Linear Coupling Research Articles

Combined effects of crab dispersion and momentum dispersion in colliders with local crab crossing scheme

In this paper, we present the effects of linear transverse-longitudinal coupling on beam size at the interaction point (IP) of a collider with a local crab crossing scheme, when time-dependent transverse deflection (crab kicks) and dispersive orbit intertwine near IP. The analytic propagation formula and the closed orbit form of the crab dispersion and momentum dispersion are derived. The nonzero momentum dispersion at crab cavities and the nonideal phase from crab cavities to IP are detailed with the derived propagation formula to predict the beam size distortion at IP with or without the beam-beam interaction. The linear results are compared with nonlinear simulation using the weak-strong beam-beam code.

Comparison of Synchronization Speed of Networks Consisting of Two Ordinary Differential Systems of Fitzhugh – Nagumo Type with Bidirectionally and Unidirectionally Linear Coupling

This work considers networks of two nodes with bidirectionally and unidirectionally linear coupling. Each node is represented by a system of ordinary differential equations of FitzHugh-Nagumo type which is obtained by simplifying the famous Hodgkin-Huxley model. From two network topologies, the existence of global attractors, and the sufficient condition under the coupling strength are sought such that the synchronization phenomenon occurs. The result shows that the network with bidirectionally linear coupling synchronizes more easily than the other. The paper also shows this theoretical result numerically and see that there is a compromise.

Spin oscillations of a single-mode polariton system driven by a plane wave

Theoretical study is performed of a single-mode polariton system with linear coupling of spin components. When combined with an ordinary two-particle interaction, the spin coupling involves a spontaneous symmetry breaking accompanied by a switch from linear to circular polarization under resonant driving. The asymmetric steady states can also lose stability, giving way to oscillatory and chaotic dynamics. Here, we explore a continuous transformation between the multistable regime, where the system is steady and locked in phase to the pump but has a broken spin symmetry, and full-span oscillations of the circular-polarization degree, owing to which the symmetry is effectively reestablished. Such oscillations are analogous to the intrinsic Josephson effect and prove to be robust against arbitrarily strong perturbations. Transitional phenomena include the Hopf bifurcation, spin bistability of limit cycles, and continuous transitions to and from dynamical chaos through series of period doubling/halving events.

Critical Quantum Metrology in the Non-Linear Quantum Rabi Model.

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.

Dynamics of scalar hair with self-interactions around a Schwarzchild black hole

In this paper, we study the dynamics of scalar hair around a Schwarzchild black hole. The scalar hair is sourced by the Gauss-Bonnet invariant with a linear coupling. We work perturbatively in the coupling constant and ignore the backreaction of the scalar hair and the Gauss-Bonnet invariant. We evolve the scalar field in the background of a Schwarzchild black hole and study the dynamical formation of scalar hair with different self-interactions. We integrate the energy and compute the energy flux of the scalar hair in terms of the canonical energy-momentum tensor and give the corresponding dependence on the self-interactions. Our results allow us to estimate the radiation and the condensation of scalar field with different self-interactions; these would improve our understanding for the dynamical scalarization of black holes and the possible configuration of the scalar hair in scalar Gauss-Bonnet gravity.

A model framework to investigate the role of anomalous land surface processes in the amplification of summer drought across Ireland during 2018

AbstractDue to its latitude and ample year‐round rainfall, Ireland is typically an energy‐limited regime in the context of soil moisture availability and evapotranspiration. However, during the summer of 2018, regions within the country displayed significant soil moisture deficits, associated with anomalous atmospheric forcing conditions, with consequent impacts on the surface energy balance. Here, we explore the utility of a physically based land surface scheme coupled with observational, global gridded reanalysis and satellite‐derived data products to analyse the spatial and temporal evolution of the 2018 summer drought event in Ireland over grassland, which represents the dominant agricultural land‐cover. While the surface–air energy exchanges were initially dominated by atmospheric anomalies, soil moisture constraints became increasingly important in regulating these exchanges, as the accumulated rainfall deficit increased throughout the summer months. This was particularly evident over the freer draining soils in the east and southeast of the country. From late June 2018, we identify a strong linear coupling between soil moisture and both evapotranspiration and vegetation response, suggesting a shift from an energy‐limited evapotranspiration regime into a dry or soil water‐limited regime. Applying segmented regression models, the study quantifies a critical soil moisture threshold as a key determinant of the transition from wet to dry evaporative regimes. These findings are important to understand the soil moisture context under which land–atmosphere couplings are strongest in water‐limited regimes across the country and should help improve the treatment of soil parameters in weather prediction models, required for subseasonal and seasonal forecasts, consequently enhancing early warning systems of summer climate extremes in the future.

Complex dynamical properties of coupled Van der Pol–Duffing oscillators with balanced loss and gain

We consider a Hamiltonian system of coupled Van der Pol–Duffing (VdPD) oscillators with balanced loss and gain. The system is analyzed perturbatively by using renormalization group (RG) techniques as well as multiple scale analysis (MSA). Both the methods produce identical results in the leading order of the perturbation. The RG flow equation is exactly solvable and the slow variation of amplitudes and phases in time can be computed analytically. The system is analyzed numerically and shown to admit periodic solutions in regions of parameter-space, confirming the results of the linear stability analysis and perturbation methods. The complex dynamical behavior of the system is studied in detail by using time-series, Poincaré-sections, power-spectra, auto-correlation function and bifurcation diagrams. The Lyapunov exponents are computed numerically. The numerical analysis reveals chaotic behaviour in the system beyond a critical value of the parameter that couples the two VdPD oscillators through linear coupling, thereby providing yet another example of Hamiltonian chaos in a system with balanced loss and gain. Further, we modify the nonlinear terms of the model to make it a non-Hamiltonian system of coupled VdPD oscillators with balanced loss and gain. The non-Hamiltonian system is analyzed perturbatively as well as numerically and shown to posses regular periodic as well as chaotic solutions. It is seen that the -symmetry is not an essential requirement for the existence of regular periodic solutions in both the Hamiltonian as well as non-Hamiltonian systems.

Linear reciprocating magnetic coupling

The magnetic system of a linear magnetic coupling on permanent magnets is studied in detail. To calculate the forces of interaction between permanent magnets, it is proposed to use the equivalent solenoid method. The possibility of optimizing the size of magnets to reduce the length of the coupling and reduce the cost of expensive magnetically rigid material is shown. Keywords: magnetic coupling, permanent magnets, equivalent solenoid method, magnetic force, traction force. alnikbltov@rambler.ru, onvk@mail.ru, vnvkv@yandex.ru

Nonlinear modal electromechanical coupling factor for piezoelectric structures containing nonlinearities

Within the linear framework, the Modal Electromechanical Coupling Factor (MEMCF) is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures. It is also an important tool to guide the piezoelectric damping design of linear structures. Advanced aircraft often fly in maneuvers, and the variable working conditions induce drastic changes in the load level on structures. Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated. To achieve a good vibration reduction effect covering all working conditions, one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures. Therefore, this paper defines the Nonlinear Modal Electromechanical Coupling Factor (NMEMCF) and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures. Three candidate definitions of the NMEMCF are given, including two frequency definitions and one energy definition. The energy definition is the most promising one. It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF. In addition, based on the energy formula, the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state. The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities. A strong correlation among the NMEMCF, geometric parameters, and energy dissipation is observed. The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping, especially for variable working conditions.

Relativistic quantum field theory of stochastic dynamics in the Hilbert space

We develop an action formulation of stochastic dynamics in the Hilbert space. By generalizing the Wiener process into 1+3-dimensional spacetime, we define a Lorentz-invariant random field. By coupling the random to quantum fields, we obtain a random-number action which has the statistical spacetime translation and Lorentz symmetries. The canonical quantization of the theory results in a Lorentz-invariant equation of motion for the state vector or density matrix. We derive the path integral formula of $S$-matrix and the diagrammatic rules for both the stochastic free field theory and stochastic $\phi^4$-theory. The Lorentz invariance of the random $S$-matrix is strictly proved. We then develop a diagrammatic technique for calculating the density matrix. Without interaction, we obtain the exact $S$-matrix and density matrix. With interaction, we prove a simple relation between the density matrices of stochastic and conventional $\phi^4$-theory. Our formalism leads to an ultraviolet divergence which has the similar origin as that in QFT. The divergence is canceled by renormalizing the coupling strength to random field. We prove that the stochastic QFT is renormalizable even in the presence of interaction. In the models with a linear coupling between random and quantum fields, the random field excites particles out of the vacuum, driving the universe towards an infinite-temperature state. The number of excited particles follows the Poisson distribution. The collision between particles is not affected by the random field. But the signals of colliding particles are gradually covered by the background excitations caused by random field.

Discrete-Time Memristor Model for Enhancing Chaotic Complexity and Application in Secure Communication.

The physical implementation of the continuous-time memristor makes it widely used in chaotic circuits, whereas the discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize the memristor model, and the discretized model also meets the three fingerprints characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling of the proposed memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication.

On dynamic coupling effects of underwater vehicle-dual-manipulator system

In this paper, a novel evaluation framework based on the proposed angular and linear dynamic coupling factors is developed to investigate the complicated dynamic coupling effects of the underwater vehicle-dual-manipulator system (UVDMS). Firstly, the rigid connection coupling effects of the vehicle-manipulator are obtained by adopting the recursive Newton–Euler algorithm, and the hydrodynamic coupling effects are analyzed including the extra added inertial, Coriolis, centripetal and damping effects. Then, the complete dynamic coupling model of UVDMS is derived as a uniform formula. Secondly, the angular and linear dynamic coupling factors are developed to numerically reflect the influence of manipulator movement on the acceleration response of the vehicle. Furthermore, the influence of link mass, length, diameter, mounted position and joint velocity on the dynamic coupling effects are analyzed by simulation study, which provide a guidance for the parameters design of the above manipulator properties. Finally, the relationship between the joint configurations and coupling effects are investigated, and coupling maps with respect to joint variables are obtained. The coupling maps provide the theoretical basis for the trajectory optimization of the manipulators to decrease the effect of dynamic couplings on the system, and the effectiveness of the proposed evaluation framework is verified by the numerical simulation results.

Spin-Peierls transition of J1−J2 and extended models with ferromagnetic J1 : Sublattice dimerization and thermodynamics of zigzag chains in β−TeVO4

The spin$-1/2$ chain with ferromagnetic exchange $J_1 < 0$ between first neighbors and antiferromagnetic $J_2 > 0$ between second neighbors supports two spin-Peierls (SP) instabilities depending on the frustration $\alpha = J_2/\vert J_1\vert$. Instead of chain dimerization with two spins per unit cell, $J_1-J_2$ models with $\alpha > 0.65$ and linear spin-phonon coupling are unconditionally unstable to sublattice dimerization with four spins per unit cell. Unequal $J_1$ to neighbors to the right and left extends the model to gapped ($\gamma > 0$) chains with conditional SP transitions at $T_{SP}$ to dimerized sublattices and a weaker specific heat $C(T)$ anomaly. The spin susceptibility $\chi(T)$ and $C(T)$ are obtained in the thermodynamic limit by a combination of exact diagonalization of small systems with $\alpha > 0.65$ and density matrix renormalization group (DMRG) calculations of systems up to $N \sim 100$ spins. Both $J_1-J_2$ and $\gamma > 0$ models account quantitatively for $\chi(T)$ and $C(T)$ in the paramagnetic phase of $\beta$-TeVO$_{4}$ for $T > 8$ K, but lower $T$ indicates a gapped chain instead of a $J_1-J_2$ model as previously thought. The same parameters and $T_{SP} = 4.6$ K generate a $C(T)/T$ anomaly that reproduces the anomaly at the $4.6$ K transition of $\beta$-TeVO$_{4}$, but not the weak $\chi(T)$ signature.

Revisiting the Dynamics of Triplet Formation in Anthraquinones.

Triplet formation pathways in 9,10-anthraquinone (AQ) and its hydroxy derivative, 1-hydroxyanthraquinone (HAQ), are studied theoretically. Dynamics simulations on the model singlet-triplet potential energy surfaces within the linear vibronic coupling framework are performed to elucidate possible internal conversion (IC) and intersystem crossing (ISC) pathways in these molecules. An ultrafast IC decay from the "bright" S4 to S1 followed by efficient ISC via S1-T4 and S1-T5 pathways fosters a high triplet quantum yield (ΦT = 0.90) in AQ. In HAQ, a new nonradiative channel of "barrierless" excited-state intramolecular proton transfer (ESIPT) opens up and competes with the IC decay to S1 upon photoexcitation to the "bright" S2. Extremely fast ESIPT on S2 reduces the efficiency of triplet formation via possible ISC pathways involving S1 and S2, resulting in a low ΦT (=0.17).

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

Theory of superconductivity mediated by Rashba coupling in incipient ferroelectrics

Experimental evidence suggests that superconductivity in ${\mathrm{SrTiO}}_{3}$ is mediated by a soft transverse ferroelectric mode which, according to conventional theories, has negligible coupling with electrons. A phenomenological Rashba-type coupling has been proposed on symmetry arguments but a microscopic derivation is lacking. Here, we fill this gap and obtain a linear coupling directly from a minimal microscopic model of the electronic structure. We find that the effective electron-electron pairing interaction has a strong momentum dependence. This yields an unusual situation in which the leading $s$-wave channel is followed by a subleading $p$-wave state which shows a stronger pairing instability than the $d$-wave state. The bare Rashba coupling constant is estimated for the lowest band of doped ${\mathrm{SrTiO}}_{3}$ with the aid of first-principles computations. Extrapolating the estimation to the multiband regime we show that it can explain bulk superconductivity. For densities where the Meissner effect has not been observed an extra softening due to inhomogeneities is needed to explain the zero resistance state.

Inflation with Einstein-Gauss-Bonnet, non-minimal, and non-minimal derivative couplings: the constant-roll condition

In our research, we consider and study the inflation theories of Einstein-Gauss-Bonnet, minimal, non-minimal, and non-minimal derivative coupling with the constant-roll condition. Given the gravitational wave event, GW170817, which produces the speed of gravitational waves that was almost equal to the speed of light in vacuum, we constrain that the speed of the tensor perturbation was nearly equal to unity, . We involve a scalar field potential whose function can be obtained from an equation of motion by choosing the Gauss-Bonnet coupling functions. We use the linear and quadratic coupling functions, which are their simplest functions. The one result obtained are able to produce observed quantities such as the spectral index for scalar perturbation, ns = 0.9642, the spectral index for tensor perturbation, nT = −5.2471 × 10−4, and tensor-scalar ratio, r = 0.0041, which are compatible with the newest Planck data using the slow-roll parameters obtained analytically.

Mean-field analysis of Stuart-Landau oscillator networks with symmetric coupling and dynamical noise.

This paper presents analyses of networks composed of homogeneous Stuart-Landau oscillators with symmetric linear coupling and dynamical Gaussian noise. With a simple mean-field approximation, the original system is transformed into a surrogate system that describes uncorrelated oscillation/fluctuation modes of the original system. The steady-state probability distribution for these modes is described using an exponential family, and the dynamics of the system are mainly determined by the eigenvalue spectrum of the coupling matrix and the noise level. The variances of the modes can be expressed as functions of the eigenvalues and noise level, yielding the relation between the covariance matrix and the coupling matrix of the oscillators. With decreasing noise, the leading mode changes from fluctuation to oscillation, generating apparent synchrony of the coupled oscillators, and the condition for such a transition is derived. Finally, the approximate analyses are examined via numerical simulation of the oscillator networks with weak coupling to verify the utility of the approximation in outlining the basic properties of the considered coupled oscillator networks. These results are potentially useful for the modeling and analysis of indirectly measured data of neurodynamics, e.g., via functional magnetic resonance imaging and electroencephalography, as a counterpart of the frequently used Ising model.

A generic model for pandemics in networks of communities and the role of vaccination.

The slogan "nobody is safe until everybody is safe" is a dictum to raise awareness that in an interconnected world, pandemics, such as COVID-19, require a global approach. Motivated by the ongoing COVID-19 pandemic, we model here the spread of a virus in interconnected communities and explore different vaccination scenarios, assuming that the efficacy of the vaccination wanes over time. We start with susceptible populations and consider a susceptible-vaccinated-infected-recovered model with unvaccinated ("Bronze"), moderately vaccinated ("Silver"), and very-well-vaccinated ("Gold") communities, connected through different types of networks via a diffusive linear coupling for local spreading. We show that when considering interactions in "Bronze"-"Gold" and "Bronze"-"Silver" communities, the "Bronze" community is driving an increase in infections in the "Silver" and "Gold" communities. This shows a detrimental, unidirectional effect of non-vaccinated to vaccinated communities. Regarding the interactions between "Gold," "Silver," and "Bronze" communities in a network, we find that two factors play a central role: the coupling strength in the dynamics and network density. When considering the spread of a virus in Barabási-Albert networks, infections in "Silver" and "Gold" communities are lower than in "Bronze" communities. We find that the "Gold" communities are the best in keeping their infection levels low. However, a small number of "Bronze" communities are enough to give rise to an increase in infections in moderately and well-vaccinated communities. When studying the spread of a virus in dense Erdős-Rényi and sparse Watts-Strogatz and Barabási-Albert networks, the communities reach the disease-free state in the dense Erdős-Rényi networks, but not in the sparse Watts-Strogatz and Barabási-Albert networks. However, we also find that if all these networks are dense enough, all types of communities reach the disease-free state. We conclude that the presence of a few unvaccinated or partially vaccinated communities in a network can increase significantly the rate of infected population in other communities. This reveals the necessity of a global effort to facilitate access to vaccines for all communities.

Energy partition between Alfvénic and compressive fluctuations in magnetorotational turbulence with near-azimuthal mean magnetic field

The theory of magnetohydrodynamic (MHD) turbulence predicts that Alfvénic and slow-mode-like compressive fluctuations are energetically decoupled at small scales in the inertial range. The partition of energy between these fluctuations determines the nature of dissipation, which, in many astrophysical systems, happens on scales where plasma is collisionless. However, when the magnetorotational instability (MRI) drives the turbulence, it is difficult to resolve numerically the scale at which both types of fluctuations start to be decoupled because the MRI energy injection occurs in a broad range of wavenumbers, and both types of fluctuations are usually expected to be coupled even at relatively small scales. In this study, we focus on collisional MRI turbulence threaded by a near-azimuthal mean magnetic field, which is naturally produced by the differential rotation of a disc. We show that, in such a case, the decoupling scales are reachable using a reduced MHD model that includes differential-rotation effects. In our reduced MHD model, the Alfvénic and compressive fluctuations are coupled only through the linear terms that are proportional to the angular velocity of the accretion disc. We numerically solve for the turbulence in this model and show that the Alfvénic and compressive fluctuations are decoupled at the small scales of our simulations as the nonlinear energy transfer dominates the linear coupling below the MRI-injection scale. In the decoupling scales, the energy flux of compressive fluctuations contained in the small scales is almost double that of Alfvénic fluctuations. Finally, we discuss the application of this result to prescriptions of ion-to-electron heating ratio in hot accretion flows.