Narrow Results

This paper provides an innovative idea to perform the analysis of entropy generation in the time-dependent flow of Williamson liquid toward an oscillating curvy porous surface. The characteristics of the transport phenomenon are improved by taking thermal and mass relaxation parameters in the energy and concentration equations respectively by utilizing a modulated form of Fourier and Fick laws known as Cattaneo–Christov heat and mass flux models. The mathematical form of the entire flow model is simplified by incorporating a curvilinear coordinate system. The obtained set of partial differential equations is then solved by the homotopy analysis method (HAM) which transforms them into convergent series form. The effects of various pertinent flow parameters on dimensionless pressure, entropy generation, velocity, and temperature fields are shown graphically. Furthermore, the variations in Sherwood number, skin friction coefficient, and local Nusselt number are presented in tabular form. It is observed from this study that the temperature and entropy generation increase with the radius of curvature parameter.

This paper presents a new analytical method for the solution of the vibration frequencies of rectangular plates with cutouts. The cutouts may be internal or bordering the edges of the plate. In this work, a newly derived exact solution for the vibrations of rectangular plates for all the possible combinations of boundary conditions is extended for the solution of the vibrations of rectangular plates with cutouts. The problem is modeled as an assembly of plates. The continuation requirements along the connecting edges are enforced as part of the solution. The accuracy of the solution is studied through comparisons with published results from other methods.

L-shaped moderately thick plates have widespread applications in diverse engineering structures. Exploring the benchmark analytic solutions for the free vibration of L-shaped moderately thick plates is important in order to accurately analyze and efficiently design structures. Nevertheless, analytical solutions, which serve as the benchmarks, have been rarely documented in previous literature due to the challenge of finding suitable solutions that satisfy both the governing higher-order partial differential equations (PDEs) and the boundary conditions of the plates. The symplectic superposition method was employed in our recently published study to present the benchmark vibration solutions of clamped rectangular moderately thick plates. In this study, we expand upon this method to solve the free vibration problem of L-shaped moderately thick plates. By employing domain decomposition, we construct an irregular domain by combining multiple rectangular domains. First, the construction of the superposition system is carried out, followed by the import of the sub-problems into the Hamiltonian system, utilizing the fundamental governing equations of the plate. Then, the sub-problems are resolved through the application of the symplectic geometry methodology in an analytical manner. Ultimately, the analytical solutions for frequencies and mode shapes are derived through ensuring the equivalence between the initial problem and the combination of sub-problems. The finite element method is used to validate and present a comprehensive analysis of the natural frequencies and mode shapes obtained from this method. This method possesses the benefits of rapid convergence and accurate precision, rendering it well suited for the analytic modeling of a broader range of plate-related problems.

In high-energy heavy-ion collisions, a nearly perfect fluid, the so-called strongly coupled quark–gluon plasma (QGP), forms. After the short period of thermalization, the evolution of this medium can be described by the laws of relativistic hydrodynamics. The time evolution of the QGP can be understood through direct photon spectra measurements, which are sensitive to the entire period between the thermalization and the freeze-out of the medium. I present a new analytic formula that describes the thermal photon radiation and it is derived from an exact and finite solution of relativistic hydrodynamics with accelerating velocity field. Then I compare my calculations to the most recent nonprompt spectrum of direct photons for $\mathrm{\text{Au}}+\mathrm{\text{Au}}$ at $\sqrt{s_{NN}}=200$GeV collisions. I have found a convincing agreement between the model and the data, which allows to give an estimate of the initial temperature in the center of the fireball. My results predict hydrodynamic scaling behavior for the thermal photon spectra of high-energy heavy-ion collisions.

In this work, a new high accuracy solution for vibrations of structures made of plate segments is presented. Each plate segment is deforming both in and out of its plane, and the edges common to two plate segments must have compatible displacements, rotations, shear forces, and moments. It is obtained by using carefully chosen series that solve the combined partial differential equations of motion, for in-plane and out-of-plane deformations for all possible combinations of edge conditions. The number of terms in the series is taken such that convergence is ensured to the number of digits as shown. Examples of the new solutions are given and compared with available solutions for the same cases.

This paper presents some new analytic thermal buckling solutions of temperature-dependent moderately thick functionally graded (FG) rectangular plates with non-Lévy-type constraints within the symplectic solution framework in the Hamiltonian system. An original problem is reduced to the superposition of two constructed subproblems that are analytically solved via the rigorous symplectic elasticity approach with mathematical techniques such as variable separation in the symplectic space and symplectic eigen expansion. The physical neutral surface is employed to remove the stretching-bending coupling in constitutive equations. The main characteristic of the present symplectic superposition strategy is on the rational derivation without assumption on solution forms, which, however, is hard to achieve by conventional semi-inverse methods. Comprehensive benchmark results are presented, including critical buckling temperatures as well as mode shapes of typical non-Lévy-type FG plates in uniform and nonlinear temperature fields, and are verified by available numerical results. The effects of boundary constraint, aspect ratio, volume fraction exponent, and thickness-to-width ratio on buckling temperatures are quantitatively investigated. The occurrence of thermal buckling is further studied by presenting a failure mode map covering a wide range of geometric parameters.

The nonlinear capacitor that obeys of a cubic polynomial voltage–charge relation (usually a power series in charge) is introduced. The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated, and the Hamiltonian of a quantum mesoscopic electrical circuit comprised by a linear inductor, a linear resistor and a nonlinear capacitor under the influence of a time-dependent external source is expressed. Using the numerical solution approaches, a good analytic approximate solution for the quantum cubic Duffing equation is found. Based on this, the persistent current is obtained antically. The energy spectrum of such nonlinear electrical circuit has been found. The dependency of the persistent current and spectral property equations to linear and nonlinear parameters is discussed by the numerical simulations method, and the quantum dynamical behavior of these parameters is studied.

Full encapsulating rock bolts are widely used in mining and civil engineering to keep the stability of underground excavations. Nevertheless, decoupling at the interface between the bolt and grout (first interface) still occurs. To disclose the loading mechanism of the bolting system and preventing decoupling at the first interface, experimental and analytic studies were conducted in this paper. First, a nonlinear shearing-slipping law is used to describe the coupling and decoupling behavior of the first interface. Then, this shearing-slipping law is merged into the anchorage body. Following this, the whole loading process is divided into two components: elastic period and elastic-plastic period. Consequently, the analytic force-deformation relation of bolts is obtained. To confirm the rationality of this solution, experimental tensile tests on bolts were performed. It shows that there was a good match between analytic results and experimental tests. With the confirmed analytic solution, a parameter study is performed to investigate the impact of shearing-slipping parameters on the bolting performance. It indicates that increasing the shearing strength of the first interface and the shearing slipping have a positive impact in improving the bearing capacity of bolts. Inversely, the softening coefficient for the post-failure stage has a negative impact on determining the bearing capacity of bolts. Overall, the shearing strength of the first interface has a major impact in determining the loading performance of bolts.

The “separability problem” in quantum information theory is a quite important and well-known hard problem. The low-dimensional system satisfies the PPT criterion. However, the high-dimensional system problem has been shown to be NP-hard problem. In general, it is very difficult to find the analytic solution of the density matrix for the high-dimensional system. Therefore, getting an analytic solution for two-qubit system is an interesting and useful problem. We propose a novel criterion for separability and entanglement-verification of two-qubit system. We expressed the density matrix by a sum of a principal density matrix and six separable density matrices. The necessary and sufficient conditions for the two-qubit system include that if the four involved coefficients $p\ge 0$, $p_0\ge 0$, $p_1\ge 0$, $p_2\ge 0$ and the principal density matrix ${\rho }_p$ are separable, then the two-qubit system is separable, otherwise the two-qubit system is entangled. Finally, our criterion results in a totally different conclusion compared to Horodecki’s criterion. We believe that the new criterion is more stringent than existing PPT methods.

In this work, a new method is used for the exact vibration analysis of plates with classical boundary conditions. Four classical edge conditions are included: C — clamped, S — Simply supported, F — free, and G — guided. For square plates, all the possibilities add up to 55 cases. The solutions for the natural frequencies of the plates are found in this paper using static analysis. Starting from the equations of motion of an isotropic rectangular thin plate supported on Winkler elastic foundation, with a positive or negative value, the solution for the vibration frequencies of the plate is equivalent to finding the values of the negative elastic foundation that will yield infinite deflection under a point load on the plate. The solution is composed of three parts, the sum of which satisfies exactly both the field equation and the boundary conditions. For zero force, the vibration frequencies are found up to the desired accuracy. Benchmark results of the first six normalized natural frequencies, of isotropic square plates, for all possible 55 combinations of classical boundary conditions are given, many for the first time.

The geodesics equations on de Sitter (dS) and anti-de Sitter (AdS) spacetimes of any dimensions, are the starting point for deriving the general form of the Boltzmann equation in terms of conserved quantities. The simple equation for the non-equilibrium Marle and Anderson–Witting models are derived and the distributions of the Boltzmann–Marle model on these manifolds are written down first in terms of conserved quantities and then as functions of canonical variables.

In this paper, the implications of considering interaction between Chaplygin gas and a barotropic fluid with constant equation of state have been explored. The unique feature of this work is that assuming an interaction $Q\propto H{\rho }_d$, analytic expressions for the energy density and pressure have been derived in terms of the hypergeometric ${}_2{\text{F}}_1$ function. It is worthwhile to mention that an interacting Chaplygin gas model was considered in 2006 by Zhang and Zhu, nevertheless, analytic solutions for the continuity equations could not be determined assuming an interaction proportional to $H$ times the sum of the energy densities of Chaplygin gas and dust. Our model can successfully explain the transition from the early decelerating phase to the present phase of cosmic acceleration. Arbitrary choice of the free parameters of our model through trial and error shows that recent observational data strongly favors $w_m=0$ and $w_m=-\frac{1}{3}$ over the $w_m=\frac{1}{3}$ case. Interestingly, the present model also incorporates the transition of dark energy into the phantom domain, however, future deceleration is forbidden.

Oceanic ridges could act as waveguides transferring tsunami energy to thousands of kilometers away, pumping large energy in to far-field regions as a secondary source. The shallow-water wave velocity $c={(gh)}^{1/2}$ can only predict the arrival time of the early signals accurately but can hardly estimate that of ridge-trapped waves. The present study provides a fast analytic prediction method to estimate the arrival time of the subsequent large trapped waves. The method is based on the energy velocity solution of trapped waves over the uniform parabolic-shaped submerged ridge. Records of two-tide gauge stations, located nearby Sand Island and Nawiliwili for the 2011 Tohoku tsunami are chosen to illustrate the application of this method. The Sand Island record shows typical open-ocean island characteristics that the maximum wave height is followed by rapid amplitude decay. While the Nawiliwili record is strongly affected by topographical trapping effect of the Hawaii Ridge, and several subsequent wave trains carrying large energy arrive within one day duration. Further investigations show that the present analytic method is able to estimate the arrival time for these distinguished subsequent trains.

This paper reports the work on the development and analysis of a model for quantum rings in which persistent currents are induced by Aharonov–Bohm (AB) or other similar effects. The model is based on a centric and annual potential profile. The time-independent Schrödinger equation including an external magnetic field and an AB flux is analytically solved. The outputs, namely energy dispersion and wavefunctions, are analyzed in detail. It is shown that the rotation quantum number $m$ is limited to small numbers, especially in weak confinement, and a conceptual proposal is put forward for acquiring the flux and eventually estimating the persistent currents in a Zeeman spectroscopy. The wavefunctions and electron distributions are numerically studied and compared to one-dimensional (1D) quantum well. It is predicated that the model and its solutions, eigen energy structure and analytic wavefunctions, would be a powerful tool for studying various electric and optical properties of quantum rings.

In this paper, we have studied the application of drug delivery in magnetohydrodynamics (MHD) peristaltic blood flow of nanofluid in a non-uniform channel. The governing equation of motion and nanoparticles are modeled under the consideration of creeping flow and long wavelength. The resulting non-linear coupled differential equation is solved with the help of perturbation. Numerical Integration has been used to obtain the results for pressure rise and friction forces. The impact of various pertinent parameters on temperature profile, concentration profile such as density Grashof number, thermal Grashof number, Brownian motion parameter, thermophoresis parameter and MHD is demonstrated mathematically and graphically. The present analysis is also applicable for three-dimensional profile.

In this paper, we present an innovative hybrid model for the valuation of equity options. Our approach includes stochastic volatility according to Heston (1993) [Review of Financial Studies6 (2), 327–343] and features a stochastic interest rate that follows a three-factor short rate model based on Hull and White (1994) [Journal of Derivatives2 (2), 37–48]. Our model is of affine structure, allows for correlations between the stock, the short rate and the volatility processes and can be fitted perfectly to the initial term structure. We determine the zero bond price formula and derive the analytic solution for European type options in terms of characteristic functions needed for fast calibration. We highlight the flexibility of our approach, by comparing the price and implied volatility surfaces of our model with the Heston model, where we in particular focus on the correlation structure. Our approach forms a comprehensive market model with an intuitive correlation structure that connects both the equity and interest market to the market volatility.

The (1+1)-dimensional higher-order Broer–Kaup (HBK) system is investigated in this paper. Painlevé test shows that there are two solution branches, one of which has the resonance -2. And an auto-Bäcklund transformation is obtained by the truncated Painlevé expansion. The new analytic solutions are presented by means of the auto-Bäcklund transformation, including the periodic and soliton-like solutions. Similarity reductions for the HBK system are given out to two ordinary differential equations (ODEs) through CK direct method.

Analytical formulations are presented for Saint-Venant's torsion of orthotropic piezoelectric hollow members. It is assumed that the cross-section consists of straight and curved segments with the same thickness. Governing equations are based on Prandtl's stress and electric displacement potential functions. Some examples are solved using the presented formulations and verified by the finite element method solutions. The results show the accuracy of the present method for torsional analysis of thin- to moderately thick-walled hollow bars.

In this paper, the vibration and primary resonance of electrostatically actuated microbridges are investigated, with the effects of electrostatic actuation, axial stress, and mid-plane stretching considered. Galerkin's decomposition method is adopted to convert the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. The homotopy perturbation method (a special case of homotopy analysis method) is then employed to find the analytic expressions for the natural frequencies of predeformed microbridges, by which the effects of the voltage, mid-plane stretching, axial force, and higher mode contribution on the natural frequencies are studied. The primary resonance of the microbridges is also investigated, where the microbridges are predeformed by a DC voltage and driven to vibrate by an AC harmonic voltage. The methods of homotopy perturbation and multiple scales are combined to find the analytic solution for the steady-state motion of the microbeam. In addition, the effects of the design parameters and damping on the dynamic responses are discussed. The results are shown to be in good agreement with the existing ones.

The cell membrane is an important organ of living cells, which has a complex structure influenced by the interaction between membrane proteins and cell membrane. On the basis of fluid motion and diffusion interaction, a simple model is proposed to evaluate quantitatively the effects of the protein size and membrane fluid velocity on the lateral diffusion of membrane proteins at the cell membrane. The study shows that the diffusion coefficient is a dominant factor on the lateral diffusion.