Presence Of Coupling Research Articles

Bulk reconstruction from generalized free fields

We propose a generalized protocol for constructing a dual free bulk theory from any boundary model of generalized free fields (GFFs). To construct the bulk operators, we employ a linear ansatz similar to the Hamilton-Kabat-Liftschytz-Lowe (HKLL) construction. However, unlike the HKLL construction, our protocol relies only on boundary data with no presupposed form for the bulk equations of motion, so our reconstructed bulk is fully emergent. For a (1+1)d bulk, imposing the bulk operator algebra as well as a causal structure is sufficient to determine the bulk operators and dynamics uniquely up to an unimportant local basis choice. We study the bulk construction for several two-sided SYK models with and without coupling between the two sides, and find good agreement with known results in the low-temperature conformal limit. In particular, we find bulk features consistent with the presence of a black hole horizon for the TFD state, and characterize the infalling fermion modes. We are also able to extract bulk quantities such as the curvature and bulk state correlators in terms of boundary quantities. In the presence of coupling between the two SYK models, we are able to observe evidence of the shockwave geometry and the traversable wormhole geometry using the two-sided mutual information between the reconstructed bulk operators. Our results show evidence that features of the geometric bulk can survive away from the low temperature conformal limit. Furthermore, the generality of the protocol allows it to be applied to other boundary theories with no canonical holographic bulk.

Fractional topology in interacting one-dimensional superconductors

We investigate the topological phases of two one-dimensional (1D) interacting superconducting wires and propose topological markers directly measurable from ground-state correlation functions. These quantities remain powerful tools in the presence of couplings and interactions. We show with the density matrix renormalization group that the double critical Ising (DCI) phase of two interacting Kitaev chains is a fractional topological phase with gapless Majorana modes in the bulk, and a one-half topological invariant per wire. Using both numerics and quantum field theoretical methods, we show that the phase diagram remains stable in the presence of an interwire hopping amplitude ${t}_{\ensuremath{\perp}}$ at length scales below $\ensuremath{\sim}1/{t}_{\ensuremath{\perp}}$. A large interwire hopping amplitude results in the emergence of two integer topological phases, stable also at large interactions. They host one edge mode per boundary shared between both wires. At large interactions, the two wires are described by Mott physics, with the ${t}_{\ensuremath{\perp}}$ hopping amplitude resulting in a paramagnetic order.

A Decentralized Technique for Autonomous Distribution Network Restoration in Presence of Coupling Neighboring Microgrids

A Decentralized Technique for Autonomous Distribution Network Restoration in Presence of Coupling Neighboring Microgrids

What Is Needed of a Scalar Field If It Is to Unify Inflation and Late Time Acceleration?

Quintessential inflation refers to scenarios in which a single scalar field is used to describe inflation and late time acceleration. This review is dedicated to the framework of quintessential inflation, with a focus on the building blocks of formalism. Consistent unification of inflation and late time acceleration using a single scalar field asks for a shallow field potential initially followed by steep behaviour thereafter and shallow again around the present epoch. The requirement of non-interference of the scalar field with thermal history dictates the steep nature of potential in the post-inflationary era, with a further restriction that late time physics be independent of initial conditions. We describe, in detail, the scaling and asymptotic scaling solutions and the mechanism of exit from the scaling regime to late time acceleration. The review includes a fresh look at scaling solutions that are central to the theme of unification of inflation and late time acceleration. As for the exit mechanism, special attention is paid to the coupling of massive neutrino matter to the scalar field, which builds up dynamically and can give rise to late time acceleration. We present a detailed analytical treatment of scalar field dynamics in the presence of coupling. We briefly discuss the distinguishing feature of quintessential inflation, namely the blue spectrum of gravity waves produced during the transition from inflation to the kinetic regime.

Amplitude-modulated spiking as a novel route to bursting: Coupling-induced mixed-mode oscillations by symmetry breaking.

Mixed-mode oscillations consisting of alternating small- and large-amplitude oscillations are increasingly well understood and are often caused by folded singularities, canard orbits, or singular Hopf bifurcations. We show that coupling between identical nonlinear oscillators can cause mixed-mode oscillations because of symmetry breaking. This behavior is illustrated for diffusively coupled FitzHugh-Nagumo oscillators with negative coupling constant, and we show that it is caused by a singular Hopf bifurcation related to a folded saddle-node (FSN) singularity. Inspired by earlier work on models of pancreatic beta-cells [Sherman, Bull. Math. Biol. 56, 811 (1994)], we then identify a new type of bursting dynamics due to diffusive coupling of cells firing action potentials when isolated. In the presence of coupling, small-amplitude oscillations in the action potential height precede transitions to square-wave bursting. Confirming the hypothesis from the earlier work that this behavior is related to a pitchfork-of-limit-cycles bifurcation in the fast subsystem, we find that it is caused by symmetry breaking. Moreover, we show that it is organized by a FSN in the averaged system, which causes a singular Hopf bifurcation. Such behavior is related to the recently studied dynamics caused by the so-called torus canards.

Numerical Investigations on Rotatry Micropolar Fluid in Hydromagnetics Permeated with Suspended Particles Saturating Porous Medium

This paper deals with the convection of micropolar fluids heated and soluted from below in the presence of suspended particles (fine dust) and uniform vertical rotation and uniform vertical magnetic field in a porous medium. Using the Boussinesq approximation, the linearized stability theory and normal mode analysis, the exact solutions are obtained for the case of two free boundaries. It is found that the presence of the suspended particles number density, the rotation parameter, stable solute, magnetic field intensity and medium permeability bring oscillatory modes which were non–existent in their absence. It is found that the presence of coupling between thermal and micropolar effects, rotation parameter, solute parameter and suspended particles may introduce overstability in the system. Graphs have been plotted by giving numerical values to the parameters accounting for rotation parameter , magnetic field solute parameter, the dynamic microrotation viscosity and coefficient of angular viscosity to depict the stability characteristics, for both the cases of stationary convection and overstability. It is found that Rayleigh number for the case of overstability and stationary convection increases with increase in rotation parameter, as well as with magnetic field intensity, solute parameter and decreases with increase in micropolar coefficients and medium permeability, for a fixed wave number, implying thereby the stabilizing effect of rotation parameter, magnetic field intensity ,solute parameter and destabilizing effect of micropolar coefficients and medium permeability on the thermosolutal convection of micropolar fluids.

Synchronization and coalescence in a dissipative two-qubit system

The possibility of detuned spins displaying synchronous oscillations in local observables is analysed in the presence of coupling, collective dissipation and incoherent pumping. We show that there exist two distinct scenarios in which synchronization can emerge, related respectively to the presence of a non-degenerate long-lived eigenmode and to the presence of a single-frequency regime. Both scenarios can arise by tuning parameters in this system, owing to the presence of coalascence. The former, known as transient synchronization, is here generalized in the presence of incoherent pumping, and is due to long-lasting coherences leading to a progressive frequency selection. On the other hand, in spite of the spins detuning, the dynamics can be governed by a single frequency. Still, we show that synchronization can be established only after a transient, when phase-locking arises. Spectral features of synchronization in these two scenarios are analysed for two-time correlations.

Leveraging deep learning to control neural oscillators.

Modulation of the firing times of neural oscillators has long been an important control objective, with applications including Parkinson's disease, Tourette's syndrome, epilepsy, and learning. One common goal for such modulation is desynchronization, wherein two or more oscillators are stimulated to transition from firing in phase with each other to firing out of phase. The optimization of such stimuli has been well studied, but this typically relies on either a reduction of the dimensionality of the system or complete knowledge of the parameters and state of the system. This limits the applicability of results to real problems in neural control. Here, we present a trained artificial neural network capable of accurately estimating the effects of square-wave stimuli on neurons using minimal output information from the neuron. We then apply the results of this network to solve several related control problems in desynchronization, including desynchronizing pairs of neurons and achieving clustered subpopulations of neurons in the presence of coupling and noise.

An efficient algorithm for inferring functional connectivity between the drive and the noisy response chaotic oscillators with significant frequency mismatch

In this study, we present a new method for assessing the functional connectivity between the drive and the noisy response chaotic oscillators with significant frequency mismatch. This method is based on the footprint of the drive oscillator on the response oscillator. Specifically, we calculate the magnitude squared coherence between the intrinsic frequency of the drive oscillator and the oscillation frequency of the dynamics of the spectral energy of the response oscillator. The spectral energy of the response oscillator is estimated using a modified S-transform algorithm with a short sliding window. We apply the proposed approach to master–slave Rossler systems and coupled Van der Pol oscillators with a frequency ratio of $$\sim $$ 1:4 and show that when the slave signal is contaminated with white Gaussian noise at different signal-to-noise ratios (SNR), the new algorithm is well suited to assess the presence of coupling with a priori known direction in noisy, unidirectionally coupled chaotic oscillators, especially in the case of weak and moderate coupling.

Methods to aggregate turbine and network impedance for wind farm resonance analysis

Small-signal sequence impedance models have been developed for different types of wind turbines and used in industry to study wind farm and high-voltage direct current (HVDC) system harmonics and resonances. Compared to other small-signal methods, a major advantage of system modelling and analysis based on sequence impedance is its scalability: an equivalent impedance model can be easily built for any complex system by aggregating the impedance of individual turbines and the network. A recent development in the small-signal sequence impedance theory is the modelling of frequency coupling to improve the accuracy of system analysis and explain a common characteristic of harmonics created by system resonance. In light of this new development, this study presents and compares different aggregation methods to build farm-level impedance models in the presence of coupling in individual turbine responses. The objective is to identify practical methods that can meet the needs of different system analyses and are easily to use. Experiences of China State Grid and TenneT with the application of sequence impedance models in renewable energy and HVDC system resonance and harmonic analysis are also discussed, along with an overview of their ongoing efforts to develop new grid codes and system analysis tools based on sequence impedances.

Quasi-Phase-Matching Efficiency Optimization for Coupled Second-Order Nonlinear Processes

It is well known how to tailor the conversion efficiency grid of a single quasi-phase-matching (QPM) grating when the involved processes are uncoupled. However, it becomes much more sophisticated in the presence of coupling between multiple processes. In this case, different processes compete for the same QPM “resources” throughout the grating, and one process can outweigh the others over a certain range of interaction. Here we propose the generalized iterative domino (GID) algorithm to meet these challenges for the first time (to our best knowledge). Instead of tailoring the strength of each “global” Fourier coefficient, GID algorithm can properly adjust the spatially varying “local” Fourier coefficients in favor of the final yield. Three methods, including cascaded single-period (C1P) structure, quasi-periodic optical superlattice (QPOS), and hyperfine aperiodic optical superlattice (HAOS) optimized by GID, are numerically and experimentally investigated under the platform of third-harmonic generation (THG). It shows that the THG efficiency of HAOS + GID can exceed the record achieved by C1P structure by 33%. This method is applicable to general wavelength converters involving with multiple coupled nonlinear processes.

Recent acoustical studies of khaen pipes

A khaen pipe is an open bamboo pipe of effective length L, with the free reed located at approximately L/4. The physical length of the pipe is greater than L, with two rectangular tuning slots cut into the pipe defining its effective length and resulting in the presence of cylindrical end sections. Properties of individual khaen pipes and collective effects of two or more pipes sounding together have been studied both experimentally and with finite element modeling software. Special attention has been given to the role of the pipe end sections and the presence of coupling between pipes played simultaneously. In addition to the modes of an open cylindrical pipe expected for the main pipe section, the khaen pipe has modes involving either an end section alone or an end section and the main section together. The presence of these resulting end sections can significantly affect both sound radiation properties and the timbre of the radiated sound. Music for the khaen almost always involves multiple pipes sounding simultaneously, and the conditions for synchronization of slightly mistuned pipes have been studied.

On convergence criteria for the coupled flow of Li–Yuan–Zhang

A one-parameter family of coupled flows depending on a parameter $\kappa>0$ is introduced which reduces when $\kappa=1$ to the coupled flow of a metric $\omega$ with a $(1,1)$-form $\alpha$ due recently to Y. Li, Y. Yuan, and Y. Zhang. It is shown in particular that, for $\kappa\not=1$, estimates for derivatives of all orders would follow from $C^0$ estimates for $\omega$ and $\alpha$. Together with the monotonicity of suitably adapted energy functionals, this can be applied to establish the convergence of the flow in some situations, including on Riemann surfaces. Very little is known as yet about the monotonicity and convergence of flows in presence of couplings, and conditions such as $\kappa\not=1$ seem new and may be useful in the future.

Theory and experiments of coherent photon coupling in semiconductor nanowire waveguides with quantum dot molecules

We present a quantum optics theory, numerical calculations, and experiments on coupled quantum dots in semiconductor nanowire waveguides. We first present an analytical Green function theory to compute the emitted spectra of two coupled quantum dots, treated as point dipoles, fully accounting for retardation effects, and demonstrate the signatures of coherent and incoherent coupling through a pronounced splitting of the uncoupled quantum dot resonances and modified spectral broadening. In the weak excitation regime, the classical Green functions used in models are verified and justified through full three-dimensional solutions of Maxwell equations for nanowire waveguides, specifically using finite-difference time-domain techniques, showing how both waveguide modes and near-field evanescent mode coupling is important. The theory exploits an ensemble-based quantum description, and an intuitive eigenmode-expansion-based Maxwell theory. We then demonstrate how the molecular resonances (in the presence of coupling) take on the form of bright and dark (or quasidark) resonances, and study how these depend on the excitation and detection conditions. To go beyond the weak excitation regime, we also introduce a quantum master-equation approach to model the nonlinear spectra from an increasing incoherent pump field, which shows the role of the pump field on the oscillator strengths and broadening of the molecular resonances, with and without pure dephasing. Next, we present experimental photoluminescence spectra for spatially separated quantum dot molecules (InAsP) in InP nanowires, which show clear signatures of pronounced splittings, although they also highlight additional mechanisms that are not accounted for in the dipole-dipole coupling model. Two different approaches are taken to control the spatial separation of the quantum dot molecules, and we discuss the advantages and disadvantages of each.

Bound states in the continuum in a bilayer photonic crystal with TE-TM cross coupling

Bound states in the continuum (BICs) in photonic crystals represent the unique solutions of wave equations possessing an infinite quality-factor. We design a type of bilayer photonic crystal and study the influence of symmetry and coupling between TE and TM polarizations on BICs. The BIC modes possess $C_{3v}$ symmetry in the x-y plane while the mirror-flip symmetry in the z-direction is broken, and they provide selective coupling into different layers by varying frequency. The enhanced TE-TM coupling due to broken mirror-flip symmetry in the z-direction gives rise to high-Q factor BIC states with unique spatial characteristics. We show the emergence of such BIC states even in the presence of coupling between the TE- and TM-like modes, which is different from the existing single polarization BIC models. We propose to study BICs in multilayer systems, and the results may be helpful in designing photonic settings to observe and manipulate BICs with various symmetries and polarizations for practical applications.

Sequential escapes: onset of slow domino regime via a saddle connection

We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable “quiescent” equilibrium to a more stable “active” equilibrium. The presence of coupling introduces dependence between the escape processes: for diffusive coupling there is a strongly coupled limit (fast domino regime) where the escapes are strongly synchronised while for intermediate coupling (slow domino regime) without partially escaped stable states, there is still a delayed effect. These regimes can be associated with bifurcations of equilibria in the low-noise limit. In this paper, we consider a localized form of non-diffusive (i.e. pulse-like) coupling and find similar changes in the distribution of escape times with coupling strength. However, we find transition to a slow domino regime that is not associated with any bifurcations of equilibria. We show that this transition can be understood as a codimension-one saddle connection bifurcation for the low-noise limit. At transition, the most likely escape path from one attractor hits the escape saddle from the basin of another partially escaped attractor. After this bifurcation, we find increasing coefficient of variation of the subsequent escape times.

Experimental investigation of performance of tri-layered magnetoelectric composites under thermal environment

The presence of coupling between electric and magnetic fields attracts various applications for magnetoelectric (ME) materials such as magnetic field sensors, energy harvesting devices, multiferroic motors, etc. ME effects are produced due to transfer of strain through bonding of ferroelectric and ferromagnetic constituent phases. ME effects are significantly affected by various parameters such as the constituent phases, geometry, connectivity schemes, etc. In the present work, a trilayered ME composite is made by sandwiching a ferroelectric material between two ferromagnetic materials at the top and the bottom. ME composites were made by varying the volume fractions of the ferromagnetic material. This work primarily focuses on understanding the temperature dependence of sensing characteristics and coupling factor of ME composites. With this in mind, initially the temperature dependent behavior of individual constituent phases are experimentally investigated. Experimental investigation reveals that the sensing characteristics and coupling factor of ME composites are significantly affected by the operating temperature and the volume fraction of the constituent phases.

Analysis of the performance of an oscillating propeller in cavitating flow

During voyages, a ship will inevitably encounter wavy conditions that cause heaving motions. These motions induce oscillations in the propeller relative to its surrounding fluid, causing the propeller to operate in off-design conditions under non-uniform inflows. These environments-induced motions will significantly alter propeller performance. To study the motions of the propeller of a surface ship in wavy conditions during actual voyages, numerical simulations were conducted on an oscillating propeller in cavitating flows by using Reynolds-averaged Navier–Stokes (RANS) approach. The rotations and oscillations of the propeller were coupled using an independently defined set of equations of motion, with the oscillations being represented as sinusoidal cyclic motions. The numerical propagation of unsteady flow fields was obtained using the overset grid technique. This approach allowed the hydrodynamic behaviours of a propeller to be fully investigated in the presence of coupling between the rotations and oscillatory motions of the propeller. The effects of non-uniform incoming flows on a propeller's unsteady load and the distribution of sheet cavitation and wake field were analysed for two different loading conditions. The results of these calculations are significant for propeller design and optimization.

Life extension of Structural Repairs – A statistical approach towards efficiency improvement

The life extension program of aircraft is taken up whenever aircraft’s intended life reaches close to its DSG (Design Service Goal). The Extended Service Goal (ESG) of an aircraft, in general, and structural repairs, in particular, is arrived at on the basis of F&DT (Fatigue & Damage Tolerance) analysis. Life extension program of aircraft consists of assessment of remaining life of all parts of the aircrafts including structural, mechanical, and electrical and avionics equipment and structural repairs. For life extension of stringer repair, as an example, it is required to re-assess the fatigue life of stringer in the presence of coupling under modified load spectrum. This is achieved by assessing the fatigue life of Web and Outer Flange (OF) part of stringers separately as per F&DT justification philosophy. Assessment of the fatigue life requires determination of stress concentration factor (Kt) for different combination of width, pitch, stringer thickness, coupling thickness and pad-up thickness of all stringer profiles available in different sections of fuselage. Determination of stress concentration factor for Web and Outer Flange of stringer profile covering entire ranges involves substantial number of Finite Element (FE) analysis. In order to optimise the number of FE runs, stress concentration factor is determined under worst repair factors combination (max. plate width; max. thickness; max. pitch; min. rivet dia.; and min. No. of rivets) resulting in conservative value. A parametric study of Web and Outer Flange data across stringer profiles were carried out and proven statistical techniques were used to find the optimal equation to predict stress concentration factor. This in turn reduced number of FE runs substantially for a given range of width, pitch, stringer thickness and so on. The use of optimal equation obtained through regression analysis is able to predict Kt within reasonable accuracy for a given range of inputs.

Dynamics and instabilities in long SRS fibre lasers with linear and ring cavities

We report results of numerical simulation of the nonlinear dynamics of SRS fibre lasers with linear and ring cavity configurations and of the specific features of manifestation of instabilities of steady-state lasing in fibres with length-periodic modulation of dispersion. The simulation is performed within the approach based on solving transport equations. The dynamics of the SRS laser with linear configuration is found to depend strongly on the coupling of counterpropagating waves at the fibre end faces and radically changes in the presence of reflections at the left or right end faces under asymmetric pumping. The existence of signal beatings in the absence of nonreciprocity (rotation) of the cavity and the presence of coupling between counterpropagating waves is demonstrated for the ring laser. A specific feature of instabilities of the propagation regime of a constant-intensity signal in a fibre with a group-velocity dispersion periodically modulated over length is their occurrence at an arbitrary dispersion sign.