Search Results (32)

Electromagnetic torques generated by mutual inductance between energized coils are widely used in aerospace applications, especially for solar panel deployment. Accurate and rapid acquisition of mutual inductance between coils is essential to provide the necessary electromagnetic force. Therefore, based on the Kalantarov–Zeitlin method and the Neumann formula, this paper presents a straightforward and efficient calculation method for mutual inductance between rectangular coils positioned arbitrarily in space. Building on this foundation, we develop a calculation method for mutual inductance between rectangular multi-turn coils using the principle of superposition. The accuracy of the proposed method’s calculations is validated using data from the published literature, and the computation time is compared with that of other methods. To further validate the accuracy of the computational method proposed in this paper, a rectangular multi-turn coil mutual inductance measurement platform has been constructed. The results indicate that the computation time of the proposed method is shorter, and the calculation outcomes closely align with those obtained from other methods as well as experimental measurements. Furthermore, the calculation accuracy exceeds 95%, providing a reliable basis for determining the electromagnetic force required for the deployment of the solar array driven by electromagnetism. Full article

This paper investigates the derivation of global shape functions in T-meshed quadrilateral patches through transfinite interpolation and local elimination. The same shape functions may be alternatively derived starting from a background tensor product of Lagrange polynomials and then imposing linear constraints. Based on the nodal points of the T-mesh, which are associated with the primary degrees of freedom (DOFs), all the other points of the background grid (i.e., the secondary DOFs) are interpolated along horizontal and vertical stations (isolines) of the tensor product, and thus, linear relationships are derived. By implementing these constraints into the original formula/expression, global shape functions, which are only associated with primary DOFs, are created. The quality of the elements is verified by the numerical solution of a typical potential problem of second order, with boundary conditions of Dirichlet and Neumann type. Full article

This research examines a fractional partial advection–dispersion model, incorporating both mobile and immobile components, employing the Hilbert reproducing algorithm under an appropriate Neumann constraint condition. To effectively formulate the model while adhering to the specified constraints, two suitable Hilbert spaces are constructed, with the time-fractional Caputo derivative being utilized in the model’s formulation. Alongside the convergence analysis, a derived approximate solution formula is presented, and a systematic computational algorithm is developed to effectively implement the solution methodology. Numerical applications related to the proposed model are presented, complemented by tables and graphical illustrations. In conclusion, significant results are analyzed, and directions for future research are outlined. Full article

With the rapid development of quantum communication technologies, controlled double-direction cyclic (CDDC) quantum communication has become an important research direction. However, how to choose an appropriate quantum state as a channel to achieve double-direction cyclic (DDC) quantum communication for multi-particle entangled states remains an unresolved challenge. This study aims to address this issue by constructing a suitable quantum channel and investigating the DDC quantum communication of two-particle states. Initially, we create a 25-particle entangled state using Hadamard and controlled-NOT (CNOT) gates, and provide its corresponding quantum circuit implementation. Based on this entangled state as a quantum channel, we propose two new four-party CDDC schemes, applied to quantum teleportation (QT) and remote state preparation (RSP), respectively. In both schemes, each communicating party can synchronously transmit two different arbitrary two-particle states to the other parties under supervisory control, achieving controlled quantum cyclic communication in both clockwise and counterclockwise directions. Additionally, the presented two schemes of four-party CDDC quantum communication are extended to situations where $n>3$ communicating parties. In each proposed scheme, we provide universal analytical formulas for the local operations of the sender, supervisor, and receiver, demonstrating that the success probability of each scheme can reach 100%. These schemes only require specific two-particle projective measurements, single-particle von Neumann measurements, and Pauli gate operations, all of which can be implemented with current technologies. We have also evaluated the inherent efficiency, security, and control capabilities of the proposed schemes. In comparison to earlier methods, the results demonstrate that our schemes perform exceptionally well. This study provides a theoretical foundation for bidirectional controlled quantum communication of multi-particle states, aiming to enhance security and capacity while meeting the diverse needs of future network scenarios. Full article

The principal aim of this paper is to introduce the extended Voigt-type function ${\mathbb{V}}_{\mu ,\nu }(x,y)$ and its counterpart extension ${\mathbb{W}}_{\mu ,\nu }(x,y)$, involving the Neumann function $Y_{\nu }$ in the kernel of the representing integral. The newly defined integral reduces to the classical Voigt functions $K(x,y)$ and $L(x,y)$, and to their generalizations by Srivastava and Miller, by the unification of Klusch. Following an approach by Srivastava and Pogány, we also present the multiparameter and multivariable versions ${\mathbb{V}}_{\mu ,\nu }^{\left(r\right)}(x,y),{\mathbb{W}}_{\mu ,\nu }^{\left(r\right)}(x,y)$ and the r positive integer of the initial extensions ${\mathbb{V}}_{\mu ,\nu }(x,y),{\mathbb{W}}_{\mu ,\nu }(x,y)$. Several computable series expansions are obtained for the discussed Voigt-type functions in terms of Humbert confluent hypergeometric functions ${\Psi }_2^{\left(r\right)}$. Furthermore, by transforming the input extended Voigt-type functions by the Grünwald–Letnikov fractional derivative, we establish representation formulae in terms of the associated Legendre functions of the second kind $Q_{\eta }^{-\nu }$ in the two-parameter and two-variable cases. Finally, functional bounding inequalities are given for ${\mathbb{V}}_{\mu ,\nu }(x,y)$ and ${\mathbb{W}}_{\mu ,\nu }(x,y)$. Particularly interesting results are presented for the Neumann function $Y_{\nu }$ and for the Struve ${\mathbf{H}}_{\nu }$ function in the form of several functional bounds. The article ends with a thorough discussion and closing remarks. Full article

To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures–Hall ensemble, extending known results obtained recently over the Hilbert–Schmidt ensemble. Full article

This paper introduces a novel collocation scheme based on an extended cubic B-spline for approximating the solution of a second-order partial integro-differential equation. The proposed scheme employs new extended cubic B-splines to discretize the second-order derivatives in the spatial domain, while discretization of spatial derivatives of lower orders is achieved using extended cubic B-spline functions. Temporal derivatives are discretized using the forward difference formula. The stability of the algorithm is assessed using the von Neumann stability method to ensure that error magnification is avoided. Furthermore, convergence analysis of the scheme is provided. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed scheme. The free parameter is optimized using $L_2$ and $L_{\infty }$ norms. The computed results are compared with those obtained from various standard numerical schemes found in the literature. Mathematical 12 is used to obtain numerical results. Full article

This paper deals with second-order differential pencils with a fixed frozen argument on a finite interval. We obtain the trace formulae under four boundary conditions: Dirichlet–Dirichlet, Neumann–Neumann, Dirichlet–Neumann, Neumann–Dirichlet. Although the boundary conditions and the corresponding asymptotic behaviour of the eigenvalues are different, the trace formulae have the same form which reveals the impact of the frozen argument. Full article

In this paper, the tensile deformation behaviors of polycrystals after relaxation were studied using the phase-field-crystal (PFC) method. Here, the free energy density map characterized the 2D energy distribution of atomic configuration effectively. The application of the Read–Shockley equation distinguished high-energy grain boundary (HEGB) and low-energy grain boundary (LEGB) in large-angle grain boundary (LAGB), and they demonstrated different migration behaviors at the early and later stages. The behaviors of small-angle grain boundary (SAGB), including its migration and grains’ rotation, were also studied. Two different mechanisms of dislocation emission and absorption were explored, which demonstrates the possibility of dislocation elevating interfacial energy. The simulated results on the topological transition of grain boundaries prompted us to propose the thinking about the applications of the Neumann–Mullins law and Euler formula. Full article

In the present paper, we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field, whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, we generalize the results found in the literature in this scenario, which has considered only the vacuum energy at zero temperature. To do this, we use the generalized zeta function method plus Abel-Plana formula and calculate the renormalized Casimir free energy as well as other thermodynamics quantities, namely, internal energy and entropy. For each one of them, we also investigate the limits of high and low temperatures. At high temperatures, we found that the renormalized Casimir free energy presents classical contributions, along with a logarithmic term. Also in this limit, the internal energy presents a classical contribution and the entropy a logarithmic term, in addition to a classical contribution as well. Conversely, at low temperatures, it is demonstrated that both the renormalized Casimir free energy and internal energy are dominated by the vacuum energy at zero temperature. It is also demonstrated that the entropy obeys the third law of thermodynamics. Full article

The work is dedicated to mathematical modelling of random diffusion flows of admixture particles in a two-phase stratified strip with stochastic disposition of phases and random thickness of inclusion-layers. The study of such models are especially important during the creation of composite layered materials, in the research of the transmission properties of filters, and in the prediction of the spread of pollutants in the environment. Within the model we consider one case of uniform distribution of coordinates of upper boundaries of the layers of which the body is made up and two more cases, i.e., of uniform and triangular distributions of the inclusion thickness. The initial-boundary value problems of diffusion are formulated for flux functions; the boundary conditions at one of the body’s surfaces are set for flux and, at the other boundary, the conditions are given for admixture concentration; the initial condition being concerned with zero and non-zero constant initial concentrations. An equivalent integro-differential equation is constructed. Its solution is found in terms of Neumann series. For the first time it was obtained calculation formulae for diffusion flux averaged over the ensemble of phase configurations and over the inclusion thickness. It allowed to investigate the dependence of averaged diffusion fluxes on the medium’s characteristics on the basis of the developed software. The simulation of averaged fluxes of admixture in multilayered $Fe-Cu$ and $\alpha Fe-Ni$ materials is made. Comparative analysis of solutions, depending on the stage of averaging procedure over thickness, is carried out. It is shown that for some values of parameters the stage of averaging procedure over thickness has almost no effect on the diffusion flow value. Full article

We propose and analyze an effective decoupling algorithm for unsteady thermally coupled magneto-hydrodynamic equations in this paper. The proposed method is a first-order velocity correction projection algorithms in time marching, including standard velocity correction and rotation velocity correction, which can completely decouple all variables in the model. Meanwhile, the schemes are not only linear and only need to solve a series of linear partial differential equations with constant coefficients at each time step, but also the standard velocity correction algorithm can produce the Neumann boundary condition for the pressure field, but the rotational velocity correction algorithm can produce the consistent boundary which improve the accuracy of the pressure field. Thus, improving our computational efficiency. Then, we give the energy stability of the algorithms and give a detailed proofs. The key idea to establish the stability results of the rotation velocity correction algorithm is to transform the rotation term into a telescopic symmetric form by means of the Gauge–Uzawa formula. Finally, numerical experiments show that the rotation velocity correction projection algorithm is efficient to solve the thermally coupled magneto-hydrodynamic equations. Full article

Due to the numerous advantages such as being convenient, safe, and contactless, wireless power transfer (WPT) is becoming the mainstream charging method for electric vehicles. This paper presents a constant current WPT system with asymmetric loosely coupled transformer for electric forklifts using lead-acid batteries. First, based on the Neumann formula, this paper analyzes the mutual inductance of the coaxial rectangular coil, and designs an asymmetric loosely coupled transformer based on the practical application requirements, which makes the secondary side light and miniaturized. Second, the WPT system is analyzed in terms of the requirements of constant current charging, and the dual-LCL compensation is proposed according to the output current and power requirements. The transfer characteristics and anti-interference capability of the topology are analyzed. The constant current output feature of the system under the condition of variable load is demonstrated. After that, a dual-active bridge secondary-side independent control strategy is proposed, the phase shift angle is adjusted to ensure constant charging current and high efficiency of the system. Finally, a wireless charging experimental platform is established in accordance with the proposed asymmetric loosely coupled transformer and WPT system. The system can achieve 45 A constant current output and 3 kW output power with 91.2% transmission efficiency. Full article

Traditional interval analysis methods for interior vibro-acoustic system with uncertain-but-bounded parameters are based on interval perturbation theory. However, the solution sets by traditional interval finite-element methods are intrinsically not capable of reflecting the actual bounds of results, due to the non-conservative approximation for neglecting the high-order terms of both Taylor and Neumann series. In order to cope with this problem, this paper introduces the concept of unimodal components from structural mechanics to factorize the uncertainties, and a new enclosing interval-finite element method (enclosing-IFEM) is proposed to predict the uncertain vibro-acoustic response. In the enclosing-IFEM, the global matrix is assembled with the mixed-nodal-element strategy (MNE), which is different from the element-by-element assembly strategy. Thus, the vibro-acoustic coupling equation can be transformed into an iterative enclosure formula, and it avoids conflicts between the Lagrange multiplier matrix and the coupling sub-block matrix. The focus of this research is to reduce the overestimation caused by dependency phenomenon in the result of the enclosing-IFEM, therefore, both Rump’s and Neumaier–Pownuk methods are analyzed in residual convergence. Furthermore, taking the results of the Monte Carlo approach and other interval finite-element methods as the cross-references, both the efficiency and accuracy of the enclosing-IFEM are examined through two numerical validation examples. Full article

In this paper, a type of high-order compact (HOC) finite difference method is developed for solving two- and three-dimensional unsteady convection diffusion reaction (CDR) equations with variable coefficients. Firstly, an HOC difference scheme is derived to solve the two-dimensional (2D) unsteady CDR equation. Discretization in time is carried out by Taylor series expansion and correction of the truncation error remainder, while discretization in space is based on the fourth-order compact difference formulas. The scheme is second-order accuracy in time and fourth-order accuracy in space. The unconditional stability is obtained by the von Neumann analysis method. Then, this scheme is extended to solve the three-dimensional (3D) unsteady CDR equation. It needs only a five-point stencil for 2D problems and a seven-point stencil for 3D problems. Moreover, the present schemes can solve the nonlinear Burgers equation. Finally, numerical experiments are conducted to show the good performances of the new schemes. Full article