coupling strengths
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2022 ◽  
Vol 7 (1) ◽  
Jun-Qing Cheng ◽  
Jun Li ◽  
Zijian Xiong ◽  
Han-Qing Wu ◽  
Anders W. Sandvik ◽  

AbstractUsing quantum Monte Carlo, exact diagonalization, and perturbation theory, we study the spectrum of the S = 1/2 antiferromagnetic Heisenberg trimer chain by varying the ratio g = J2/J1 of the intertrimer and intratrimer coupling strengths. The doublet ground states of trimers form effective interacting S = 1/2 degrees of freedom described by a Heisenberg chain. Therefore, the conventional two-spinon continuum of width ∝ J1 when g = 1 evolves into to a similar continuum of width ∝ J2 when g → 0. The intermediate-energy and high-energy modes are termed doublons and quartons which fractionalize with increasing g to form the conventional spinon continuum. In particular, at g ≈ 0.716, the gap between the low-energy spinon branch and the high-energy band with mixed doublons, quartons, and spinons closes. These features should be observable in inelastic neutron scattering experiments if a quasi-one-dimensional quantum magnet with the linear trimer structure and J2 < J1 can be identified. Our results may open a window for exploring the high-energy fractional excitations.

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 201
Xu Ni ◽  
Kejia Yi ◽  
Yiming Jiang ◽  
Ancai Zhang ◽  
Chengdong Yang

This paper discusses consensus control of nonlinear coupled parabolic PDE-ODE-based multi-agent systems (PDE-ODEMASs). First, a consensus controller of leaderless PDE-ODEMASs is designed. Based on a Lyapunov-based approach, coupling strengths are obtained for leaderless PDE-ODEMASs to achieve leaderless consensus. Furthermore, a consensus controller in the leader-following PDE-ODEMAS is designed and the corresponding coupling strengths are obtained to ensure the leader-following consensus. Two examples show the effectiveness of the proposed methods.

Electronics ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 153
Balamurali Ramakrishnan ◽  
Mahtab Mehrabbeik ◽  
Fatemeh Parastesh ◽  
Karthikeyan Rajagopal ◽  
Sajad Jafari

A memristor is a vital circuit element that can mimic biological synapses. This paper proposes the memristive version of a recently proposed map neuron model based on the phase space. The dynamic of the memristive map model is investigated by using bifurcation and Lyapunov exponents’ diagrams. The results prove that the memristive map can present different behaviors such as spiking, periodic bursting, and chaotic bursting. Then, a ring network is constructed by hybrid electrical and chemical synapses, and the memristive neuron models are used to describe the nodes. The collective behavior of the network is studied. It is observed that chemical coupling plays a crucial role in synchronization. Different kinds of synchronization, such as imperfect synchronization, complete synchronization, solitary state, two-cluster synchronization, chimera, and nonstationary chimera, are identified by varying the coupling strengths.

Tuncer Kaya

In this work, the values of critical coupling strengths of the Ising lattices which are changing their lattice structure (or non-self-dual) under decimation transformations, such as the honeycomb, the triangular and the body centered cubic Ising lattices, are obtained by a modified real space renormalization group approach (RSRG). This modification is necessary to obtain a proper relation between the coupling strengths of the original and the decimated lattices. Indeed, we have achieved to obtain a proper renormalized coupling strength relation for honeycomb and triangular lattices readily, since the decimation transformation of the honeycomb lattice produces the triangular lattice or vice versa. Here, the problem of having physically untractable interactions between degrees of freedom in the renormalized Hamiltonian, which leads eventually to inevitable approximations in the treatment, except for the 1D Ising chain, has been solved with a proper approximation. Especially for the 3D Ising lattices, the physically untractable interactions appearing in the renormalized Hamiltonian make the mathematical treatment too cumbersome. As a result, there is not enough research dealing with the 3D Ising lattices using RG theory. Our approximation is based on using the simple relation [Formula: see text], which is, of course, a very relevant first-order approximation, if [Formula: see text]. With the help of this approximation, decimation transformation process produces only pairwise interactions in the renormalized Hamiltonian instead of having four spins, six spins, or even eight spin interactions which appear naturally if all the terms are kept in the renormalized Hamiltonians of the Ising lattices in 2D and higher dimensions. Without this approximation, one cannot apply analytic RG treatment feasibly to even simple cubic lattice, let alone applying it to the body centered cubic lattice. Using this modified RG approach, the values of critical coupling strengths of the honeycomb, the triangular and the body centered cubic Ising lattices are obtained analytically as [Formula: see text], [Formula: see text] and [Formula: see text] respectively. Apparently, these estimations are really close to the results obtained from cumbersome exact treatments which are [Formula: see text], [Formula: see text] and [Formula: see text] for the honeycomb, the triangular and the body centered cubic lattices.

Yuhui Luo ◽  
Chunhua Zeng ◽  
Baowen Li

Abstract We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function (VACF) and mean squared displacement (MSD) of a single particle, we find that for the steady state, diffusions are ballistic at short times and then become normal for most of parameter regimes. However, for certain parameter regimes, both VACF and MSD suggest that the transition between superdiffusion and subdiffusion takes place at intermediate times, and diffusion becomes normal at long times. Via the power spectrum density corresponding to the transitions, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we theoretically propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles and for identifying cancer cells or healthy ones.

Jinniu Hu ◽  
Ying Zhang ◽  
Hong Shen

Abstract The $\Xi$-nuclear potential is investigated in the quark mean-field (QMF) model based on recent results of the $\Xi^-+^{14}\rm{N}$ ($_{\Xi^-}^{15}\rm{C}$) system. The experimental data on the binding energy of $1p$-state $\Xi^-$ hyperon in $_{\Xi^-}^{15}\rm{C}$ hypernuclei in KISO, IBUKI, E07-T011, E176-14-03-35 events are merged as $B_{\Xi^-}(1p)=1.14\pm0.11$ MeV. With this constraint, the coupling strengths between the $\omega$ vector meson and $\Xi$ hyperon are fixed in three QMF parameter sets. At the same time, the $\Xi^-$ binding energy of $1s$ state in $_{\Xi^-}^{15}\rm{C}$ is predicted as $B_{\Xi^-}(1s)=5.66\pm0.38$ MeV with the same interactions, completely consistent with the data from the KINKA and IRRAWADDY events. Finally, the $\Xi$-nuclear potential is calculated in the symmetric nuclear matter in the framework of QMF models. It is $U_{\Xi }=-11.96\pm 0.85$ MeV at nuclear saturation density, which will be essential to determine the onset density of $\Xi$ hyperon in neutron star.

Mahdis Dadfar ◽  
Rahman Sheikhhoseini ◽  
Mohadeseh Jafarian ◽  
Alireza Esmaeili

Abstract Background Dynamic knee valgus (DKV) is a common lower extremity movement disorder among females. This study aimed to investigate kinematic couplings between lower extremity joints in female junior athletes with DKV during single and double-leg landing and gait. Methods Twenty-six physically active female junior athletes (10–14 years old) with DKV were recruited. Kinematic couplings between rearfoot, tibia, knee, and hip were extracted using eight Vicon motion capture cameras and two force plates. Zero-lag cross-correlation coefficient and vector coding were used to calculate kinematic couplings between joints during physical tasks. Paired t-test and Wilcoxon tests were run to find significant couplings between joint motions and coupling strengths. Bonferroni posthoc was used to determine significance with α ≤ 0.05. Results The results showed that the strongest kinematic relationship existed between rearfoot eversion/inversion and tibial internal/external rotation during all three tasks. Correlations of the rearfoot supination/pronation with tibial rotations, knee, and hip motions in sagittal, frontal, and transverse planes were very strong to strong during double-leg landing and moderate to weak during gait. A weak correlation was observed between rearfoot supination/pronation and hip adduction/abduction during single-leg landing. Conclusions Coupling relationships between rearfoot, knee, and hip vary by the task intensity and alignment profiles in female juniors with DKV.

2021 ◽  
He Tian ◽  
Hunter C. Davis ◽  
J. David Wong-Campos ◽  
Linlin Z. Fan ◽  
Benjamin Gmeiner ◽  

All-optical electrophysiology can be a powerful tool for studying neural dynamics in vivo, as it offers the ability to image and perturb membrane voltage in multiple cells simultaneously. The "Optopatch" constructs combine a red-shifted archaerhodopsin (Arch)-derived genetically encoded voltage indicator (GEVI) with a blue-shifted channelrhodopsin actuator (ChR). We used a video-based pooled screen to evolve Arch-derived GEVIs with improved signal-to-noise ratio (QuasAr6a) and kinetics (QuasAr6b). By combining optogenetic stimulation of individual cells with high-precision voltage imaging in neighboring cells, we mapped inhibitory and gap junction-mediated connections, in vivo. Optogenetic activation of a single NDNF-expressing neuron in visual cortex Layer 1 significantly suppressed the spike rate in some neighboring NDNF interneurons. Hippocampal PV cells showed near-synchronous spikes across multiple cells at a frequency significantly above what one would expect from independent spiking, suggesting that collective inhibitory spikes may play an important signaling role in vivo. By stimulating individual cells and recording from neighbors, we quantified gap junction coupling strengths. Together, these results demonstrate powerful new tools for all-optical microcircuit dissection in live mice.

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2224
Haiping Gao ◽  
Jian Zhu ◽  
Xianyong Li ◽  
Xing Chen

In this paper, several multi-layer-coupled star-composed networks with similar symmetrical structures are defined by using the theory of graph operation. The supra-Laplacian matrix of the corresponding multi-layer networks is obtained according to the master stability equation (MSF). Two important indexes that reflect the synchronizability of these kinds of networks are derived in the case of bounded and unbounded synchronized regions. The relationships among the synchronizability, the number of layers, the length of the paths, the branchings, and the interlayer and intralayer coupling strengths in the two cases are studied. At the same time, the simulation experiments are carried out with the MATLAB software, and the simulated images of the two symmetrical structure networks’ synchronizability are compared. Finally, the factors affecting the synchronizability of multi-layer-coupled star-composed networks are found. On this basis, optimization schemes are given to improve the synchronizability of multi-layer-coupled star-composed networks and the influences of the number of central nodes on the networks’ synchronizability are further studied.

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2201
Vinh Le Duc ◽  
Joanna K. Kalaga ◽  
Wiesław Leoński ◽  
Mateusz Nowotarski ◽  
Konrad Gruszka ◽  

We consider two PT-symmetric models, consisting of two or three single-mode cavities. In both models, the cavities are coupled to each other by linear interactions, forming a linear chain. Additionally, the first and last of such cavities interact with an environment. Since the models are PT-symmetric, they are described by non-Hermitian Hamiltonians that, for a specific range of system parameters, possess real eigenvalues. We show that in the models considered in the article, the steering generation process strongly depends on the coupling strengths and rates of the gains/losses in energy. Moreover, we find the values of parameters describing the system for which the steering appears.

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