Modern Physics Letters B

In this paper, a low-voltage and low-voltage power rail-to-rail operational amplifier is designed based on the research progress of low-voltage and low-voltage power rail-to-rail operational amplifier. Based on the level shift technology, the problem of limited common mode input range caused by constant threshold voltage under low voltage is effectively solved. Based on the SMIC 0.18 $\mu$m complementary metal-oxide semiconductor (CMOS) process, the operational amplifier has a slew rate of 9.3 V/$\mu$s and an establishment time of 0.41 $\mu$s. The power consumption of the operational amplifier is 0.52 mW. The effective area of the layout is about $310\times 190\mu$m².

In this research paper, we scrutinize the novel traveling wave solutions and other solutions with conformable, M-truncated and beta fractional derivatives for the nonlinear fractional Hirota–Maccari system. In order to acquire the analytical solutions, the Riccati–Bernoulli sub-ODE technique is implemented. Presented method is the very powerful technique to get the novel exact soliton and other solutions for nonlinear partial equations in sense of both integer and fractional-order derivatives. Mathematical properties of different kinds of fractional derivatives are given in this paper. A comparative approach is presented between the solutions with the fractional derivatives. For the validity of the solutions, the constraints conditions are determined. To illustrate the physical meaning of the presented equation, the 2D and 3D graphs of the acquired solutions are successfully charted by selecting appropriate values of parameters.

Nonlinear evolution equations play enormous significant roles to work with complicated physical phenomena located across the nature world. The Schrödinger type equations bearing nonlinearity are important models that flourished with the wide-ranging arena concerning plasma physics, nonlinear optics, fluid flow and the theory of deep-water waves. In this exploration, we retrieve the soliton and other solutions in an appropriate form to the coupled nonlinear Schrödinger equations by means of the improved tanh method and the rational $(G^{\prime }/G)$-expansion method. The suggested system of nonlinear Schrödinger equations is turned into a differential equation of a single variable through executing some operations. Thereupon, successful implementation of the advised techniques regains the abundant exact traveling wave solutions. The obtained solutions are figured out in the profiles of three-dimensional (3D), two-dimensional (2D) and contour by assigning suitable values of the involved unknown constants. These diverse graphical appearances enable the researchers to understand the underlying mechanisms of intricate phenomena of the leading equations. The individual performances of the employed methods are praiseworthy which deserve further application to unravel any other nonlinear partial differential equations arising in various branches of science.

In this paper, we investigate the structural design of beam splitters with high total transmission efficiency in the two-dimensional (2D) GaSb (Gallium Antimonide)-based photonic crystals, and several optimal structures for $1\times 2$ and $1\times 4$ Y-shaped beam splitters have been provided. Using our proposed alternating iteration algorithm, by introducing several microstructures in the bend and Y-shaped junction areas to achieve topology optimization, the design of Y-shaped beam splitters with high total transmission efficiency at 1550 nm makes great progress. The splitter structures are designed on 2D GaSb-based photonic crystals with a triangular lattice of air holes immersed in the GaSb. All designs are simulated numerically and analyzed by using the finite element method. The optimized structures of $1\times 2,1\times 4$ Y-shaped beam splitters show that our optimization technique is efficient and simple. And the total transmission efficiencies both over $72\%$ at output ports are obtained, which indicates that our method is relatively efficient to other methods in some related reports.

Biological, social and man-made systems often harbor various types of higher-order interaction, whose presence may substantially impact the dynamics on these systems. As a special random walk, paradigmatic trapping problem is still scarcely explored on networks encoding higher-order interactions. In this paper, applying simplicial networks produced by edge corona product as test bed, we explore how the higher-order interaction impact trapping process. Specifically, an immobile trap is first deployed at an initial node of the networks and average trapping time (ATT) is derived analytically to measure trapping efficiency of standard weight-dependent random walk. Then, delayed random walk incorporating delay phenomenon into random walk process is introduced into the networks and closed form solution of ATT is still obtained for quantifying trapping efficiency. The obtained analytical solutions of ATT in both scenarios show that ATT grows sub-linearly with network size but its leading scaling is quantitatively dependent on the parameter specifying building block of networks. Besides, analytical expression of ATT obtained in the latter scenario shows that the parameter $p$ manipulating delayed random walk does not affect the leading scaling of ATT but can quantitatively modify its prefactor. Therefore, introduction of delay phenomenon still can modulate trapping efficiency quantitatively in the presence of higher-order interaction. This work may pave the way for modulating trapping process and related dynamical processes on general networks modeling higher-order interactions.

To examine the hybrid nanomaterial transportation within a permeable region, a numerical approach was applied. The permeable domain was filled with a mixture of water with hybrid nanomaterial (Fe₃O${}_4+$ MWCNT). The wavy below wall experiences uniform flux but the top circular wall maintains at cold temperature. Magnetic field in $x$-direction was applied and non-Darcy formulation was applied for applying permeability effect. Gravity forces help the transportation of hybrid nanomaterial and magnetic forces reduce the speed of nanomaterial. Imposing nanomaterial can decline the irreversibility. For simulation of equations, CVFEM was applied and Bejan and Nu numbers were calculated. Verification test depicts the nice agreement and contours for irreversibility have been presented. By imposing Ha, the Be augments about 4.36% while Nu declines around 13.32%. By selecting greater Da, the Nu intensifies around 8.95% while Be declines about 4.35%. Nu elevates around 93.78% with an augment of Ra while Be drops around 52.75%.

Multilayer networks have received considerable attention because a network with one layer cannot be used to describe a complex system with multiple relationships inside it. In this paper, we encapsulate the high-speed railway network into dynamic multilayer infrastructures based on the information of train operations and the railway network topology constrained by geographic factors. In our multilayer railway network, each station defines a node and each train route defines a layer. In order to identify key stations in a multilayer network, we first propose some performance metrics to evaluate the importance of stations. Then, an information fusion method based on the Dempster–Shafer evidence theory is introduced. Through this method, the importance of each node in different layers can be fused, and the results of fusion are used to determine the importance of the stations in the whole multilayer network. Finally, some numerical experiments are discussed to illustrate the usefulness of the proposed method. The results developed in this study could provide guidance for improving traffic managements under emergencies.

In this paper, exact solutions of nonlinear Schrödinger equation with third-order dispersion in constant potential are achieved. This equation plays an important role in mathematical physics such as nonlinear optics. To deal with the mentioned equation, Bernoulli $(G/G)$-expansion method has been proposed by exerting some transformation and using homogenous balance. On the other hand, $(G/G)$-expansion method has also been used to obtain the addition results and find out the differences between the proposed method and the applied method. As a result of this study, the solutions of these two methods are expressed by hyperbolic function solutions and trigonometric function solutions. To have acceptable concept of dynamic structures of begotten results and find relation between these solutions and certain parameters, some figures are illustrated when the potential is taken as different values, which show us bright soliton and periodic wave. To complete our study, the Lagrangian and Hamiltonian of nonlinear Schrödinger equation with third-order dispersion are also established.

In this paper, the models of the Al${}_x$Ga${}_{1-x}$N nanowire array (NWA) are established through the Finite Difference Time Domain (FDTD). The results show that the best resonance-enhanced light absorption is obtained at $P=240$ nm, $D=160$ nm and $H=1000$ nm array structures, and the maximum can be close to 99% at a resonance wavelength of approximately 235 nm. With the external field, the peak collection efficiency rises to 32.75%.

In this paper, we introduce a class of treelike networks generated by motifs with single root node. We study the spectral properties of treelike networks by studying the behaviors of the corresponding adjacency matrix and Laplacian matrix. First, we get the adjacency matrix and Laplacian matrix of this treelike network. Then, we analyze symmetry of eigenvalues, multiplicity of eigenvalue $0$ and prove that its largest eigenvalue is strictly monotonically increasing and convergent. Finally, we introduce a new method to prove that the largest eigenvalue of the Laplacian matrix is strictly monotonically increasing and convergent. Also, we obtain that its smallest nonzero eigenvalue is strictly monotonically decreasing and convergent.

The complete classification of solutions to the Riemann problem of the good Jaulent–Miodek equation is investigated by Whitham modulation theory. The one-phase and two-phase periodic wave solutions and the corresponding Whitham equations are derived based on the Lax pair of the good Jaulent–Miodek equation and the finite-gap integration method. In particular, the N-phase periodic wave solutions are proposed by algebro-geometric approach. Then the basic wave structures of rarefaction waves and DSWs are proposed analytically and graphically, which makes it possible to establish the classification of all the possible wave patterns evolving from initial discontinuities. The asymptotic results given by Whitham modulation theory are in excellent agreement with direct numerical simulations. Finally, a detailed description of the shallow-water dam break problem is demonstrated to find the possible physical significance of the wave patterns found in this work.

In this paper, a (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation is studied from the governing equations of dusty plasma by means of multiscale analysis and reduced perturbation method. We utilize the generalized exponential rational function method to give various forms of analytical solutions with free parameters of the corresponding equation by using Mathematica software calculation. Then, appropriate parameter values are selected to draw the three-dimensional (3D) diagram and contour diagram of the analytic solutions. We also give the influence of these physical parameters on wave amplitude, waves profile, and stability of waves. The results show the generalized method is a reliable mathematical method to solve similar nonlinear equations in mathematical physics and these solutions can enrich the physical behavior of the equation in dusty plasma.