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<jats:p>Based on the framework of Kaniadakis’ statistics and its related kinetic theory, the Jeans instability for self-gravitational systems in the background of Eddington-inspired Born–Infield (EiBI) gravity is revisited. A dispersion relation generalizing the Jeans modes is derived by modifying the Maxwellian distribution to a family of power law distributions parameterized by the <jats:italic>κ</jats:italic> parameter. It is established that the <jats:italic>κ</jats:italic>-deformed Kaniadakis distribution has significant effects on the Jeans modes of the collisionless EiBI-gravitational systems. And as expected, in the limitation <jats:italic>κ</jats:italic> → 0, the corresponding results for Maxwellian case are recovered. The related result in the present work is valuable for the investigations involving the fields of astrophysics such as neutron stars, accretion disks, and relevant plasma physics, <jats:italic>etc</jats:italic>.</jats:p>

<jats:p>We report an attempt to reveal the nonlinear dynamic behavior of a classical rotating pendulum system subjected to combined excitations of constant force and periodic excitation. The unperturbed system characterized by strong irrational nonlinearity bears significant similarities to the coupling of a simple pendulum and a smooth and discontinuous (SD) oscillator, especially the phase trajectory with coexistence of Duffing-type and pendulum-type homoclinic orbits. In order to learn the effect of constant force on this pendulum system, all types of phase portraits are displayed by means of the Hamiltonian function with large constant excitation especially the transitions of complex singular closed orbits. Under sufficiently small perturbations of the viscous damping and constant excitation, the Melnikov method is used to analyze the global structure of the phase space and the feature of trajectories. It is shown, both theoretically and numerically, that this system undergoes a homoclinic bifurcation and then bifurcates a unique attracting rotating limit cycle. Finally, the estimation of the chaotic threshold of the rotating pendulum system with multiple excitations is calculated and the predicted periodic and chaotic motions can be shown by applying numerical simulations.</jats:p>

<jats:p>Complexity and abundant dynamics may arise in locally-active systems only, in which locally-active elements are essential to amplify infinitesimal fluctuation signals and maintain oscillating. It has been recently found that some memristors may act as locally-active elements under suitable biasing. A number of important engineering applications would benefit from locally-active memristors. The aim of this paper is to show that locally-active memristor-based circuits can generate periodic and chaotic oscillations. To this end, we propose a non-volatile locally-active memristor, which has two asymptotically stable equilibrium points (or two non-volatile memristances) and globally-passive but locally-active characteristic. At an operating point in the locally-active region, a small-signal equivalent circuit is derived for describing the characteristics of the memristor near the operating point. By using the small-signal equivalent circuit, we show that the memristor possesses an edge of chaos in a voltage range, and that the memristor, when connected in series with an inductor, can oscillate about a locally-active operating point in the edge of chaos. And the oscillating frequency and the external inductance are determined by the small-signal admittance <jats:italic>Y</jats:italic>(i<jats:italic>ω</jats:italic>). Furthermore, if the parasitic capacitor in parallel with the memristor is considered in the periodic oscillating circuit, the circuit generates chaotic oscillations.</jats:p>

<jats:p>Designing tunable molecular devices with different charge carriers in single-molecule junctions is crucial to the next-generation electronic technology. Recently, it has been demonstrated that the type of charge carriers depends on and can be tuned by controlling the molecular length and the number of interfacial covalent bonds. In this study, we show that the type of charge carriers can also be tuned by controlling the material and shape of electrodes. N-heterocyclic carbenes (NHCs) have attracted attention because of their ability to form strong, substitutional inert bonds in a variety of metals. Also, NHCs are more stable than the widely used thiol group. Therefore, we use electrodes to tune the type of charge carriers in a series of NHCs with different side groups. The <jats:italic>ab initio</jats:italic> calculations based on non-equilibrium Green’s formalism combined with density functional theory show that the dominant charge carrier switches from electrons to holes when gold electrodes are changed into platinum ones. The nature of the charge carriers can be identified by variations in the transport spectra at the Fermi level (<jats:italic>E</jats:italic> <jats:sub>F</jats:sub>), which are caused by the side groups. The projections of transport spectra onto the central molecules further validate our inferences. In addition, the transmission coefficient at <jats:italic>E</jats:italic> <jats:sub>F</jats:sub> is found to be dependent on the atomic interface structure. In particular, for the NHC without methyl or ethyl side groups, connecting a protruding atom on the electrode surface significantly enhances the transportability of both electrode materials. Overall, this study presents an effective approach to modifying transport properties, which has potential applications in designing functional molecular devices based on NHCs.</jats:p>

<jats:p>We investigate the alignment dependence of the strong laser dissociation dynamics of molecule <jats:inline-formula> <jats:tex-math> <?CDATA ${{\rm{C}}}_{2}{{\rm{H}}}_{2}^{2+}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">C</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msubsup> <mml:mi mathvariant="normal">H</mml:mi> <mml:mn>2</mml:mn> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_11_113202_ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> in the frame of real-time and real-space time-dependent density function theory coupled with nonadiabatic quantum molecular dynamics (TDDFT-MD) simulation. This work is based on a recent experiment study “ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene” [Wolter <jats:italic>et al</jats:italic>, <jats:italic>Science</jats:italic> <jats:bold>354</jats:bold>, 308–312 (2016)]. Our simulations are in excellent agreement with the experimental data and the analysis confirms that the alignment dependence of the proton dissociation dynamics comes from the electron response of the driving laser pulse. Our results validate the ability of the TDDFT-MD method to reveal the underlying mechanism of experimentally observed and control molecular dissociation dynamics.</jats:p>

<jats:p>A fully developed electromagnetohydrodynamic (EMHD) flow through a microchannel with patterned hydrodynamic slippage on the channel wall is studied. The flow is driven by the Lorentz force which originates from the interaction between an externally imposed lateral electric field and a perpendicular magnetic field. The governing equations for the velocity with patterned slip boundary conditions are solved analytically by perturbation techniques under the assumption of small Reynolds number <jats:italic>Re</jats:italic>. In addition, the numerical solutions for the velocity are obtained by using the finite-difference method, and they are found to be in good agreement with the analytical solutions within admissible parameter range. The effects of different parameters on the velocity and volume flow rate due to patterned hydrodynamic slippage are discussed in detail, including wave-number <jats:italic>K</jats:italic>, Hartmann number <jats:italic>Ha</jats:italic>, amplitude <jats:italic>δ</jats:italic> of the patterned slip length, and normalized electric field strength <jats:italic>S</jats:italic>. The results show that patterned slippage over microchannel walls can induce transverse flows, which will increase the mixing rates in microfluidic devices. In addition, we also find that precise flow control can be achieved by controlling the magnetic flux and the wave-number and also by well choosing the electric field intensity. Our analysis can be used for designing the efficient micro-fluidic mixers.</jats:p>

<jats:p>We propose an on-chip reconfigurable micro-ring to engineer the spectral-purity of photons. The micro-ring resonator is designed to be coupled by one or two asymmetric Mach–Zehnder interferometers and the coupling coefficients hence the quality-factors of the pump and the converted photons can be dynamically changed by the interferometer’s internal phase-shifter. We calculate the joint-spectrum function and obtain the spectral-purity of photons and Schmidt number under different phases. We show that it is a dynamical method to adjust the spectral-purity and can optimize the spectral-purity of photons up to near 100%. The condition for high-spectral-purity photons is ensured by the micro-ring itself, so it overcomes the trade-off between spectral purity and brightness in the traditional post-filtering method. This scheme is robust to fabrication variations and can be successfully applied in different fabrication labs and different materials. Such high-spectral-purity photons will be beneficial for quantum information processing like Boson sampling and other quantum algorithms.</jats:p>

<jats:p>A traditional single-pixel camera needs a large number of measurements to reconstruct the object with compressive sensing computation. Compared with the 1/0 matrices in classical measurement, the 1/−1 matrices in the complementary measurement has better property for reconstruction computation and returns better reconstruction results. However, each row of the 1/−1 matrices needs two measurements with the traditional single-pixel camera which results into double measurements compared with the 1/0 matrices. In this paper, we consider the pseudo complementary measurement which only takes the same amount of measurements with the row number of some properly designed 1/0 matrix to compute the total luminous flux of the objective and derives the measurement data of the corresponding 1/−1 matrix in a mathematical way. The numerical simulation and experimental result show that the pseudo complementary measurement is an efficient tool for the traditional single-pixel camera imaging under low measurement rate, which can combine the advantages of the classical and complementary measurements and significantly improve the peak signal-to-noise ratio.</jats:p>

<jats:p>Polarization-insensitive multiple transparency windows are obtained with a graphene-based complementary metamaterial structure in terahertz regions, which is composed of two kinds of monolayer graphene perforated in shapes of a cross and four identical split rings that construct a resonator. The geometric parameters of resonators are different from each other. Numerical and theoretical results show that the quantum effect of Autler–Townes splitting is the key factor for appearance of transparency windows within the resonant dips. Further investigation demonstrates that by employing the fourfold-symmetry graphene complementary structure, polarization-independent transparency windows can be achieved. Moreover, multiple transparency windows can be separately manipulated over a broad frequency range via adjusting the chemical potential of the corresponding graphene resonators, and the bandwidth as well as resonance strength can also be tuned by changing the relative displacement between resonators each consisting of a cross and four split rings. The proposed metamaterial structure may be utilized in some practical applications with requirements of no polarization-varied loss and slowing the light speed.</jats:p>

<jats:p>We propose a two-dimensional metal grating with rhombus particles on a gold film structure for refractive index sensing due to its perfect absorption at near-infrared wavelength. Via two-dimensional metal grating coupling, the incident light energy is effectively transformed into the surface plasmons which propagate along the upper surface of the gold film and interact with the surrounding environment in a wide range. The plasmonic resonance mechanism of the structure is discussed in detail by theoretical analysis and finite-difference time-domain method. After optimizing the geometrical parameters, the designed structure shows the sensing performance with a refractive index sensitivity of 1006 nm/RIU. More importantly, this plasmonic refractive index sensor achieves an ultra wide refractive index sensing range from 1.0 to 2.4 with a stable sensing performance. The promising simulation results of the structure show that the sensor has a broad application prospect in the field of biology and chemistry.</jats:p>