Weakly-coupled Systems Research Articles

Spontaneous symmetry breaking and vortices in a tri-core nonlinear fractional waveguide

We introduce a waveguiding system composed of three linearly-coupled fractional waveguides, with a triangular (prismatic) transverse structure. It may be realized as a tri-core nonlinear optical fiber with fractional group-velocity dispersion (GVD), or, possibly, as a system of coupled Gross–Pitaevskii equations for a set of three tunnel-coupled cigar-shaped traps filled by a Bose–Einstein condensate of particles moving by Lévy flights. The analysis is focused on the phenomenon of spontaneous symmetry breaking (SSB) between components of triple solitons, and the formation and stability of vortex modes. In the self-focusing regime, we identify symmetric and asymmetric soliton states, whose structure and stability are determined by the Lévy index of the fractional GVD, the inter-core coupling strength, and the total energy, which determines the system’s nonlinearity. Bifurcation diagrams (of the supercritical type) reveal regions where SSB occurs, identifying the respective symmetric and asymmetric ground-state soliton modes. In agreement with the general principle of the SSB theory, the solitons with broken inter-component symmetry prevail with the increase of the energy in the weakly-coupled system. Three-components vortex solitons (which do not feature SSB) are studied too. Because the fractional GVD breaks the system’s Galilean invariance, we also address mobility of the vortex solitons, by applying a boost to them.

Bias-Voltage-SSHI Interface Circuit for Strong Coupling Piezoelectric Energy Systems

Compared with the standard extraction interface circuit (SEH), the harvested energy and harvested power of synchronized switching harvesting interface circuits (SSHI) and synchronous charge extraction interface circuit (SECE) cannot improve more effectively. This paper proposes a Bias-Voltage-SSHI Interface Circuit (BV-SSHI), consisting of a single peak voltage detection switch and a rectifier, to solve this problem. The proposed BV-SSHI improves the output voltage by biasing the voltage of the piezoelectric energy harvester and obtains similar harvested power as SSHI. Simulation results show that the BV-SSHI can obtain more harvested energy and harvested power than SEH under weak, medium, and strong coupling systems. Results show that the higher harvester's voltage and the larger phase difference cause the electrical restoring force (χV) to significantly weaken the vibration displacement, especially under strong coupling systems. Thus, the gain effect of the SSHI and SECE is weakened. The experimental results of the medium coupling systems show that the BV-SSHI can obtain 247.2% harvested energy and 121.2% maximum harvested power compared with SEH. The BV-SSHI can achieve at least 142.4% harvested energy and 100.3% maximum harvested power compared with what SSHI and SECE can achieve.

A numerical approach for a two-parameter singularly perturbed weakly-coupled system of 2-D elliptic convection–reaction–diffusion PDEs

In this work, we consider the numerical approximation of a two dimensional elliptic singularly perturbed weakly-coupled system of convection–reaction–diffusion type, which has two different parameters affecting the diffusion and the convection terms, respectively. The solution of such problems has, in general, exponential boundary layers as well as corner layers. To solve the continuous problem, we construct a numerical method which uses a finite difference scheme defined on an appropriate layer-adapted Bakhvalov–Shishkin mesh. Then, the numerical scheme is a first order uniformly convergent method with respect both convection and diffusion parameters. Numerical results obtained with the algorithm for some test problems are presented, which show the best performance of the proposed method, and they also corroborate in practice the theoretical analysis.

Interface design of the thermoelectric transport properties of phosphorene-tetrathiafulvalene nanoscale devices.

Interface design and energy band engineering are two key strategies for improving the thermoelectric conversion efficiency of low dimensional nanoscale devices. By using first-principle-based density functional theory combined with a non-equilibrium Green function method, the thermoelectric properties of a single tetrathiafulvalene (TTF) molecule coupled with armchair phosphorene nanoribbons (APNRs) within different interface modes have been investigated. The results indicate that phonon transport can be dramatically suppressed in this intermediate weak-coupling system due to strong interfacial phonon scattering behavior, where very few phonons can propagate through two nonbonded interface regions from left side lead to a TTF molecule and then to right side lead. Furthermore, connecting a thiophene group at both the head and tail of the intermediate TTF molecule can significantly enhance the power factor (S2σ) of such a weak-coupling system based on an out-of-plane electronic transmission mechanism, and there is obvious charge transfer from S atoms to upper and lower APNRs. Compared to a single regular method, composite interface co-design can achieve more accurate control of thermal/electrical transmission performance. Electrical conductance can be effectively improved with low phonon thermal conductance being maintained at the same time, and an excellent thermoelectric figure of merit (ZT) of 0.73 has been obtained near 0.6 eV.

A Primary-Side Method for Ultrafast Determination of Mutual Coupling Coefficient in Milliseconds for Wireless Power Transfer Systems

This article presents a systematic frequency-sweeping based method for fast and accurate determination of mutual coupling coefficient in a series–series wireless power transfer system. The novel contributions involve a sensitivity analysis to evaluate the robustness of the proposed method and an evaluation of several adaptive frequency step functions to minimize detection time with an accuracy of less than 1% error. It is found that the proposed method is the most sensitive when the frequency is swept from the lower frequency boundary in a weakly-coupled system. Several adaptive frequency step functions are evaluated and compared. A power factor reference and an adaptive frequency step function are designed in a systematic way to achieve the dual purposes of minimum detection time and high accuracy. The experimental results obtained from the hardware setups show that the mutual coupling coefficients under a range of conditions can be estimated within 7 ms and with errors typically less than 1.0%.

Review Map of Comparative Designs for Wireless High-Power Transfer Systems in EV Applications: Maximum Efficiency, ZPA, and CC/CV Modes at Fixed Resonance Frequency Independent From Coupling Coefficient

This article proposes a review map for comparative designs of wireless high-power transfer (WHPT) systems using single- and double-resonance blocks. In-depth analyses and key guidelines are provided to design high-efficiency WHPT systems while keeping zero-phase-angle/unity-power-factor and constant <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</i> current/voltage supply to the load. Basic single- and double-resonance blocks based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC-</i> resonant circuits are analyzed. Then, resonant <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S-</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T-</i> blocks are recommended as the best transmission blocks for competitive designs. The proposed approach is applied to map recent developments on the wireless charging technologies for electric vehicles (EVs), especially for weak-coupling systems and dynamic-charging technologies. The proposed design approach offers a systematic and effective methodology to quickly evaluate current technologies and solutions for WHPTs in EVs applications. In extension, this article indicates different control strategies for WHPTs, especially for optimal-efficiency tracking. Design guidelines and control strategies are provided to achieve the maximum efficiency at a standard resonance frequency against variations from loads and coupling coefficients in operation which can easily map to recent research works and future research directions. Experimental verifications of dominant designs are also presented to validate the proposed approach. The map for comparative designs and control structures presented in this article aims to serve as a guideline and to ease the initial steps for other researchers in this area.

Stabilization of the Weakly Coupled Wave-Plate System with One Internal Damping

We study a stabilization problem of a system coupled by a wave and a Euler–Bernoulli plate equation. Only one of the two equations is directly damped. Under some assumptions on the damping and the coupling terms, we prove that sufficiently smooth solutions of the system decay logarithmically without any geometric conditions on the damping domain. The proofs of these decay results rely on the interpolation inequalities for a coupled elliptic-parabolic system and the estimate of the resolvent operator for that system. The main tools to derive the desired interpolation inequalities are global Carleman estimates.

Homogenization of Coupled Fast-Slow Systems via Intermediate Stochastic Regularization

In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter varepsilon such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with ergodic invariant measure. Convergence of the slow process to the solution of a homogenized stochastic differential equation (SDE) in the limit varepsilon to zero, with explicit formulas for drift and diffusion coefficients, has so far only been obtained for the case that the fast dynamics evolve independently. In this paper we give sufficient conditions for the convergence of the first moments of the slow variable in the coupled case. Our proof is based upon a new method of stochastic regularization and functional-analytical techniques combined via a double limit procedure involving a zero-noise limit as well as considering varepsilon to zero. We also give exact formulas for the drift and diffusion coefficients for the limiting SDE. As a main application of our theory, we study weakly-coupled systems, where the coupling only occurs in lower time scales.

Scrambling and Lyapunov exponent in spatially extended systems

Scrambling of information in a quantum many-body system, quantified by the out-of-time-ordered correlator (OTOC), is a key manifestation of quantum chaos. A regime of exponential growth in the OTOC, characterized by a Lyapunov exponent, has so far mostly been observed in systems with a high-dimensional local Hilbert space and in weakly-coupled systems. Here, we propose a general criterion for the existence of a well-defined regime of exponential growth of the OTOC in spatially extended systems with local interactions. In such systems, we show that a parametrically long period of exponential growth requires the butterfly velocity to be much larger than the Lyapunov exponent times a microscopic length scale, such as the lattice spacing. As an explicit example, we study a random unitary circuit with tunable interactions. In this model, we show that in the weakly interacting limit the above criterion is satisfied, and there is a prolonged window of exponential growth. Our results are based on numerical simulations of both Clifford and universal random circuits supported by an analytical treatment.

The cosmological heavy ion collider: Fast thermalization after cosmic inflation

Heavy-ion colliders have revealed the process of “fast thermalization”. This experimental break-through has led to new theoretical tools to study the thermalization process at both weak and strong coupling. We apply this to the reheating epoch of inflationary cosmology, and the formation of a cosmological quark gluon plasma (QGP). We compute the thermalization time of the QGP at reheating, and find it is determined by the energy scale of inflation and the shear viscosity to entropy ratio η/s; or equivalently, the tensor-to-scalar ratio and the strong coupling constant at the epoch of thermalization. Thermalization is achieved near-instantaneously in low-scale inflation and in strongly coupled systems, and takes of order or less than a single e-fold of expansion for weakly-coupled systems or after high-scale inflation. We demonstrate that the predictions of inflation are robust to the physics of thermalization, and find a stochastic background of gravitational waves at frequencies accessible by interferometers, albeit with a small amplitude.

Unexpected magnetic phase in the weakly ordered spin- 12 chain cuprate Sr2CuO3

We present the magnetic phase diagram of a spin-1/2 chain antiferromagnet Sr$_2$CuO$_3$ studied by ultrasound phase-sensitive detection technique. We observe an enhanced effect of external magnetic field on the ordering temperature of the system, which is in the extreme proximity to the quantum critical point. Inside the N\'eel ordered phase, we detect an additional field-induced continuous phase transition, which is unexpected for a collinear Heisenberg antiferromagnet. This transition is accompanied by softening of magnetic excitation mode observed by electron-spin resonance, which can be associated with a longitudinal (amplitude) mode of the order parameter in a weakly-coupled system of spin-1/2 chains. These results suggest transition from a transverse collinear antiferromagnet to an amplitude-modulated spin density wave phase induced by magnetic field.

Excellent thermoelectric performance in weak-coupling molecular junctions with electrode doping and electrochemical gating

Excellent thermoelectric performance in molecular junctions requires a high power factor, a low thermal conductance, and a maximum figure of merit ( ZT ) near the Fermi level. In the present work, we used density functional theory in combination with a nonequilibrium Green’s function to investigate the thermoelectric performance of carbon chain-graphene junctions with both strong-coupling and weak-coupling contact between the electrodes and the molecules. The results revealed that a room temperature ZT of 4 could be obtained for the weak-coupling molecular junction, approximately one order of magnitude higher than that reached by the strong-coupling junction. The reason for this is that strong interfacial scattering suppresses most of the phonon modes in weak-coupling systems, resulting in ultralow phonon thermal conductance. The influence of electrode width, electrode doping, and electrochemical gating on the thermoelectric performance of the weak-coupling system was also investigated, and the results revealed that an excellent thermoelectric performance can be obtained near the Fermi level.

Attractive polaron formed in doped nonchiral/chiral parabolic system within ladder approximation

We investigate the properties of attractive polaron formed by a single impurity dressed with the particle-hole excitations in a three-dimensional (3D) doped (extrinsic) parabolic system. Base on the single particle-hole variational ansatz, we study the pair propagator, self-energy, and the non-self-consistent medium T-matrix. The non-self-consistent T-matrix discussed in this paper contains only the open channel since we do not consider the shift of center-of-mass due to the resonance (e.g., induced by the magnetic field). The scattering form factor is discussed in detail for the chiral case and compared to the non-chiral one. The effects of the bare coupling strength, which is momentum-cutoff-dependent, are also discussed. We found that the pair propagator and the related quantities, like the self-energy, spectral function, induced effective mass, and residue (spectral weight), all exhibit some novel features in the low-momentum regime which are different from the high one. That also related to the polaronic instabilities as well as the many-body fluctuation and nonadiabatic/adiabatic dynamics. The effects of chirality and the finite-temperature (much lower than the critical one) are studied in detail, and our results can also be used in exploring other weak-coupling systems with mobile impurity.

Reply to “Comment on ‘Superconductivity at low density near a ferroelectric quantum critical point: Doped SrTiO3 ”'

In our paper (W\"olfle and Balatsky, Phys. Rev. B 98, 104505 (2018)) we presented a microscopic theory of superconductivity for doped SrTiO$_{3}$ by proposing two pairing mechanisms acting simultaneously with relative strength depending on the closeness to the ferroelectric quantum critical point. The first mechanism rests on the dynamically screened Coulomb interaction, and the second assumed a coupling to the soft transverse optical phonon. In their comment Ruhman and Lee point out an error in our estimate of the deformation potential coupling to the soft mode. We agree that this type of coupling cannot explain the gigantic isotope effect observed experimentally, so that a different coupling mechanism needs to be found. As for the first pairing mechanism, Ruhman and Lee maintain the view expressed in their paper (Ruhman and Lee, Phys. Rev. B 94, 224515 (2016)) that the energy range over which the usual longitudinal optical phonon mediated interaction operates is limited by the Fermi energy. We object to this view and in this reply present evidence that the cutoff energy is much larger. In a weak coupling system such as SrTiO$_{3}$ the cutoff is given by the energy beyond which quasiparticles cease to be well defined.

Fluctuation theorem for entropy production at strong coupling**Project supported by the National Natural Science Foundation of China (Grant Nos. 11674360, 11734018, 11835011, and 11965012) and the Applied Basic Research Project of Yunnan Province, China (Grant No. 2017FB004).

Fluctuation theorems have been applied successfully to any system away from thermal equilibrium, which are helpful for understanding the thermodynamic state evolution. We investigate fluctuation theorems for strong coupling between a system and its reservoir, by path-dependent definition of work and heat satisfying the first law of thermodynamics. We present the fluctuation theorems for two kinds of entropy productions. One is the informational entropy production, which is always non-negative and can be employed in either strong or weak coupling systems. The other is the thermodynamic entropy production, which differs from the informational entropy production at strong coupling by the effects regarding the reservoir. We find that, it is the negative work on the reservoir, rather than the nonequilibrium of the thermal reservoir, which invalidates the thermodynamic entropy production at strong coupling. Our results indicate that the effects from the reservoir are essential to understanding thermodynamic processes at strong coupling.

Bang-Bang Property of Time Optimal Control for a Kind of Microwave Heating Problem

In this paper, the bang–bang property and the existence of the solution for the time optimal control of a specific kind of microwave heating problem are studied. The mathematical model for the time optimal control problem (P) of microwave heating is formulated, in which the governing equations of the controlled system are the weak coupling system of Maxwell equations and the heat equation. Based on a new observability estimate of the heat controlled system, the controllability of the system is derived by proving the null controllability of an equivalent system. The existence of the time optimal control of microwave heating is acquired under some stated assumptions, enabling the bang–bang property of the time optimal control problem (P) to be achieved.

Study of mode localization in an umbrella antenna with tensile ropes

The umbrella antenna is a typical periodic structure in nature, and as its ribs are made of CFRP (carbon fibre reinforced plastic), the presence of irregularities in dimension, stiffness and mass is unavoidable during manufacturing process, which will result in mode localization of the antenna. Excessive mode localization will damage the reflector precision and endanger safety of the antenna, so how to suppress mode localization of the ribs is important for umbrella design. Combined with the development of an umbrella antenna, mode localization of the structure is studied. Firstly, dynamic equations of an umbrella antenna with tensile ropes are derived. Then, based on the ribs stiffness test results, further mode localization simulation and test are conducted. The final simulation and test results show that, when stiffness of the tensile ropes reaches to 3N/mm, the antenna structure will change from a weak coupling system to a strong coupling system and mode localization of the ribs are effectively suppressed.

Modeling and intelligent optimization of social collective behavior with online public opinion synchronization

Today, the public opinion synchronization on the network platform is becoming one of important issues worthy of careful study. In this paper, we take synchronization evolution phenomenon as an objective and adopt artificial bee colony (ABC) to evaluate network synchronization effects with optimization theory to find out an appropriate network structure. Firstly, we use the Kuramoto oscillators as a metaphor of the social system collective behavior. Secondly, combined with the social network characteristics obtained from the data of Sina Micro-Blog, a synchronization evolution model of Internet public opinion based on Kuramoto one is established. Subsequently, evolutionary multi-objective optimization model is set up and the ABC method is used to optimize the level of network synchronization, the synchronization starting time and the cost of public opinion synchronization. Finally, case analysis on “Double Eleven” Internet Marketing as well as Cadmium Poisoned Rice Event demonstrates that the synchronization performance of weak coupled system can be enhanced by offering reasonable configuration of the connection cost and the synchronization duration cost. In addition, a certain degree of increase in input cost can promote the synchronization performance and extend the synchronization duration significantly.

A simple first-order shear deformation theory for vibro-acoustic analysis of the laminated rectangular fluid-structure coupling system

This paper presents a simple first-order shear deformation theory (SFSDT), which is used for the first time to analyze the vibro-acoustic characteristics of the laminated rectangular plate-cavity coupling system filled with air or water. The proposed theory contains only four unknowns and has greater application scope and higher computation accuracy compared with the classical plate theory (CPT). The admissible functions of displacements and sound pressure of the fluid-structure coupling system are expressed as superposition of the periodic functions based on the Fourier series method. Combined with the artificial virtual spring technology, the proposed theory could be used to analyze the composite coupling system under various combinations of classical boundary conditions or arbitrary elastic boundary conditions. Based on the free vibration analysis of the laminated rectangular plate in-vacuo, both the natural characteristics analysis and the forced response analysis under the excitation of a unit point force or a unit point sound source are carried out. The differences between the weak coupling system with air as medium and the strong coupling system with water as medium are discussed in detail and some new results and new conclusions have been given, which could be the benchmark for the future research.

On the Benefit of Different Additional Regularity for the Weakly Coupled Systems of Semilinear Effectively Damped Waves

This paper is devoted to study the global existence of small data solutions to the Cauchy problem for weakly coupled systems of semilinear effectively damped waves, where the data have different additional regularities and different power nonlinearities.