New integrable B₂ model with off-diagonal boundary reflections is proposed. The general solutions of the reflection matrix for the B₂ model are obtained by using the fusion technique. We find that the reflection matrix has 7 free boundary parameters, which are used to describe the degree of freedom of boundary couplings, without breaking the integrability of the system. The new quantization conditions will induce the novel structure of the energy spectrum and the boundary states. The corresponding boundary effects can be studied based on the results in this paper. Meanwhile, the reflection matrix of high rank models associated with B_n algebra can also be obtained by using the method suggested in this paper.

With the advent of the information age of networks, the study about rumor propagation in social networks has become increasingly significant. In this paper, a rumor propagation model with nonlinear functions and time delay in social networks is proposed. First, according to the next-generation matrix method, we work out the basic reproduction number. Second, we discuss the existence of the rumor-prevailing equilibrium points. Third, we demonstrate the stabilities of equilibrium points and analyze the sufficient conditions for Hopf bifurcation. Finally, the correctness of the theory is verified and several vital conclusions are obtained by numerical simulations.

This paper focuses on the issue of resilient dynamic output-feedback (DOF) control for ${{ \mathcal H }}_{\infty }$ synchronization of chaotic Hopfield networks with time-varying delay. The aim is to determine a DOF controller with gain perturbations ensuring that the ${{ \mathcal H }}_{\infty }$ norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound. A delay-dependent criterion for the ${{ \mathcal H }}_{\infty }$ synchronization is derived by employing the Lyapunov functional method together with some recent inequalities. Then, with the help of some decoupling techniques, sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases. Lastly, an example is used to illustrate the applicability of the results obtained.

We generalize the $\bar{\partial }$-dressing method to investigate a (2+1)-dimensional lattice, which can be regarded as a forced (2+1)-dimensional discrete three-wave equation. The soliton solutions to the (2+1)-dimensional lattice are given through constructing different symmetry conditions. The asymptotic analysis of one-soliton solution is discussed. For the soliton solution, the forces are zero.

The consideration of measuring instruments as macroscopic bodies leads to neglect of the microscopic processes that occur during measurements. This disregard is not justified in general cases. As an example of measurements using microscopic instruments, the scattering of a photon by an electron with electron interference at two slits (Compton effect) was used. The amount of information that can be obtained in such a process is inversely proportional to the wavelength of the incident photon. At large photon wavelengths (soft measurements), the pure state of the electron can be disrupted by an arbitrarily small extent; accordingly, the amount of information extracted in such an experiment is also arbitrarily small. It is shown that the energy price for a bit obtained in such a measurement tends toward a constant value for increasing the photon wavelength. Microscopic instruments can be used in situations where energy costs for measurements are important.

A fast scheme to generate Greenberger-Horne-Zeilinger states between different cavities in circuit QED systems is proposed. To implement this scheme, we design a feasible experimental device with three qubits and three cavities. In this device, all the couplings between qubit and qubit, cavity and qubit are tunable and are independent with frequencies, and thus the shortcut to adiabaticity technique can be directly applied in our scheme. It is demonstrated that the GHZ state can be generated rapidly with high fidelity in our scheme.

The dynamics of entanglement and quantum discord (QD) between two two-level atoms interacting with two dissipative coupled cavities in the presence of initial atom-cavity correlations is investigated. In comparison with the result of the initial factorized state, we show that the initial state contained quantum correlation of atom-cavity is most robust against the dissipative environment, and the initial atom-cavity correlations, especially the quantum correlation, play a constructive role in the generation of atomic entanglement and QD. Simultaneously, the comparison between Markovian and non-Markovian dynamics, and the influences of inter-cavity hopping rate are also taken into account and analyzed.

We present a formulation of quantum mechanics based on the theory of orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis where the expansion coefficients are orthogonal polynomials in the energy and physical parameters. Information about the corresponding physical systems (both structural and dynamical) are derived from the properties of these polynomials. We demonstrate that an advantage of this formulation is that the class of exactly solvable quantum mechanical problems becomes larger than in the conventional formulation (see, for example, table 3 in the text). We limit our investigation in this work to the Askey classification scheme of hypergeometric orthogonal polynomials and focus on the Wilson polynomial and two of its limiting cases (the Meixner–Pollaczek and continuous dual Hahn polynomials). Nonetheless, the formulation is amenable to other classes of orthogonal polynomials.

We study the Schwinger mechanism in the presence of an additional uniformly oriented, weak super Gaussian of integer order 4N + 2. Using the worldline approach, we determine the relevant critical points to compute the leading order exponential factor analytically. We show that increasing the parameter N gives rise to a strong dynamical enhancement. For N = 2, this effect turns out to be larger compared to a weak contribution of the Sauter type. For higher orders, specifically, for the rectangular barrier limit, i.e. $N\to \infty $, we approach the Lorentzian case as an upper bound. Although the mentioned backgrounds significantly differ in Minkowski spacetime, we show that the found coincidence applies due to identical reflection points in the Euclidean instanton plane. In addition, we also treat the background in perturbation theory following recent ideas. By doing so, we show that the parameter N determines whether the weak contribution behaves perturbatively or nonperturbatively with respect to the field strength ratio, and, hence, reveals an interesting dependence on the background shape. In particular, we show that for backgrounds, for which higher orders in the field strength ratio turn out to be relevant, a proposed integral condition is not fulfilled. In view of these findings, the latter may serve as an indicator for the necessity for higher-order contributions.

In this paper, we study the thermodynamics and the weak cosmic censorship conjecture of the nonlinear electrodynamics black hole under the scattering of a charged complex scalar field. According to the energy and charge fluxes of the scalar field, the variations of this black hole’s energy and charge can be calculated during an infinitesimal time interval. With scalar field scattering, the variation of the black hole is calculated in the extended and normal phase spaces. In the normal phase space, the cosmological constant and the normalization parameter are fixed, and the first and second laws of thermodynamics can also be satisfied. In the extended phase space, the cosmological constant and the normalization parameter are considered as thermodynamic variables, and the first law of thermodynamics is valid, but the second law of thermodynamics is not valid. Furthermore, the weak cosmic censorship conjecture is both valid in the extended and normal phase spaces.

In this paper, we study the evolution of a spatially flat universe composed of Tsallis agegraphic dark energy (TADE) and a pressureless dark matter (DM), by assuming that there is a sign-changeable interaction between TADE and DM. The density, deceleration parameter and the equation of state parameters (EoS) show satisfactory behaviors in the model. By analysis we find that the accelerated expansion of the universe can be achieved at the late time if model parameters δ > 2 and −2/3 < β < 0. Also, we investigate the interacting TADE model by means of statefinder diagnostic and $w\mbox{--}w^{\prime} $ analysis.

We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime. These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass. The Hawking mass of this family of ellipsoids tends to $-\infty $. In contrast, we show that the Hayward mass converges to a finite value. Moreover, a positive mass type theorem is established. The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are. This result could be extended for asymptotically Schwarzschild manifolds. And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.

We investigate phase-plane analysis of general relativistic orbits in a gravitational field of the Reissner–Nordström-type regular black hole spacetime. We employ phase-plane analysis to obtain different phase-plane diagrams of the test particle orbits by varying charge q and dimensionless parameter β, where β contains angular momentum of the test particle. We compute numerical values of radii for the innermost stable orbits and corresponding values of energy required to place the test particle in orbits. Later on, we employ similar analysis on an Ayón–Beato–García (ABG) regular black hole and a comparison regarding key results is also included.

A design of ultrathin crystalline silicon solar cells patterned with α-NaEr_0.2Y_0.8F₄ upconversion nanosphere (NSs) arrays on the surface was proposed. The light trapping performance of α-NaEr_0.2Y_0.8F₄ NSs with different ratios of sphere diameter to sphere pitch was systematically studied by COMSOL Multiphysics. The influence of different NS diameters and ratio to the average optical absorption of ultrathin crystalline silicon solar cell was calculated, as well as the short circuit current densities. The results show that the average optical absorption of solar cells with 2.33 μm silicon covered by α-NaEr_0.2Y_0.8F₄ NSs of 100 nm in diameter and 5.2 in ratio has improved by 8.5% compared to planar silicon solar cells with the same thickness of silicon. The light trapping performance of different thicknesses of silicon solar cells with the optimized configuration of NSs was also discussed. The results indicate that our structure enhances the light absorption. The presented model will be the basis for further simulations concerning frequency upconversion of α-NaEr_0.2Y_0.8F₄ materials.

The separate spin evolution quantum hydrodynamics (SSE-QHD) model is used to investigate the energy behavior for ion acoustic waves in degenerate quantum plasma. Numerical results show that the energy flow speed decreases with spin polarization parameter. It is also shown that it decreases with the increasing rate up to a certain range of wave number and then it goes to zero asymtotically. It is observed that Bohm potential suppresses the energy flow speed. It is also noticed that the energy flow speed deviates from the group velocity even in the absence of Bohm potential effect. However, the contribution of of Bohm poential effect  in spin polarized plasma reduces the extent of deviation.

We propose a new microfluid chip for transporting micro and nano particles. The device consists of chemical stripe pathways full of fuel species, which can be realized in experiments by chemical surface reactions that form spatiotemporal patterns. A mesoscopic model is constructed to simulate the transport dynamics of nanodimers passing through the chip. It is found that the increases of the volume fraction and radius of the dimer both decrease the first reach time although the underlying mechanisms are different: the volume fraction affects the probability of touching and entering the chip while the radius determines the self-propulsion within the chip. The transport efficiency is influenced by the size of the particles.

The current article investigates the impact of the bioconvection in an unsteady flow of magnetized Cross nanofluid with gyrotactic microorganisms and activation energy over a linearly stretched configuration. The analysis has been performed by utilizing the realistic Wu's slip boundary and zero mass flux conditions. The effects of nonlinear thermal radiation and the activation energy are also addressed. The governing flow equations are deduced to a dimensionless form by considering suitable transformations which are numerically targeted via a shooting algorithm. The physical visualization of each physical parameter governing the flow problem has been displayed graphically for distribution of velocity, temperature, concentration and motile microorganisms. The numerical treatment for the variation of skin friction coefficient, local Nusselt number, local Sherwood number and motile density number is performed in tabular forms.

In the present study, we consider the q-homotopy analysis transform method to find the solution for modified Camassa-Holm and Degasperis-Procesi equations using the Caputo fractional operator. Both the considered equations are nonlinear and exemplify shallow water behaviour. We present the solution procedure for the fractional operator and the projected solution procedure gives a rapidly convergent series solution. The solution behaviour is demonstrated as compared with the exact solution and the response is plotted in 2D plots for a diverse fractional-order achieved by the Caputo derivative to show the importance of incorporating the generalised concept. The accuracy of the considered method is illustrated with available results in the numerical simulation. The convergence providence of the achieved solution is established in $\hslash $-curves for a distinct arbitrary order. Moreover, some simulations and the important nature of the considered model, with the help of obtained results, shows the efficiency of the considered fractional operator and algorithm, while examining the nonlinear equations describing real-world problems.

The economic and financial systems consist of many nonlinear factors that make them behave as the complex systems. Recently many chaotic finance systems have been proposed to study the complex dynamics of finance as a noticeable problem in economics. In fact, the intricate structure between financial institutions can be obtained by using a network of financial systems. Therefore, in this paper, we consider a ring network of coupled symmetric chaotic finance systems, and investigate its behavior by varying the coupling parameters. The results show that the coupling strength and range have significant effects on the behavior of the coupled systems, and various patterns such as the chimera and multi-chimera states are observed. Furthermore, changing the parameters' values, remarkably influences on the oscillators attractors. When several synchronous clusters are formed, the attractors of the synchronized oscillators are symmetric, but different from the single oscillator attractor.

Car taillights are ubiquitous during the deceleration process in real traffic, while drivers have a memory for historical information. The collective effect may greatly affect driving behavior and traffic flow performance. In this paper, we propose a continuum model with the driver's memory time and the preceding vehicle's taillight. To better reflect reality, the continuous driving process is also considered. To this end, we first develop a unique version of a car-following model. By converting micro variables into macro variables with a macro conversion method, the micro car-following model is transformed into a new continuum model. Based on a linear stability analysis, the stability conditions of the new continuum model are obtained. We proceed to deduce the modified KdV-Burgers equation of the model in a nonlinear stability analysis, where the solution can be used to describe the propagation and evolution characteristics of the density wave near the neutral stability curve. The results show that memory time has a negative impact on the stability of traffic flow, whereas the provision of the preceding vehicle's taillight contributes to mitigating traffic congestion and reducing energy consumption.

Solving nonlinear evolution partial differential equations has been a longstanding computational challenge. In this paper, we present a universal paradigm of learning the system and extracting patterns from data generated from experiments. Specifically, this framework approximates the latent solution with a deep neural network, which is trained with the constraint of underlying physical laws usually expressed by some equations. In particular, we test the effectiveness of the approach for the Burgers' equation used as an example of second-order nonlinear evolution equations under different initial and boundary conditions. The results also indicate that for soliton solutions, the model training costs significantly less time than other initial conditions.

We explore some interesting phenomena in a simple non-Hermitian ladder system. Special modes with energy eigenvalues closely related to the inter-chain-coupling strength appear in the non-Hermitian ladder system. We show that a phase transition occurs whereby special modes with pure real eigenvalues can switch to special modes with pure imaginary eigenvalues, when the inter-chain-coupling strength changes from symmetric to asymmetric. We find that the density profiles of all the special modes are completely identical under certain conditions, even if the inter-chain-coupling strength is added into the non-Hermitian ladder system in different ways. Moreover, we also demonstrate that the different inter-chain couplings are fundamentally equivalent to adding different on-site potential energies into the non-Hermitian ladder system.

We study the skew information-based coherence of quantum states and derive explicit formulas for Werner states and isotropic states in a set of autotensors of mutually unbiased bases (MUBs). We also give surfaces of skew information-based coherence for Bell-diagonal states and a special class of X states in both computational basis and in MUBs. Moreover, we depict the surfaces of the skew information-based coherence for Bell-diagonal states under various types of local nondissipative quantum channels. The results show similar as well as different features compared with relative entropy of coherence and l₁ norm of coherence.

The standard model is a successful theory but is lacking a mechanism for neutrino mass generation as well as a solution to the naturalness problem. In the models that are proposed to simultaneously solve the two problems, heavy Majorana neutrinos and top partners are usually predicted to lead to a new decay mode of the top partner mediated by the heavy Majorana neutrinos: $T\to b\,{W}^{+}\to b\,{{\ell }}^{+}{{\ell }}^{+}q\bar{q^{\prime} }$. In this paper, we will study the observability of such a new signature via the pair production process of a top partner ${pp}\to T\bar{T}\to 2b+{{\ell }}^{\pm }{{\ell }}^{\pm }+4j$ in a model independent way. By performing Monte Carlo simulations, we present the 2σ exclusion limits of the top partner mass and mixing parameters at the HL-LHC.

We present complete next-to-leading-order (NLO) QCD correction and electro-weak (EW) correction to the production cross section of Higgs-Boson in association with two hard quark jets by using Monte-Carlo numerical calculation program, HAWK, for various photon parton distribution functions at the Large Hadron Collider with center of mass energy 7, 8, 13, and 14 TeV without and with typical vector-Boson-fusion cuts on the tagging jets. In our calculation we include complete contribution from the full set of t-channel, u-channel and s-channel Feynman diagrams, and corresponding interferences as well as NLO QCD and EW corrections.

We give a pedagogical analysis on K-matrix models describing the πN scattering amplitude, in S₁₁ channel at low energies. We show how the correct use of analyticity in the s-channel and crossing symmetry in t- and u-channels leads to a much improved analytic behavior in the negative s region, in agreement with the prediction from chiral perturbation amplitudes in its validity region. The analysis leads again to the conclusion that a genuine N*(890) resonance exists.

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger-Pauli equation and show that the spectrum of energy is a function of the Aharonov-Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.

We revisit the novel symmetries in ${ \mathcal N }=2$ supersymmetric quantum mechanical models by considering specific examples of coupled systems. Further, we extend our analysis to a general case and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry. Thus, we are able to provide a proof of the conjecture which points out the existence of more than one set of discrete symmetry transformations corresponding to the Hodge duality operator. Moreover, we derive on-shell nilpotent symmetries for a generalized superpotential within the framework of supervariable approach.

Five-dimensional (5D) fission potential energy surfaces (PES) for uranium nuclei are investigated based on the macroscopic-microscopic Lublin-Strasbourg drop model in the three-quadratic-surface parametrization, and the heights of static fission barriers are obtained. Asymmetric and symmetric fission paths are presented on the 5D PES of ²³⁶U for different nuclear shapes. The calculated barrier heights, E_A and E_B, are quite consistent with the experimental data for all even-even nuclei of uranium isotopes, from ²³⁰U to ²⁴⁴U.

Effective lambda-proton and lambda-neutron potentials, restored from theoretical scattering phases through Gel'fand-Levitan-Marchenko theory, are tested on a lambda hypertriton through three-body calculations. The lambda hypertriton is treated as a three-body system consisting of lambda-proton, lambda-neutron and proton-neutron subsystems. Binding energy and root mean square radius are computed for the ground state of lambda hypertriton (${J}^{\pi }=1/{2}^{+}$). In coordinate space, the dynamics of the system is described using a set of coupled hyperradial equations obtained from the differential Faddeev equations. By solving the eigenvalue problem derived from this set of coupled hyperradial equations, the binding energy and root mean square matter radius computed are found to be −2.462 MeV and 7.00 fm, respectively. The potentials are also shown to display a satisfactory convergence behaviour.

On the basis of a charged BTZ black hole, we add an extra term in the metric function to describe the contribution from nonlinear electrodynamics. In this way we artificially construct a (2 + 1)-dimensional black hole in general relativity coupled with a nonlinear electrodynamics source. The thermodynamic quantities and Smarr formula are derived. It is found that this black hole has T − S criticality like that of an RN-AdS black hole. Further modifying the metric function, we obtain a (2 + 1)-dimensional black hole possessing P − V critical behaviors similar to that of van der Waals fluid. To our knowledge, this is the first example of (2 + 1)-dimensional black holes having this kind of critical behavior.

Motivated by recent work, nonmonotonic behaviors of photon sphere radius can be used to reflect black hole phase transition for Reissner-Nordström-AdS (RN-AdS) black holes, we study the case of five-dimensional charged Gauss-Bonnet-AdS black holes in the reduced parameter space. We find that the nonmonotonic behaviors of photon sphere radius still exist. Using the coexistence line calculated from P-V plane, we capture the photon sphere radius of saturated small and large black holes (the boundary of the coexistence phase), then illustrate the reduced coexistence region. The results show that, reduced coexistence region decreases with charge Q but increases with Gauss-Bonnet coefficient α. When the charge vanishes, reduced coexistence region does not vary with Gauss-Bonnet coefficient α any more. In this case, the Gauss-Bonnet coefficient α plays the same role as the charge of five-dimensional RN-AdS black holes. Also, the situation of higher dimension is studied in the end.

The impedance spectroscopy, electrical conductivity and electric modulus of bulk phenol red were measured, as a function of both frequency and temperature. Artificial neural networks (ANNs) were used for modeling its electrical properties. The two parts (real and imaginary) of its complex impedance (Z*) were analyzed and the activation energy related to the electrical relaxation process was evaluated. Nyquist curves were plotted showing semicircles for the different temperatures. The AC electrical conductivity follows a power law σ_ac(ω) α ω^η. The maximum barrier height B_m was derived for specific temperatures. A plausible mechanism for the AC conduction of bulk phenol red was deduced from the temperature reliance of the frequency exponent. The dielectric data was analyzed using electric modulus as a tool. In addition, ANNs were used to model the impedance parts and the total electrical conductivity. Numerous runs were tried, to obtain the best performance. The training and prediction results were compared to the equivalent experimental results, with a good match obtained. An equation describing the experimental results was obtained mathematically, based on the use of ANNs. The outputs demonstrated that ANNs are an admirable tool for modeling experimental results.

To describe two correlated events, the Alice–Bob (AB) systems were constructed by Lou through the symmetry of the shifted parity, time reversal and charge conjugation. In this paper, the coupled AB system of the Kadomtsev–Petviashvili equation, which is a useful model in natural science, is established. By introducing an extended Bäcklund transformation and its bilinear formation, the symmetry breaking soliton, lump and breather solutions of this system are derived with the aid of some ansatze functions. Figures show these fascinating symmetry breaking structures of the explicit solutions.

Investigating the dynamic characteristics of nonlinear models that appear in ocean science plays an important role in our lifetime. In this research, we study some features of the paired Boussinesq equation that appears for two-layered fluid flow in the shallow water waves. We extend the modified expansion function method (MEFM) to obtain abundant solutions, as well as to find new solutions. By using this newly modified method one can obtain novel and more analytic solutions comparing to MEFM. Also, numerical solutions via the Adomian decomposition scheme are discussed and favorable comparisons with analytical solutions have been done with an outstanding agreement. Besides, the instability modulation of the governing equations are explored through the linear stability analysis function. All new solutions satisfy the main coupled equation after they have been put into the governing equations.

It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation, modified KdV equation, KdV–Burgers equation and Sharma–Tasso–Olver equation, demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well.

Under investigation in this paper is a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics. Soliton and one-periodic-wave solutions are obtained via the Hirota bilinear method and Hirota–Riemann method. Magnitude and velocity of the one soliton are derived. Graphs are presented to discuss the solitons and one-periodic waves: the coefficients in the equation can determine the velocity components of the one soliton, but cannot alter the soliton magnitude; the interaction between the two solitons is elastic; the coefficients in the equation can influence the periods and velocities of the periodic waves. Relation between the one-soliton solution and one-periodic wave solution is investigated.

In our previous work (Meng et al 2020 Phys. Rev. A 101 023838), we discover the phenomenon that the quantum entanglement on the driving threshold line remains a constant in a three-mode optomechanical phonon laser system. In this paper, to find the conditions under which the constant boundary entanglement shows up, we explicitly study how this boundary entanglement depends on various parameters through numerical integrations. The results show that the necessary and sufficient condition is a resonant frequency match between the optical frequency difference and the mechanical vibrational frequency, and this constant value is proportional to the multiplication of the square of the optomechanical coupling strength and the resonant driving threshold power.

In practical quantum key distribution (QKD) systems, a single photon-detector (SPD) is one of the most vulnerable components. Faint after-gate attack is a universal attack against the detector. However, the original faint after-gate attack can be discovered by monitoring the photocurrent. This paper presents a probabilistic generalization of the attack, which we refer to as probabilistic faint after-gate attack, by introducing probability control modules. Previous countermeasures for photocurrent monitoring may fail in detecting the eavesdropper under some specific probabilities. To mitigate this threat, we provide a method to determine the detectable boundary in the limitation of precision of photocurrent monitoring, and investigate the security of QKD systems under such boundaries using the weak randomness model.

Now, there have been many different methods to calculate one-loop amplitudes. Two of them are the unitarity cut method and the generalized unitarity cut method. In this short paper, we present an explicit connection between these two methods, especially how the extractions of triangle and bubble coefficients are equivalent to each other.