flow was excited by a vibrating quartz tuning fork with a resonance frequency of about 24 kHz. It was found that for velocities of the tuning fork oscillations from 0.046 to 0.16 m/s, the He II flow can be both quasistable laminar and turbulent. Transitions between these flow regimes were observed. When the velocity of the tuning fork oscillations increases more rapidly, the velocity at which the quasistable flow becomes unstable and undergoes a transition to a turbulent flow is higher. Mechanisms for the dissipation of the energy of the oscillating tines of the tuning fork in the quasistable laminar flow regime are analyzed. It is found that there is an additional mechanism for dissipation of the energy of the oscillating tuning fork beyond internal friction in the quartz. This mechanism is associated with mutual friction owing to scattering of thermal excitations of He II on quantized vortices and leads to a cubic dependence of the exciting force on the fluid velocity.

Description: We study the dynamics of a qubit-resonator system, when the resonator is driven by two signals. The interaction of the qubit with the high-amplitude driving we consider in terms of the qubit dressed states. Interaction of the dressed qubit with the second probing signal can essentially change the amplitude of this signal. We calculate the transmission amplitude of the probe signal through the resonator as a function of the qubit's energy and the driving frequency detuning. The regions of increase and attenuation of the transmitted signal are calculated and demonstrated graphically. We present the influence of the signal parameters on the value of the amplification, and discuss the values of the qubit-resonator system parameters for an optimal amplification and attenuation of the weak probe signal.

Description: The previously derived equations for the components of the order parameter (OP) of dense superfluid neutron matter (SNM) with anisotropic spin-triplet p-wave pairing and with taking into account the effects of magnetic field and finite temperatures are reduced to the single equation for the one-component OP in the limit of zero magnetic field. Here this equation is solved analytically for arbitrary parametrization of the effective Skyrme interaction in neutron matter and as the main results the energy gap (in the energy spectrum of neutrons in SNM) is obtained as nonlinear function of temperature T and density n in two limiting cases: for low temperatures near T = 0 and in the vicinity of phase transition temperature T c 0 ( n ) for dense neutron matter from normal to superfluid state. These solutions for the energy gap are specified for generalized BSk21 and BSk24 parametrizations of the Skyrme forces (with additional terms dependent on density n ) and figures are plotted on the interval 0.1 n 0 〈 n 〈 2.0 n 0 , where n 0 = 0.17 fm −3 is nuclear density.

Description: An analysis of known experimental literature data on the temperature dependence of magnetic susceptibility of beryllium. It is shown that this dependence can be explained if we take into account that beryllium has an electron topological transition of 3½ kind near the Fermi level.

Description: The electronic structure and optical properties of the SmNi 5– x Cu x ( x = 0, 1, 2) compounds are studied. The band spectra of the studied intermetallics were calculated with LDA + U + SO method supplementing the local density approximation with a correction for strong electron interaction on the shell of the rare-earth element. Optical properties were studied by ellipsometry method in the wide wavelength range. It was found that the substitution of copper for nickel leads to local changes in the optical conductivity spectra. Both the spectroscopic measurements and theoretical calculations demonstrate the presence of a broad absorption band around 4 eV associated with the Cu 3 d → Ni 3 d electron transitions and increasing with the grown of copper content. The experimental dispersion curves of optical conductivity in the interband absorption region were interpreted using the results of the calculations.