Modern Physics Letters B

We know energy and mass of a particle can be connected by $E=m{c}^2$. What is the physical basis of this relation? Historically, it was thought to be based on the principle of relativity (PR). A careful examination of the literature, however, indicated that this understanding is not true. Einstein did not derive this relation from PR. Instead, his argument was mainly based on thought experiments, which focused on the similarity between radiation and matter. Following this hint, we suspect that the mass–energy equivalence could be based on the quantum property of wave–particle duality. We know photon and electron can behave as a particle as well as a wave. Such a wave property could make the particle behave differently from Newtonian mechanics. Indeed, using a wave model which treats particles as excitations of the vacuum, we show that the mass–energy equivalence relation can be directly derived based on the quantum relations of Planck and de Broglie. This wave hypothesis has several advantages; not only can it explain naturally why particles can be created in the vacuum; it also predicts that a particle cannot travel faster than the speed of light. This hypothesis can also be tested in experiment.

This paper aims to study lump solutions to a class of (2+1)-dimensional nonlinear PDE systems, which involve the fourth-order Hirota derivative term: $D_t^2{D}_x{D}_y$. This Hirota derivative term generates higher-order derivatives of the temporal variable. Lump solutions to the resulting new class of nonlinear PDE systems are studied in detail via the Hirota bilinear method.

In this communication, design of asymmetrical multiple open slot loaded microstrip antenna for WiBro/WiMAX/WLAN band operation is presented. The substrate material is chosen as FR4 (${𝜀}_r=4.3$, $tan\delta =0.027$) and fed by coaxial feeding. This antenna is able to radiate at four resonating bands. The antenna is radiating between 2.29 and 2.39 GHz, which is suitable for Wireless Broadband, WiBro. In parallel to this design, this antenna is also radiating in (5.16–5.36 GHz and 5.725–5.825 GHz) range which cover Wireless Local Area Network, WLAN (5.2/5.8 GHz) bands. Moreover, this antenna is radiating in (3.28–3.65 GHz, 5.45–5.65 GHz) range which is suitable for Worldwide Interoperability for Microwave Access, WiMAX (3.5/5.5) GHz bands. Measured results have proven that there is a good agreement with the simulated results of farfield patterns, reflection coefficient, peak gain of the proposed asymmetrical multiple open slot loaded microstrip antenna. The volume of this design is $39\times 45\times 1.6{\mathrm{\text{mm}}}^3$. Radiation pattern is noticed as stable at all obtained resonating frequencies. Maximum gain of 4.2 dBi is achieved between 3.28 and 3.65 GHz frequency band.

The model of electrostatic Micro-Electromechanical System (MEMS) is considered without/with an external pressure. The model represents nonlinear elliptic or parabolic problem due to the steady or non-steady state problem, respectively. To obtain exact solutions in an explicit form, the symmetry analysis is considered. With symmetries, the transformations are obtained and by means of these transformations, solvable equations are hold. The obtained results have a major role in the literature so that the considered equation is seen in a large-scale applications.

The performance of thermoelectric (TE) thin films strongly depends on the substrates. In our previous study, we investigated the power factor (PF) 1.78 mW/$(\mathrm{\text{m}}\cdot {\mathrm{\text{K}}}^2)$ at 700 K in ${\mathrm{\text{MoO}}}_{2+x}$ thin film grown on single crystalline Si, comparable to the state of art in other TE thin films. Such boosted PF originates mainly from the significantly enhanced Seebeck coefficient, correlated with the contribution of the Si substrate. In this paper, the PF has been prominently optimized up to 12.5 mW/$(\mathrm{\text{m}}\cdot {\mathrm{\text{K}}}^2)$ at 668 K by adjusting the thickness of ${\mathrm{\text{MoO}}}_{2+x}$ film in the ${\mathrm{\text{MoO}}}_{2+x}$/Si system, which could be understood in the frame work of parallel slab model. Experimentally, the effective TE properties were susceptible to the substrate–film interface. The existence of Mo in ${\mathrm{\text{MoO}}}_{2+x}$ film might limit the formation of ${\mathrm{\text{SiO}}}_2$ interfacial layer. These results suggest a simple, low-cost, scalable technique route to explore highly effective TE devices.

In this paper, we propose a two-party and a three-party controlled quantum key agreement (QKA) protocols with three-qubit GHZ states and Bell measurements. Compared with previous protocols, the significant change of our schemes is that a supervisor is introduced for controlling the agreement process to improve the controllability. Moreover, our protocols ensure each communication participant contribute equally to the agreement keys, and all participants can negotiate the shared keys without exchanging classical bits between them. The performance analysis shows that our protocols can be immune to outsider and participant attack.

The periodic solutions for the $(2+1)$-dimensional complex modified Korteweg–de Vries (cmKdV) equation are obtained by using the Darboux transformation (DT). Starting with a periodic seed, we get two types of periodic solutions that are respectively, induced by different properties of the parameter $l_2$, namely, the periodic line wave solutions for $l_2=\alpha \in ℝ$ and the breather solutions for $l_2=\alpha {\lambda }_1$. Especially, for each type, two different kinds of solutions can be obtained via choosing different constrains, namely, $c-2\gamma \ge 0$ or $c-2\gamma <0$. The detailed dynamical characteristics of these solutions are also analyzed, including period, velocity, extreme values, amputations and the rules of temporal evolutions.

A hybrid protocol is proposed which utilizes secure clustering and hybrid soft computing to improve the network lifetime. Ant colony optimization (ACO) and Particle swam optimization (PSO) with crossover operator are used to design a hybrid soft computing-based inter-cluster data aggregation. Initially, cluster heads are selected based upon adaptive threshold function. Recommendation-based signatures are then assigned to every aggregated data. Then, tree-based data aggregation comes in action and collects sensing information directly from cluster heads by utilizing short distance obtained from the hybrid soft computing. The use of compressive sensing reduces the packet size which is going to be transmitted in the sensor network. Extensive analysis shows that the hybrid protocol considerably enhances network lifetime by conserving the energy in more efficient manner than other protocols at present deployed for sensor networks.

We propose a new approach of many-particle quantum hydrodynamics to describe a system of interacting magnetic skyrmions in the external fields. The model is based on the description of skyrmions as a fluid of point-like particles. The equations of many-particle quantum hydrodynamics are obtained for a system of skyrmions with induced dipole moments and charges. The dipole–dipole interaction between dipoles and the Coulomb interaction between charges are taken into account. The influence of quantum effects in the form of the Bohm quantum potential is obtained. The contribution of Magnus effect to the dynamics of dipoles current density is predicted. The electron–skyrmion interactions are considered, based on a two-fluid model of quantum hydrodynamics with separate description of spin-up and spin-down electrons on the background of skyrmion lattice. The proposed model can be further used to study the dynamical effects in a system of skyrmions in the external fields.

There are two ways to choose the generating functions of the gauge transformations $T_D(\mathrm{\Phi })={({\mathrm{\Phi }}^{-1})}_x^{-1}\partial {\mathrm{\Phi }}^{-1}$ and $T_I(\mathrm{\Psi })={\mathrm{\Psi }}^{-1}{\partial }^{-1}{\mathrm{\Psi }}_x$, when dicussing the gauge transformations for the constrained modified KP hierarchy. The first is to select the (adjoint) eigenfunctions, while the second is the (adjoint) wave functions. In this paper, we will mainly discuss the gauge transformations obtained by the second method. The corresponding successive applications are considered. Also, we investigate the results of the gauge transformation derived through the union of these two methods.

${\mathrm{\text{Bi}}}_2{\mathrm{\text{Se}}}_3$ is a ${\mathrm{\text{Pn}}}_2{\mathrm{\text{Ch}}}_3$ compound (where Pn = Bi and Sb, Ch = Te, Se, and S), which has attracted increasing attention as a candidate for use in thermoelectric applications. Previous studies demonstrated the advantage of ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Se}}}_3$ thermoelectric materials, despite an inferior thermoelectric performance. Herein, a series of ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Se}}}_{3-x}$ ($x=0.05$, 0.10, 0.15, 0.20, and 0.25) thermoelectric materials were prepared by powder compaction sintering. The effects of phase structures and microstructure of the ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Se}}}_{3-x}$ bulk material were analyzed by X-ray diffraction, scanning electron microscopy, and energy-dispersive X-ray spectroscopy. The thermoelectric properties, including Seebeck coefficient, electrical conductivity, and thermal conductivity, were measured systematically. The results show that carrier concentration increased with decreasing Se content, which in turn affected the electrical transport properties. Low Se contents gave larger power factor (PF) values than the pristine ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Se}}}_3$ sample, the maximum PF value being $540\mu {\mathrm{\text{Wm}}}^{-1}{\mathrm{\text{K}}}^{-2}$ at 320 K for ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Se}}}_{2.85}$. The variation in PF was attributed to the variations in electrical conductivity $(\sigma )$ and Seebeck coefficient $(\alpha )$ upon optimizing Se content. The ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Se}}}_{3-x}$ samples showed an enhanced thermoelectric figure of merit (ZT) with increasing measurement temperature, due to the increased $\left|\alpha \right|$ value, $\sigma$, and decreased $\kappa$. The ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Se}}}_{0.90}$ sample exhibited the highest ZT (0.28) at 575 K, while ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Se}}}_{0.85}$ exhibited the lowest ZT (0.14) at 325 K. This indicated that tuning Se content was an effective way to enhance carrier concentration.

We present a three-dimensional (3D) perfect metamaterial absorber (PMA) for temperature sensing application in terahertz region. The PMA consists of a 3D metal resonator structure array and a continuous metal film separated by an indium antimonide (InSb) layer. The numerical simulations demonstrate that the PMA can achieve perfect absorption (about 99.9%) with the high $Q$-factor of about 18.8 at 2.323 THz when the temperature is 300 K (room temperature). Further simulation results indicate that this terahertz PMA is polarization-insensitive and wide-angle for both transverse electric (TE) and transverse magnetic (TM) waves. The electric field and surface current distributions of the unit-cell structure indicate that the perfect absorption is originated from the excitation of the fundamental magnetic and electric dipole resonance mode. Since the permittivity of the InSb is sensitive to the external temperature, the resonance absorption frequency of the PMA can be dynamically adjusted. The temperature sensitivity of the PMA is about 15.24 GHz/K, which may have potential prospects in temperature sensing and detection.

A hybrid large eddy simulation (LES)/assumed subgrid probability density function (PDF) closure model was employed to investigate the structural characteristics of the combustion flow field in an ethylene-fueled supersonic combustor with a rear-wall-expansion cavity. The wall pressure distribution from numerical simulation was compared with experimental data, and the numerical results are in good agreement with the experimental data. The spatial distribution characteristics of combustion heat release in the flow field are obtained from the simulation results. The reaction heat release zone is mainly distributed in the cavity. The cavity shear layer forms a concentrated reaction zone that produces a large amount of chemical heat release, thus further maintaining local stable combustion and forming a flame base. The front part of the cavity shear layer has the highest temperature in the whole flow field. There is still excess fuel reaching the cavity rear wall and producing a certain intensity of reaction. In addition, a dispersed small flame intermittently forms in the downstream near-wall region. The premixed combustion mode dominates the cavity recirculation zone, while the combustion in the downstream region evidently shows a non-premixed mode.

Resonance dispersion mixing technology is a new process developed in recent years. The main function of the technology is each scale vortex caused by the vibration, which is a multiscale phenomenon that includes macroscopic vortices and mesoscopic vortices. For mesoscopic vortices, due to the lack of sufficient resolution, current commercial software filter and average these vortices, so it is difficult to meet the needs of research. Based on this, the paper proposes a lattice Boltzmann Method (LBM) to simulate the mesoscopic vortices. The LBM is a mesoscale research method, so it has sufficient resolution to study mesoscopic vortices. The paper mainly simulated the process of splitting and evolution of mesoscopic vortices, studied the effects of parameters such as simulation interval, viscosity, vibration frequency on mesoscopic vortices. The results show that the selection of the simulation interval has a certain influence on the evolution of the vortices. The viscosity of the flow field plays a decisive role in the vortices, for there is no vortex generation when the viscosity exceeds a certain threshold. The excitation frequency controls the development process of the vortices, larger frequency can significantly reduce the micro-mixing characteristic time to increase mixing efficiency. Different from the previous theoretical analysis literature, this paper gives visual numerical simulation results.