AbstractMathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations (FPDEs) corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n-truncated representation is substituted into the original system and it is assumed the (n − 1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some real-world applications. Finally, highlights and some closing comments are attached.

In this paper, a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota’s bilinear form and symbolic computation, lump and interaction solutions between lump and solitary wave are obtained, which include a periodic-shape lump solution, a parabolic-shape lump solution, a cubic-shape lump solution, interaction solutions between lump and one solitary wave, and between lump and two solitary waves. The spatial structures called the bright lump wave and the bright-dark lump wave are discussed. Interaction behaviors of two bright-dark lump waves and a periodic-shape bright lump wave are also presented. Their interactions are shown in some 3D plots.

AbstractIn this article, flow and heat transfer inside a corrugated cavity is analyzed for natural convection with a heated inner obstacle. Thermal performance is analyzed for CuO–water inside a partially heated domain by defining the constraint along the boundaries. For nanofluid analysis, the Koo and Kleinstreuer Li (KKL) model is implemented to deal with the effective thermal conductivity and viscosity. A heated thin rod is placed inside the corrugated cavity and the bottom portion of the corrugated cavity is partially heated. The dimensionless form of nonlinear partial differential equations are obtained through the compatible transformation along with the boundary constraint. The finite element method is executed to acquire the numerical solution of the obtained dimensional system. Streamlines, isotherms and heat transfers are analyzed for the flow field and temperature distribution. The Nusselt number is calculated at the surface of the partially heated domain for various numerical values of emerging parameters by considering the inner obstacle at cold, adiabatic and heated conditions. The computational simulation was performed by introducing various numerical values of emerging parameters. Important and significant results have been attained for temperature and velocities (in both x- and y-directions) at the vertically and horizontally mean positions of the corrugated duct.

This study investigates the (3+1)-dimensional soliton equation via the Hirota bilinear approach and symbolic computations. We successfully construct some new lump, lump-kink, breather wave, lump periodic, and some other new interaction solutions. All the reported solutions are verified by inserting them into the original equation with the help of the Wolfram Mathematica package. The solution’s visual characteristics are graphically represented in order to shed more light on the results obtained. The findings obtained are useful in understanding the basic nonlinear fluid dynamic scenarios as well as the dynamics of computational physics and engineering sciences in the related nonlinear higher dimensional wave fields.

Two nonlocal Alice–Bob Sawada–Kotera (ABSK) systems, accompanied by the parity and time reversal invariance are studied. The Lax pairs of two systems are uniformly written out in matrix form. The periodic waves, multiple solitons, and soliton molecules of the ABSK systems are obtained via the bilinear method and the velocity resonant mechanism. Though the interactions among solitons are elastic, the interactions between soliton and soliton molecules are not elastic. In particular, the shapes of the soliton molecules are changed explicitly after interactions.

AbstractIn this article, the analysis of Tsallis holographic dark energy (which turns into holographic dark energy for a particular choice of positive non-additivity parameter δ) in modified f (T, B) gravity with the validity of thermodynamics and energy conditions for a homogeneous and isotropic FLRW Universe has been studied. The enlightenment of the field equation towards f(T,B)=&agr;Tm+βBn, made possible by the fact that the model is purely accelerating, corresponds to q = −0.54 (Mamon and Das 2017 Eur. Phys. J. C 77 49). The generalized second law of thermodynamics is valid not only for the same temperature inside the horizon, but also for the apparent horizon for a change in temperature. The essential inspiration driving this article is to exhibit the applicability that the holographic dark energy achieved from standard Tsallis holographic dark energy and the components acquired from f(T, B) gravity are identical for the specific bounty of constants. The analysis of energy conditions confirms that the weak energy condition and the null energy condition are fulfilled throughout the expansion, while violation of the strong energy condition validates the accelerated expansion of the Universe. With the expansion, the model becomes a quintessence dominated model. The dominant energy condition is not observed initially when the model is filled with genuine baryonic matter, whereas it appears when the model is in the quintessence dominated era.

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.

AbstractWe study the behavior of information spreading in the XY model, using out-of-time-order correlators (OTOCs). The effects of anisotropic parameter γ and external magnetic field λ on OTOCs are studied in detail within thermodynamical limits. The universal form which characterizes the wavefront of information spreading still holds in the XY model. The butterfly speed vB depends on (γ, λ). At a fixed location, the early-time evolution behavior of OTOCs agrees with the results of the Hausdorff–Baker–Campbell expansion. For long-time evolution, OTOCs with local operators decay as for power law t−1, but those with nonlocal operators show different and nontrivial power law behaviors. We also observe temperature dependence for OTOCs when (γ = 0, λ = 1). At low temperature, the OTOCs with nonlocal operators show divergence over time.

AbstractIn this work, we study the theory of inflation with the non-minimally coupled quadratic, standard model Higgs, and hilltop potentials, through &xgr;&phi;2R term in Palatini gravity. We first analyze observational parameters of the Palatini quadratic potential as functions of &xgr; for the high-N scenario. In addition to this, taking into account that the inflaton field &phi; has a non-zero vacuum expectation value v after inflation, we display observational parameters of well-known symmetry-breaking potentials. The types of potentials considered are the Higgs potential and its generalizations, namely hilltop potentials in the Palatini formalism for the high-N scenario and the low-N scenario. We calculate inflationary parameters for the Palatini Higgs potential as functions of v for different &xgr; values, where inflaton values are both &phi; > v and &phi; < v during inflation, as well as calculating observational parameters of the Palatini Higgs potential in the induced gravity limit for high-N scenario. We illustrate differences between the Higgs potential&rsquo;s effect on &xgr; versus hilltop potentials, which agree with the observations for the inflaton values for &phi; < v and &xgr;, in which v < 1 for both these high and low N scenarios. For each considered potential, we also display ns &minus; r values fitted to the current data given by the Keck Array/BICEP2 and Planck collaborations.

We develop a variational theory for a dipolar condensate in an elongated (cigar shaped) confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.

AbstractWe explore the existence of monogamy relations in terms of R&eacute;nyi-&agr; entanglement. By using the power of the R&eacute;nyi-&agr; entanglement, we establish a class of tight monogamy relations of multiqubit entanglement with larger lower bounds than the existing monogamy relations for &agr; &ge; 2, the power &eegr; > 1, and 2>&agr;&ge;7&minus;12, the power &eegr; > 2, respectively.

AbstractIntroducing the top partner is a common way to cancel the largest quadratically divergent contribution to the Higgs mass induced by the top quark. In this work, we study single top partner production in the tZ channel at e&gamma; collision in the littlest Higgs model with T-parity (LHT). Since it is well known that polarized beams can enhance the cross section, we analyze the signal via polarized electron beams, and photon beams. we have selected two decay modes for comparison, based on the leptonic or the hadronic decays of the W and Z from the top partner. We then construct a detailed detector simulation, and choose a set of cuts to enhance signal significance. For mode A(B), the capacity for exclusion in this process at s &equals; 3 TeV is comparable to the current experimental limits with L &equals; 1000 (500) fb&minus;1. If the integrated luminosity can be increased to 3000 fb&minus;1, the top partner mass mT&plus; can be excluded up to 1350 (1440) GeV at 2&sgr; level. We also considered the initial state radiation effect, and find that this effect reduces the excluding ability of the e&gamma; collision on the the top partner mass by approximately 10 GeV. Moreover, the ability to exclude the LHT parameter space at e&gamma; collision complements the existing research.

We propose a systematic way of finding solutions to the classical Yang&ndash;Mills equation with nontrivial topology. This approach is based on one of the Wightman axioms for quantum field theory, which is referred to as the form invariance condition in this paper. For a given gauge group and a spacetime with certain isometries, thanks to this axiom that imposes strong constraints on the general ansatz, a systematic way of solving the Yang&ndash;Mills equation can be obtained in both flat and curved spacetimes. In order to demonstrate this method, we recover various known solutions as special cases, as well as producing new solutions not previously reported in the literature.

AbstractIn this work, we study damped ion acoustic solitary wave structures in magnetized dense plasmas. The collisional effects of ions with electrons and neutrals are considered. The trapping effects of electrons and Landau quantization are included in the plasma model under consideration. We assume that magnetic field is quantized such that the condition kBT<&hbar;&ohgr;ce is satisfied. We have derived the damped Korteweg&ndash;de Vries (dKdV) equation by using small amplitude reductive perturbation technique. The time-dependent analytical and numerical solutions of the dKdV equation are presented. For numerical solutions we apply a two level finite difference scheme with the help of the Runge Kutta method. The effects of variations of different plasma parameters on the propagation characteristics of damped solitary structures in the presence of collisions are discussed.

In this paper, four optical filter topologies based on metal&ndash;insulator&ndash;metal waveguides are proposed and the designed structures are investigated numerically using finite-difference time-domain method. Triangular-shaped adjunctions have been added to the filter structures to improve their transmission spectrum. These improved structures consist of air as the insulator and silver as the metal. The relative permittivity of metal has been described via the Drude, Drude&ndash;Lorentz, and Palik models. The first filter&rsquo;s transmission spectrum shows an acceptable transmittance. In the second optimized filter, the transmission spectrum has been improved. The transmittance spectrum can be tuned through adjusting the edge of the triangle in these four optimized filters. As a result, the bandwidths of resonance spectra can be adjusted. The theory of such tapered structures will be investigated by the tapered transmission line and will be solved with the transfer matrix method. This method shows a better performance and higher transmission efficiency in comparison with the basic structures. On the other hand, the final filter has been chosen as the best one because of its hexagonal resonator. The main reason for having a better result is due to a longer interaction length in comparison with the circular resonator. This in turn creates much better energy coupling and results in higher transmission.

This study aims to investigate the time-dependent squeezing of nanofluid flow, comprising carbon nanotubes of dual nature, e.g. single-walled carbon nanotubes, and multi-walled carbon nanotubes, between two parallel disks. Numerical simulations of the proposed novel model are conducted, accompanied by Cattaneo-Christov heat flux in a Darcy-Forchheimer permeable media. Additional impacts of homogeneous&ndash;heterogeneous reactions are also noted, including melting heat. A relevant transformation procedure is implemented for the transition of partial differential equations to the ordinary variety. A computer software-based MATLAB function, bvp4c, is implemented to handle the envisioned mathematical model. Sketches portraying impacts on radial velocity, temperature, and concentration of the included parameters are given, and deliberated upon. Skin friction coefficient and local Nusselt number are evaluated via graphical illustrations. It is observed that the local inertia coefficient has an opposite impact on radial velocity and temperature field. It is further perceived that melting and radiation parameters demonstrate a retarding effect on temperature profile.

AbstractRecently, Wu et al (2019 Int. J. Theor. Phys.58 1854) found a serious information leakage problem in Ye and Ji&rsquo;s quantum private comparison protocol (2017 Int. J. Theor. Phys.56 1517), that is, a malicious participant can steal another&rsquo;s secret data without being detected through an active attack means. In this paper, we show that Wu et al&rsquo;s active attack is also effective for several other existing protocols, including the ones proposed by Ji et al and Zha et al (2016 Commun. Theor. Phys.65 711; 2018 Int. J. Theor. Phys.57 3874). In addition, we propose what a passive attack means, which is different from Wu et al&rsquo;s active attack in that the malicious participant can easily steal another&rsquo;s secret data only by using his own secret data after finishing the protocol, instead of stealing the data by forging identities when executing the protocol. Furthermore, we find that several other existing quantum private comparison protocols also have such an information leakage problem. In response to the problem, we propose a simple solution, which is more efficient than the ones proposed by Wu et al, because it does not consume additional classical and quantum resources.