Repulsive Coupling Research Articles

Collective Dynamical Behaviors of Nonlocally Coupled Brockett Oscillators

In this study, we consider a network of nonlocally coupled Brockett oscillators (BOs) with attractive and repulsive (AR) couplings to illustrate the existence of diverse collective dynamical behaviors, whereas previous studies solely concentrated on synchronization. In the absence of coupling, the individual BO oscillator shows stable periodic oscillations (POs) or stable steady state (SS) depending on the critical values of the parameters. We first begin by examining the collective dynamics by setting the critical value of the parameters at the active (PO) region. A diverge collective dynamical states are manifested for a fixed nonlocal coupling range with rising coupling magnitude. Notably, the lower coupling strength exhibits two distinct dynamical patterns at lower and higher transients. At lesser transients, for example, transient dynamics of desynchronization, chimera, and traveling wave states are observed. At larger time periods, the transient dynamics disappear with the emergence of a synchronized state. Increasing the coupling strength results in a unique state of traveling wave or synchronized state for smaller and larger time periods depending on the coupling strength. Increasing the coupling strength further gives rise to clustering behaviors. Importantly, the considered system attains cluster oscillation death (COD) through a cluster oscillatory state (COS). Finally, there exists a chimera death at a larger coupling strength. The observed dynamical transitions are further demonstrated through the two‐parameter analysis by setting different critical thresholds.

Noise-induced swarming of active particles.

We report on the effect of spatially correlated noise on the velocities of self-propelled particles. Correlations in the random forces acting on self-propelled particles can induce directed collective motion, i.e., swarming. Even with repulsive coupling in the velocity directions, which favors a disordered state, strong correlations in the fluctuations can align the velocities locally leading to a macroscopic, turbulent velocity field. On the other hand, while spatially correlated noise is aligning the velocities locally, the swarming transition to globally directed motion is inhibited when the correlation length of the noise is nonzero, but smaller than the system size. We analyze the swarming transition in d-dimensional space in a mean field model of globally coupled velocity vectors.

Heterogeneity induced splay state of amplitude envelope in globally coupled oscillators.

Splay states of the amplitude envelope are stably observed as a heterogenous node is introduced into the globally coupled identical oscillators with repulsive coupling. With the increment of the frequency mismatches between the heterogenous nodes and the rest identical globally coupled oscillators, the formal stable splay state based on the time series becomes unstable, while a splay state based on the new-born amplitude envelopes of time series is stably observed among the rest identical oscillators. The characteristics of the splay state based on the amplitude envelope are numerically and theoretically presented for different parameters of the coupling strength ϵ and the frequency mismatches Δω for small coupling strength and large frequency mismatches. We expect that all these results could reveal the generality of splay states in coupled nonidentical oscillators and help to understand the rich dynamics of amplitude envelopes in multidisciplinary fields.

Extreme events in a complex network: Interplay between degree distribution and repulsive interaction.

The role of topological heterogeneity in the origin of extreme events in a network is investigated here. The dynamics of the oscillators associated with the nodes are assumed to be identical and influenced by mean-field repulsive interactions. An interplay of topological heterogeneity and the repulsive interaction between the dynamical units of the network triggers extreme events in the nodes when each node succumbs to such events for discretely different ranges of repulsive coupling. A high degree node is vulnerable to weaker repulsive interactions, while a low degree node is susceptible to stronger interactions. As a result, the formation of extreme events changes position with increasing strength of repulsive interaction from high to low degree nodes. Extreme events at any node are identified with the appearance of occasional large-amplitude events (amplitude of the temporal dynamics) that are larger than a threshold height and rare in occurrence, which we confirm by estimating the probability distribution of all events. Extreme events appear at any oscillator near the boundary of transition from rotation to libration at a critical value of the repulsive coupling strength. To explore the phenomenon, a paradigmatic second-order phase model is used to represent the dynamics of the oscillator associated with each node. We make an annealed network approximation to reduce our original model and, thereby, confirm the dual role of the repulsive interaction and the degree of a node in the origin of extreme events in any oscillator associated with a node.

Ferromagnetism with Strong Perpendicular Magnetic Anisotropy in Epitaxial SrMn0.3Ir0.7O3 Perovskite Films

Strong Coulomb repulsion and spin-orbit coupling are known to give rise to exotic physical phenomena in transition metal oxides. Here, we report magnetic characteristics of a ${\mathrm{Sr}\mathrm{Mn}}_{0.3}{\mathrm{Ir}}_{0.7}{\mathrm{O}}_{3}$ perovskite thin film, having both 3d and 5d elements on the $B$ sites, with a strong perpendicular magnetic anisotropy (PMA), which is rare in perovskite oxide thin films. The ${\mathrm{Sr}\mathrm{Mn}}_{0.3}{\mathrm{Ir}}_{0.7}{\mathrm{O}}_{3}$ films have been epitaxially deposited on (001)-oriented ${\mathrm{Sr}\mathrm{Ti}\mathrm{O}}_{3}$ single-crystal substrates by pulsed-laser deposition, exhibiting a para-to-ferromagnetic transition at about 110 K. The average valence of $\mathrm{Mn}$ and $\mathrm{Ir}$ cations are estimated as +3.61 and +4.17, respectively, by x-ray photoelectron spectroscopy. X-ray absorption spectroscopy reveals that $\mathrm{Mn}$ ${e}_{g}$ electrons occupy preferentially the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital, which produces the observed PMA in the framework of spin-orbital coupling. The ${\mathrm{Sr}\mathrm{Mn}}_{0.3}{\mathrm{Ir}}_{0.7}{\mathrm{O}}_{3}$ thin film shows a large effective anisotropy constant of about 1.2 \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ erg ${\mathrm{cm}}^{\ensuremath{-}3}$ at 10 K, which is found to decrease with decreasing tetragonality c/a of the film. First-principles calculations reveal that $\mathrm{Mn}$ and $\mathrm{Ir}$ cations provide opposite magnetizations in ${\mathrm{Sr}\mathrm{Mn}}_{0.3}{\mathrm{Ir}}_{0.7}{\mathrm{O}}_{3}$ and the $\mathrm{Mn}$ ${e}_{g}$ orbital polarization comes from both lattice distortion and oxygen octahedron rotation. The ${\mathrm{Sr}\mathrm{Mn}}_{0.3}{\mathrm{Ir}}_{0.7}{\mathrm{O}}_{3}$ thin film with strong PMA may have applications in future low-power-consumption oxide spintronic devices.

Symmetric synchronization behavior of multistable chaotic systems and circuits in attractive and repulsive couplings

This paper studies the synchronization behavior of multistable chaotic systems with coexisting symmetric attractors. Specifically, the focus is on the attractive and repulsive couplings of the attractors in single-variable couplings. It is shown that in the self-couplings, both attractors have the same synchronization pattern either in the attractive or repulsive coupling. In the cross-couplings, the synchronization pattern of the attractors is dependent on the variables involved in the coupling and the symmetry transformation. If the coupling scheme is defined such that only one of the variables in the coupling participates in the symmetry transformation, the synchronization patterns of the symmetric attractors are symmetric in the attractive and repulsive couplings. The master stability function is applied to four chaotic systems with different symmetry transformations to represent the results. The corresponding chaotic circuit of two coupled symmetric systems is also implemented and their symmetric responses are shown.

Effect of mobility on collective phase dynamics of nonlocally coupled oscillators with a phase lag.

Nonlocally coupled oscillators with a phase lag self-organize into various patterns, such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, whereas it destroys coherence for a repulsive coupling. The transition behaviors are discussed in terms of the timescales of synchronization and diffusion of the oscillators. We also find a novel spatiotemporal pattern at the border between coherent and incoherent states.

Amplitude death in multiplex networks with competing attractive and repulsive interactions

Amplitude death (AD) phenomenon is one of the most striking and ubiquitous collective behaviors of coupled dynamical networks, in which all the dynamical units will cease their oscillations totally when the coupling occurs. Various appealing works have been devoted to the study of AD in the single-layer networks from theoretical and experimental perspectives in the last decades. However, it is still unclear under which conditions AD can be induced in the multiplex networks. In this work, we investigate the onset of AD of coupled systems connected via multiplex network architectures in the presence of competing attractive and repulsive intralayer and interlayer interactions. We first theoretically derive the critical condition of AD for a class of generalized multiplex network models. Then we apply it to calculate the stable AD regions for the case of a single-layer network of Stuart–Landau oscillators and observe that in the single-layer ring network, AD only can occur for small networks regardless of how to tune the proportion of repulsive coupling. Whereas, for the single-layer all-to-all network, AD always can appear, and the larger the network size or the proportion of repulsive coupling, the smaller the required coupling strength for AD is. Finally, we show in the three-layer multiplex network of Stuart–Landau oscillators that the stable AD regions can be concluded to four types based on the intralayer and interlayer network topologies. In particular, even if AD does not exist separately in each layer network, it can be reached by choosing appropriately interlayer interaction in the three-layer multiplex network. Our study sheds a new insight into the generation of AD phenomenon and gives a general framework to analyze the steady state behaviors of coupled systems in the multiplex networks.

Flexible patterns of information transfer in frustrated networks of phase oscillators

Brain networks are characterized by flexible patterns of pairwise correlations and information exchange between different brain regions. Such dynamic patterns are crucial for an efficient response of the brain to environmental and cognitive demands. We here propose that the collective oscillations in the brain can provide a mechanism to control dynamical interactions and the exchange of information across brain networks. In particular, we show that the phase difference between oscillatory activities in different brain regions determines the transmission of neural signals. To further corroborate this, we study a network of coupled oscillators with repulsive couplings and show that the amount of information transfer between the nodes is determined by the phase differences. The emergence of multiple (locally) stable states due to the frustration makes it possible to change the patterns of information transfer between the nodes by means of the switching between different stable states. Our results indicate that frustration can be the mechanism through which large-scale brain networks control the effective connectivity and the routes for the information transfer between different brain regions.

Observation of a multitude of correlated states at the surface of bulk 1T−TaSe2 crystals

Is it possible to have a single crystal that hosts a variety of correlated surface states? Layered transition metal dichalcogenides such as bulk 1$T$-TaSe${}_{2}$ offer a unique platform for accomplishing this since the electrons in each charge density wave (CDW) unit cell are susceptible to both Coulomb repulsion and interlayer coupling. By using scanning tunneling microscopy and spectroscopy, the authors identify here a multitude of correlated surface states that exist on bulk 1$T$-TaSe${}_{2}$ with properties ranging all the way from Mott insulating to strongly metallic Kondo behavior. 1$T$-TaSe${}_{2}$ thus simulates the full range of the periodic Anderson model within a single crystal by combining electron correlations with variable interlayer coupling.

Explosive synchronization in coupled nonlinear oscillators on multiplex network

We report the emergence of explosive synchronization in a multiplex network where oscillators on the first layer are coupled with attractive coupling and those on the second layer, coupled with repulsive coupling. With Stuart-Landau and FitzHugh-Nagumo oscillators as the nodal dynamics, we consider non-local and mean-field intralayer couplings. We establish that explosive synchronization occurs in the multiplex network in the presence of Gaussian noise, and the transition is first order with hysteresis to a state of complete intra-layer and in-phase interlayer synchronization. The width of the hysteresis depends on the range of intralayer attractive coupling, strength of interlayer coupling and noise. We also see how to have control over this induced transition so that the explosive nature, if undesirable, can be converted to continuous type by tuning the strength of repulsive coupling or noise.

Vibronic recovering of functionality of quantum cellular automata based on bi-dimeric square cells with violated condition of strong Coulomb repulsion.

Strong Coulomb repulsion between the two charges in a square planar mixed-valence cell in quantum cellular automata (QCA) allows us to encode the binary information in the two energetically beneficial diagonal distributions of the electronic density. In this article, we pose a question: to what extent is this condition obligatory for the design of the molecular cell? To answer this question, we examine the ability to use a square-planar cell composed of one-electron mixed valence dimers to function in QCA in a general case when the intracell Coulomb interaction U is not supposed to be extremely strong, which means that it is comparable with the characteristic electron transfer energy (violated strong U limit). Using the two-mode vibronic model treated within the semiclassical (adiabatic) and quantum-mechanical approaches, we demonstrate that strong vibronic coupling is able to create a considerable barrier between the two diagonal-type charge configurations, thus ensuring bistability and polarizability of the cells even if the Coulomb barrier is not sufficient. The cases of weak and moderate Coulomb repulsion and strong vibronic coupling are exemplified by consideration of the cation radicals of the two polycyclic derivatives of norbornadiene [C12H12]+ and [C17H16]+ with the terminal C=C chromophores playing the role of redox sites. By using the detailed ab initio data, we reveal the main characteristics of the bi-dimeric cells composed of these molecules and illustrate the pronounced effect of the vibronic recovery clearly manifesting itself in the shape of the cell-cell response function. Revealing such "vibronic recovery" of strong localization when the strong U limit is violated suggests a way to a significant expansion of the class of molecular systems suitable as QCA cells.

Elastic scattering and boron, lithium, and α -particle production in the Be9 + V51 reaction

Background: Experimental and theoretical investigation of breakup coupling effects due to different cluster structures ($^{8}\mathrm{Be}+n$ and $^{5}\mathrm{He}+\ensuremath{\alpha}$), relative importance of neutron or $^{5}\mathrm{He}/\ensuremath{\alpha}$ transfer, and their contribution to $\ensuremath{\alpha}$ production are important to understand reaction mechanism in a weakly bound projectile ($^{9}\mathrm{Be}$) near the Coulomb barrier.Purpose: Breakup coupling effect on elastic scattering and measurement of angular distributions and energy spectra of $\ensuremath{\alpha}$ particles produced through breakup, transfer, and complete fusion processes to disentangle their relative contributions and to investigate the relative importance of breakup followed by fusion (breakup-fusion) are compared to transfer.Methods: Elastic scattering, inclusive $\ensuremath{\alpha}$ production, lithium, and boron production cross sections have been measured for the $^{9}\mathrm{Be}+^{51}\mathrm{V}$ system above Coulomb barrier energies. Continuum-discretized-coupled-channels (CDCC) breakup coupling effect using $^{8}\mathrm{Be}+n$ and $^{5}\mathrm{He}+\ensuremath{\alpha}$ cluster configurations have been investigated. Coupled reaction channels (CRC) calculations for $1\mathit{p}, 1\mathit{d}$, and $1\mathit{n}$ stripping and $1\mathit{p}, 1\mathit{d}$ pickup leading to $^{8}\mathrm{Li}+^{52}\mathrm{Cr}, ^{7}\mathrm{Li}+^{53}\mathrm{Cr}, ^{8}\mathrm{Be}+^{52}\mathrm{V}$, and $^{10}\mathrm{B}+^{50}\mathrm{Ti}, ^{11}\mathrm{B}+^{49}\mathrm{Ti}$, respectively, were performed and compared with the experimental data. Theoretical calculations for the estimation of various reaction channels contributing to $\ensuremath{\alpha}$ production have been performed with CDCC and CRC methods using the fresco code.Results: Global optical model parameters for the $^{9}\mathrm{Be}$ projectile describe the elastic scattering data very well and the optical model fit improves the ${\ensuremath{\chi}}^{2}$ slightly. CRC calculations show a major contribution in the production of lithium through $1\mathit{p}, 1\mathit{d}$ stripping and boron through $1\mathit{p}, 1\mathit{d}$ pickup reactions. $\ensuremath{\alpha}$ production angular and energy distributions are obtained, and direct $\ensuremath{\alpha}$ production is described with contributions from noncapture breakup, breakup-fusion, and transfer reactions.Conclusions: Breakup coupling for $^{5}\mathrm{He}+\ensuremath{\alpha}$ and $^{8}\mathrm{Be}+n$ cluster structures shows a repulsive and attractive coupling effect on elastic scattering, respectively. The $^{8}\mathrm{Be}+n$ cluster structure also shows a dipole polarization effect by suppressing the Coulomb rainbow compared to the $^{5}\mathrm{He}+\ensuremath{\alpha}$ cluster structure. Kinematic analysis of the $\ensuremath{\alpha}$ particles energy spectra suggest that $\ensuremath{\alpha}$ production is dominated by breakup-fusion over cluster transfer. CRC calculations suggest that $1\mathit{p}, 1\mathit{d}$ stripping and pickup reactions are a major contributor to lithium and boron production cross sections.

Impact of repulsive coupling in exhibiting distinct collective dynamical states

Impact of repulsive coupling in exhibiting distinct collective dynamical states

Counterflow dynamics of two correlated impurities immersed in a bosonic gas

The counterflow dynamics of two correlated impurities in a double well coupled to a one-dimensional bosonic medium is explored. We determine the ground-state phase diagram of the system according to the impurity-medium entanglement and the impurities' two-body correlations. Specifically, bound impurity structures reminiscent of bipolarons for strong attractive couplings as well as configurations with two clustered or separated impurities in the repulsive case are identified. The interval of existence of these phases depends strongly on the impurity-impurity interactions and external confinement of the medium. Accordingly the impurities' dynamical response, triggered by suddenly ramping down the central potential barrier, is affected by the medium's trapping geometry. In particular, for a box-confined medium, repulsive impurity-medium couplings lead, due to attractive induced interactions, to the localization of the impurities around the trap center. In contrast, for a harmonically trapped medium the impurities perform a periodic collision and expansion dynamics further interpreted in terms of a two-body effective model. Our findings elucidate the correlation aspects of the collisional physics of impurities which should be accessible in recent cold-atom experiments.

Swarmalators under competitive time-varying phase interactions

Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to the fascinating bidirectional interplay between phase and spatial dynamics. Although different coupling topologies have already been considered, here we introduce time-varying competitive phase interaction among swarmalators where the underlying connectivity for attractive and repulsive coupling varies depending on the vision (sensing) radius. Apart from investigating some fundamental properties like conservation of center of position and collision avoidance, we also scrutinize the cases of extreme limits of vision radius. The concurrence of attractive–repulsive competitive phase coupling allows the exploration of diverse asymptotic states, like static π, and mixed phase wave states, and we explore the feasible routes of those states through a detailed numerical analysis. In sole presence of attractive local coupling, we reveal the occurrence of static cluster synchronization where the number of clusters depends crucially on the initial distribution of positions and phases of each swarmalator. In addition, we analytically calculate the sufficient condition for the emergence of the static synchronization state. We further report the appearance of the static ring phase wave state and evaluate its radius theoretically. Finally, we validate our findings using Stuart–Landau oscillators to describe the phase dynamics of swarmalators subject to attractive local coupling.

Hydrodynamics and transport in the long-range-interacting φ 4 chain

We present a simulation study of the one-dimensional φ 4 lattice theory with long-range interactions decaying as an inverse power r −(1+σ) of the intersite distance r, σ > 0. We consider the cases of single and double-well local potentials with both attractive and repulsive couplings. The double-well, attractive case displays a phase transition for 0 < σ ⩽ 1 analogous to the Ising model with long-range ferromagnetic interactions. A dynamical scaling analysis of both energy structure factors and excess energy correlations shows that the effective hydrodynamics is diffusive for σ > 1 and anomalous for 0 < σ < 1, where fluctuations propagate superdiffusively. We argue that this is accounted for by a fractional diffusion process and we compare the results with an effective model of energy transport based on Lévy flights. Remarkably, this result is fairly insensitive on the phase transition. Nonequilibrium simulations with an applied thermal gradient are in quantitative agreement with the above scenario.

Two-gap s± -wave superconductivity at an oxide interface

After half a century of debate, superconductivity in doped ${\mathrm{SrTiO}}_{3}$ has come to the fore again with the discovery of interfacial superconductivity in the ${\mathrm{LaAlO}}_{3} /{\mathrm{SrTiO}}_{3}$ heterostructures. While these interfaces share the interesting properties of bulk ${\mathrm{SrTiO}}_{3}$ , quantum confinement generates a complex band structure involving bands with different orbital symmetries whose occupancy is tunable by electrostating doping. Multigap superconductivity has been predicted to emerge in ${\mathrm{LaAlO}}_{3} /{\mathrm{SrTiO}}_{3}$ at large doping, with a Bose-Einstein condensation character at the Lifshtiz transition. In this article, we report on the measurement of the upper critical magnetic field ${\mathrm{H}}_{\mathrm{c}2}$ of superconducting (110)-oriented ${\mathrm{LaAlO}}_{3} /{\mathrm{SrTiO}}_{3}$ heterostructures and evidence a two-gap superconducting regime at high doping. Our results are quantitatively explained by a theoretical model based on the formation of an unconventional ${\mathrm{s}}_{\ifmmode\pm\else\textpm\fi{}}$-wave superconducting state with a repulsive coupling between the two condensates.

Stability of rotatory solitary states in Kuramoto networks with inertia.

Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and oscillates with a different frequency. Such chimera-type patterns with an incoherent state formed by a single oscillator were observed in various oscillator networks; however, there is still a lack of understanding of how such states can stably appear. Here, we study the stability of solitary states in Kuramoto networks of identical two-dimensional phase oscillators with inertia and a phase-lagged coupling. The presence of inertia can induce rotatory dynamics of the phase difference between the solitary oscillator and the coherent cluster. We derive asymptotic stability conditions for such a solitary state as a function of inertia, network size, and phase lag that may yield either attractive or repulsive coupling. Counterintuitively, our analysis demonstrates that (1) increasing the size of the coherent cluster can promote the stability of the solitary state in the attractive coupling case and (2) the solitary state can be stable in small-size networks with all repulsive coupling. We also discuss the implications of our stability analysis for the emergence of rotatory chimeras.

Controlling synchrony in an array of the globally coupled FitzHugh–Nagumo type oscillators

A feedback method of controlling synchrony in globally coupled oscillators is described. The technique is based on injecting a negative replica of the mean field into the array. The feedback force either desynchronizes the oscillators via compensation of the attractive coupling or causes the repulsive coupling of the oscillators. Both mechanisms result in low level of the mean field. Clustering of the oscillators is observed in the region of repulsive coupling. Numerical and analytical investigations have been carried with an array of the mean-field coupled FitzHugh–Nagumo type oscillators.