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In this study, an improved multiobjective optimization approach is proposed for optimal structural-vibrational design solution of bi-directional thermal-dependent functionally graded cylindrical shells (FGCS). The first-order shear deformation theory is first applied for the dynamic modeling, and the eigenvalue equations are obtained by the Rayleigh–Ritz method. The obtained results are compared with the literature to verify the accuracy of the analytical method. On this basis, characterization studies are carried out to obtain the important influencing parameters and their value ranges. Subsequently, the numerical experiments are carried out using Design Expert to obtain multivariate polynomials for several objective functions along with the important design variables (fundamental frequency, mass and cost). In order to avoid settling into local optima, a hybrid PSO-GWO technique is used to search for Pareto optimum solutions in space. The results show that the bi-directional graded index ranging from 0 to 1 significantly influences the fundamental frequency of the system. The graded indexes and material distribution are identified as key design variables. The ideal bi-directional graded index and material distribution for functionally graded ceramic shells (FGCS) in a thermal environment are determined. The optimization process aims to balance the conflicting objectives of maximizing frequency while simultaneously minimizing both mass and cost. By addressing these trade-offs, the final design achieves an effective compromise that meets the desired performance goals and economic constraints. [ABSTRACT FROM AUTHOR]

Due to their structural characteristics, stay cables are inherently susceptible to vibrations. Addressing this issue, the research explores the dynamics of a two‐cable network system, emphasizing the impact of composite vibration control methods. A system consisting of two horizontal cables is presented, each fitted with negative stiffness dampers (NSDs) at their anchored ends and interconnected by a cross‐tie. A complex eigenvalue equation, formulated based on displacement boundary conditions and the continuity of displacement and force, is validated through numerical simulations. The multimode damping effects of the dual NSDs and cross‐tie on the two‐cable network are explored through parameter analysis and optimization. The results demonstrate that reducing the stiffness of the cross‐tie improves the fundamental modal damping ratio, whereas increasing its stiffness or positioning it close to the cable's midpoint enhances the vibration frequency. The incorporation of NSDs into the hybrid system significantly increases the maximum damping ratio while lowering the optimal damping coefficient. This study presents a method for calculating the range of negative stiffness values, providing insights into the selection of installation positions and stiffness for the cross‐tie, thereby facilitating the design of highly effective multimode vibration control solutions for stay cables. [ABSTRACT FROM AUTHOR]

This study delves into the thermomechanical vibration behavior of functionally graded porous nanoplates under extreme thermal temperature and humidity conditions. The equation of motion of the nanoplate was derived using advanced theories in elasticity and deformation. The nanoplate consists of metal (SUS304) on the bottom surface and ceramic (Ni3S4) on the top surface, with the material distribution changing according to the power law across the plate thickness. The nanoplate was modeled with uniform and symmetric distributions of porosity reaching as high as 60%. Upon incorporating the thermal and moisture loads from the humid surroundings into the equations of motion derived from Hamilton's principle, the equations were solved using Navier's method and simplified to the eigenvalue equation. Analyzed within a broad framework are the thermomechanical vibration behavior of the nanoplate, temperature impact, humidity influence, porosity and its distribution, material grading parameter effects, and nonlocal integral elasticity effects. Observations indicate that variations in thermal temperature, humidity, and nonlocal parameters can lower the thermomechanical vibration frequency of the nanoplate, whereas porosity has the opposite effect. The effects mentioned are influenced by factors, such as the porosity ratio, porosity distribution, material ratios, and the size of the nonlocal parameter in the plate. The primary objective of this work is to uncover the nonlinear frequency response of nanoplates with high porosity in conditions characterized by high temperature and humidity. [ABSTRACT FROM AUTHOR]

The inverse reactor period α is a fundamental mode eigenvalue of the α-mode nonlinear Boltzmann eigenvalue equation that considers delayed neutron contributions. Thus far, several Monte Carlo methods, including the α-k, weight balancing, and transition rate matrix methods, have been developed to calculate α. This study presents a new Monte Carlo method for predicting α by using the derivatives of the k-eigenvalue with respect to α. Formulae are derived to calculate the first and second derivatives using the differential operator sampling method. The key feature of the new proposed method is its ability to estimate the uncertainty of the predicted α by considering the uncertainty of the k-eigenvalue and its derivatives with respect to α. [ABSTRACT FROM AUTHOR]

We consider the propagation of smooth solitary waves in a two-dimensional generalization of the Camassa–Holm equation. We show that transverse perturbations to one-dimensional solitary waves behave similarly to the KP-II theory. This conclusion follows from our two main results: (i) the double eigenvalue of the linearized equations related to the translational symmetry breaks under a transverse perturbation into a pair of the asymptotically stable resonances and (ii) small-amplitude solitary waves are linearly stable with respect to transverse perturbations. [ABSTRACT FROM AUTHOR]

This article presents unified and efficient stochastic modal decomposition methods to solve stochastic structural static and dynamic problems. We extend the idea of deterministic modal decomposition method for structural dynamic analysis to stochastic cases. Standard/generalized stochastic eigenvalue equations are adopted to calculate the stochastic subspaces for stochastic static/dynamic problems and they are solved by an efficient reduced‐order method. The stochastic solutions of both static and dynamic equations are approximated by stochastic bases of the stochastic subspaces. Original stochastic static/dynamic equations are then transformed into a set of single‐degree‐of‐freedom (SDoF) stochastic static/dynamic equations, which are efficiently solved by the proposed non‐intrusive methods. Specifically, a non‐intrusive stochastic Newmark method is developed for the solution of SDoF stochastic dynamic equations, and the element‐wise division of sample vectors is used to solve the SDoF stochastic static equations. All of these methods have low computational effort and are weakly sensitive to the stochastic dimension, thus the proposed methods avoid the curse of dimensionality successfully. Two numerical examples, including two‐ and three‐dimensional spatial problems with low and high stochastic dimensions, are given to show the efficiency and accuracy of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the results for the ground state of a Klein–Gordon oscillator under gravitational effects in a topologically charged Ellis–Bronnikov wormhole derived recently. We show that the authors failed to truncate a power-series and, consequently, could not obtain the desired solution to a differential equation. For this reason, their analytical expression for the ground-state eigenvalue is incorrect, a fact that affects all the conclusions drawn by the authors for the physical problem. [ABSTRACT FROM AUTHOR]

AbstractIn this article, longitudinal wave (P-wave) band structures of functionally graded viscoelastic phononic crystals (PnCs) with exponential distribution properties are analytically investigated via an exact method. Differing from the laminated model, displacement and stress vectors of normal incident P-wave are obtained exactly by utilizing a stress-transform technique and the state space method. According to the continuous condition and Bloch theory, the eigenvalue equation of band structure is derived by applying transfer matrix method. The storage modulus is considered to be frequency-dependent while the loss modulus is neglected for the consideration of components viscoelasticity. Dispersion curves, obtained from the calculation of eigenvalue equation, are validated by the results of exist laminated model and transmission spectra which are also present to reveal the propagation characteristic of normal incident P-wave. Numerical examples indicate that band width and center frequencies of band gaps can be effectively altered by changing magnitude of exponential function, ratio between initial modulus and final modulus. Other new band gaps are opened as well as wider band width are achieved with the increase of gradient index к. The exact analytical solution presented in this paper can be the benchmark for those approximation solutions. [ABSTRACT FROM AUTHOR]

This paper investigates the free vibration of functionally graded material (FGM) sandwich plates supported by different boundary conditions and influenced by a three-parameter viscoelastic foundation and hygro-thermal changes. Three types of FGM sandwich plates are studied and discussed, in which the FGM layers vary according to the power law rule and consist of ceramic and metal materials. An efficient and simple four-variable integral higher-order shear deformation theory (HSDT) is employed to model the analytical solution of the considered problem. Hamilton principle is implemented to obtain the plates' governing equations and to derive the eigenvalue equation for the free vibration study. The model is verified by comparing numerical results with previous studies on the vibration of exponentially graded plates. New results are presented in this paper showing the influences of different boundary conditions, hygro-thermal changes, viscoelastic parameters, vibration modes, material exponents, and geometric dimensions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain the sharp estimate for the lowest positive eigenvalue for the Camassa-Holm equation y ″ = 1 4 y + λ m (t) y , with the Neumann-Dirichlet boundary conditions, where potential m admits to change sign. We first study the optimal lower bound for the smallest positive eigenvalue in the measure differential equations. Then based on the relationship between the minimization problem of the smallest positive eigenvalue for the ODE and the one for the MDE, we find the explicit optimal lower bound of the smallest positive eigenvalue for this indefinite Camassa-Holm equation. [ABSTRACT FROM AUTHOR]

We performed uncertainty analysis and further numerical studies on the data-enabled physics-informed neural network (DEPINN). The purpose of DEPINN is to accurately and efficiently use a small amount of prior data to solve the neutron diffusion eigenvalue equations based on the physics-informed neural network. However, in practical engineering experiments, these prior data are acquired through different kinds of sensors, which are inevitably polluted by noise. Numerical results of three typical benchmark problems show that the classical DEPINN is not so robust with respect to noise. To improve the noise robustness, we propose an interval loss function to deal with the noisy prior data term; the weight of the noisy prior data term is also set to be noise dependent. Numerical results show that the proposed framework effectively enhances the robustness of DEPINN and improves the efficiency of utilizing the noisy prior data and thus promotes the engineering application of DEPINN. [ABSTRACT FROM AUTHOR]

• The symplectic method is applied to derive the analytical solution of micropolar plane annular sector in polar coordinate. • The solution to an eigenproblem of the Hamiltonian operator matrix is obtained in form of the Bessel and power functions. • The analytical solutions of the micropolar plane annular sector under the different boundary conditions are obtained. • Size-dependent behaviors in the micropolar plane annular sector are captured. The symplectic approach is utilized to derive the solutions of the plane annular sector in micropolar elasticity. According to the Hellinger-Reissner variational principle, the Hamiltonian canonical equations are obtained for the plane problem in an annular sectorial region. Through the method of separation of variables, we obtain an eigenvalue equation of the Hamiltonian operator matrix which is a system of linear differential equations with variable coefficients. By the method of series solutions, its general solutions can be expressed as the linear combination of Bessel functions and power functions. The corresponding eigensolutions for three types of homogeneous boundary conditions are derived. According to the adjoint symplectic orthogonality of the eigensolutions, the solution of the micropolar plane annular sector is expressed as a series expansion of eigensolutions. Numerical analyses are presented to demonstrate the validity of the proposed method and confirm its ability to accurately capture the size effect. [ABSTRACT FROM AUTHOR]

In this paper, we study that the algebraic multiplicity of the zero Laplacian eigenvalue of a connected uniform hypergraph. We give the algebraic multiplicity of the zero Laplacian eigenvalue of a hyperstar. For a loose hyperpath, we characterize the algebraic multiplicity of the zero Laplacian eigenvalue by the multiplicities of points in the affine variety defined by the Laplacian eigenvalue equations. We compute the algebraic multiplicities of the zero Laplacian eigenvalue of a loose hyperpath. We also show that the algebraic multiplicity of the zero Laplacian eigenvalue is not smaller than the number of irreducible components of the eigenvariety associated with the zero Laplacian eigenvalue for a loose hyperpath. [ABSTRACT FROM AUTHOR]

We study the transport properties of Dirac fermions in ABC trilayer graphene (ABC-TLG) superlattices. More specifically, we analyze the impact of varying the physical parameters-the number of cells, barrier/well width, and barrier heights-on electron tunneling in the ABC-TLG. In the initial stage, we solved the eigenvalue equation to determine the energy spectrum solutions for the ABC-TLG superlattices. Subsequently, we applied boundary conditions to the eigenspinors and employed the transfer matrix method to calculate transmission probabilities and conductance. For the two-band model, we identified the presence of Klein tunneling, with a notable decrease as the number of cells increased. The introduction of interlayer bias opened a gap as the number of cells increased, accompanied by an asymmetry in scattered transmission. Increasing the barrier/well width and the number of cells resulted in an amplified number of gaps and oscillations in both two-band and six-band cases. We observed a corresponding decrease in conductance as the number of cells increased, coinciding with the occurrence of a gap region. Our study demonstrates that manipulating parameters such as the number of cells, the width of the barrier/well, and the barrier heights provides a means of controlling electron tunneling and the occurrence of gaps in ABC-TLG. Specifically, the interplay between interlayer bias and the number of cells is identified as a crucial factor influencing gap formation and transmission asymmetry. [ABSTRACT FROM AUTHOR]

The accuracy of any observable derived from multi-scale simulations based on Frozen-Density Embedding Theory (FDET) is affected by two inseparable factors: (i) the approximation for the E xcT nad [ ρ A , ρ B ] component of the FDET energy functional and (ii) the choice of the density ρB(r) for which the FDET eigenvalue equation for the embedded wavefunction is solved. A procedure is proposed to estimate the relative significance of these two factors. Numerical examples are given for four weakly bound intermolecular complexes. It is shown that the violation of the non-negativity condition is the principal source of error in the FDET energy if ρB is the density of the isolated environment, i.e., it is generated without taking into account the interactions with the embedded species. Reduction of both the magnitude of the violation of the non-negativity condition and the error in the FDET energy can be pragmatically achieved by means of the explicit treatment of the electronic polarization of the environment. [ABSTRACT FROM AUTHOR]

Vibration behaviors of elastically supported functionally graded (FG) sandwich beams resting on elastic foundations under moving loads are investigated. The transformed-section method is first applied to establish the bending vibration equations of FG sandwich beams, then the Chebyshev collocation method is used to study free and forced vibrations. Two types of sandwich beams with FG faces-isotropic core and isotropic faces-FG core are considered. The material properties of FG materials are assumed to vary across the beam thickness according to a simple power function. Regarding the free vibration analysis, bending vibration frequencies are calculated numerically by forming a matrix eigenvalue equation. As for the forced vibration analysis, the backward differentiation formula method is employed to solve the time-dependent ordinary differential equations to obtain the dynamic deformations of the beam. To ensure the accuracy of the proposed model, some calculated results are compared with those in the published literature. Parametric studies are then performed to demonstrate the effects of material gradient indexes, stack types, layer thickness ratios, slenderness ratios, excitation frequency and speed of moving loads, and foundation and support stiffness parameters on the dynamic characteristics of FG sandwich beams. [ABSTRACT FROM AUTHOR]

The SL (2 , Z) -symmetry of Cherednik's spherical double affine Hecke algebras in Macdonald theory includes a distinguished generator which acts as a discrete time evolution of Macdonald operators, which can also be interpreted as a torus Dehn twist in type A. We prove for all twisted and untwisted affine algebras of type ABCD that the time-evolved q-difference Macdonald operators, in the t → ∞ q-Whittaker limit, form a representation of the associated discrete integrable quantum Q-systems, which are obtained, in all but one case, via the canonical quantization of suitable cluster algebras. The proof relies strongly on the duality property of Macdonald and Koornwinder polynomials, which allows, in the q-Whittaker limit, for a unified description of the quantum Q-system variables and the conserved quantities as limits of the time-evolved Macdonald operators and the Pieri operators, respectively. The latter are identified with relativistic q-difference Toda Hamiltonians. A crucial ingredient in the proof is the use of the "Fourier transformed" picture, in which we compute time-translation operators and prove that they commute with the Pieri operators or Hamiltonians. We also discuss the universal solutions of Koornwinder-Macdonald eigenvalue and Pieri equations, for which we prove a duality relation, which simplifies the proofs further. [ABSTRACT FROM AUTHOR]

The paper deals with the combined effect of non-Newtonian saturating fluid and horizontal flow rate on the thermal convection in a highly permeable, porous plane layer saturated with a power-law model. Asymmetric boundary conditions are assumed, with a cooled free surface at the top and a heated, impermeable, rigid wall at the bottom. The generalised Forchheimer equation is employed to model the power-law fluid movement. Convection cells emerge in the power-law fluid because of vertical temperature gradient imposed by the thermal boundaries. The onset of this scenario can be studied using linear stability theory, which leads to an eigenvalue problem. The latter is solved either numerically, employing shooting schemes, or analytically, using one-order Galerkin approach. The present study is considered an extension of the classical Prats problem. When the Peclet number, which defines the flow rate, is negligible, the configuration switches to the special case of Darcy-Rayielgh instability. The results show that the form drag exhibits a stronger stabilizing influence in shear-thinning fluids compared to shear-thickening and Newtonian ones since the saturating fluid is described by the power-law model. This scenario appears in the specific range of the Peclet number. In general, this investigation can be used to understand the heat transfer process in subsurface hydrocarbon reservoirs where the fluid may exhibit non-Newtonian behaviour. [ABSTRACT FROM AUTHOR]

We develop the Euclidean time method of the variational quantum eigensolver for solving the generalized eigenvalue equation A | ϕ n ⟩ = λ n B | ϕ n ⟩ , where A and B are hermitian operators, and | ϕ n ⟩ and λ n are called the eigenvector and the corresponding eigenvalue of this equation, respectively. For the purpose, we modify the usual Euclidean time formalism, which was developed for solving the time-independent Schrödinger equation. We apply our formalism to three numerical examples for test. It is shown that our formalism works very well in all numerical examples. We also apply our formalism to the hydrogen atom and compute the electric polarizability. It turns out that our result is slightly less than that of the perturbation method. [ABSTRACT FROM AUTHOR]

The approximate solution to the Schrödinger equation of exotic doubly muonic helium-like systems has been obtained using a simple matrix method based on hydrogenic s-states. Each system considered consists of a positively charged nucleus surrounded by 2 negatively charged muons XZ+μμ-- (2≤Z≤36). The present work aims to obtain approximate ground-state energies of the systems and to decompose the energies in terms of the basis states used. Here, the wave function was expressed as a linear combination of 15 eigenfunctions, each written as the product of two hydrogenic s-states. The elements of the Hamiltonian matrix were calculated and finally, the energy eigenvalue equation was numerically solved to obtain the ground-state energies of the systems with their corresponding eigenvectors. From the results, ground-state energies of all systems were in agreement with others from the literature, with percentage differences between 0.03% and 2.05%. The analysis of the probability amplitudes from the eigenvectors showed that the 1s1s state made the largest contribution to the ground state energies of the systems, approaching 90.99%, 96.98% and 98.54% for He2+μμ--, Li3+μμ--, and Be4+μμ--, respectively. [ABSTRACT FROM AUTHOR]

The unrestricted Hartree‐Fock method is extended to correlation calculation within the density‐matrix functional theory. The method is derived from an entropic cumulant functional for the correlation energy. The eigenvalue equations for the spin‐orbitals are modified by the orbital occupation numbers. The Euler equation for the occupation numbers results in the Fermi‐Dirac distribution, which is very efficient to update as soon as the orbital eigenvalue equations are solved. The method is demonstrated on the ground state of O2. [ABSTRACT FROM AUTHOR]

By recasting the non-linear frequency-dependent GW quasiparticle equation into a linear eigenvalue problem, we explain the appearance of multiple solutions and unphysical discontinuities in various physical quantities computed within the GW approximation. Considering the GW self-energy as an effective Hamiltonian, it is shown that these issues are key signatures of strong correlation in the (N ± 1)-electron states and can be directly related to the intruder state problem. A simple and efficient regularization procedure inspired by the similarity renormalization group is proposed to avoid such issues and speed up the convergence of partially self-consistent GW calculations. [ABSTRACT FROM AUTHOR]

The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported. We present a simple strategy for truncating the commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian H ̄ . The qUCCSD method for the electronic ground state includes up to double commutators for the amplitude equations and up to cubic commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double commutators for the singles–singles block of H ̄ , single commutators for the singles–doubles and doubles–singles blocks, and the bare Hamiltonian for the doubles–doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Møller–Plesset perturbation theory. [ABSTRACT FROM AUTHOR]

The 3D problem became the basis for modeling the critical states and shapes of bifurcation buckling of longitudinal force and torque-stressed nanotubes. The homogeneous system of ordinary differential equations built on the theory of rectilinear elastic rods was formulated. Its nontrivial solutions result in critical torque or longitudinal force levels at preset values of one of those entities. The closed-form solutions under chosen boundary conditions indicate that only spatial curves as variable diameter spirals with the left or right orientation consistent with that of the torque can be stability loss modes. The spiral is single-wound without longitudinal force, regardless of the tube length. If the tube is also prestressed with axial compression or tension, the bifurcation spiral is multi-wound; its number is determined by the eigenvalue of the equations, which increases with growing forces and tube length. [ABSTRACT FROM AUTHOR]

We obtain new concavity results, up to a suitable transformation, for a class of quasi-linear equations in a convex domain involving the p-Laplace operator and a general nonlinearity satisfying concavity-type assumptions. This provides an extension of results previously known in the literature only for the torsion and the first eigenvalue equations. In the semilinear case p = 2 the results are already new since they include new admissible nonlinearities. [ABSTRACT FROM AUTHOR]

The outer disc region of most spiral galaxies (approximately 50 per cent of all disc galaxies) shows warping above the galactic mid-plane and is primarily asymmetric by nature. In this work, we explore analytically the effect of the gas component on asymmetric warps in a realistic self-gravitating collision-less disc residing in a cold oblate dark matter halo's potential field. We consider the disc to be composed of gravitationally coupled stars and gas components. The quadratic eigenvalue equation describing the shape and frequency of the bending mode is formulated and solved numerically. Two stable ground-state bending modes m  = 0 and m  = 1, representing the U-shape and the mostly observed S-shaped warp in the galactic disc are superimposed linearly to generate and examine the asymmetric warps in the disc. The resulting asymmetry in warp is measured by asymmetric index (A asym) by varying physical parameters such as the mass of the gas components and the halo flattening parameter. It is shown that the gas fraction in the disc has a negligible contribution to the generation of asymmetric warp in the disc. The disc residing in a spherical dark matter halo is found to be more asymmetry than that in the counterpart oblate halo. [ABSTRACT FROM AUTHOR]

In this work, perforated and restrained nanobeams with deformable boundary conditions are modeled based on the non-local strain gradient elasticity theory with the elastic medium effect. In this approach in which the Fourier infinite series and Stokes' transformation are used together, the nanobeam is detached into parts from the two boundary points with the main part. Then using elastic force boundary conditions, a system of linear equations in terms of nonlinearity, elastic medium parameter, spring coefficients and small size effects are derived and the eigenvalue solution of these equations is also presented. The nonlinear stability of restrained nanobeam is examined and the effects of size parameters, perforation and elastic spring coefficients are studied. To reveal the accuracy and effectiveness of the offered model, several numerical applications are solved for the nonlinear stability response of restrained nanobeams with elastic medium effects. The outcomes of this method validated that the presented approach is appropriate for the stability behavior of rigid and restrained nanobeams with perforated cross section. [ABSTRACT FROM AUTHOR]

A self-gravitating, differentially rotating galactic disc under vertical hydrostatic equilibrium is supported by the vertical pressure gradient force against the gravitational collapse. Such discs are known to support various bending modes, for example warps, corrugation, or scalloping (typically, higher order bending modes) of which m  = 1 bending modes (warps) are the most prevalent ones in galactic discs. Here, we present a detailed theoretical analysis of the bending instability in realistic models of disc galaxies in which an exponential stellar disc is under vertical equilibrium and residing in a cold rigid dark matter halo. A quadratic eigenvalue equation describing the bending modes is formulated and solved for the complete eigen spectrum for a set of model disc galaxies by varying their physical properties such as disc scale-height, and dark matter halo mass. It is shown that the vertical pressure gradient force can excite unstable bending modes in such a disc as well as large scale discrete modes. Further, it is shown that the unstable eigen modes in a thinner disc grow faster than those in a thicker disc. The bending instabilities are found to be suppressed in discs dominated by massive dark matter halo. We estimate the growth time-scales and corresponding wavelength of the m  = 1 unstable bending modes in Milky Way like galaxies and discuss its implication. [ABSTRACT FROM AUTHOR]

The conveyance of fluid through pipes is a common occurrence in practical applications, and the dynamic stability of such systems has been a subject of interest for many decades. In this paper, we investigate the dynamic stability of a cantilevered pipe conveying fluid, considering the lateral distributed load as a critical factor. To achieve this, we employ the differential quadrature method to solve the eigenvalue equations for various load patterns. Remarkably, we observe excellent agreement with exact solutions and the Argand diagram. By analyzing the relationship between circular frequency and dimensionless velocity, we demonstrate that the descending distributed load pattern exhibits the highest stability. For certain conditions, it is possible to enhance stability. The results obtained in this study provide valuable insights for improving the stability of cantilevered pipe conveying fluid through a different approach. [ABSTRACT FROM AUTHOR]

This paper investigates the size-dependent vibration and buckling behavior of nanoplates described by the nonlocal Kirchhoff model analytically. The nonlocal and local constitutive relations, governing equations and boundary conditions are comprehensively discussed. A shifted governing equation in terms of local stress resultants with associated local boundary conditions is chosen in the current work. The direct separation of variables method is formulated based on the Hamiltonian dual form of the governing differential equation to address the eigenvalue problems of nonlocal rectangular plates with each edge either simply supported or clamped. The closed-form eigen-solutions are acquired for the first time for the cases where two adjacent clamped edges exist. The validity and accuracy of the present approach are verified by comparison with published analytical and numerical results. Parametric studies are performed to investigate the influences of nonlocal parameter and boundary conditions on the size-dependency of natural frequencies and critical buckling loads of nanoplates. [ABSTRACT FROM AUTHOR]

We devise an efficient scheme to determine vibrational properties from Path Integral Molecular Dynamics (PIMD) simulations. The method is based on zero-time Kubo-transformed correlation functions and captures the anharmonicity of the potential due to both temperature and quantum effects. Using analytical derivations and numerical calculations on toy-model potentials, we show that two different estimators built upon PIMD correlation functions fully characterize the phonon spectra and the anharmonicity strength. The first estimator is associated with the force–force quantum correlators and, in the weak anharmonic regime, yields reliable zero-point motion frequencies and thermodynamic properties of the quantum system. The second one is instead connected to displacement–displacement correlators and accurately probes the lowest-energy phonon excitations, regardless of the anharmonicity strength of the system. We also prove that the use of generalized eigenvalue equations, in place of the standard normal mode equations, leads to a significant speed-up in the PIMD phonon calculations, both in terms of faster convergence rate and smaller time step bias. Within this framework, using ab initio PIMD simulations, we compute phonon dispersions of diamond and of the high-pressure I41/amd phase of atomic hydrogen. We find that in the latter case, the anharmonicity is stronger than previously estimated and yields a sizeable red-shift in the vibrational spectrum of atomic hydrogen. [ABSTRACT FROM AUTHOR]

We introduce the unitary almost-Mathieu operator, which is obtained from a two-dimensional quantum walk in a uniform magnetic field. We exhibit a version of Aubry–André duality for this model, which partitions the parameter space into three regions: a supercritical region and a subcritical region that are dual to one another, and a critical regime that is self-dual. In each parameter region, we characterize the cocycle dynamics of the transfer matrix cocycle generated by the associated generalized eigenvalue equation. In particular, we show that supercritical, critical, and subcritical behavior all occur in this model. Using Avila's global theory of one-frequency cocycles, we exactly compute the Lyapunov exponent on the spectrum in terms of the given parameters. We also characterize the spectral type for each value of the coupling constant, almost every frequency, and almost every phase. Namely, we show that for almost every frequency and every phase the spectral type is purely absolutely continuous in the subcritical region, pure point in the supercritical region, and purely singular continuous in the critical region. In some parameter regions, we refine the almost-sure results. In the critical case for instance, we show that the spectrum is a Cantor set of zero Lebesgue measure for arbitrary irrational frequency and that the spectrum is purely singular continuous for all but countably many phases. [ABSTRACT FROM AUTHOR]

The eigenvalues are HT ht and HT ht , where I R i is the radius of the sphere, I V SB l sb i and I V SB t sb i are the longitudinal and transverse sound velocities of the sphere, and I f i is the frequency. [Extracted from the article]

This paper focused on propagation characteristics of a single mode supporting waveguide enclosed by metallic sidewalls periodically loaded with lossless single negative (SNG) metamaterial slabs along axial direction. The gap between two successive SNG slabs is filled with a double positive (DPS) material. For the analysis, the periodic structure is assumed having symmetric unit cell (UC) and simplified as a two-port network which is one-half of the symmetric UC. Scattering parameters (S-parameters) are defined by even/odd mode analysis of the symmetric UC, and then the total S-parameters are calculated by solving the cascade connection of N unit cells. Eigenvalue equations are also obtained to explicit the solutions of band edge and pass/stopband diagrams in the microwave regime. Since a SNG can be either epsilon-negative (ENG) or mu-negative (MNG), S-parameters and dispersion behavior are illustrated with numerical examples and discussed for each periodic structure constructed with ENG or MNG slabs. [ABSTRACT FROM AUTHOR]

A direct method for simultaneously updating mass and stiffness matrices of the undamped piezoelectric smart structural models based on incomplete modal measured data is presented. By applying the generalized singular value decomposition and some matrix derivatives, the optimal approximate mass and stiffness matrices which satisfy the required eigenvalue equation and the orthogonality relation are found under the Frobenius norm sense. The method is computationally efficient as neither iteration nor eigenanalysis is required. Numerical results are included to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The dynamic characteristics and thermal buckling behaviors of a multi-span honeycomb sandwich panel with arbitrary boundaries are studied comprehensively in this paper. The concept of artificial springs is proposed and it was found that arbitrary boundaries can be achieved by adjusting the stiffness of artificial springs. The hinges which connect the base plates of this structure are simulated by massless torsion springs. The displacement field of the panel is expressed as a series of admissible functions which is a set of characteristic orthogonal polynomials generated directly by employing the Gram–Schmidt process. The stresses induced by the temperature change in the multi-span panel are considered, and then the eigenvalue equations of free vibration and thermal buckling are derived by using the Rayleigh–Ritz method. The theoretical formulations of the present research are validated by comparing the results of this paper with those obtained from the available literature and ABAQUS software. Subsequently, the influences of structural parameters on the critical buckling temperature and natural frequencies are investigated comprehensively, and some useful conclusions about dynamic optimization design for multi-span honeycomb sandwich panels are drawn from the present study. [ABSTRACT FROM AUTHOR]

The localization accuracy is susceptible to the received signal strength indication (RSSI) fluctuations for RSSI-based wireless localization methods. Moreover, the maximum likelihood estimation (MLE) of the target location is nonconvex, and locating target presents a significant computational complexity. In this paper, an RSSI-based access point cluster localization (APCL) method is proposed for locating a moving target. Multiple location-constrained access points (APs) are used in the APCL method to form an AP cluster as an anchor node (AN) in the wireless sensor network (WSN), and the RSSI of the target is estimated with several RSSI samples obtained by the AN. With the estimated RSSI for each AN, the solution for the target location can be obtained quickly and accurately due to the fact that the MLE localization problem is transformed into an eigenvalue problem by constructing an eigenvalue equation. Simulation and experimental results show that the APCL method can meet the requirement of high-precision real-time localization of moving targets in WSN with higher localization accuracy and lower computational effort compared to the existing classical RSSI-based localization methods. [ABSTRACT FROM AUTHOR]

• A method for complex band structure computation of phononic crystals is proposed. • Local optimization semi-Cartesian grid is proposed to improve the grid quality near the interface. • Floquet transform is applied to transform the elastic wave equation into quadratic eigenvalue equation. • Complex band structures of phononic crystals with sharp-edged scatterer shapes are computed and analyzed. In this paper, we propose a finite element method based on the Floquet transform and local optimization semi-Cartesian grid to compute the complex band structure of phononic crystals. Floquet transform is applied to transform the elastic wave equation into a quadratic eigenvalue equation. Value-periodic test function independent of the interface is defined to derive the weak formulation. The local optimization semi-Cartesian grid is proposed to improve the quality of triangular elements near the interface. Our results are in good agreement with ones obtained by other mature methods, and the purely propagative mode coincides with the traditional band diagram. In addition to simple scatterer shapes such as circle or square, the proposed method is able to calculate the complex band structures of phononic crystals with complicated scatterer shapes. Numerical experiments demonstrated the effectiveness of this method in the computation of anisotropic inhomogeneous medium. The complex band structures under different lattice types, scatterer shapes, material properties, rotation angle and modes are obtained, and their effects on the width and number of band gaps are analyzed. [ABSTRACT FROM AUTHOR]

We consider the zero-dispersion limit for the Benjamin-Ono equation on the torus for bell shaped initial data. Using the approximation by truncated Fourier series, we transform the eigenvalue equation for the Lax operator into a problem in the complex plane. Then, we use the steepest descent method to get asymptotic expansions of the Lax eigenvalues. As a consequence, we determine the weak limit of solutions as the dispersion parameter goes to zero, as long as the initial data is an even bell shaped potential. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the propagation behavior of electromagnetic waves through coaxial optical fiber bounded with DB-boundaries. For this purpose, an eigenvalue equation is derived by using suitable DB-boundary conditions to determine the allowed values of propagation constant β for each propagating mode. Moreover, we have analyzed the electric field and power distribution patterns through coaxial optical fiber for different propagating modes and dimensions, respectively. Our results show that small dimensional guide confinement remains maximum close to the lower interface of the guide, whereas, for larger dimensions, it shifts toward the upper interface. Investigations show that high power is confined by H12 mode compared to H11 mode, and, therefore, shows contrary behavior compared to commonly used fibers. [ABSTRACT FROM AUTHOR]

In this work, we investigate complete stability behaviors of the Rosenzweig–MacArthur predator–prey model with delayed harvesting of the prey. The unharvested system exhibits either a steady‐state or an oscillatory dynamics for the coexistence of the species. We explore how the delayed harvesting affects the dynamics of these two modes by analyzing the system stability in effort‐delay bi‐parameter plane. Some novel dynamical scenarios and intricate dynamics are obtained. Analytical conditions for different stability scenarios are derived by examining the associated quasi‐polynomial eigenvalue equation. For invariant harvesting effort, the time delay induces four stability scenarios: stability invariance, instability invariance, stability change, and stability switching. On the other hand, the effort instigates five stability scenarios: stability invariance, instability invariance, stability change, instability change, and instability switching, when the delay strength is fixed. Majority of literatures on harvesting reported that harvesting stabilizes predator–prey interactions. However, we will show that the delayed harvesting can destabilize the system. One of the novelties of the study is to unveil the occurrence of effort‐induced chaos via period‐doubling mechanism. Interestingly, the effort‐induced switching phenomena and chaos do not occur for non‐delayed harvesting. [ABSTRACT FROM AUTHOR]

We discuss results obtained recently for a quantum-mechanical model given by a neutral particle with a magnetic quadrupole moment in a radial electric field and a scalar potential proportional to the radial variable in cylindrical coordinates that also includes the noninertial effects of a rotating reference frame. We show that the conjectured allowed values of the cyclotron frequency are a mere artifact of the truncation of the power series used to solve the radial eigenvalue equation. Our analysis proves that the analytical expression for the eigenvalues is incorrect. [ABSTRACT FROM AUTHOR]

A new approach to solving eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to computing structured pseudospectra and their extremal points, and to structured matrix nearness problems such as computing the distance to instability or to singularity under structured perturbations. The perturbation structure can be a general linear structure. We focus on the practically important cases of large matrices with a given sparsity pattern and on perturbation matrices with given range and corange. It is known that analogous eigenvalue optimization for unstructured complex matrices favorably works with rank-1 matrices. The novelty of the present paper is that structured eigenvalue optimization can still be performed with rank-1 matrices, which yields a significant reduction of storage and in some cases of the computational cost. Optimizers are shown to be rank-1 matrices orthogonally projected onto the given structure. This is used in the numerical algorithms. The numerical approach comes in two different versions. If the rank-1 matrices projected onto the structure form a manifold and if the orthogonal projection onto the corresponding tangent spaces is known and computationally inexpensive, as is the case for matrices with given range and corange, then the method relies on a gradient system on this manifold. Otherwise, in particular for matrices with a given sparsity pattern, the method relies on the orthogonal projection of the free gradient onto the tangent space of the manifold of complex rank-1 matrices. The solution of this rank-1 system is then projected onto the structure. It is shown that there is a bijective correspondence between the stationary points of the gradient system on the structure space and of the rank-1 system. Near a local minimizer the rank-1 tangent projection is very close to the identity map, and so the computationally favorable rank-1 projected system behaves locally like the gradient system. Numerical experiments illustrate the two approaches for large matrices with a given sparsity pattern and for perturbation matrices with given range and corange. [ABSTRACT FROM AUTHOR]

In this paper, we argue that the results shown in [Mod. Phys. Lett. A 34, 1950319 (2019)] are not correct. The truncation of the Frobenius method only yields some particular bound states from which one cannot derive any sound physical conclusion. The existence of allowed model parameters is an artifact of such procedure. Besides, the authors failed to obtain most of the solutions given by the truncation of the Frobenius series as well as their connection with the actual eigenvalues of the problem. [ABSTRACT FROM AUTHOR]

We obtain eigenvalue equations satisfied by various elliptic modular graphs with five links where two of the vertices are unintegrated. Solving them leads to several nontrivial algebraic identities between these graphs. [ABSTRACT FROM AUTHOR]

The key to decreasing reradiation interference (RRI) of power transmission lines on adjacent radio stations is to clarify the RRI resonance mechanism. Aiming at the defects of existing RRI resonance analysis methods, including frequency limitation and lack of physical explanation, a RRI resonance analysis method based on characteristic mode (CM) theory is proposed in this paper. Firstly, based on the generalized eigenvalue equation, a set of characteristic currents with orthogonal relationship and their eigenvalues for power transmission lines are solved, and combined with Poynting's theorem, the CM radiation characteristics are analyzed. Secondly, under specific external excitation, CM-related parameters are obtained through modal decomposition. Finally, the total energy radiated by power transmission lines is decomposed into the superposition of energy radiated by each CM, and the mechanism of RRI resonance is clarified from the perspective of CM. The simulation results show that compared with the IEEE guide and the generalized resonance theory, the method in this paper is effective and independent of observation points, which can provide a theoretical support for further research on the RRI suppression measures. [ABSTRACT FROM AUTHOR]

We study the viscosity solutions to the first eigenvalue equation. We consider Ω a bounded B-regular domain in C n and we prove that the Dirichlet problem Λ 1 (D C 2 u) = f in Ω and u = φ on ∂ Ω admits a unique viscosity solution. We also deal with viscosity theory for operators which are comparable to the first eigenvalue operator. [ABSTRACT FROM AUTHOR]

The q-Toda equation is derived from replacing ordinary derivatives with q-derivatives in the famous Toda equation. In this paper, we associate an extension of the q-Toda equation with matrix eigenvalue problems, and then show applications of its time-discretization to computing matrix eigenvalues. With respect to the Lotka–Volterra system, we also have the similar discussion on the case of the Toda equation. [ABSTRACT FROM AUTHOR]