Modern Physics Letters B

Due to the influence of diverse factors, travel time is highly uncertain. Travelers are eager to find the most reliable path in multimodal networks to reduce the penalty caused by late arrival. However, the research considering the traveler preferences in multimodal transportation networks to solve the reliable path problem with given budgets is limited. Thus, we propose two multimodal reliable path models to find personalized and reliable paths. First, we build a multimodal network based on smart card data to incorporate the multimodal transfers between public and private transportation and solve corresponding parking issues effectively. Next, we build a multimodal time-reliable path model to find time-reliable paths. Further, considering traveler preferences, we design a multimodal utility-reliable path model to find personalized and reliable paths. A novel two-factor reliability bound convergence algorithm is developed to solve the proposed models and proved for its theoretical feasibility. Finally, a real-world case study is used to verify the effectiveness and efficiency of the proposed models and algorithm.

In this paper, the solitary solutions of the (1 + 1)-dimensional Benjamin–Bona–Mahony and strain wave equations are set up by employing the simplest equation method for the first time. By determining the value of parameters, the images of the traveling wave solutions are displayed, and they intuitively reflect that choosing different Bernoulli equations will affect the form of solutions. The validity and wider applicability of the method for solving known wave phenomena models are verified, moreover, the solution structure is enriched.

In this paper, a novel four-dimensional fractional-order chaotic system is proposed, and its dynamic characteristics are analyzed by equilibrium points, phase diagram, Lyapunov exponent spectrum and bifurcation diagram. Then, the electronic circuit of the chaotic system is designed and implemented by PSpice. The results of numerical simulation are in good agreement with the analog circuit simulation. In addition, the four-dimensional fractional-order system is implemented with field programmable gate array (FPGA). Finally, the synchronization of two four-dimensional chaotic systems with different initial values is realized by finite time control method, and it is also realized by FPGA. The design of fractional-order system based on hardware concerned in this paper will provide a certain theoretical basis for its application in the fields of secure communication, image encryption and so on.

The dynamics of Bose–Einstein condensates in a one-dimensional ring optical lattice is related to the interplay of the open system conditions and the initial atomic distribution. The circulation evaluation model based on the relative atomic density on each site is established to analyze the circulation strength under low dissipation. The direction of the circulation due to the symmetry breaking can be manipulated by changing the primary atomic distribution and the number of lattice sites. The effect of the atomic interaction on the atom flow in the optical ring lattice is analyzed to maintain the current interval rotation behavior.

The Jacobi elliptic function expansion method is one of the most powerful tools for exploring exact solutions of nonlinear partial differential models, which is used in this work to characterize the interaction between one long longitudinal wave and one short transverse wave propagation in a generalized elastic medium. First, we applied a wave transform to the proposed system of equations and obtained an ordinary differential equation. We obtain the values of involved free parameters after performing necessary operations, then substitute the obtained values to the ordinary differential equation by considering the constructed solutions to the ordinary and then to the partial differential equation. As a result, different structures of solutions are constructed such as solitary dark–bright, dark, bright, singular, trigonometric function, Jacobi elliptic function, and hyperbolic function solutions. In order to illustrate the tsunami and tidal oscillations, we draw 3D surfaces and 2D graphics for the obtained solutions by giving a specific value for the involved parameters under the given conditions.

In this paper, based on the Hodgkin–Huxley (H-H) neuron model, three distinct types of noises are introduced into the input of the neuron. The noises are Gaussian white noise (GWN), Lévy noise and Colored noise, separately. The phenomenon of stochastic resonance under and above threshold in one-dimensional H-H neuron is discussed. First, the responses of H-H neuron to different input signal frequency, amplitude and constant offset stimulation are researched. The neuron membrane potential diagram and spectrum diagram are given. Then, the mutual information rate (MIR) is taken as the evaluation index. The results show that adding a noise of certain intensity can increase the response of neuron to the orignal signal and the MIR between the output and input of neuron has unimodal property, which proves the existence of stochastic resonance under and above the threshold. We also find that neurons have frequency selectivity and different transmission performance for different amplitude of input signals. In addition, the constant offset stimulus should not be too large. Finally, it is discovered that the adaptability of subthreshold stochastic resonance and suprathreshold stochastic resonance (SSR) characteristics characteristics of one-dimensional H-H neurons induced by three distinct types of noises is different. What is more important is that the results of this paper will be instrumental in the future researching on the affect of these three noises in the stochastic resonance of neuron networks.

Galerkin method for scrutinizing the treatment of system during solidification of water has been implemented in existence of alumina nanoparticle. Cylinder and blade shapes of nanoparticles have been dispersed in to water in considering concentration less than 0.04. With neglecting the gravity force impact during freezing process, there exist only energy equations which should involve phase change term as mathematical model. Such equation has been coupled with equation for fraction of solid phase and final equations have been solved numerically. The configuration of grid has been considered variable according to position of ice front. As amount of $m$ increases, the freezing period declines around 10.7% owing to greater conductivity of Nanoparticle Enhanced Phase Change Material (NEPCM). With dispersing nanoparticles, the required time for solidification declines around 47.7%.

Optical properties of a new two-dimensional (2D) Dirac carbon material Phagraphene have been investigated by first-principles calculations based on density functional theory (DFT). We have studied the complex dielectric function, absorption spectrum and reflection spectrum of Phagraphene under different polarizations. Our results show that optical properties of this 2D Dirac carbon material show strong anisotropy under different polarized light. Phagraphene has a high real part of static dielectric function, which indicates that the material has considerable carrier mobility and conductivity and is expected to have a wide application in the next generation new nanoelectronic devices. In addition, Phagraphene has a wide-frequency optical response in the range from zero frequency to ultraviolet, showing its promising prospect of being applied in optoelectronic devices.

This study investigates the Hamiltonian amplitude equation by using the generalized exponential rational function method. As a result, a variety of soliton solutions have been established with different wave structures such as optical exponential, dark, singular, periodic, periodic-singular, and hyperbolic solutions. 2D and 3D graphics of certain acquired solutions are drawn with the help of computer program. By picking appropriate values for the free parameters in the obtained solutions, the physical phenomena for these obtained solutions are graphically studied and depicted.

This paper reveals optical soliton solutions to fiber Bragg gratings (FBGs) with dispersive reflectivity having Kerr law of nonlinear refractive index. Bragg gratings are no doubt a technological spectacle that sustained balance between dispersion and the nonlinear effects that leads to a stable transmission of solitons across intercontinental distances. FBGs as sensor elements are used for measuring numerous engineering parameters such as temperature, strain, pressure, tilt, displacement, acceleration, load. Two recently developed mechanisms such as the unified method and extended sinh-Gordon equation expansion method (ShGEEM) are successfully employed to secure optical pulses in the shapes of the bright, dark, singular, complex combo, periodic, and plane wave solutions. The achieved solutions contain key applications in engineering and physics. These solutions define the wave performance of the governing models. By selecting suitable parametric values, the dynamics of the evaluated results are exemplified by sketching their 2-dimensional, 3-dimensional, and contour profiles to understand the real phenomena for such sort of nonlinear models. The novelty of the gained outcomes is manifested by a detailed comparison with the results that already exist.

Materials with ultralow lattice thermal conductivity have attracted considerable interest in thermoelectrics and thermal management. Here, we have studied the lattice thermal conductivities in the layered material, hafnium germanium tetratelluride HfGeTe₄, by the first-principles calculations and revealed an ultralow out-of-plane lattice thermal conductivity of $0.3 \mathrm{\text{W}}\cdot {\mathrm{\text{m}}}^{-1}\cdot {\mathrm{\text{K}}}^{-1}$ at 300 K. HfGeTe₄ also had a large anisotropy in its lattice thermal conductivities, and the ${\kappa }_{xx}$/${\kappa }_{yy}$ ratio reached as high as 10.4 at 300 K. By analyzing its phonon dispersion, group velocities, and lifetimes, we find that the ultralow lattice thermal conductivity of HfGeTe₄ was mainly due to the small group velocities and short lifetimes of phonons, which was essentially caused by its heavy elements and complex layered crystal structure. Considering that HfGeTe₄ is a semiconductor with a moderate band gap, HfGeTe₄ would be a potential thermoelectric material. Our work sheds light on future studies on the thermoelectric properties of HfGeTe₄.

In this paper, the aluminum nitride (AlN) and gallium-doped aluminum nitride (AlGaN) films are adopted to fabricate the 3.5 GHz solidly mounted resonator (SMR) devices. A reactive radio frequency (RF) magnetron sputtering system and a co-puttering subsystem were used to deposit AlN and AlGaN thin films as piezoelectric layers. The sputtering parameters were fixed as sputtering pressure of 35 mTorr and sputtering power of 200 W for AlN piezoelectric layers. For the co-sputtering parameters, the sputtering pressure was set 10 mTorr, and the sputtering powers of Al and GaN targets were 175 W and 25 W, respectively, to deposit AlGaN piezoelectric layers. The X-ray diffraction (XRD) patterns showed that as compared with the 2$𝜃$ values of the diffraction peaks of AlN thin films, those of AlGaN thin films shifted to lower values. Even the diffraction intensity of (002) peak of AlGaN thin film was higher than that of AlN film, both AlN and AlGaN thin films presented the strongly $c$-axis orientated crystallization. The energy dispersive X-ray spectrometer (EDS) analysis showed that the content of Ga element in the AlGaN thin film, ($\mathrm{\text{Ga}}=(\mathrm{\text{Al}}+\mathrm{\text{Ga}})$), was about 19%. SEM images showed that the obtained AlN and AlGaN thin films exhibited uniform grain sizes and smooth surfaces. Finally, both the frequency responses of the fabricated SMR devices were measured using a network analyzer and the difference in their efficiencies were well compared. The frequency response of the fabricated SMR device with ${\text{Al}}_{0.81}$${\text{Ga}}_{0.19}$N thin film showed the center frequency of 3.51 GHz, the return loss $S_{11}$ of −10.466 dB, quality factor $Q$ of 170.952, electromechanical coupling coefficient $k_t^2$ of 4.026%, and FoM value of 6.838, respectively. The results show that the frequency response of SMR device has been improved by Ga doped in AlN thin film, although the $Q$ value is still less than that of obtained using single crystalline AlGaN thin film.