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By applying nonequilibrium Green's function combined with density functional theory, we investigate the electronic transport properties of carbon-doped p-n nanojunction based on hexagonal boron nitride armchair nanoribbons. The calculated I-V curves show that both the center and edge doping systems present obvious negative differential resistance (NDR) behavior and excellent rectifying effect. At low positive bias, the edge doping systems possess better NDR performance with larger peak-to-valley ratio (∼105), while at negative bias, the obtained peak-to-valley ratio for both of the edge and center doping systems can reach the order of 107. Meanwhile, center doping systems present better rectifying performance than the edge doping ones, and giant rectification ratio up to 106 can be obtained in a wide bias range. These outstanding transport properties are explained by the evolution of the transmission spectra and band structures with applied bias, together with molecular projected self-consistent Hamiltonian eigenvalues and eigenstates. [ABSTRACT FROM AUTHOR]

Rytov's theory of thermally generated radiation is used to find the noise in two-dimensional passive guides based on an arbitrary distribution of lossy isotropic dielectric. To simplify calculations, the Maxwell curl equations are approximated using difference equations that also permit a transmission-line analogy, and material losses are assumed to be low enough for modal losses to be estimated using perturbation theory. It is shown that an effective medium representation of each mode is valid for both loss and noise and, hence, that a one-dimensional model can be used to estimate the best achievable noise factor when a given mode is used in a communications link. This model only requires knowledge of the real and imaginary parts of the modal dielectric constant. The former can be found by solving the lossless eigenvalue problem, while the latter can be estimated using perturbation theory. Because of their high loss, the theory is most relevant to plasmonic waveguides, and its application is demonstrated using single interface, slab, and slot guide examples. The best noise performance is offered by the long-range plasmon supported by the slab guide. [ABSTRACT FROM AUTHOR]

Rapid execution is required in operation-oriented applications in underwater acoustic modelling. In this paper, the GPU graphic pipeline is used to accelerate the calculation of high-resolution sound field image in the normal mode model of underwater acoustic propagation. The computer times of the proposed graphic pipeline method, the MATLAB code, and the C# code are compared for a stratified shallow water waveguide using the KRAKEN model at different frequencies. The research validates that the graphic pipeline method outperforms the classic CPU-based methods in terms of execution speed at the frequencies where the eigenvalue equation in normal mode models can be solved. [ABSTRACT FROM AUTHOR]

A slowly varying modes solution of Wentzel–Kramers–Brillouin type is derived for the problem of sound propagation in a slowly varying two-dimensional duct with homentropic inviscid sheared mean flow and acoustically lined walls of slowly varying impedance. The modal shape function and axial wavenumber are described by the Pridmore-Brown eigenvalue equation. The slowly varying modal amplitude is determined in the usual way by an equation resulting from a solvability condition. For a general mean flow, this equation can be solved in the form of an incomplete adiabatic invariant. Due to conservation of specific mean vorticity along streamlines, two simplifications prove possible for a linearly sheared mean flow: (i) an analytically exact approximation for the mean flow, and (ii) a complete adiabatic invariant for the acoustics. For this last configuration some example cases are evaluated numerically, where the Pridmore-Brown eigenvalue problem is solved by a Galerkin projection combined with an efficient nonlinear iteration. [ABSTRACT FROM AUTHOR]

Due to superior characteristics added to composite structures by using graphene-platelets (GPLs) as nanofillers, this article investigates torsional buckling analysis of functionally graded graphene-platelets reinforced composite (FG-GPLRC) porous cylindrical shell within the framework of the first-order shear deformation theory (FSDT). The relationship between coefficients of porosity and mass density is determined based on the typical mechanical property of an open-cell metal foam. The modified Halpin-Tsai micromechanics model is employed to estimate the effective modulus of elasticity and the rule of mixtures to compute density and Poisson's ratio of the shell material. First-order shear deformation theory and Rayleigh-Ritz method are employed to establish the related eigenvalue equations in order to calculate the critical buckling torque. The accuracy of the applied approach is examined by comparing the numerical results with those published in the available literature and also with the simulation results of ABAQUS. Additionally, the effects of various matrix materials, internal porosities and GPLs distribution patterns, size and concentration of porosities, GPLs weight fraction, graphene plates dimensional ratios, geometric factors such as mid-radius to thickness ratio and length to mid-radius on the torsional performance of FG-GPLRC porous cylindrical shell are inspected. The results of this article can be regarded as practical designing hints for engineers analyzing the mechanical behavior of innovative composite structures. [ABSTRACT FROM AUTHOR]

In magnetic hyperthermia, the effectiveness for tumour cell destruction is measured by the specific loss power. Theoretically, within the medically accepted ranges for the amplitude and frequency of the applied magnetic field, if energy losses in nanofluids occur through magnetic relaxation processes, the specific loss power is calculated based on the linear response theory. In this theory, the specific loss power depends on the effective magnetic relaxation time of the colloidal nanoparticle system which involves either the Brownian relaxation time or the Néel relaxation time. All theoretical approaches to the Néel relaxation time show that it depends directly on the diffusional relaxation time and inversely on the smallest non-vanishing eigenvalue of the Fokker-Planck equation, where the damping constant is expressed one way or another by a value, generally unknown, which in most cases is approximated. This paper shows through a numerical experiment how the damping constant influences the specific loss power, referring to some benchmarks on how to choose the most accurate value of this constant in the case of magnetite nanoparticles, mostly used in magnetic hyperthermia applications. Following an uninspired choice of the damping constant value, the simulated or calculated data can deviate from the experimentally determined data, even if, in general, the model is correct and as close as possible to reality. [ABSTRACT FROM AUTHOR]

This paper studies the vibration behaviors of bidirectional functionally graded (BDFG) Timoshenko beams based on the Chebyshev collocation method. The material properties of the beam are assumed to vary simultaneously in the beam length and thickness directions. The Chebyshev differentiation matrices are used to reduce the ordinary differential equations into a set of algebraic equations to form the eigenvalue problem for free vibration analysis. To validate the accuracy of the proposed model, some calculated results are compared with those obtained by other investigators. Good agreement has been achieved. Then the effects of slenderness ratios, material distribution types, gradient indexes, and restraint types on the natural frequency of BDFG beams are examined. Through the parametric study, the influences of the various geometric and material parameters on the vibration characteristics of BDFG beams are evaluated. [ABSTRACT FROM AUTHOR]

A triaxial core rotating around the middle axis, i.e. two-axis, is cranked around the one-axis, due to the coupling of an odd proton from a high j orbital. Using the Bargmann representation of a new and complex boson expansion of the angular momentum components, the eigenvalue equation of the model Hamiltonian acquires a Schrödinger form with a fully separated kinetic energy. From a critical angular momentum, the potential energy term exhibits three minima, two of them being degenerate. Spectra of the deepest wells reflects a chiral-like structure. Energies corresponding to the deepest and local minima respectively, are analytically expressed within a harmonic approximation. Based on a classical analysis, a phase diagram is constructed. It is also shown that the transverse wobbling mode is unstable. The wobbling frequencies corresponding to the deepest minimum are used to quantitatively describe the wobbling properties in 135Pr. Both energies and e.m. transition probabilities are described. [ABSTRACT FROM AUTHOR]

We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schrödinger eigenvalue equation HΨ ≡ (Δ2 + V)Ψ = EΨ on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal coordinate system. We apply the method, as an example, to revisit the Tremblay and Winternitz (2010) derivation of the Painlevé VI potential for a 3rd order superintegrable flat space system that separates in polar coordinates and, as new results, we give a listing of the possible potentials on the two-sphere that separate in spherical coordinates and all two-hyperbolic (two-sheet) potentials separating in horocyclic coordinates. In particular, we show that the Painlevé VI potential also appears for a 3rd order superintegrable system on the two-sphere that separates in spherical coordinates, as well as a 3rd order superintegrable system on the two-hyperboloid that separates in spherical coordinates and one that separates in horocyclic coordinates. Our aim is to develop tools for analysis and classification of higher order superintegrable systems on any 2D Riemannian space, not just Euclidean space. [ABSTRACT FROM AUTHOR]

Transverse vibration of rectangular composite plates with multiple distributed composite patches is analyzed in this paper. Because of the geometric discrepancy between the plate and patch, analytical solutions are usually hard to achieve. The present model is formulated by using the Rayleigh–Ritz method and adopting various types of modal shape functions of uniform beam as admissible functions for different boundary conditions. The total system energies are calculated by adding the energies of the substrate plate and the energies of the patches. By imposing the displacement-matching condition at the patch domains, the coordinate systems of the substrate plate and patches are coupled. By means of the present method, it is very convenient and efficient to build the system governing equations and solve the eigenvalue problem. For the composite patches, they are also assumed to be symmetrically layered and have the same layer stacking sequence with the substrate laminate. The effects of layer stacking sequence, modulus ratio, aspect ratio, and boundary conditions on the natural frequencies are investigated and discussed. The results are also compared with the existed benchmark solutions and FEM solutions for validation. The numerical results demonstrate that the proposed approach is computationally very efficient and accurate and can be used as a tool to solve transverse vibration problems of composite plate with multiple composite patches. [ABSTRACT FROM AUTHOR]

We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to a three-term recurrence relation for the coefficients of the power series that, under suitable truncation, yields exact analytical eigenvalues and eigenfunctions for particular values of a model parameter. From these solutions some researchers have derived a variety of predictions like allowed angular frequencies, allowed field intensities and the like. We also solve the eigenvalue equation numerically by means of the variational Ritz method and compare the resulting eigenvalues with those provided by the truncation condition. In this way we prove that those physical predictions are merely artifacts of the truncation condition. [ABSTRACT FROM AUTHOR]

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale. [ABSTRACT FROM AUTHOR]

For Hermitian and non-Hermitian Hamiltonian matrices H, we present the Schr¨odinger equation for qudit (spin-j system, N-level atom) with the state vector |ψ〉 in a new form of the linear eigenvalue equation for the matrix ℋ = (H ⊗ 1N) and the probability eigenvector |p〉 identified with quantum states in the probability representation of quantum mechanics. We discuss the possibility to experimentally detect the difference between the system states described by the solutions, corresponding to the Schrödinger equation with Hermitian and non-Hermitian Hamiltonians, by measuring the probabilities of artificial spin-1/2 projections m = ± 1/2, sets of which are identified with qudit states. We show that different symmetries of systems, including 𝒫𝒯 -symmetry and broken 𝒫𝒯 -symmetry, are determined by a set of N complex eigenvalues of the Hamiltonian matrix H. [ABSTRACT FROM AUTHOR]

Introduction: Borderline personality influenced by numerous factors is considered as a complex network. Purpose of the study was to conduct a research on borderline personality traits (BPT) using network dynamics for research on factors influencing BPT. Materials and Methods: The statistical population included monozygotic and dizygotic twins (N=500; Mean age=23.46 years; 74.40% female; Iranian). The research instruments were self-report for participants. We used a threshold for correlations to remove links which represented weak relations. After creating a sparse network, Inverse Participation Ratio (IPR) method was used to extract affective nodes. Results: In total sample and monozygotic twins, nodes of secure attachment to mother and father had a profound effect on network stability (Prevention of sings) and node of secure attachment to father had the greatest impact on the given stability among dizygotic twins. Nodes of interpersonal problems, emotional neglect, and insecure attachment to father were among the most important ones affecting all groups in no stability of network (moving towards signs). Conclusion: Given the dominance of environmental factors within threshold conditions, the influence of environment on heritability for BPT was confirmed. [ABSTRACT FROM AUTHOR]

The Schrödinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional time steps of order greater than two necessarily have negative steps and cannot be used for this class of diffusive problems. However, there exist methods which use fractional complex time steps with positive real parts which can be used with only a moderate increase in the computational cost. We analyze the performance of this class of schemes and propose new methods which outperform the existing ones in most cases. On the other hand, if the gradient of the potential is available, methods up to fourth order with real and positive coefficients exist. We also explore this case and propose new methods as well as sixth-order methods with complex coefficients. In particular, highly optimized sixth-order schemes for near integrable systems using positive real part complex coefficients with and without modified potentials are presented. A time-stepping variable order algorithm is proposed and numerical results show the enhanced efficiency of the new methods. [ABSTRACT FROM AUTHOR]

Real-time detection of heavy metal ions in water was implemented by using a composite optical waveguide (COWG) based polarimetric interferometer. The COWG was made by local deposition of a tapered nanometric layer of high-index materials onto a single-mode slab glass waveguide, and it is a low-cost robust waveguide with a locally large modal birefringence. The COWG-based polarimetric interferometer operates with a single incident laser beam and uses the transverse electric and transverse magnetic modes as the sensing and reference beams, respectively, and it can easily detect 0.1 ppm lead(II) ions in water via nonspecific adsorption on the tapered layer of TiO2. The excellent linearity was obtained between the lead(II) concentration and the ratio of concentration to the phase-difference change (Δ[lowercase_phi_synonym]), suggesting that adsorption of lead(II) ions on the TiO2 film follows the Langmuir isotherm model. The saturation adsorption leads to Δ[lowercase_phi_synonym]max = 7.485π. By use of the eigenvalue equations for a homogeneous waveguide to fit the measured refractive-index (RI) sensitivity of the interferometer, the equivalent thickness of Teq = 26.05 nm for the tapered TiO2 layer used was achieved. With Teq = 26.05 nm and Δ[lowercase_phi_synonym]max = 7.485π and the thickness of 0.264 nm for the lead(II) adlayer, the adlayer RI was derived to be nad ≈ 1.945 at the maximum coverage. [ABSTRACT FROM AUTHOR]

Vibration analysis of vessels conveying blood flow embedded in viscous fluid is studied based on the modified strain gradient theory. The viscoelastic vessels are simulated as a non-classical Euler-Bernoulli beam theory. Employing Hamilton's principle, the governing equations for size-dependent vessels are derived. The Galerkin method is used in order to transform the resulting equations into general eigenvalue equations. The effects of the blood flow profile and its modification factors, red blood cells (RBCs) and hematocrit are considered in the blood flow. Besides, the influences of the constitutional material gradient scale, blood flow, internal pressure, structural damping coefficient, viscous fluid substrate and various boundary conditions on the natural frequencies and critical buckling velocities are studied. It is revealed that as the hematocrit, fluid viscosity of substrate, internal pressure and mass ratio increase, the natural frequencies and critical buckling velocities decrease. Furthermore, the results indicated that the strain gradient theory predicts the highest natural frequencies and critical buckling velocities among others. The results are compared with those available in the literature and good agreement has been observed. [ABSTRACT FROM AUTHOR]

Laplace's tidal equations govern the angular dependence of oscillations in stars when uniform rotation is treated within the so-called traditional approximation. Using a perturbation expansion approach, I derive improved expressions for the eigenvalue associated with these equations, valid in the asymptotic limit of large spin parameter q. These expressions have a relative accuracy of order q −3 for gravito-inertial modes, and q −1 for Rossby and Kelvin modes; the corresponding absolute accuracy is of order q −1 for all three mode types. I validate my analysis against numerical calculations, and demonstrate how it can be applied to derive formulae for the periods and eigenfunctions of Rossby modes. [ABSTRACT FROM AUTHOR]

This paper presents a proof of the existence of novel bound states of the two-photon quantum Rabi model at the collapse point. The two-photon Rabi model is interesting not only for its important role on non-linear light–matter interaction, but also for the exhibition of the many-energy-levels degenerating process called the 'spectral collapse'. The squeezing property of the two-photon annihilation and creation operators is the origin for this phenomenon which is well studied without the energy-slitting term ω0. However, many numerical studies have pointed out that with the presence of ω0, some low-level isolated states exist while other high energy states collapse to , which is known as incomplete spectral collapse. From the eigenvalue equation in real space, a pair of second order differential equations, which are similarly to the Schrödinger equation, are derived at the collapse point. These differential equations provide an explanation to the existence of isolated bound states below with the presence of the spin slitting ω0 and a better numerical method to generate those bound states. [ABSTRACT FROM AUTHOR]

The Hartree–Fock (HF) equation for atoms with closed (sub)shells is transformed with the pseudospectral (PS) method into a discrete eigenvalue equation for scaled orbitals on a finite radial grid. The Fock exchange operator and the Hartree potential are obtained from the respective Poisson equations also discretized using the PS representation. The numerical solution of the discrete HF equation for closed-(sub)shell atoms from He to No is robust, fast and gives extremely accurate results, with the accuracy superior to that of the previous HF calculations. A very moderate number of 33 to 71 radial grid points is sufficient to obtain total energies with 14 significant digits and occupied orbital energies with 12 to 14 digits in numerical calculations using the double precision (64-bit) of the floating-point format.The electron density at the nucleus is then determined with 13 significant digits and the Kato condition for the density and s orbitals is satisfied with the accuracy of 11 to 13 digits. The node structure of the exact HF orbitals is obtained and their asymptotic dependence, including the common exponential decay, is reproduced very accurately. The accuracy of the investigated quantities is further improved by performing the PS calculations in the quadruple precision (128-bit) floating-point arithmetic which provides the total energies with 25 significant digits while using only 80 to 130 grid points. [ABSTRACT FROM AUTHOR]

This paper investigates the time-local discretization, using Gaussian quadrature, of a class of diffusive operators that includes fractional operators, for application in fractional differential equations and related eigenvalue problems. A discretization based on the Gauss–Legendre quadrature rule is analyzed both theoretically and numerically. Numerical comparisons with both optimization-based and quadrature-based methods highlight its applicability. In addition, it is shown, on the example of a fractional delay differential equation, that quadrature-based discretization methods are spectrally correct, i.e. that they yield an unpolluted and convergent approximation of the essential spectrum linked to the fractional derivative, by contrast with optimization-based methods that can yield polluted spectra whose convergence is difficult to assess. [ABSTRACT FROM AUTHOR]

The linear stability and energy stability of the plane Poiseuille flow with the isotropic and anisotropic slip boundary conditions are theoretically analyzed and numerically calculated in this paper. The asymptotic expansions of the critical parameters for the linear stability and energy stability are derived from the eigenvalue equations characterizing the least stable modes. The critical Reynolds number for the linear stability based on 1.5 times of the bulk mean streamwise velocity is found to be R l 2 D ≈ (1 + 2741 l 2 ) R 0 2 D when the non-dimensional isotropic slip length l ≪ 1, where R 0 2 D ≈ 5772 is the critical Reynolds number under the no-slip boundary condition. The critical Reynolds numbers for the linear stability are calculated for a wide range of anisotropic slip lengths and are found to be no larger than their counterparts in the isotropic slip cases with the same streamwise slip lengths. In the energy stability analyses of the two-dimensional and three-dimensional plane Poiseuille flows with the isotropic slip boundary condition, the critical Reynolds numbers are found to be R l E 2 D ≈ (1 + 14.95 l 2 ) R 0 E 2 D and R l E 3 D ≈ (1 + 8.37 l 2 ) R 0 E 3 D , where R 0 E 2 D ≈ 87.6 and R 0 E 3 D ≈ 49.6 are their counterparts under the no-slip boundary condition. In the three-dimensional plane Poiseuille flow with the anisotropic slip boundary condition, the critical Reynolds number for the energy stability increases with the increase in streamwise slip length lx and with the decrease in spanwise slip length lz, and its first-order approximation is R l x , l z E 3 D ≈ [ 1 + 2.41 ( l x − l z ) ] R 0 E 3 D . [ABSTRACT FROM AUTHOR]

The bending vibration behavior of a non-uniform axially functionally graded Euler-Bernoulli beam is investigated based on the Chebyshev collocation method. The cross-sectional and material properties of the beam are assumed to vary continuously across the axial direction. The Chebyshev differentiation matrices are used to reduce the ordinary differential equations into a set of algebraic equations to form the eigenvalue problem associated with the free vibration. Some calculated results are compared with numerical results in the published literature to validate the accuracy of the present model. A good agreement is observed. The effects of the taper ratio, volume fraction index, and restraint types on the natural frequency of axially functionally graded beams with non-uniform cross section are examined. [ABSTRACT FROM AUTHOR]

We present a classical and a quantum constant of motion used to study the behavior of an electron moving in the vicinity of a tridimensional charged nanostructure with electric dipole. It is the generalization of the bidimensional version studied in a previous work. The classical case is found by using two approaches: the Hamilton Jacobi equation and a Newtonian treatment. The quantum case is obtained by separating the Schrödinger equation in spherical coordinates. We use three quantum numbers to classify the states. The angular part is solved by using an expansion of spherical harmonics to get an eigenvalue equation for the new constant of motion. The solution shows that the probability density of the electron shifts toward the values where 𝜃 < π 2 . The eigenvalue λ is near the value l(l + 1) of the angular momentum, but their difference grows if the electric dipole increases, so that the effect is small for a cluster like (GaAs)3 but very important for fullerenes like RbC60 and LiC60. The radial part is solved using the shooting method and we find the ground state, and first and second excited states. [ABSTRACT FROM AUTHOR]

The present work focuses on the effect of rotational restraints on the shear buckling of symmetrically laminated curved composite panels. The Sanders–Koiter shell theory and a first-order shear deformation scheme were used for the mathematical representation of the deformation kinematics of cylindrical shells. The eigenvalue buckling equations were obtained using the principle of minimum total potential energy and by employing the Ritz method. The solution for the deformed shape was approximated as a series of trigonometric functions compatible with the essential boundary conditions of the problem. The effect of the rotational and torsional springs was incorporated by adding their corresponding potential energy to the total potential energy of the panel-loading system. Using the developed formulation, the effect of the influential parameters such as aspect ratio, panel curvature and restraint stiffness on the buckling strength of a specific class of laminates was studied extensively. To present the results in a more insightful manner, non-dimensional parameters were used in parametric studies. To normalize the effect of torsional elements, a new non-dimensional parameter was introduced. [ABSTRACT FROM AUTHOR]

The investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is taken into account here. The buckling mode of the member flange is defined by rotation angle a flange about the line of its connection with the web. The channel column under investigation is made of unidirectional fibre-reinforced laminate. Two approaches to member orthotropic material modelling are performed: the homogenization with the aid of theory of mixture and periodicity cell or homogenization upon the Voigt–Reuss hypothesis. The fundamental differential equation of local buckling is derived with the aid of the stationary total potential energy principle. The critical buckling stress corresponding to a number of buckling half-waves is assumed to be a minimum eigenvalue of the equation. Some numerical examples dealing with columns are given here. The analytical results are compared with the finite element stability analysis carried out by means of ABAQUS software. The paper is focused on a close analytical solution of the critical buckling stress and the associated buckling mode while the web–flange cooperation is assumed. [ABSTRACT FROM AUTHOR]

Starting from the hyperoctahedral multivariate hypergeometric function of Heckman and Opdam (associated with the B C n root system), we arrive—via partial confluent limits in the sense of Oshima and Shimeno—at solutions of the eigenvalue equations for the quantum Toda chain with one-sided boundary perturbations of Pöschl-Teller type and for the hyperbolic quantum Calogero-Sutherland system in a Morse potential. With the aid of corresponding degenerations of the (bispectral dual) difference equations for the Heckman-Opdam hyperoctahedral hypergeometric function, it is deduced that the eigensolutions in question are holomorphic in the spectral variable. [ABSTRACT FROM AUTHOR]

We complete the stability study of general-relativistic spherically symmetric polytropic perfect fluid spheres, concentrating our attention on the newly discovered polytropes containing region of trapped null geodesics. We compare the methods of treating the dynamical stability based on the equation governing infinitesimal radial pulsations of the polytropes and the related Sturm–Liouville eigenvalue equation for the eigenmodes governing the pulsations, to the methods of stability analysis based on the energetic considerations. Both methods are applied to determine the stability of the polytropes governed by the polytropic index n in the whole range 0 < n < 5 , and the relativistic parameter σ given by the ratio of the central pressure and energy density, restricted by the causality limit. The critical values of the adiabatic index for stability are determined, together with the critical values of the relativistic parameter σ. For the dynamical approach, we implemented a numerical method which is independent on the choice of the trial function, and compare its results with the standard trial function approach. We found that the energetic and dynamic method give nearly the same critical values of σ. We found that all the configurations having trapped null geodesics are unstable according to both methods. [ABSTRACT FROM AUTHOR]

The 1/8 BPS D6ℛ4 coupling in type II string theory compactified on T2 receives contributions from worldsheet instantons and anti-instantons wrapping the T2, up to genus three in string perturbation theory. These involve contributions separately from bound states of instantons and anti-instantons, which are qualitatively similar to such contributions to the 1/2 and 1/4 BPS couplings. At genus two, the D6ℛ4 coupling also receives contributions from instanton/anti-instanton bound states unlike the 1/2 and 1/4 BPS couplings, which is a consequence of a T-duality invariant eigenvalue equation a term in the coupling satisfies. We solve this eigenvalue equation to obtain the complete structure of the worldsheet (anti)instanton contributions. In the type IIB theory, strong weak coupling duality leads to certain contributions involving bound states of D string (anti)instantons wrapping the T2. [ABSTRACT FROM AUTHOR]

The free vibration of axially functionally graded (FG) tapered Timoshenko curved beams is studied with the numerical approach. By using the non-uniform rational B-spline (NURBS) basis functions, the exact geometry and the generalized displacement field are formulated. Variable geometric parameters and material properties, including the curvature, cross-sectional area, area moment of inertia, mass density, and Young's modulus, are expanded as functions of the coordinate in a parametric domain. Based on Hamilton's principle, the weak formulation is derived by applying a refined constitutive relation which considers the thickness effect. Natural frequencies and mode shapes are obtained from the eigenvalue equation. Circular, elliptic, and parabolic curved beams are considered in numerical examples. The obtained results are in good agreement with those in the existing studies and those calculated by the finite element software ANSYS. Moreover, the effects of the material gradient, taper ratio, slenderness ratio, and height-span ratio on vibration behaviors are discussed. [ABSTRACT FROM AUTHOR]

We consider solutions of the eigenvalue equation at zero energy for a class of non-local Schrödinger operators with potentials decreasing to zero at infinity. Using a path integral approach, we obtain detailed results on the spatial decay at infinity of both L 2 and resonance solutions. We highlight the interplay of the kinetic term and the potential in these decay behaviours, and identify the decay mechanisms resulting from specific balances of global lifetimes with or without the potential. [ABSTRACT FROM AUTHOR]

By studying solutions of various forms of the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT)-based characteristic mode (CM) formulations, we have found that the proper choice of the weighting operator of the generalized eigenvalue equation is crucial in developing formulations that are immune from spurious solutions. Spurious modes of the Chang–Harrington surface formulation for CMs of lossless material bodies are shown to be solutions of a reverse problem where the material parameters of the background and the object are swapped. These unwanted modes can be avoided by removing the integral operators of the interior of the object from the weighting operator of the generalized eigenvalue equation. We also illustrate that to obtain physically meaningful eigenvalues with orthogonal far-field patterns, it is necessary to define that weighting operator so that it connects the eigensolutions to radiated power. [ABSTRACT FROM AUTHOR]

In this paper, the spin-one Duffin–Kemmer–Petiau equation in (1 + 3) dimensions with a modified Kratzer potential is considered in the non-commutative space framework. The energy eigenvalue equation and the corresponding eigenfunctions are derived analytically. Furthermore, the energy shift due to the space non-commutativity effect is also obtained using the perturbation theory. In particular, it is shown that the degeneracy of the initial spectral line is broken, where the space non-commutativity plays the role of a magnetic field. This behavior is very similar to the Zeeman effect. [ABSTRACT FROM AUTHOR]

A semi-analytical finite element numerical mode-matching (FNMM) method is developed to simulate microscopic structures of metasurfaces on the interfaces of the 3-D multilayered structure. Similar to the recently developed spectral element NMM method, the FNMM method reduces the original 3-D problem into a series of 2-D waveguide eigenvalue problems plus a 1-D layered medium problem, which can be analytically described by a recursion procedure. The 2-D eigenvalue problems in the horizontal directions are solved numerically by the mixed finite element method (MFEM) to remove the spurious modes in the conventional FEM. Therefore, it can effectively and accurately simulate electromagnetic wave interactions with the detail metasurfaces, especially for thick layers. Metasurfaces embedded on the interfaces of 3-D structures are treated by the generalized impedance boundary conditions, thus enabling their rapid yet accurate computation. This method is applied to characterize metasurfaces consisting of microscopic patterns with complex geometric construction with details much smaller than the wavelength. Numerical experiments indicate that the FNMM method is highly efficient and accurate for the microscopic metasurface models. [ABSTRACT FROM AUTHOR]

The present work discusses mechanical behaviors of an axially functionally graded (AFG) beam in micro scales subjected to a moving mass. The AFG microbeam is exposed to hygrothermal environments with a uniform temperature rise and a moisture concentration rise. The material properties of AFG microbeam are assumed to vary along the axial direction of the beam according to a power-law function and are temperature dependent. A microbeam model is developed based on a refined first order shear deformation theory (FSDT) in conjunction with the closed-form solution technique, in which the modified couple stress theory is implemented to account for size effect. The minimum energy strategy is applied to derive the eigenvalue equations associated to buckling and free vibrations of the microbeams, while the equations of motion related to the dynamic response are obtained by adoption of Lagrange method and solved using the Newmark- β method. A ceramic-metal AFG microbeam with simply-supported end constraints is taken as a numerical illustration to show the effects of hygrothermal environments, small scale on the mechanical behaviors of AFG microbeams subjected to a moving mass. • Mechanical response of AFG microbeams under hygrothermal environments is investigated. • A refined first order shear deformation theory is used. • Modified couple stress theory is employed. • Temperature-dependent material properties are considered. • The microbeams traversed by a mass. [ABSTRACT FROM AUTHOR]

While variation of the energy functional yields the Schrödinger equation in the usual, linear case, no such statement can be formulated in the general nonlinear situation when the Hamiltonian depends on its eigenvector. In this latter case, as we illustrate by sample numerical calculations, the points of the energy expectation value hypersurface where the eigenvalue equation is satisfied separate from those where the energy is stationary. We show that the variation of the energy at the eigensolution is determined by a generalized Hellmann–Feynman theorem. Functionals, other than the energy, can, however be constructed, that result the nonlinear Schrödinger equation upon setting their variation zero. The second centralized moment of the Hamiltonian is one example. [ABSTRACT FROM AUTHOR]

In a recent paper, Castellanos-Jaramillo and Castellanos-Moreno proposed a simple quantum-mechanical model for an electron in the vicinity of an ionized nanostructure with a permanent electric dipole. They chose the interaction of the electron with the charge and the dipole in such a way that the resulting Schrödinger equation is separable into radial and angular parts. In this comment, we show that those authors did not solve the angular eigenvalue equation with proper periodic boundary conditions and that they also made a mistake in the elimination of the first derivative in the radial equation. Such errors invalidate their results of the Einstein coefficients for the G a A s 3 system considered. [ABSTRACT FROM AUTHOR]

This paper introduces a cascadic adaptive finite element method for nonlinear eigenvalue equations arising from quantum physics following the multilevel correction strategy. Instead of the classical scheme, which requires solving nonlinear eigenvalue equations on a series of adaptive spaces directly, the new scheme consists of several smoothing processes on an adaptive space sequence and nonlinear eigenvalue equations being solved in a very low dimensional space. The main feature of the proposed scheme is that large-scale nonlinear eigenvalue problem solving is avoided, and the associated smoothing process can be executed efficiently based on the appropriate number of smoothing steps. Thus, efficiency can be enhanced by the proposed cascadic adaptive method. The good performance of the new finite element strategy is examined by various numerical experiments. [ABSTRACT FROM AUTHOR]

Toward a unified algebraic theory for mean-field Hamiltonian describing paired- and unpaired-mode effects, in this paper, we propose a generalized Hartree–Bogoliubov mean-field Hamiltonian in terms of fermion pair and creation-annihilation operators of the SO (2 N + 1) Lie algebra. We diagonalize the generalized Hartree–Bogoliubov mean-field Hamiltonian and throughout its diagonalization we can first obtain the unpaired mode amplitudes which are given by the self-consistent field parameters appeared in the Hartree–Bogoliubov theory together with the additional self-consistent field parameter in the generalized Hartree–Bogoliubov mean-field Hamiltonian and by the parameter specifying the property of the SO (2 N + 1) group. Consequently, it turns out that the magnitudes of these amplitudes are governed by such parameters. Thus, it becomes possible to make clear a new aspect of such results. We construct the Killing potential in the coset space SO (2 N) U (N) on the Kähler symmetric space which is equivalent to the generalized density matrix. We show another approach to the fermion mean-field Hamiltonian based on such a generalized density matrix. We derive an SO (2 N + 1) generalized Hartree–Bogoliubov mean-field Hamiltonian operator and a modified Hartree–Bogoliubov eigenvalue equation. We discuss on the mean-field theory related to the algebraic mean-field theory based on the generalized density matrix and the coadjoint orbit leading to the nondegenerate symplectic form. [ABSTRACT FROM AUTHOR]

The linear theory stability of different collisionless plasma sheath structures, including the classic sheath, inverse sheath and space-charge limited (SCL) sheath, is investigated as a typical eigenvalue problem. The three background plasma sheaths formed between a Maxwellian plasma source and a dielectric wall with a fully self-consistent secondary electron emission condition are solved by recent developed 1D3V (one-dimensional space and three-dimensional velocities), steady-state, collisionless kinetic sheath model, within a wide range of Maxwellian plasma electron temperature Te. Then, the eigenvalue equations of sheath plasma fluctuations through the three sheaths are numerically solved, and the corresponding damping and growth rates γ are found: (i) under the classic sheath structure (i.e. Te (the first threshold)), there are three damping solutions (i.e. γ1, γ2 and γ3, 0 > γ1 > γ2 > γ3) for most cases, but there is only one growth-rate solution γ when Te → Tec due to the inhomogeneity of sheath being very weak; (ii) under the inverse sheath structure, which arises when Te > Tec, there are no background ions in the sheath so that the fluctuations are stable; (iii) under the SCL sheath conditions (i.e. Te ≥ Te SCL the second threshold), the obvious ion streaming through the sheath region again emerges and the three damping solutions are again found. [ABSTRACT FROM AUTHOR]

Transferring knowledge from a source domain to a target domain by domain adaptation has been an interesting and challenging problem in many machine learning applications. The key problem is how to match the data distributions of the two heterogeneous domains in a proper way such that they can be treated indifferently for learning. We propose a covariance matching approach DACoM for semi-supervised domain adaptation. The DACoM embeds the original samples into a common latent space linearly such that the covariance mismatch of the two mapped distributions is minimized, and the local geometric structure and discriminative information are preserved simultaneously. The KKT conditions of DACoM model are given as a nonlinear eigenvalue equation. We show that the KKT conditions could at least ensure local optimality. An efficient eigen-updating algorithm is then given for solving the nonlinear eigenvalue problem, whose convergence is guaranteed conditionally. To deal with the case when homogeneous information could only be matched nonlinearly, a kernel version of DACoM is further considered. We also analyze the generalization bound for our domain adaptation approaches. Numerical experiments on simulation datasets and real-world applications are given to comprehensively demonstrate the effectiveness and efficiency of the proposed approach. The experiments show that our method outperforms other existing methods for both homogeneous and heterogeneous domain adaptation. [ABSTRACT FROM AUTHOR]

While the literature on numerical methods (e.g. finite elements and, to a certain extent, virtual elements) concentrates on convex elements, there is a need to probe beyond this limiting constraint so that the field can be further explored and developed. Thus, in this paper, we employ the virtual element method for non-convex discretizations of elastodynamic problems in 2D and 3D using an explicit time integration scheme. In the formulation, a diagonal matrix-based stabilization scheme is proposed to improve performance and accuracy. To address efficiency, a critical time step is approximated and verified using the maximum eigenvalue of the local (rather than global) system. The computational results demonstrate that the virtual element method is able to consistently handle general nonconvex elements and even non-simply connected elements, which can lead to convenient modeling of arbitrarily-shaped inclusions in composites. • Exploring arbitrarily-shaped polygons/polyhedra in computational mechanics. • The VEM is established for elastodynamics with explicit time integration. • Novel diagonal matrix-based stabilization scheme improves VEM performance (and accuracy). • The critical time step is evaluated using the maximum eigenvalue of a system of equations. [ABSTRACT FROM AUTHOR]

Quantum signatures of classical chaos in the spectral properties of non-relativistic quantum billiards are well understood by now based on the semiclassical and the random matrix theory aproach. The experimental detection of relativistic phenomena featured by graphene implicated an increasing interest in the properties of graphene billiards and relativistic quantum billiards consisting of massless spin-1/2 particles governed by the Dirac equation and confined to a planar domain. Confinement is attained by imposing appropriate boundary conditions on the wave function components. We chose those proposed for neutrino billiards. By now numerical studies have been performed on the spectral properties of neutrino billiards of various shapes. Our main focus is the question to what extent the semiclassical approach in terms of trace formulae applies to such systems. We derive trace formulae for circular and elliptical neutrino billiards. The associated eigenvalue equations have been solved analytically for the circular billiard. We present analytical solutions for elliptical neutrino billiards. [ABSTRACT FROM AUTHOR]

The onset of convection in a porous layer saturated by a power-law fluid is here investigated. The walls are considered to be isothermal, isobaric and permeable in such a way that a vertical throughflow is described. The threshold for a buoyancy-driven cellular flow is investigated by means of a linear stability analysis. This study consists in introducing disturbances with small amplitude. The disturbances are plane waves, i.e. a normal modes stability analysis of the basic stationary solution is performed. The resulting problem is an ordinary differential equation eigenvalue problem which is solved numerically by coupling the Runge–Kutta method with the shooting method. Results are presented in the form of marginal stability curves and their critical points representing the values of the control parameters such that the growth rate of the disturbances is zero. It is found that, among roll disturbances, the most unstable modes are stationary and uniform with infinite wavelength. For this reason, an asymptotic analysis for vanishing wave numbers is carried out. The results of this asymptotic analysis are obtained analytically displaying a very good agreement with the numerical solution. It is found that vertical throughflow plays a destabilising role for pseudoplastic fluids and a stabilising role for dilatant fluids. [ABSTRACT FROM AUTHOR]

Closed combustion devices like gas turbines and rockets are prone to thermoacoustic instabilities. Design engineers in the industry need tools to accurately identify and remove instabilities early in the design cycle. Many different approaches have been developed by the researchers over the years. In this work we focus on the Helmholtz wave equation based solver which is found to be relatively fast and accurate for most applications. This solver has been a subject of study in many previous works. The Helmholtz wave equation in frequency space reduces to a nonlinear eigenvalue problem which needs to be solved to compute the acoustic modes. Most previous implementations of this solver have relied on linearized solvers and iterative methods which as shown in this work are not very efficient and sometimes inaccurate. In this work we make use of specialized algorithms implemented in SLEPc that are accurate and efficient for computing eigenvalues of nonlinear eigenvalue problems. We make use of the n-tau model to compute the reacting source terms in the Helmholtz equation and describe the steps involved in deriving the Helmholtz eigenvalue equation and obtaining its solution using the SLEPc library. • Software for the early identification of thermoacoustic instabilities in closed combustion devices with arbitrary geometry. • Helmholtz wave equation in frequency space leading to a nonlinear eigenvalue formulation. • SLEPc's nonlinear eigensolver is fast and accurate, and can be run in parallel for large-scale problems. [ABSTRACT FROM AUTHOR]

Optical eigenvalues of the eigenvalue equation associated with the nonlinear Schrödinger equation (NLSE) are invariant during propagation in nonlinear dispersive fiber. Optical eigenvalue communication is expected to be a technology for overcoming the Kerr nonlinear limit. Several modulation methods based on optical eigenvalue have been proposed. In this paper, we demonstrate an arbitrary optical eigenvalue modulation scheme by numerical simulations and experiments. Based on the proposed scheme, the generation and transmission of a 65 536-ary eigenvalue-modulated signal is demonstrated by numerical simulation. Moreover, we experimentally demonstrate modulation, transmission, and demodulation of a 16-ary eigenvalue-modulated signal. The 16-ary signal represented by combinations of four eigenvalues can be successfully transmitted through a 100-km standard single-mode fiber line. [ABSTRACT FROM AUTHOR]

We consider the non-linear eigenvalue equations characterizing L p into L q Sobolev embeddings of second order for Navier boundary conditions at both ends of a line segment. We give a complete description of the s-numbers and the extremal functions in the general case (p , q) ∈ (1 , ∞) 2 . Among other results, we show that these can be expressed in terms of those of related first order embeddings, if and only if 1 p + 1 q = 1. Our findings shed new light on the surprising nature of higher order Sobolev spaces in the Banach space setting. [ABSTRACT FROM AUTHOR]