Understanding the effects of point liquid loading on transversely isotropic poroelastic media is crucial for advancing geomechanics and biomechanics, where precise modeling of fluid-structure interactions is essential. This paper presents a comprehensive analysis of infinite transversely isotropic poroelasticity under a fluid source, based on Biot’s theory, aiming to uncover new and previously unexplored insights in the literature. We begin our study by deriving a general solution for fluid-saturated, transversely isotropic poroelastic materials in terms of harmonic functions that satisfy sixth-order homogeneous partial differential equations, using potential theory and Almansi’s theorem. Based on these general solutions and potential functions, we construct a Green’s function for a point fluid source, introducing three new harmonic functions with undetermined constants. These constants are determined by enforcing continuity and equilibrium conditions. Substituting these into the general solution yields fundamental solutions for poroelasticity that provide crucial support for a wide range of project problems. Numerical results and comparisons with existing literature are provided to illustrate physical mechanisms through contour plots. Our observations reveal that all components tend to zero in the far field and become singular at the concentrated source. Additionally, the contours exhibit rapid changes near the point fluid source but display gradual variations at a distance from it. These findings highlight the intricate behavior of the system under point liquid loading, offering valuable insights for further research and practical applications.
Renormalization group analysis has been proposed to eliminate secular terms in perturbation solutions of differential equations and thus expand the domain of their validity. Here we extend the method to treat periodic orbits or limit cycles. Interesting normal forms could be derived through a generalization of the concept ’resonance’, which offers nontrivial analytic approximations. Compared with traditional techniques such as multi-scale methods, the current scheme proceeds in a very straightforward and simple way, delivering not only the period and the amplitude but also the transient path to limit cycles. The method is demonstrated with several examples including the Duffing oscillator, van der Pol equation and Lorenz equation. The obtained solutions match well with numerical results and with those derived by traditional analytic methods.
In this paper, the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system, which is described by four component nonlinear evolution equations (NLEEs). On the background of the Jacobian elliptic function, we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the model spectrum problem. Then, with the help of the one-fold Darboux transformation and two-fold Darboux transformation, rogue waves on a dn-periodic background and cn-periodic background are derived, respectively. Finally, the corresponding complex dynamical properties and evolutions of the four components are illustrated graphically by choosing suitable parameters.
In this paper, we investigate the effect of exceptional points (EPs) on the violation of Leggett–Garg inequality (LGI) and no-signaling-in-time (NSIT) conditions and compare the different effects between the Hamiltonian EP (HEP) and Liouvillian EP (LEP) on those violations. We consider an open system consisting of two coupled qubits and each qubit is contacted with a thermal bath at a different temperature. In the case of omitting quantum jumps, we find that the system exhibits a second-order HEP, which separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI and NSIT conditions can be violated in both regimes and not violated at the HEP. In the case of without omitting quantum jumps, we find that the system exhibits a third-order LEP, which also separates the parameter space into an overdamped regime and an underdamped regime. In this situation, the LGI can only be violated in the underdamped regime with large coupling strength between the qubits. Conversely, the NSIT conditions can be violated in both regimes, as well as at the LEP, except in the overdamped regime with small coupling strength between the qubits. Comparing the violations of the LGI and NSIT conditions with HEP and LEP, we find that the quantum jumps would reduce the generation of coherence, enhance the decoherence, and lead to narrower parameter regimes that the LGI and NSIT conditions can be violated. Furthermore, in both cases, the NSIT conditions can be violated in a wider parameter regime than the LGI.
We present a theoretical scheme to realize two-dimensional (2D) asymmetric diffraction grating in a five-level inverted Y-type asymmetric double semiconductor quantum wells (SQWs) structure with resonant tunneling. The SQW structure interacts with a weak probe laser field, a spatially independent 2D standing-wave (SW) field, and a Laguerre–Gaussian (LG) vortex field, respectively. The results indicate that the diffraction patterns are highly sensitive to amplitude modulation and phase modulation. Because of the existence of vortex light, it is possible to realize asymmetric high-order diffraction in the SQW structure, and then a 2D asymmetric grating is established. By adjusting the detunings of the probe field, vortex field, and SW field, as well as the interaction length, diffraction intensity, and direction of the 2D asymmetric electromagnetically induced grating (EIG) can be controlled effectively. In addition, the number of orbital angular momenta (OAM) and beam waist parameter can be used to modulate the diffraction intensity and energy transfer of the probe light in different regions. High-order diffraction intensity is enhanced and high-efficiency 2D asymmetric diffraction grating with different diffraction patterns is obtained in the scheme. Such 2D asymmetric diffraction grating may be beneficial to the research of optical communication and innovative semiconductor quantum devices.
We analyze the steady-state characteristics of a damped harmonic oscillator (system) in the presence of a non-Markovian bath characterized by Lorentzian spectral density. Although Markovian baths presume memoryless dynamics, the introduction of complex temporal connections by a non-Markovian environment radically modifies the dynamics of the system and its steady-state behaviour. We obtain the steady-state Green’s function and correlation functions of the system using the Schwinger–Keldysh formalism. In both rotating and non-rotating wave approximation, we analyzed various emergent properties like effective temperature and distribution function. We also explore the impact of dissipation and non-Markovian bath on the quantum Zeno and anti-Zeno effects. We show that a transition between Zeno to anti-Zeno effect can be tuned by bath spectral width and the strength of dissipation.
Recently, large-scale trapped ion systems have been realized in experiments for quantum simulation and quantum computation. They are the simplest systems for dynamical stability and parametric resonance. In this model, the Mathieu equation plays the most fundamental role for us to understand the stability and instability of a single ion. In this work, we investigate the dynamics of trapped ions with the Coulomb interaction based on the Hamiltonian equation. We show that the many-body interaction will not influence the phase diagram for instability. Then, the dynamics of this model in the large damping limit will also be analytically calculated using few trapped ions. Furthermore, we find that in the presence of modulation, synchronization dynamics can be observed, showing an exchange of velocities between distant ions on the left side and on the right side of the trap. These dynamics resemble that of the exchange of velocities in Newton’s cradle for the collision of balls at the same time. These dynamics are independent of their initial conditions and the number of ions. As a unique feature of the interacting Mathieu equation, we hope this behavior, which leads to a quasi-periodic solution, can be measured in current experimental systems. Finally, we have also discussed the effect of anharmonic trapping potential, showing the desynchronization during the collision process. It is hoped that the dynamics in this many-body Mathieu equation with damping may find applications in quantum simulations. This model may also find interesting applications in dynamics systems as a pure mathematical problem, which may be beyond the results in the Floquet theorem.
We present a calculation by including the relativistic and off-shell contributions to the interaction potentials between two spin-1/2 fermions mediated by the exchange of light spin-0 particles, in both momentum and coordinate spaces. Our calculation is based on the four-point Green's function rather than the scattering amplitude. Among the sixteen potential components, eight that vanish in the non-relativistic limit are shown to acquire nonzero relativistic and off-shell corrections. In addition to providing relativistic and off-shell corrections to the operator basis commonly used in the literature, we introduce an alternative operator basis that facilitates the derivation of interaction potentials in the coordinate space. Furthermore, we calculate both the long-range and short-range components of the potentials, which can be useful for future experimental analyses at both macroscopic and atomic scales.
This work demonstrates that once a large number of pion is condensed in a high-energy hadron collision, the gamma-ray spectrum from π0 decay takes on a typical broken power-law shape, which has been documented in many astronomical observations, but we have not yet recognized it. We show that this pion condensation is caused by a large number of soft gluons condensed in protons.
Relic gravitational waves (RGWs) from the early Universe carry crucial and fundamental cosmological information. Therefore, it is of extraordinary importance to investigate potential RGW signals in the data from observatories such as the LIGO-Virgo-KAGRA network. Here, focusing on typical RGWs from the inflation and the first-order phase transition (by sound waves and bubble collisions), effective and targeted deep learning neural networks are established to search for these RGW signals within the real LIGO data (O2, O3a and O3b). Through adjustment and adaptation processes, we develop suitable Convolutional Neural Networks (CNNs) to estimate the likelihood (characterized by quantitative values and distributions) that the focused RGW signals are present in the LIGO data. We find that if the constructed CNN properly estimates the parameters of the RGWs, it can determine with high accuracy (approximately 94% to 99%) whether the samples contain such RGW signals; otherwise, the likelihood provided by the CNN cannot be considered reliable. After testing a large amount of LIGO data, the findings show no evidence of RGWs from: 1) inflation, 2) sound waves, or 3) bubble collisions, as predicted by the focused theories. The results also provide upper limits of their GW spectral energy densities of h2Ωgw ∼ 10−5, respectively for parameter boundaries within 1) [β ∈ (−1.87, −1.85) × α ∈ (0.005, 0.007)], 2) [β/Hpt ∈ (0.02, 0.16) × α ∈ (1, 10) × Tpt ∈ (5*109, 1010) Gev], and 3) [β/Hpt ∈ (0.08, 0.2) × α ∈ (1, 10) × Tpt ∈ (5 * 109, 8 * 1010) Gev]. In short, null results and upper limits are obtained, and the analysis suggests that our developed methods and neural networks to search for typical RGWs in the LIGO data are effective and reliable, providing a viable scheme for exploring possible RGWs from the early Universe and placing constraints on relevant cosmological theories.
This work revisits the analysis of charged Casimir wormhole solutions within the framework of Einstein–Gauss–Bonnet (EGB) gravity, addressing a critical inconsistency in the approach presented by Farooq et al. Specifically, we show that their use of four-dimensional Casimir and electric field energy densities are incompatible with the higher-dimensional nature of EGB gravity, which requires D ≥ 5. We provide the correct formulation for the energy densities and revise the wormhole properties under this framework, offering a refined perspective on the interplay between extra dimensions and Casimir effects in EGB gravity.
This study explores the dynamics of charged Hayward black holes, focusing on the effects of electric charge and the length factor on accretion disk characteristics. Our results show that increasing both parameters reduces the size of the event horizon and innermost stable circular orbits (ISCO) radius, with the electric charge exerting a more pronounced influence. Additionally, the length factor and electric charge can effectively replicate the spin of a Kerr black hole. Both parameters also affect the electromagnetic radiation emitted from the accretion disk, increasing the flux, temperature, and radiative efficiency. The peak radiation occurs in the soft x-ray band, with higher values of electric charge and length factor enhancing disk luminosity and shifting the peak to higher frequencies. These findings can offer valuable insights into the accretion processes around black holes and their observable signatures, particularly in x-ray astronomy.
The QCD axion bubbles can form due to an explicit breaking of the Peccei–Quinn symmetry in the early Universe. In this paper, we investigate the modified formation of a QCD axion bubble in the presence of an axionlike particle (ALP), considering its resonant conversion to a QCD axion. We consider a general scenario where the QCD axion mixes with ALP before the QCD phase transition. In this scenario, the energy density of the ALP can be adiabatically transferred to the QCD axion at a temperature TR, resulting in the suppression of the cosmic background temperature TB at which the energy density of the QCD axion equals that of the radiation. The QCD axion bubbles form when the QCD axions arise during the QCD phase transition. Finally, we briefly discuss the impact of the formation of QCD axion bubbles on the formation of primordial black holes.
This research examines the dynamics of a cosh-Gaussian laser pulse travelling through a vacuum and its impact on electron acceleration. We examine the impact of several critical factors, such as laser electric field amplitude, decentered parameter, beam waist, and laser chirp parameter, on the energy gain of electrons using coupled momentum equations. Our results indicate that the energy acquisition of electrons escalates with the amplitude of the laser electric field, decentered parameter, and chirp parameter. An appropriate beam waist is essential for attaining energy-efficient electron acceleration in a vacuum. Through the optimization of these parameters, we get a maximum electron energy gain of 2.80 GeV. This study highlights the significance of customized laser pulse attributes in improving electron acceleration and aids in the progression of high-energy particle physics.
A mid-infrared femtosecond pulse laser with a single cycle and high intensity is an ideal driving light source for generating isolated attosecond pulses. Due to current experimental limitations, it is difficult to directly achieve this type of laser light source in the laboratory. In this paper, we obtain such an ideal light source by adding a Ti sapphire pulse to the combined pulse laser consisting of two mid-infrared pulses. Specifically, by combining the synthesized pulse consisting of 8 fs/1200 nm/1.62 × 1014 W cm−2 and 12 fs/1800 nm/2.71 × 1014 W cm−2 with an additional 8 fs/800 nm/1.26 × 1014 W cm−2 Ti sapphire pulse, the resulting electric field waveform is very close to that of a 1170 nm femtosecond pulse with an intensity of 1.4 × 1015 W cm−2, a single-cycle pulse width, and a carrier-envelope phase of 0.25π. Numerical simulations show that both cases produce high-order harmonic emission spectra with broadband supercontinuum spectra, however, the bandwidth of the supercontinuum spectra and the harmonic intensities in the synthesized pulses are significantly better than those in the single 1170 nm pulse. After inverse Fourier transform, we obtain 66 as a high-intensity isolated attosecond pulse, whose intensity is five orders of magnitude higher than that of a monochromatic field. Here, the phase differences between three combined pulse lasers have little effect on the numerical simulation results when they vary in the range of 0.3π.
The noise feature of a single-mode class-A laser amplifier is investigated by solving the Maxwell–Bloch equations of motion in the presence of the fluctuation force of cavity Langevin. The aim is to calculate the simultaneous fluctuations that are superimposed on the amplitude and phase of the cavity electric field, as well as the atomic population inversion. The correlation function of these fluctuations yields the amplitude, phase, and spontaneous emission noise fluxes, respectively. The amplitude and spontaneous emission noise fluxes exhibit the Lorentzian profiles in both the below-threshold state and the injection-locking region of the above-threshold state. While noise is typically viewed negatively in science and engineering, this research highlights its positive role as a valuable tool for measuring the optical properties of a laser amplifier. For instance, the degree of first-order temporal coherence (DFOTC) is derived by taking the Fourier transform of the amplitude noise flux. The damping rate of DFOTC is associated with the coherence time of the light emitted by the laser amplifier. Furthermore, the uncertainty relation between noise bandwidth and coherence time is confirmed. Finally, it is demonstrated that the input pumping noise flux, together with the output amplitude and spontaneous emission noise fluxes, satisfy the principle of flux conservation.
The properties of the non-trivial quantum state in an all-optical environment come mainly from the higher-order quantum electrodynamics effect, which remains one of the few unverified predictions of this theory due to its weak signal. Here, we propose a scheme specifically designed to detect this quantum vacuum, where a tightly focused pump laser interacts with an optical frequency comb (OFC) in its resonant cavity. When the OFC pulse passes through the vacuum polarized by the high-intensity pump laser, its carrier frequency and envelope change. This can be intuitively understood as the asymmetric photon acceleration induced by the ponderomotive force of the pump laser. By leveraging the exceptional ultrahigh frequency and temporal resolution of the OFC, this scheme holds the potential to improve the accuracy of quantum vacuum signal. Combining theoretical and simulation results, we discuss possible experimental conditions, and the detectable OFC signal is shown to be orders of magnitude better than the instrumental detection threshold. This shows our scheme can be verified on the forthcoming laser systems.
In this work, Langevin dynamics simulations were carried out to thoroughly investigate the swapping process of composite knots under tension in a cuboid nanochannel. From our analysis, the free energy profiles of knot swapping under different conditions were extracted from the overall probability distribution of the relative distance between the centers of composite knots. In addition, the impact of the stretching force, confinement size, and bending stiffness on the free energy profiles was directly identified. Especially, the influence of topology structure is for the first time reported. The increasing stretching force in a fixed confinement or the confinement size under a constant stretching force does not alter their respective equilibrium populations at the separate state and the entangled state. In contrast, a bending stiffness larger than 15 enhanced the formation of the entangled state. The topology structure of the 51 knot, which was different from the 52 knot, resulted in forming a metastable state in the free energy profiles. The increasing stretching forces yielded an enhancement of the following free energy barrier.
The Richtmyer–Meshkov (RM) instability plays an important role in various natural and engineering fields such as inertial confinement fusion. In this study, the effect of relaxation time on the RM instability under reshock impact is investigated using a two-component discrete Boltzmann method. The hydrodynamic and thermodynamic characteristics of the fluid system are comprehensively analyzed from the perspectives of the density gradient, vorticity, kinetic energy, mixing degree, mixing width and non-equilibrium intensity. Simulation results indicate that for longer relaxation time, the diffusion and dissipation are enhanced, the physical gradients decrease, and the growth of the interface is suppressed. Furthermore, the non-equilibrium manifestations show complex patterns, driven by the competitive physical mechanisms of the diffusion, dissipation, shock wave, rarefaction wave, transverse wave and fluid instabilities. These findings provide valuable insight into the fundamental mechanism of compressible fluid flows.
The ion channel in neurons is the basic component of signal transmission in the nervous system. The ion channel has important effects on the potential of neuron release and dynamic behavior in neural networks. Ion channels control the flow of ions into and out of the cell membrane to form an ion current, which makes the excitable membrane produce special potential changes and become the basis of nerve and muscle activity. The blockage of ion channels has a significant effect on the dynamics of neurons and networks. Therefore, it is very meaningful to study the influence of ion channels on neuronal dynamics. In this work, a hybrid ion channel is designed by connecting a charge-controlled memristor (CCM) with an inductor in series, and a magnetic flux-controlled memristor (MFCM), capacitor, and nonlinear resistor are connected in parallel with the mixed ion channel to obtain the memristor neural circuit. Furthermore, the oscillator model with a hybrid ion channel and its energy function are calculated, and a map neuron is obtained by linearizing the neuron oscillator model. In addition, an adaptive regulation method is designed to explore the adaptive regulation of energy on the dynamic behaviors of the map neuron. The results show that the dynamics of a map neuron with a hybrid ion channel can be controlled by parameters and external magnetic fields. This study is also used to research synchronization between map neurons and collective behaviors in the map neurons network.
