This study delves into the role of the neuromuscular junction in communication between nerves and muscles, as well as the importance of sarcomeres in muscle contraction. A mechanical device and circuit model is developed to simulate the movement of sarcomeres and the biophysical properties of skeletal muscles, including membrane potential and channel currents. The model integrates electromagnetic, kinetic, and elastic potential energy, which is verified by Helmholtz’s theorem. By using memristors to simulate the neuromuscular junction, the coupling of neuronal circuits with muscle cell circuits is achieved, and dynamic analysis is conducted. Adjusting Hamiltonian energy parameters can modulate oscillation patterns and beam displacement, optimizing the coupling strength between neurons and muscle cells. The study demonstrates that by manipulating energy ratios, it is possible to control the interactions between muscle cells.
In order to investigate physically meaning localized nonlinear waves on the periodic background defined by Weierstrass elliptic ℘-function for the (n + 1)-dimensional generalized Kadomtsev–Petviashvili equation by Darboux transformation, the associated linear spectral problem with the Weierstrass function as the external potential is studied by utilizing the Lamé function. The degenerate solutions of the nonlinear waves have also been obtained by approaching the limits of the half-periods ω1 and ω2 of ℘(x). At the same time, the evolution and nonlinear dynamics of various nonlinear waves under different parameter regimes are systematically discussed. The findings may open avenues for related experimental investigations and potential applications in various nonlinear science domains, such as nonlinear optics and oceanography.
This paper investigates the physical significance of the infinitely many K- and τ-symmetries associated with the soliton and complex solutions of the sine-Gordon (sG) equation. It is shown that the K-symmetries are linear combinations of wave center translation symmetries, while the τ-symmetries combine both wave center translation and wave number translation symmetries. Only a subset of the K- and τ-symmetries are independent, indicating that these symmetries are not incomplete. A special one-soliton solution of the sG equation is derived by using the generalized symmetries.
The investigation centers on a generalized Toda lattice equation featuring four potentials. Initially, the continuous counterpart is first established using the continuous limit approach. Subsequently, leveraging its 3 × 3 matrix spectrum problem, the discrete generalized (m, 3N − m)-fold Darboux transformation (DT) is formulated for this discrete system. Finally, the derived generalized DT is employed to generate precise rational solutions and hybrid rational-exponential solutions, which are thoroughly analyzed and graphically illustrated. These novel findings may offer insights into the lattice dynamical phenomena described by Toda lattice equation.
Official and civil information, as distinct information sources, significantly influence public behavior and the dynamics of epidemic transmission. In this paper, we propose a three-layer ${U}_{1}{A}_{1}{U}_{1}-{U}_{2}{A}_{2}{U}_{2}-SIS$ coupled model to analyze the co-evolution process of official information dissemination, civil information dissemination and epidemic transmission, considering the interdependencies between the information dissemination channels. The first layer describes the official information dissemination process. The second layer models the civil information dissemination process, considering the effects of perceived risk costs and the role of the correlation between official and civil information. The third layer represents the epidemic transmission process, highlighting the impact of the correlation between official and civil information on epidemic transmission. Then, using the microscopic Markov chain approach, we describe the information-epidemic coupled dynamics and derive the epidemic outbreak threshold. Our research demonstrates that a stronger positive correlation between official and civil information raises the epidemic threshold and suppresses the scale of epidemic transmission. Furthermore, individuals’ adoption of civil information should involve a more thorough assessment of the infection risk based on their personal circumstances, which can contribute to more effective epidemic control. Moreover, enhancing infected individuals’ accurate comprehension of official information can effectively curb the transmission of the epidemic. Our study highlights the importance of both official and civil information dissemination in epidemic management and provides insights for policymakers in developing effective public health and communication strategies.
In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations (in the sense of having three-soliton solutions) of the KdV type and mKdV type that were found by Jarmo Hietarinta in the 1980s. Examples of non-integrable bilinear equations of the KdV type are also given.
We propose an effective surface plasmon resonance system designed to achieve both negative and positive Goos–Hänchen shifts in reflected light. This system comprises a metal film and an underlying medium, where the real part of the permittivity of the underlying medium must be less than unity. Surface plasmon polaritons can be excited at the lower surface of the metal when light is incident from the air onto the upper surface of the metal. The excitation of surface plasmon polaritons leads to the exploration of the Goos–Hänchen shift (G–HS). Control over the negative and positive (G–HS) is investigated via the wavelength of the incident light. The magnitude of the G–HS is strongly dependent on the incident wavelength. A remarkable enhancement of both negative and positive G–HS in the reflected light is achieved at certain wavelengths and incident angles. Our system paves the way for exploring different characteristics of optical switching and micro-sensors with very high precision.
We investigate phase-controlled bound states in a one-dimensional photonic waveguide coupled to an artificial giant atom at two distant sites. Specifically, we identify the bound state out of the continuum (BOC) and the bound state in the continuum (BIC) and derive the exact existence condition for the BOC. Furthermore, we analytically determine the BIC’s frequency and photonic distribution profile. Remarkably, our analysis reveals quantum beats in both atomic and photonic dynamics, arising from coherent oscillations between the BIC and BOC. These results establish a novel approach for manipulating waveguide quantum electrodynamics via engineered bound states, with potential applications in quantum information processing.
In 2021, LHCb collaboration reported a very narrow state in the D0D0π+ mass spectrum just below the D*+D0 mass threshold. We consider the influence of the Castillejo–Dalitz–Dyson (CDD) pole in the scattering amplitude to derive a general treatment for the two-body final state interaction near its threshold. The line shape (or the energy dependent event distribution) are then obtained, where the parameters can be fixed by fitting to the experimental data on the D0D0π+ mass spectrum. Within our method the data are quite well reproduced. The pole structure in the complex energy plane indicates that the Tcc state has a large portion of elementary degree of freedom (e.g. the compact tetraquark component) inside its hadron wave function. The compositeness as a measure of molecule component in its wave function is predicted to be $0.2{3}_{-0.09}^{+0.40}$. Clearly, the non-molecular component takes a non-negligible or even dominant portion.
We investigate the application of the on-shell unitarity method to compute the anomalous dimensions of effective field theory operators. We compute one-loop anomalous dimensions for the dimension-7 operator mixing in low-energy effective field theory (LEFT). The on-shell method significantly simplifies the construction of scattering amplitudes. By leveraging the correspondence between the anomalous dimensions of operator form factors and the double-cut phase-space integrals, we bypass the need for direct loop integral calculations. The resulting renormalization group equations derived in this work provide crucial insights into the scale dependence of the LEFT dimension-7 Wilson coefficients, which will aid in precision experimental fitting of these coefficients.
The observed identical π7/2−[514] band and near-identical π1/2−[521] band in 251Md and 255Lr are investigated using the cranked shell model (CSM) with the particle-number-conserving (PNC) pairing method. The experimental kinematic moments of inertia (MOIs) J(1) for each band are reproduced well by the PNC-CSM calculations. A remarkable identity is exhibited for the variation of the calculated MOIs J(1) versus the frequency between 251Md and 255Lr, which is attributed to the identical contributions of the alignment from the blocked proton orbitals π[514]7/2 (π[521]1/2) in 251Md and 255Lr. The slight differences of J(1) at high frequency ℏω > 0.2 MeV for the near-identical π1/2−[521] band are due to the contributions of the direct term j(1)(μ) and the interference term j(1)(μν) based on the neutron orbital ν9/2−[734]. The B(E2) values are lower in 251Md than in 255Lr while the pairing gaps are almost the same for the π7/2−[514] and π1/2−[521] bands. The behaviors of the B(E2) values (pairing gaps) versus frequency are predicted to exhibit a remarkable similarity in 251Md and 255Lr.
This research paper seeks to investigate the characteristics of almost Riemann solitons and almost gradient Riemann solitons within the framework of generalized Robertson–Walker (GRW) spacetimes that incorporate imperfect fluids. Our study begins by defining specific properties of the potential vector field linked to these solitons. We examine the potential vector field of an almost Riemann soliton on GRW imperfect fluid spacetimes, establishing that it aligns collinearly with a unit timelike torse-forming vector field. This leads us to express the scalar curvature in relation to the structures of soliton and spacetime. Furthermore, we explore the characteristics of an almost gradient Riemann soliton with a potential function ψ across a range of GRW imperfect fluid spacetimes, deriving a formula for the Laplacian of ψ. We also categorize almost Riemann solitons on GRW imperfect fluid spacetimes into three types: shrinking, steady, and expanding, when the potential vector field of the soliton is Killing. We prove that a GRW imperfect fluid spacetime with constant scalar curvature and a Killing vector field admits an almost Riemann soliton. Additionally, we demonstrate that if the potential vector field of the almost Riemann soliton is a ν(Ric)-vector, or if the GRW imperfect fluid spacetime is ${{ \mathcal W }}_{2}$-flat or pseudo-projectively flat, the resulting spacetime is classified as a dark fluid.
Light sub-GeV dark matter (DM) particles up-scattered by high-energy cosmic rays (CRs) (referred to as CRDM) can be energetic and become detectable by conventional DM direct detection experiments. Nevertheless, current CRDM theoretical frameworks remain limited by model-dependent parameterizations, whereas the effective operators provides a model-independent computing framework. In this work, we systematically investigate the general relativistic DM-nucleus spin-independent interactions. We first construct effective operators for dark matter with spin up to two, i.e. spin-1/2 fermionic DM (χ), the scalar DM (φ), the vector DM (Vμ), spin-3/2 fermionic DM ($\Psi$) and spin-2 DM (Tμν). We then derive the CRDM flux and the nuclear recoil event rate based on these operators, and employ nuclear recoil data from the LUX-ZEPLIN (LZ) experiment to constrain all effective operators. We set stringent constraints on the CRDM-nucleon scattering cross section for sub-GeV DM. Especially, our results show that the exclusion limits from the spin-2 Tμν operator differ by as much as ten orders of magnitude from those calculated using constant cross section.
The chiral gravitational wave background (GWB) can be produced by axion-like fields in the early universe. We perform parameter estimation for two types of chiral GWB with the LISA-Taiji network: axion-dark photon coupling and axion-Nieh–Yan coupling. We estimate the spectral parameters of these two mechanisms induced by the axion and determine the normalized model parameters using the Fisher information matrix. For highly chiral GWB signals that we choose to analyze in the mHz band, the normalized model parameters are constrained with a relative error less than 6.7% (dark photon coupling) and 2.2% (Nieh–Yan coupling) at the one-sigma confidence level. The circular polarization parameters are constrained with a relative error around 21% (dark photon coupling) and 6.2% (Nieh–Yan coupling) at the one-sigma confidence level.
Gravitational collapse and bubble evolution in the asymptotic Friedmann–Lemaître–Robertson–Walker (FLRW) Universe is an intriguing and intricate problem. We systematically analyze the dynamics of contact Schwarzschild–FLRW (McVittie) spacetimes, focusing on their general junction conditions and introducing a novel function to simplify the extrinsic curvature and surface stress–energy tensor. Both static and dynamic scenarios are explored, including special cases such as Schwarzschild, FLRW, and Einstein–Straus configurations using our general framework. Numerical calculations further investigate the evolution of concentric McVittie spacetimes under various initial conditions, incorporating Λ-CDM cosmological models to better reflect realistic cosmic backgrounds. These results offer deep insights into the interplay between the McVittie mass parameter, initial peculiar velocity, and the influence of dark energy, providing a unified perspective for understanding gravitational collapse and bubble evolution in cosmology and astrophysics.
The existence of absolute parametric instability in an inhomogeneous plasma is revisited in a one-dimensional three-wave model. Non-resonant daughter waves are considered to match the conditions of radio-frequency (RF)-plasma interactions in magnetically confined plasma. Our model shows that such absolute instability has an extremely high threshold and cannot be induced for typical RF-plasma interactions, even if the linear growth rate of the instability achieves the level of ion-cyclotron frequency. As a result, we suggest that it is appropriate to neglect absolute instability when non-resonant daughter waves are involved.
The theory of statistical physics relies on ergodicity, whereby in large or interacting systems lacking integrability, trajectories eventually explore nearly all points in the phase space. It has been believed that chaotic dynamics provide a possible pathway to ergodicity. Here, we examine the phase space density distributions and their recurrence in the harmonic oscillator, the linear and nonlinear Mathieu equations, the Lorenz attractor, and the Nosé–Hoover model. We show that in models with periodic or quasiperiodic dynamics, sharp peaks can be found in the phase space density distributions. However, for the chaotic dynamics, their distributions display totally different behaviors. We understand these differences using recurrence plots. Our results show that while chaotic dynamics provide an efficient way for the trajectory to explore a large portion of the phase space, which is necessary for ergodicity, the chaotic dynamics are not sufficient for this goal. For instance, despite the Nosé–Hoover model being chaotic, it is not sufficiently large for ergodicity. Therefore, our results may lead to an important conclusion, which is that ergodicity may be realized from large chaotic systems. These findings in these simple models can be explored in experiments in the future, which may provide some key insights into ergodic dynamics.
We study the thermoelectric transport of a series-coupled double quantum dots (SDQDs) system, based on the hierarchical equations of motion approach. The thermocurrent as a function of the energy level of QDs gives rise to a sign-changing phenomenon. The temperature difference between the two leads can enhance the thermocurrent. Moreover, the sign changing also generates in thermocurrent as a function of temperature due to the transition from the many-body Kondo resonant tunneling process to the single electron process of the SDQDs system. The inter-dot coupling strength between two QDs not only affects the value of the thermocurrent but also influences the characteristic temperature at which the sign changing of thermocurrent emerges. In a weak coupling regime, the thermocurrent firstly is enhanced by inter-dot coupling strength due to the ‘t-enhanced Kondo effect’ and then decreases with inter-dot coupling strength due to the effective antiferromagnetic interaction between the two QDs. In the middle coupling regime, the forming coherence bonding and antibonding orbitals channels and the residual Kondo effect co-dominate the transport process. The thermocurrent firstly decreases, then increases, and finally decreases with temperature. However, the thermocurrent shows a transition from increasing to decreasing behavior with temperature in the strong coupling regime. Although the inter-dot coupling strength t has a complex impact on the SDQDs system, the characteristic temperature kBTc, at which a sign changing appears, indicates a quantitative relationship with the value of the inter-dot coupling strength t by an identical amount of the Kondo correlation being partially destroyed.
We have analyzed magnetic order in the one-dimensional Kondo lattice with classical localized spins. To identify relevant low-energy configurations, we combine the exact diagonalization of the electronic system with a dissipative evolution, described by the Landau–Lifshitz-Gilbert equation. We find that spiral states always relax into a more complex form of noncollinear order, characterized by a periodic modulation of the relative angles between neighboring spins. A finite-size scaling analysis shows that the amplitude of the modulation and the gain in free energy remain finite in the thermodynamic limit. Importantly, the wavelength of the modulation is determined by the Fermi wavevector of the unperturbed spiral. This suggests that complex noncollinear order originates from an instability of the unperturbed spirals, which, in the presence of a weak pairing term, may hinder topological superconductivity. Our final phase diagram is obtained by comparing the modulated spiral states with various complex collinear configurations proposed in the literature.
Coupled oscillator systems often exhibit collective dynamics as a consequence of their mutual heterogeneous interactions. Recent studies have highlighted the importance of shear diversity, an inhomogeneous pattern, in influencing the collective behavior of complex systems. Here, we investigate the quenching dynamics occurring within a network of limit-cycle oscillators that are globally coupled by taking into account both the shear diversity and the heterogeneous natural frequencies that are assumed to be statistically independent. Beyond the phase-only model considered in previous studies, we propose a general approach for identifying the critical criteria, demonstrating the instability of the incoherent state, by retaining the responses of both amplitudes and phases. This study advances the understanding of the role of heterogeneous couplings in interacting dynamical agents, offering valuable insights into the quenching phenomena observed in complex systems.
