Components Of Tensor Research Articles

CALCULATION OF SHELLS BASED ON THE MIXED FEM VARIANT WITH TENSOR-VECTOR APPROXIMATION OF THE DESIRED VALUES

An algorithm for calculating thin shells based on the mixed finite element method (FEM) in a two-dimensional formulation is proposed. To correctly take into account possible displacements of the shell as a rigid body, the algorithm implements the developed tensor-vector form of the interpolation procedure of the desired values, which were chosen as the tensors of deformations and curvature at the point of the middle surface and the displacement vectors of this point. The discretization element was a quadrangular fragment of the middle surface with unknown nodes in the form of location and their first derivatives, as well as components of strain and curvature tensors among the inner surface at the nodes of the finite element. After minimizing the modified mixed functional, a 36?36 finite element stiffness matrix is formed. In order to verify the developed algorithm, a number of test problems were solved for calculating a fragment of an elliptical cylinder with an analytical solution, as well as for calculating a shell with spring supports that allow the ellipsoidal shell to move as an absolutely rigid body. Analysis of the obtained results showed that when calculating a fragment of an elliptical cylinder, the calculation scheme of which makes it possible to obtain an analytical solution, the numerical values of bending moments and normal stresses completely coincide with the values calculated from the condition of static equilibrium. An analysis of the calculation results for an ellipsoidal shell with spring supports led to the conclusion that the developed tensor-vector interpolation procedure in the mixed FEM version allows one to correctly take into account the displacements of shells as solids and obtain an adequate assessment of their stress-strain state.

Cortical morphological networks for profiling autism spectrum disorder using tensor component analysis.

Atypical neurodevelopmental disorders such as Autism Spectrum Disorder (ASD) can alter the cortex morphology at different levels: (i) a low-order level where cortical regions are examined individually, (ii) a high-order level where the relationship between two cortical regions is considered, and (iii) a multi-view high-order level where the relationship between regions is examined across multiple brain views. In this study, we propose to use the emerging multi-view cortical morphological network (CMN), which is derived from T1-w magnetic resonance imaging (MRI), to profile autistic and typical brains and pursue new ways of fingerprinting 'cortical morphology' at the intersection of 'network neuroscience'. Each CMN view models the pairwise morphological dissimilarity at the connection level using a specific cortical attribute (e.g., thickness). Specifically, we set out to identify the inherently most representative morphological connectivities shared across different views of the cortex in both autistic and normal control (NC) populations using tensor component analysis. We thus discover the connectional profiles of both populations shared across different CMNs of the left and right hemispheres, respectively. One of the most representative morphological cortical attributes for assessing the abnormal brain structures in patients with ASD is cortical thickness. The most representative morphological connectivities in multi-view CMN population of normal control and ASD subjects, respectively, and in both left and right hemispheres within the temporal, frontal, and insular lobes of individuals with ASD. These representative connectivities are corresponded to specific clinical features observed in individuals with ASD.

Curvature analysis of concircular trajectories in doubly warped product manifolds

<p>The aim of this research paper was to explore the various characteristics of the doubly warped product manifold, focusing particularly on aspects such as the Hessian, Riemannian curvature, Ricci curvature, and concircular curvature tensor components. By examining the necessary conditions that would classify the manifold as Riemann-flat, Ricci-flat, and concircularly-flat, the study aimed to expand our understanding of these concepts. To achieve this, the research incorporated the application of these findings to a generalized Robertson-Walker doubly warped product manifold scenario. This approach allowed us to identify and analyze the specific circumstances under which the manifold displayed concircular flatness.</p>

Коэффициенты электромагнитных связанностей композита "пьезоэлектрик / феррит" с учетом реальной структуры и начальных напряжений

New improved analytical solutions are obtained for tensors of effective pyro– electro–magneto–elastic properties of a piezoactive composite at initial stress-strain state (resulting from initial loading) that account for real two-point correlation functions of an irregular quasi-periodic random structure. The calculations of effective coefficients of electromagnetic and magnetoelectric coupling of the transversal isotropic unidirectional fibrous composite "PZT-4/ferrite" with an axisymmetric tensor of initial strain of the composite are presented. An increase in the absolute values of the effective coefficients is observed at negative (compressive) values of the initial strain tensor components of the composite.

ATOMISTIC AND CONTINUAL DETERMINATION OF STRESS FIELDS AT A CRACK TIP IN ANISOTROPIC ENVIRONMENT WITH CUBIC SYSTEM

The article presents a comparative analysis of stresses associated with a crack tip in an anisotropic medium with cubic symmetry of elastic properties under mixed mode loading conditions, using two different approaches: atomistic and continuum approaches. The atomistic approach is based on the use of the molecular dynamics method implemented in the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The continuum approach is based on the classical theory of elasticity of anisotropic media, in which the mechanical fields associated with the crack tip are represented using series that generalize the well-known representation of M. Williams to the case of anisotropic media. Using the method of molecular dynamics, a large series of calculations of loading of single-crystal copper and aluminum plates with a face-centered crystal lattice, weakened by a central crack, was carried out using the embedded atom potential (EAM). Molecular dynamics modeling is aimed at determining atomistic stresses and strains near the crack tip. The calculated atomistic stresses were compared with the stress field determined by the continuum theory of elasticity of anisotropic media for crystal lattices with cubic symmetry of elastic properties. A comparative analysis was carried out for the angular dependences of the stress and strain tensor components at different distances from the crack tip for the entire range of mixed strain modes: from perfect normal tension to loadings close to perfect transverse shear. It is established that the fields found on the basis of two fundamentally different approaches (discrete and continuum) are fully consistent with each other. It is demonstrated that the mathematical methods of continuum fracture mechanics can be used to describe stress, strain, and displacement fields at the atomistic level.

Computer homogenization of porous piezoceramics of different ferrohardness with random porous structure and inhomogeneous polarization field

The article is concerned with the homogenization problems, in which the effective moduli of porous piezoceramic composites are determined taking into account the inhomogeneity of the polarization field. The homogenization problems are solved by the finite element method in the framework of the theory of effective moduli and the Hill energy principle using the ANSYS package. To this end, in static problems of electroelasticity, the displacements and electric potential, which are linear in spatial variables, are specified on the boundary of a representative volume to provide constant stress and electric induction fields for a homogeneous reference medium. After solving a set of boundary value problems under different boundary conditions and determining the volume-averaged stress components and the electric induction vector, a complete set of effective moduli for the piezoelectric composite is calculated. A representative volume of the piezocomposite is created in the form of a regular finite element mesh consisting of cubic elements. Pores in the representative volume are assumed to be filled with a piezoelectric material with extremely small moduli. Finite elements with pore properties are selected according to a simple random algorithm. The inhomogeneous polarization field is found by solving an electrostatic problem, in which the polarization process in the representative volume is modeled based on a simplified linear formulation. The local coordinate systems for individual finite elements of the composite matrix are specified by the directions of the polarization vectors. In the following, when solving the problems of electroelasticity, these local coordinate systems associated with the elements of the piezoelectric matrix allow recalculating the material properties according to the formulas of transformation of the tensor components as the coordinate systems rotate. In addition, consideration is given to different models describing the change in the moduli of the material from an unpolarized state to a polarized one as a function of the polarization vector. Computational experiments were carried out for three types of piezoceramics: soft ferroelectric piezoceramics PZT-5H, piezoceramics PZT-4 of medium ferrohardness, and piezoceramics PZT-8 with higher degree of ferrohardness. The dependences of the effective moduli on porosity are compared for different laws of polarization inhomogeneity and different kinds of piezoceramic material of the composite matrix.

FEATURES OF THE CONSTRUCTION OF THE STIFFNESS MATRIX OF THE SPATIAL HEXAGONAL FINITE ELEMENT FOR COMPOSITE MATERIAL WITH DISCRETE INCLUSIONS BASED ON THE MOMENT SCHEME

An approach to numerical modeling of the stress-strain state of composite structures with discrete inclusions is presented in the paper. The finite element method is used as the main method, namely its modification – the moment finite-element scheme. The moment scheme, in contrast to the classic scheme of finite elements, allows to avoid such negative properties as not taking in consideration the rigid rotation of the finite element and “false” shear. If both the material of the matrix and the material of the reinforcing inclusions are weakly compressible, then problems arise due to the fact that some elastic constants approach very large values. The Taylor series expansion of the components of the displacement vector, the components of the strain tensor, and the volume change function is used in order to eliminate the mentioned shortcomings, after that, according to the moment scheme, certain sums are removed from these expansions. Homogenization of the material with lamellar inclusions, a small proportion of spherical inclusions, and a large proportion of spherical inclusions is used for modeling the elastic properties of the composite. The chaotic nature of the location of inclusions after homogenization makes it possible to present a non-homogeneous composite material as a homogeneous quasi-isotropic one. The described approaches are used in the construction of the stiffness matrix of the spatial hexagonal finite element. The obtained expressions for the stiffness matrix are done in the software package for calculating structures from composite materials. The calculation of a thick-walled pipe under the action of internal pressure from a composite material with lamellar inclusions, a small proportion of spherical inclusions, and a large proportion of spherical inclusions was carried out using the software package. For different volume fractions of discrete inclusions, the numerical convergence of the results with different finite element meshes has been investigated, which shows great congruence with analytical solutions.

ON THE RECONSTRUCTION OF PRESTRESS FIELDS IN A HOLLOW CYLINDER

The present research is devoted to the development of the theoretical foundations of nondestructive acoustic method for identifying inhomogeneous prestress fields in a hollow cylinder, depending on the probing loading type. A linearized model of steady oscillations of an elastic body in the presence of an inhomogeneous prestress field of arbitrary nature is considered in the standard and weak formulations. On the basis of this model, we formulate a problem for a cantilever-clamped prestressed hollow cylinder that performs steady axisymmetric vibrations under three types of probing loading. A corresponding weak formulation of the problem in the cylindrical coordinate system is presented, in which six independent components of the prestress tensor are taken into account. At that, a case of prestress fields obtained by applying some initial mechanical external static load is considered. In the presence and absence of prestresses of various types, amplitude-frequency dependences are analyzed, and resonant and natural frequencies are found in a wide frequency range. Numerical calculations were carried out using the FEM on a non-uniform grid; mesh refinement is carried out in the vicinity of the boundary points, where the type of boundary conditions changes. Based on the numerical solution of an auxiliary set of direct problems, seven types of prestress fields are constructed, differing in the types of initial loading, most often encountered in practice. To assess the possibility of implementing the procedure for reconstructing prestresses of each of the considered types, a sensitivity analysis was additionally performed, which showed that for some prestress types there are frequencies and types of probing loading for which the presence of prestress is practically not manifested. The sensitivity analysis performed made it possible to implement the optimal method of probing loading when solving the inverse coefficient problem. The statement of the new inverse problem on the restoration of arbitrary inhomogeneous prestress fields in the considered finite hollow cylinder is formulated. When restoring the prestress of a given structure, the inverse problem is reduced to finding a set of parameters from an ill-conditioned algebraic system, which was studied with the help of the A.N. Tikhonov regularization method. Additional data for solving the inverse problem was obtained on the basis of probing both via a single load and via combined probing modes. It has been found that it is most effective to use a combined loading mode and use a sufficiently wide frequency range when selecting sounding frequencies. The results of computational experiments on the reconstruction of six components of the prestress tensor are presented and analyzed, and recommendations are proposed for choosing the optimal modes of acoustic sounding.

Onsager Reciprocal Relation between Anomalous Transverse Coefficients of an Anisotropic Antiferromagnet.

Whenever two irreversible processes occur simultaneously, time-reversal symmetry of microscopic dynamics gives rise, on a macroscopic level, to Onsager's reciprocal relations, which impose constraints on the number of independent components of any transport coefficient tensor. Here, we show that in the antiferromagnetic YbMnBi_{2}, which displays a strong temperature-dependent anisotropy, Onsager's reciprocal relations are strictly satisfied for anomalous electric (σ_{ij}^{A}) and anomalous thermoelectric (α_{ij}^{A}) conductivity tensors. In contradiction with what was recently reported by Pan etal. [Nat. Mater. 21, 203 (2022)NMAACR1476-112210.1038/s41563-021-01149-2], we find that σ_{ij}^{A}(H)=σ_{ji}^{A}(-H) and α_{ij}^{A}(H)=α_{ji}^{A}(-H). This equality holds in the whole temperature window irrespective of the relative weights of the intrinsic or extrinsic mechanisms. The α_{ij}^{A}/σ_{ij}^{A} ratio is close to k_{B}/e at room temperature but peaks to an unprecedented magnitude of 2.9k_{B}/e at ∼150 K, which may involve nondegenerate carriers of small Fermi surface pockets.

Controlled light energy and perfect absorption in twisted bilayer graphene.

We theoretically study the components of the dynamical optical conductivity tensor and associated finite-frequency dielectric response of bilayer graphene (BLG), where one graphene layer can slide in-plane or commensurably twist on top of the other. Our results reveal that even slight deviations from the conventional AA, AB, or AC stacking orders yield a finite transverse conductivity. Upon calculating the optical conductivity of the BLG at any arbitrary interlayer displacement, Δ, and chemical potential, µ, it is utilized for a layered device with an epsilon-near-zero (ENZ) insert and metallic back plate. We find that both Δ and µ can effectively control the polarization, energy flow direction, and absorptivity of linearly polarized incident light. By appropriately tailoring Δ and µ, near-perfect absorption and tunable dissipation can be accessible through particular angles of incidence and a broad range of ENZ layer thicknesses. Our findings can be applied to the design of programmable optoelectronics devices.

Estimating the Inertia Tensor Components of an Asymmetrical Spacecraft When Removing It from the Operational Orbit at the End of Its Active Life

The paper presents a method for estimating the inertia tensor components of a spacecraft that has expired its active life using measurement data of the Earth’s magnetic field induction vector components. The implementation of this estimation method is supposed to be carried out when cleaning up space debris in the form of a clapped-out spacecraft with the help of a space tug. It is assumed that a three-component magnetometer and a transmitting device are attached on space debris. The parameters for the rotational motion of space debris are estimated using this measuring system. Then, the known controlled action from the space tug is transferred to the space debris. Next, measurements for the rotational motion parameters are carried out once again. Based on the available measurement data and parameters of the controlled action, the space debris inertia tensor components are estimated. It is assumed that the measurements of the Earth’s magnetic field induction vector components are made in a coordinate system whose axes are parallel to the corresponding axes of the main body axis system. Such an estimation makes it possible to effectively solve the problem of cleaning up space debris by calculating the costs of the space tug working body and the parameters of the space debris removal orbit. Examples of numerical simulation using the measurement data of the Earth’s magnetic field induction vector components on the Aist-2D small spacecraft are given. Thus, the purpose of this work is to evaluate the components of the space debris inertia tensor through measurements of the Earth’s magnetic field taken using magnetometer sensors. The results of the work can be used in the development and implementation of missions to clean up space debris in the form of clapped-out spacecraft.

Probing magnetoelectric effect in the spin-modulated magnet Fe2GeO4

The distinct spin amplitude wave was reported in a highly frustrated magnetic compound Fe2GeO4, which is very different from observations on other members of the M2GeO4 (M = Fe, Co, and Ni) family, raising interest in this compound for some additional emergent phenomena. In particular, this non-uniform spin order allows the intrinsic connection between ferroelectric polarization and magnetically gradient structure to probe the potential linear magnetoelectric (ME) effect. In this work, we address this issue and investigate the magnetism of Fe2GeO4 single crystal that hosts two successive anomalies at antiferromagnetic (AFM) Néel temperatures T N1 ∼ 7.5 K and T N2 ∼ 6.7 K, respectively. Our results reveal a remarkable metamagnetic transition in the magnetization as a function of the magnetic field, occurring at a critical magnetic field H c ∼ 4.1 T when applied along the [110] and [1–10] directions, while such transition along the [001] direction is pointedly absent. Further exploration uncovers two predominant off-diagonal ME coefficients αyz and αzy in the incommensurate AFM phase between T N1 and T N2. Additionally, all components of the linear ME tensor remain non-vanishing in the canting AFM phase below T N2. This indicates the ME mechanisms for the two phases that may be driven by different magnetic structures. All these presented results are sufficient for us to draw a non-trivial ME phase diagram, which is beneficial to understanding the ME behavior of Fe2GeO4. Therefore, our study implies that Fe2GeO4, an unusual frustrated magnet, provides a platform for manipulating the fascinating ME effect in the spinel structure.

Neighbor List Artifacts in Molecular Dynamics Simulations.

Molecular dynamics (MD) simulations are widely used in biophysical research. To aid nonexpert users, most simulation packages provide default values for key input parameters. In MD simulations using the GROMACS package with default parameters, we found large membranes to deform under the action of a semi-isotropically coupled barostat. As the primary cause, we identified overly short outer cutoffs and infrequent neighbor list updates that resulted in missed nonbonded interactions. Small but systematic imbalances in the apparent pressure tensor then induce unphysical asymmetric box deformations that crumple the membrane. We also observed rapid oscillations in averages of the instantaneous pressure tensor components and traced these to the use of a dual pair list with dynamic pruning. We confirmed that similar effects are present in MD simulations of neat water in atomistic and coarse-grained representations. Whereas the slight pressure imbalances likely have minimal impact in most current atomistic MD simulations, we expect their impact to grow in studies of ever-larger systems with coarse-grained representation, in particular, in combination with anisotropic pressure coupling. We present measures to diagnose problems with missed interactions and guidelines for practitioners to avoid them, including estimates for appropriate values for the outer cutoff rl and the number of time steps nstlist between neighbor list updates.

Determination of internal efforts in the base finite elements of SAFEM

The principles of calculating the internal efforts of a circular finite element in the semi-analytical finite element method (FEM) based on the obtained components of the stress tensor and the peculiarities of the approach associated with the use of the moment scheme of the finite element (FEM) are considered. Formulas for determining longitudinal, shear forces, bending and torque moments have been obtained.
 A special place, among the variety of objects considered with the help of analytical and numerical methods, is occupied by bodies of revolution of complex shape and cross-sectional structure, formed by the movement of some creative surface along a closed or opened line without breaks. The selected geometric class is used as natural structures of nodes and details in construction of mechanical engineering. The sufficiently wide distribution of the specified forms in the construction and machine-building industries, on the one hand, and the possibility of significantly simplifying the solving relationships by taking into account their geometric features, on the other hand, provide a basis for the development and use of various modifications of the finite element method (FEM). The semi-analytical finite element method (SAFEM) is one such approach that has gained widespread use for solving problems whose objects are prismatic bodies and bodies of revolution of complex shape and cross-sectional structure. Due to the introduction of additional hypotheses that do not reduce the accuracy of the approximation, the representation of deformations and stresses in physical terms and in accordance with the moment scheme of the finite element (MSFE), on the one hand, it is possible to avoid the time-consuming procedure of numerical integration over the cross-sectional area of the finite element (FE), on the other hand - maintain the high efficiency of 3D discretization.
 Despite the large number of publications devoted to the semi-analytical method of finite elements, the question of determining internal forces, which are often component factors of the strength criteria laid down in state building codes, is inappropriately neglected. The use of SAFEM in combination with МSFЕ creates some mathematical features of calculating internal longitudinal, shearing forces and moments.

An Intensity Tensor and Electric Field Gradient Tensor for Fe3+ at M1 Sites of Aegirine–Augite Using Single-Crystal Mössbauer Spectroscopy

An intensity tensor of quadrupole doublets and an electric field gradient tensor for Fe3+ at M1 sites in aegirine–augite ((Ca0.16Na0.86)∑1.02(Mg0.13Fe2+0.04Fe3+0.72 Al0.07)∑0.96Si2.01O6) are determined using single-crystal Mössbauer spectroscopy. The components of the intensity tensor are IXX = 0.670 (19), IYY = 0.353 (14), IXY = −0.113 (37) and IZZ = 0.477 (33). The components of the electric field gradient tensor (VXX, VYY and VZZ) for Fe3+ at M1 sites in aegirine–augite are −5.96 × 109, −4.65 × 1010 and 5.23 × 1010 C/m3, respectively. Comparisons of the intensity tensor of aegirine–augite with those of aegirine and augite (Wo40En45Fs16) that have already been reported and the IXX, IYY, IXY and IZZ intensity tensor components of aegirine–augite in this study are almost the same as those of aegirine, but different from those of augite. While the M2 sites of aegirine–augite and aegirine are fully occupied with Na+ and Ca2+ ions, the M2 sites of augite are not fully occupied with Ca2+. The compositional dependency of the intensity tensor components suggests that the intensity tensor components for Fe3+ at the M1 site of a solid solution between aegirine and augite are dependent on the occupancy of large cations such as Ca2+ and Na+ at M2 sites.

Symmetry invariants of higher orders in magnetoelastic energy for a trigonal easy-plane antiferromagnet

In expansion of the thermodynamic potential for a trigonal easy-plane antiferromagnet such as iron borate, FeBO3, magnetoelastic invariants of a higher order in the components of the deformation tensor and the antiferromagnetic vector with respect to those traditionally used were taken into account. Such invariants make it possible to describe new effects observed in iron borate crystals and composites based on them.

Invariance embedded physics-infused deep neural network-based sub-grid scale models for turbulent flows

In this paper, we present two novel physics-infused neural network (NN) architectures that satisfy various invariance conditions for constructing efficient and robust Deep Learning (DL)-based sub-grid scale (SGS) turbulence models for use in Large Eddy Simulation (LES) procedures widely used in various fluid engineering applications. The first architecture, called tensor basis neural networks (TBNN), recently proposed in the context of Reynolds-averaged Navier–Stokes (RANS) modeling, and introduced herein for SGS modeling of wall-bounded turbulence, embeds the analytical expansion of the SGS turbulence stresses into integrity basis tensors composed of the symmetric and anti-symmetric parts of the resolved velocity gradient tensor, thus incorporating the Galilean, rotational and reflectional invariances. In our second approach, a relatively simple yet powerful architecture, called Galilean Invariance embedded Neural Network (GINN) incorporates the Galilean invariance, and takes in as inputs the independent components of the integrity basis tensors in addition to the invariant inputs in a single input layer. Explicit filtering of data from direct simulations of the canonical channel flow at two friction Reynolds numbers Reτ≈395 and 590 provided accurate data for training and testing these models. Both sets of models are used to predict the SGS stresses for feature datasets generated with different filter widths, and at different Reynolds numbers. The GINN model yields less prediction error on test datasets (mean squared error ∼0.4) compared to the TBNN model (mean squared error ∼0.5). Upon comparison, it is revealed that GINN has better feature extraction capacity owing to its ability to establish relations between and extract information from cross-components of the integrity basis tensors and the SGS stresses. Based on their predictive performance, both models proposed herein have shown great promise for use in a posteriori actual LESs. The present work illustrates the significance of physics infusion as well as invariance embedding into NN architecture for constructing efficient and robust DL-based SGS turbulent models in achieving superior predictive efficacy.

The similarity theory of free turbulent shear flows of viscoelastic fluids

A new theory is formulated for the description of the conformation state of the polymer chains in free turbulent shear flows of viscoelastic fluids. Using self-similarity arguments and new scaling relations for the turbulent flux of conformation tensor we show the existence of minimum and maximum solvent dissipation reduction asymptotes, and four different polymer deformation regimes. The similarities with the maximum drag reduction asymptote of turbulent pipe flow is discussed and new scaling laws are obtained for all components of the mean conformation tensor at each deformation regime. Analytical solutions for the self-similar transverse profiles of the conformation tensor components are also obtained, providing the complete solution for the mean flow problem at the far field. The analysis is developed for both planar jets and wakes and covers the two limits of shear flows, with large and small velocity differences, respectively. Comparisons of the new theoretical results with several direct numerical simulations employing the FENE-P rheological model show excellent agreement.

DFT studies on structural stability, vibrational and linear and nonlinear optical properties of low-dimensional zinc sulfide: from the 3D bulk to the 2D monolayer and the 1D zigzag single-walled nanotubes

Through first-principles calculations, we investigate structural stability, vibrational and linear and nonlinear optical properties of the zinc sulfide (ZnS) in different periodic forms ranging from the 3D bulk to the 2D hexagonal monolayer and their corresponding 1D zigzag single-walled nanotubes. To first order, the electronic wave function on the ground state was constructed using linear combinations of Gaussian-type functions at the DFT/B3LYP level. Then, the Raman and IR spectrum is computed by adopting a Coupled-Perturbed-Hartree–Fock/Kohn–Sham (CPHF/KS) approach. Cohesive, relaxation, and rolling energies, elastic and piezoelectric constants, electronic and nuclear contributions to the polarizability tensor, and nonlinear first and second-order hyperpolarizability tensor components are reported. Our study shows that 3D and 2D forms are stable and show semiconducting behavior, good piezoelectric responses, and fascinating linear and nonlinear optical properties. For 1D single-walled nanotubes, dynamic stability is observed only for the smallest (6,0) nanotubes. For n > 6, imaginary mode frequencies in the simulated IR and Raman spectra indicate dynamic instability. A scanning mode procedure along the largest imaginary vibrational mode is applied in order to determine the stable structures of the largest (14,0), (18,0) and (22,0) ZnS nanotubes. After that, no more imaginary phonon frequencies are detected in their vibrational spectra. Their potential energy surface contains two minima between a saddle point corresponding to a slightly distorted nanotube structure. Our study proves that the zinc sulfide nanostructures possess diverse physical properties so useful for potential applications in nanoelectronics and for nanodevices.

Contribution of Lighthill tensor components to far-field acoustic pressure

We numerically investigate the contribution of different components of the Lighthill tensor to the far-field acoustic pressure arising from laminar flow noise around a rigid cylinder. Computational fluid dynamics simulations were used to obtain the flow field, from which the time histories of the velocity components were stored to calculate the Lighthill tensor. The acoustic pressure was then calculated based on the Lighthill source distribution and free-field Green's function. The contribution and characteristics of the different components of the Lighthill tensor to the far-field pressure are described.