Showing papers on "Antisymmetric relation published in 2007"
TL;DR: In this paper, it was shown that the rotating black holes in an arbitrary number of dimensions possess the same hidden symmetry as the four-dimensional Kerr metric, besides the spacetime symmetries generated by the Killing vectors they also admit the (antisymmetric) Killing-Yano and symmetric Killing tensors.
Abstract: We demonstrate that the rotating black holes in an arbitrary number of dimensions and without any restrictions on their rotation parameters possess the same hidden symmetry as the four-dimensional Kerr metric. Namely, besides the spacetime symmetries generated by the Killing vectors they also admit the (antisymmetric) Killing-Yano and symmetric Killing tensors.
136 citations
TL;DR: In this paper, the authors present results from direct numerical simulations showing the suppression of the large-scale drift motion of an ensemble of charged particles in a nonuniform turbulent magnetic field.
Abstract: We present results from direct numerical simulations showing the suppression of the large-scale drift motion of an ensemble of charged particles in a nonuniform turbulent magnetic field. We find that when scattering is negligible, the ensemble average drift velocity is in the direction predicted by the usual guiding center theory. When scattering is very strong, we find that all large-scale drift motions vanish. For an intermediate amount of scattering we find that the antisymmetric drift velocity is typically suppressed by a larger amount than the antisymmetric drift coefficient. We show that the total drift motion of the ensemble is not necessarily completely contained in the antisymmetric part of the diffusion tensor. Because of the occurrence of scattering, knowledge of the spatial variation of the symmetric part of the diffusion tensor is also needed to fully describe the total drift motion of the ensemble.
107 citations
TL;DR: In this paper, the symmetric formation of twin vortices occurs close to the cylinder synchronized with the oscillatory component of the flow and gives rise to an antisymmetric arrangement of vortex structures further downstream.
103 citations
TL;DR: The antisymmetric sparse grid discretization to the electronic Schrodinger equation is applied and costs, accuracy, convergence rates and scalability are compared with respect to the number of electrons present in the system.
Abstract: We present a sparse grid/hyperbolic cross discretization for many-particle problems. It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results in a sparse grid discretization. Here, depending on the norms involved, different variants of sparse grid techniques for many-particle spaces can be derived that, in the best case, result in complexities and error estimates which are independent of the number of particles. Furthermore we introduce an additional constraint which gives antisymmetric sparse grids which are suited to fermionic systems. We apply the antisymmetric sparse grid discretization to the electronic Schrodinger equation and compare costs, accuracy, convergence rates and scalability with respect to the number of electrons present in the system.
89 citations
TL;DR: Antisymmetric orbit functions on the Euclidean space are antisymmetrized exponential functions as discussed by the authors, which are closely related to irreducible characters of a compact semisimple Lie group.
Abstract: In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corresponding to a Coxeter-Dynkin diagram. Properties of such functions are described. These functions are closely related to irreducible characters of a compact semisimple Lie group $G$ of rank $n$. Up to a sign, values of antisymmetric orbit functions are repeated on copies of the fundamental domain $F$ of the affine Weyl group (determined by the initial Weyl group) in the entire Euclidean space $E_n$. Antisymmetric orbit functions are solutions of the corresponding Laplace equation in $E_n$, vanishing on the boundary of the fundamental domain $F$. Antisymmetric orbit functions determine a so-called antisymmetrized Fourier transform which is closely related to expansions of central functions in characters of irreducible representations of the group $G$. They also determine a transform on a finite set of points of $F$ (the discrete antisymmetric orbit function transform). Symmetric and antisymmetric multivariate exponential, sine and cosine discrete transforms are given.
79 citations
TL;DR: In this paper, a new hyperbolic displacement model was proposed to account for parabolic distributions of transverse shear stresses and satisfy zero shear stress conditions at the top and bottom surfaces of the plate.
Abstract: Buckling and free vibration analysis of simply supported symmetric and antisymmetric cross-ply thick composite plates on elastic foundation are examined by a new hyperbolic displacement model in this paper. In this new model, inplane displacements vary as a hyperbolic function across the plate thickness, so account for parabolic distributions of transverse shear stresses and satisfy zero shear stress conditions at the top and bottom surfaces of the plate. In the analysis, the foundation is modeled as two parameter Pasternak type foundation, and Winkler type if the second foundation parameter is zero. The equation of motion for thick laminated rectangular plates resting on elastic foundation and subjected to inplane loads is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then buckling loads and fundamental frequencies are found by solving the results of eigenvalue problems. The numerical results obtained through the present analysis for free vib...
64 citations
TL;DR: In this article, the authors presented a damage assessment technique to extract damage information from the complicated PZT signals that could not be interpreted in time domain, and the results showed that the changes of power spectrum density in characteristic frequency band of symmetric and antisymmetric modes are proportional to the delamination size in quasi-isotropic Gr/Ep laminates.
Abstract: Piezo-ceramic transducers of the surface mounted type are commonly used for structural health monitoring (SHM) techniques. But, there is a disadvantage to use piezo-ceramic transducers of the surface mounted type in Lamb wave application. Due to the symmetric and antisymmetric Lamb wave modes generated by the surface mounted piezo-ceramic transducers simultaneously, the received signals are very complex and it is difficult to extract damage information from the signals. In this paper, the practical method for SHM was proposed using piezo-ceramic transducers of the surface mounted type and Lamb wave. In order to overcome the difficulties in the signal processing of the simultaneous modes, the symmetric and antisymmetric modes were separated by using the two sensors bonded on the opposite surfaces at the same point. Also, spectral analyses of the separated symmetric and antisymmetric Lamb waves showed that each mode propagated with different frequency characteristics in the exciting frequency range. By making use of these findings, the changes of power spectrum density in characteristic frequency band of symmetric and antisymmetric modes are proportional to the delamination size in quasi-isotropic Gr/Ep laminates. Therefore, this paper presents the damage assessment technique to extract damage information from the complicated PZT signals that could not be interpreted in time domain.
59 citations
TL;DR: In this article, spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps (cores), equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC), is studied.
Abstract: We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps (cores), equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling (the model may also be interpreted in terms of spatial solitons in parallel planar optical waveguides with a periodic modulation of the refractive index). Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral band gaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bistability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. In addition to the fundamental solitons, branches of twisted (odd) solitons in the AA system, and twisted bound states of fundamental solitons in both AA and RR systems, are found too. The impact of a phase mismatch, $\ensuremath{\Delta}$, between the OLs in the two cores is also studied. It is concluded that $\ensuremath{\Delta}=\ensuremath{\pi}∕2$ only mildly deforms the picture, while $\ensuremath{\Delta}=\ensuremath{\pi}$ changes it drastically, replacing the symmetry-breaking bifurcations by pseudobifurcations, with the branch of asymmetric solutions asymptotically approaching its symmetric or antisymmetric counterpart (in the AA and RR system, respectively), rather than splitting off from it. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing different spin states of the same atom) are coupled by linear interconversion. In that case, the symmetry-breaking bifurcations in the AA and RR models switch their character, if the interspecies nonlinear interaction becomes stronger than the intraspecies nonlinearity.
58 citations
TL;DR: From the EPR findings it has been shown that the compound [Cu(3)(PhPyCNO)(3)(OCH(3))(Cl)(ClO(4))] () having isosceles magnetic symmetry or lower (delta not equal 0), the antisymmetric exchange is important and DeltaE > hv.
Abstract: The use of phenyl 2-pyridyl ketoxime (PhPyCNO)/X−
“blends” (X− = OH−, Cl−, ClO4−) in copper chemistry has yielded trinuclear clusters that have been characterized as inverse-9-metallacrown-3 accommodating one or two anions. The magnetic behaviour has shown a large antiferromagnetic interaction. The discrepancy between the Brillouin curve and the experiment has been assigned to the influence of the antisymmetric interaction. By introducing in the magnetization formula the antisymmetric terms derived from the fitting of the susceptibility data the simulated curve become almost superimposable to the experimental one. From the EPR findings it has been shown that the compound [Cu3(PhPyCNO)3(OCH3)(Cl)(ClO4)] (1) having isosceles magnetic symmetry or lower (δ
≠ 0), the antisymmetric exchange is important (G
≠ 0) and ΔE > hv. The structures of the two complexes have been determined by single-crystal X-ray crystallography.
58 citations
TL;DR: The authors analyze a new approach for Jp* obtained by factorization of the matrix Delta within the bounds on its off-diagonal elements imposed by the positivity conditions of the two-particle reduced density matrix.
Abstract: The authors have investigated the description of the dispersion interaction within the Piris natural orbital functional (PNOF) theory. The PNOF arises from an explicit antisymmetric approach for the two-particle cumulant in terms of two symmetric matrices, Δ and Λ. The functional forms of these matrices are obtained from the generalization of the two-particle system expressions, except for the off-diagonal elements of Δ. The mean value theorem and the partial sum rule obtained for the off-diagonal elements of Δ provide a prescription for deriving practical functionals. In particular, the previous employed approximation {Jpp∕2} for the mean values {Jp*} affords several molecular properties but it is incapable to account for dispersion effects. In this work, the authors analyze a new approach for Jp* obtained by factorization of the matrix Δ within the bounds on its off-diagonal elements imposed by the positivity conditions of the two-particle reduced density matrix. Additional terms for the matrix elements...
49 citations
TL;DR: The role of the different components of the AS in the low-temperature magnetic behavior of V15 was analyzed, and a perfect fit was reached to the experimental data on the staircaselike dependence of magnetization versus field in the whole temperature range including extremely low temperature.
Abstract: In this article, the low-temperature static (adiabatic) magnetization data of the nanoscopic V-15 cluster present in K-6[(V15As6O42)-As-IV(H2O)]center dot 8H(2)O is analyzed. The cluster anion, which attracted much attention in the past, contains a triangular V-3(IV) array causing frustration as a function of applied field and temperature. In the analysis, a three-spin (S = 1/2) model of V-15 was employed that includes isotropic antiferromagnetic exchange interaction and antisymmetric (AS) exchange in the most general form compatible with the trigonal symmetry of the system. It was shown that, along with the absolute value of AS exchange, the orientation of the AS vector plays a significant physical role in spin-frustrated systems. In this context, the role of the different components of the AS in the low-temperature magnetic behavior of V-15 was analyzed, and we were able to reach a perfect fit to the experimental data on the staircaselike dependence of magnetization versus field in the whole temperature range including extremely low temperature. Furthermore, it was possible for the first time to precisely estimate the two components of the AS vector coupling constant in a triangular unit, namely, the effective in-plane component, D, and the perpendicular part, D-n.
TL;DR: In this article, the lower lying states of a hydrogenic impurity, located at the centre of an infinite barrier lens-shaped quantum dot (LSQD), are calculated analytically in parabolic rotational coordinates.
Abstract: The lower-lying states of a hydrogenic impurity, located at the centre of an infinite barrier lens-shaped quantum dot (LSQD), are calculated analytically in parabolic rotational coordinates. The solutions are obtained directly using the Frobenius method and by transforming the separated differential equations into the Whittaker equation. Results are given for both symmetric and asymmetric LSQDs. It is found that the energy states of the system are positive for a very small LSQD and decrease as the size of the dot increases. They become negative as the size increases, and approach the energy states of a free hydrogen atom. Also symmetric and antisymmetric eigenfunctions have been constructed for a hydrogenic impurity in a symmetric LSQD. Antisymmetric eigenfunctions can be used as eigenfunctions of a hydrogenic impurity located at the surface of a semi-LSQD.
TL;DR: In this paper, the applicability and accuracy of a recently developed differential quadrature (DQ) methodology, for nonlinear analysis of composite plates, was explored and comparative studies were made between two approaches for different cases.
TL;DR: In this article, the symmetric and antisymmetric multivariate sine and cosine functions are studied, which are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space.
Abstract: Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms involving the symmetric and antisymmetric multivariate sine and cosine functions.
TL;DR: In this article, a matrix-integral system derived from antisymmetric inner products involving the potential operators is constructed and solved for the Schrodinger equation with computational complexity competitive with current methods.
Abstract: The wavefunction for the multiparticle Schr\"odinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions, and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods.
TL;DR: In this article, an analytical formulation and solution for the stress analysis of simply supported antisymmetric angle-ply composite and sandwich plates was presented. But the results were not reported in the literature based on a higher order refined computational model with twelve degrees of freedom.
TL;DR: In this paper, the reduced form of displacement field is developed for long antisymmertic angle-ply composite laminates subjected to extensional and/or torsional loads.
TL;DR: Based on the three-dimensional linear elastic equations and magnetoelectroelastic constitutive relations, propagation of symmetric and antisymmetric Lamb waves in an infinite magneto-elastic plate is investigated in this paper.
TL;DR: In this article, the relation of vector Proca field formalism and antisymmetric tensor-field formalism for spin-one resonances in the context of the large NC inspired chiral resonance Lagrangian systematically up to the order O(p6) was studied.
Abstract: We study the relation of vector Proca field formalism and antisymmetric tensor-field formalism for spin-one resonances in the context of the large NC inspired chiral resonance Lagrangian systematically up to the order O(p6) and give a transparent prescription for the transition from vector to antisymmetric tensor Lagrangian and vice versa. We also discuss the possibility to describe the spin-one resonances using an alternative “mixed” first order formalism, which includes both types of fields simultaneously, and compare this one with the former two. We also briefly comment on the compatibility of the above lagrangian formalisms with the high-energy constraints for a concrete VVP correlator.
TL;DR: In this paper, the authors define and study symmetric and antisymmetrized multivariate exponential functions, defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable.
Abstract: We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found.
TL;DR: It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix.
Abstract: A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincare sphere are studied.
TL;DR: In this paper, the anti-self-dual (ASD) Lagrangians on path spaces have been used for variational resolution of nonlinear PDEs of the form Λu + Au + ∂φ(u) + f = 0.
Abstract: The theory of anti-self-dual (ASD) Lagrangians, introduced in [6], is developed further to allow for a variational resolution of nonlinear PDEs of the form Λu + Au + ∂φ(u) + f = 0 where φ is a convex lower-semicontinuous function on a reflexive Banach space X, f ∈ X*, A : D(A) ⊂ X X* is a positive linear operator, and where Λ : D(λ) ⊂ X X* is a nonlinear operator that satisfies suitable continuity and antisymmetry properties. ASD Lagrangians on path spaces also yield variational resolutions for nonlinear evolution equations of the form u(t) + Λu(t) + Au(t) + ∂φ(u(t)) + f = 0 starting at u(0) = u0. In both stationary and dynamic cases, the equations associated to the proposed variational principles are not derived from the fact that they are critical points of the action functional, but because they are also zeroes of the Lagrangian itself. For that we establish a general nonlinear variational principle that has many applications, in particular to Navier-Stokes-type equations, to generalized Choquard-Pekar Schrodinger equations with nonlocal terms, as well as to complex Ginsburg-Landau-type initial-value problems. The case of Navier-Stokes evolutions is more involved and will be dealt with in [9]. The general theory of antisymmetric Hamiltonians and its applications is developed in detail in an upcoming monograph (7). © 2007 Wiley Periodicals, Inc.
TL;DR: In this paper, the collective state space of two dipole-dipole interacting four-level atoms was shown to contain a four-dimensional decoherence-free subspaces.
Abstract: Decoherence-free subspaces (DFS's) in systems of dipole-dipole interacting multilevel atoms are investigated theoretically. It is shown that the collective state space of two dipole-dipole interacting four-level atoms contains a four-dimensional DFS. We describe a method that allows us to populate the antisymmetric states of the DFS by means of a laser field, without the need for a field gradient between the two atoms. We identify these antisymmetric states as long-lived entangled states. Further, we show that any single-qubit operation between two states of the DFS can be induced by means of a microwave field. Typical operation times of these qubit rotations can be significantly shorter than for a nuclear spin system.
Journal Article•
TL;DR: Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied and the problem of preservation of these properties by n-ary operations is considered.
Abstract: Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n-ary operations is considered. Namely, with the use of fuzzy relations R 1 ,.. R n and n-argument operation F on the interval [0,1], a new fuzzy relation R F = F(R 1 ,..,R n ) is created. Characterization theorems concerning the problem of preservation of fuzzy relations properties are given. Some conditions on aggregation functions are weakened in comparison to those previously given by other authors.
TL;DR: In this paper, the authors show that the spin triplet superconductivity in non-centrosymmetric systems is stabilized by antisymmetric spin-orbit coupling even if the magnetic field is absent.
Abstract: We show that the nonuniform state [Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state] of the spin triplet superconductivity in noncentrosymmetric systems is stabilized by antisymmetric spin–orbit coupling even if the magnetic field is absent. The transition temperature of the spin triplet superconductivity is reduced by the antisymmetric spin–orbit coupling in general. This pair breaking effect is shown to be similar to the Pauli pair breaking effect due to magnetic field for the spin singlet superconductivity, in which FFLO state is stabilized near the Pauli limit (or Chandrasekhar–Clogston limit) of external magnetic field. Since there are gapless excitations in nonuniform superconducting state, some physical quantities such as specific heat and penetration depth should obey different temperature-dependences from those in the uniform superconductivity. We discuss the possibility of the realization of nonuniform state in CePt 3 Si.
TL;DR: This work puts forward existence of surface breathers, which represent two-frequency modes localized about the array edges, and provides classification of the modes based on the anti-continuum limit, and discusses relation between surface and bulk modes.
Abstract: We present the complete set of symmetric and antisymmetric (edge and corner) surface modes in finite one- and two-dimensional arrays of waveguides. We provide classification of the modes based on the anti-continuum limit, study their stability and bifurcations, and discuss relation between surface and bulk modes. We put forward existence of surface breathers, which represent two-frequency modes localized about the array edges.
TL;DR: The DFT calculations show that the origin of the problem is a drastic, 2 orders of magnitude decrease of the infrared intensity of the C=C antisymmetric stretching upon electron addition, and no infrared band can be easily associated to this mode in charge-transfer (CT) solids with rho approximately > 0.5.
Abstract: We have combined DFT calculations with single-crystal polarized infrared spectra to reinvestigate the assignment of the CC antisymmetric stretching mode b2uν18 of p-chloranil (CA). The frequency of this mode indeed seems to display a nonlinear dependence on the average charge on the CA molecule (ρ), at variance with the behavior of the antisymmetric CO stretching frequency. The DFT calculations show that the origin of the problem is a drastic, 2 orders of magnitude decrease of the infrared intensity of the CC antisymmetric stretching upon electron addition. Therefore, no infrared band can be easily associated to this mode in charge-transfer (CT) solids with ρ ≳ 0.5. On the other hand, a linear relationship between ρ and the b2uν18 frequency is found in quasi-neutral CT complexes of CA.
TL;DR: In this article, a two-dimensional (2D) electron gas layer interacting with a slab of conductive material is treated in the local limit and the frequency of the coupled mode corresponding to the extended 2D plasmon interacting with the background plasmons is obtained.
Abstract: We present a calculation for a two-dimensional (2D) electron gas layer interacting with a slab of conductive material We treat the plasmons in the slab in the local limit and obtain the frequency of the coupled mode corresponding to the extended 2D plasmon interacting with the background plasmons in the presence of a conducting surface The dispersion equation of a double quantum well is obtained and we show how the split symmetric and antisymmetric modes are formed and modified by the localized surface plasmon For a single layer, we show that when a one-dimensional (1D) periodic electrostatic potential is applied to the surface, each of the symmetric and antisymmetric modes will be further split by the interaction with the 1D modulation, leading to folding of plasmon dispersion curves for different modes For double layers, we show that the coupled 2D and surface plasmons may result in radiated energy Our analysis is based on a calculation of the surface response function obtained using a transfer-matrix method
TL;DR: In this article, the authors numerically studied a new type of infrared resonator structure, whose unit cell consists of paired split-ring resonators (SRRs), at different resonant frequencies, the magnetic dipoles induced from the two SRRs within one unit cell can be parallel or antiparallel, respectively.
Abstract: In this paper, we numerically study a new type of infrared resonator structure, whose unit cell consists of paired split-ring resonators (SRRs). At different resonant frequencies, the magnetic dipoles induced from the two SRRs within one unit cell can be parallel or antiparallel, which are defined as symmetric and antisymmetic modes, respectively. Detailed simulation indicates that the symmetric mode is due to magnetic coupling to resonators, in which the effective permeability could be negative. However, the antisymmetric mode originating from strong electric coupling may contribute to negative effective permittivity. Our new electromagnetic resonators with pronounced magnetic as well as electric responses could provide a new pathway to design negative index materials (NIMs) in the optical region.
TL;DR: A neural network is developed to predict cut-off dimensionless frequencies of the antisymmetric circumferential waves propagating around an elastic circular cylindrical shell of different radius ratio b/a (a, outer radius; b, inner radius).
Abstract: A neural network is developed to predict cut-off dimensionless frequencies of the antisymmetric circumferential waves (Ai) propagating around an elastic circular cylindrical shell of different radius ratio b/a (a, outer radius; b, inner radius). The useful data to train and test the performances of the model are determinated from calculated trajectories of natural modes of resonances or extracted from time-frequency representations of Wigner-Ville of the acoustic backscattered time signal obtained from a computation. In this work, the studied tubes are made of aluminum or stainless steel. The material density, the radius ratio b/a, the index i of the antisymmetric waves, and the propagation velocities in the tube, are selected like relevant entries of the model of neural network. During the development of the network, several configurations are evaluated. The optimal model selected is a network with two hidden layers. This model is able to predict the cut-off dimensionless frequencies with a mean relative error (MRE) of about 1%, a mean absolute error (MAE) of 3.10-3 k 1a, and a standard error (SE) of 10-3 k1a(k1a is the dimensionless frequency, k1 is the wave number in water)