Vertical Symmetry Plane Research Articles

Legume: A free implementation of the guided-mode expansion method for photonic crystal slabs

We describe legume, a free electromagnetic solver that implements the guided-mode expansion method for patterned multilayer waveguides, or photonic crystal slabs. legume has a built-in tool for automatic differentiation, which makes it suitable for the inverse design of photonic crystal structures with desired physical properties. Compared to a previous version of the method (M. Minkov et al., 2020 [12]), here we introduce several new features of the code, we discuss additional technical aspects of the method and its numerical implementation. The novel features that are treated in this paper include: (i) the separation of modes according to their mirror symmetry with respect to a vertical symmetry plane of the photonic structure, (ii) the problem of polarization mixing in coupling to far-field radiation modes, and (iii) the description of active two-dimensional layers through a suitably formulated radiation-matter coupling Hamiltonian, allowing to describe the physics of both weakly and strongly coupled exciton-photon modes, the latter leading to photonic crystal polariton eigenmodes. Detailed and direct comparisons with rigorous coupled-wave analysis simulations are used to test the accuracy of the method and the numerical efficiency of the code. These newly added features of the legume code significantly increase the prospective applications of guided-mode expansion, making it a very practical and versatile tool enabling the design of advanced photonic structures and the description of radiation-matter interaction. Program summaryProgram Title:legumeCPC Library link to program files:https://doi.org/10.17632/kf3cwknx4d.1Developer's repository link:https://github.com/fancompute/legumeLicensing provisions: MITProgramming language: PythonNature of problem: Dispersion and radiative losses of photonic eigenmodes in patterned multilayer waveguides/photonic crystal slabs/periodic metasurfaces. Interaction of photonic modes with exciton resonances leading to exciton-polaritons. Inverse design by optimization of the parameters.Solution method: Finite-basis expansion using a basis of guided modes of an effective homogeneous waveguide, perturbation theory to describe coupling with far-field radiation. Quantum theory of excitons, photons and their interaction to describe the occurrence of exciton-polaritons. Automatic differentiation via Autograd to implement inverse design. In this upgraded version of the legume code we implement symmetrization with respect to a vertical mirror plane and light-matter interaction for exciton-polaritons. Inverse design has been described previously, here we focus on the new features and applications of the code.

Dynamics of a vibrating screen with two motor-vibrators

A method for calculating a vibrating screen with two motor vibrators is proposed. The first part of the article is devoted to the issue of synchronizing the rotation of the rotors of both drives. Their opposite rotation creates a directed force passing through the center of gravity of the screen and perpendicular to the plane of the vibrator axes. The interaction of forces in this plane determines the phase mismatch of the rotation angles of the vibrators θ. An expression is obtained for determining the angle θ depending on the frequency of their rotation vibrators ω. It is shown that at ω > 100 rad/s, motor-vibrators operate in self-synchronizing mode. In the second part of the article a dynamic calculation of the screen was carried out. Linear vibrations in the vertical plane of symmetry of the screen and rotational vibrations around a perpendicular to this plane are investigated. The Lagrange equation of the second kind is compiled without considering inelastic resistances. They are considered at the last stage of the calculation in the form of the imaginary part of the complex modulus of elastic bonds. The amplitude-frequency characteristic of the screen was constructed considering the rotation mismatch angle of the vibrators θ. Stabilization of the oscillation amplitude at high frequencies is shown.

SYSTEM IDENTIFICATION OF AIRCRAFT LONGITUDINAL MOTION BY MEANS OF FLIGHT SIMULATOR DATA

In presented article, an exemplary problem of identifying parameters of an aircraft's motion within the vertical plane of symmetry is solved. The data was collected by FlightGear simulator for a Pilatus PC-9M aircraft flight case. After submitting a sequence of commands to pitch elevator and engine thrust, the simulator records five parameters of longitudinal motion at certain frequency. The collected data are further used to build a state-space model of the flight through least-squares estimation. The obtained numerical results are compared with the experimental ones and are overlaid graphically. Charts depicting elevator angle to trim are derived in addition. A source code developed in GNU Octave is applied with the help of which the problem was solved.

The generalized E-DVA method: a new approach for multi-modal pushover analysis under multi-component earthquakes with local variables maximization

Pushover analysis is a common nonlinear static procedure, performed to evaluate seismic response of civil structures. This approach allows considering the structural nonlinear behavior under earthquake loading in a simplified yet effective way; however, in its classic formulation, it is limited by restrictive and unrealistic assumptions. Thus, the basic method is inadequate for the accurate analysis of buildings without a vertical plane of symmetry and/or for multi-component earthquakes, where torsion effects cannot be neglected. Furthermore, standard pushover analysis only comprises one dominant mode of vibration; higher modes, and therefore their effects, are not accounted for. For all these reasons, the standard technique is generally not considered suitable for the assessment of buildings at high risk of natural-technological (NaTech) events, such as nuclear facilities in areas of high seismic activity. To overcome these limitations, a multi-modal pushover analysis procedure is here tested and validated on the data from a non-symmetric structure (the SMART case study) under multi-component earthquakes. In detail, the procedure applies a linear combination of modal load patterns, defined according to the well-established Direct Vectorial Addition (DVA) method. With respect to other existing multi-modal pushover analysis techniques, elliptical response envelopes are employed to calculate the corresponding combination factors. Innovatively, the identification of the dominant modes for the load pattern is not limited to the classic maximization of the forces at the basis of a structure but rather generalized to shear and displacement maximization at different heights and locations throughout the whole structural frame.

Numerical Study of Mixed Convection of Buoyant Twin Jet

Abstract The effect of mixed convection of twin vertical jets is investigated numerically in this paper. The results are presented specifically for flows affected by buoyancy for two parallel jets of same velocities ranging between 0.25 m/s and 5.0 m/s and temperatures between 295 K and 320 K. Both jets generate a slow flow with a temperature difference (with the ambient flow) less or equal to 32 °C (305 K). Predictions of dynamical and thermal parameters are obtained for the merging and combining regions. This study reveals that the trajectory of the two jets is strongly influenced by the ratio of buoyancy to inertial forces. Results indicate that, relative to isotherm jets, the location along the vertical symmetry plane at which the two jets merge (merging point) decreases with increasing jet inlet temperature. It was also found that the location of the merging point is shifted toward the confining wall as the velocity of the jets increases. The behavior law (linear regression), relating to the expansion of the jet, is not verified in the developed region for each value of the inlet velocity and temperature. This is explained by the fact that natural convection is more predominant than forced convection. The results show that the self-similarity of the cross profiles of the mean velocity and the behavior law relating to the expansion of the jet are obtained throughout the developed region.

Reflection Symmetry Detection in Earth Observation Data.

The paper presents a new algorithm for reflection symmetry detection, which is specialized to detect maximal symmetric patterns in an Earth observation (EO) dataset. First, we stress the particularities that make symmetry detection in EO data different from detection in other geometric sets. The EO data acquisition cannot provide exact pairs of symmetric elements and, therefore, the approximate symmetry must be addressed, which is accomplished by voxelization. Besides this, the EO data symmetric patterns in the top view usually contain the most useful information for further processing and, thus, it suffices to detect symmetries with vertical symmetry planes. The algorithm first extracts the so-called interesting voxels and then finds symmetric pairs of line segments, separately for each horizontal voxel slice. The results with the same symmetry plane are then merged, first in individual slices and then through all the slices. The detected maximal symmetric patterns represent the so-called partial symmetries, which can be further processed to identify global and local symmetries. LiDAR datasets of six urban and natural attractions in Slovenia of different scales and in different voxel resolutions were analyzed in this paper, demonstrating high detection speed and quality of solutions.

The accuracy of approximating P-wave traveltimes in orthotropic media using VTI equations

SUMMARY Analysis of azimuthally varying non-hyperbolic moveout of P-wave traveltimes in orthotropic media can provide valuable information for reservoir fracture characterization and seismic data processing. Moveout velocities and azimuthal orientation of the two vertical symmetry planes plus anellipticity parameters defined for the three symmetry planes of an orthotropic medium can be estimated from the inversion of P-wave traveltimes measured in long-spread, wide-azimuth seismic surveys. Several orthotropic moveout equations have been developed to this date that can be used in the traveltime data inversion. The accuracy of the inversion results is primarily determined by the complexity of the equation and the assumptions (i.e. elastic or acoustic) made to derive it. Here, we show that often simpler moveout equations derived for transverse isotropy media with vertical axis of symmetry (VTI) can be used to estimate anellipticity parameters of the orthotropic media with high accuracy. We make an accuracy comparison analysis between non-hyperbolic moveout equations that are widely used in modelling P-wave traveltimes in VTI media. Our comparison analysis is based on the accuracy of estimating anellipticity parameters defined for two vertical [η(1) and η(2)] and one horizontal [η(3)] symmetry planes of a wide range of orthotropic media. The anellipticity parameters are estimated from the inversion of numerical traveltimes that are generated for a single and horizontal orthotropic layer. We show that for the survey geometry used in this analysis, most of the moveout equations can produce reliable estimates of the anellipticity parameters η(1) and η(2). Despite the availability of traveltime data from wide-azimuths and long source–receiver offsets, none of the moveout equations can estimate η(3) as accurate as η(1) and η(2) estimations. We show that while all the equations produce mostly accurate estimates of η(1) and η(2), generalized moveout approximation (GMA) provides the greatest accuracy. We also assess the validity of using GMA to invert P-wave traveltimes for three anellipticity parameters in terms of anisotropy in the background medium, fracture weakness, source–receiver offset (group angle) and traveltime data coverage in both the vertical (dip) and horizontal (azimuthal) planes. We show that, for a reasonable offset range, GMA can be reliably used to estimate anellipticity parameters η(1) and η(2) for an orthotropic medium that is constructed by intensive fracturing of a host medium with strong VTI anisotropy.

Umbilic points of slowness surface in elastic orthorhombic media

AbstractFor 3D seismic data processing, azimuth plays an important role, especially in complex subsurface regions. In such regions, elliptical or anelliptical orthorhombic models are commonly used to describe wave propagation. In these models, the behaviour of the slowness surface needs more detailed analysis. Umbilic points defined by the equal principal curvatures exist in a complex 3D model. In the vicinity of the umbilic points, the traveltime surface has the shifted hyperbola form that needs to be considered in processing operations like velocity analysis. Fractured media characterized by the orthorhombic model are more likely to have umbilic points, and it is important to address their positions. If exists, umbilic points can provide additional constraints in inverting for model parameters. Through a defined condition, we examine the position of the umbilic point and derive their explicit formulas. We analyse umbilic points for elliptical and anelliptical orthorhombic models in the numerical example. For the elliptical orthorhombic model, the formulas for the umbilic point position on different symmetry planes are derived and corresponding conditions are also identified. Further, we numerically examine umbilic point positions for anelliptical orthorhombic models and observe that the umbilic points are located out of two vertical symmetry planes. Moreover, caused by interference from two neighbouring umbilic points, a more significant deviation in traveltime is found in the anelliptical orthorhombic model.

The E-DVA method for multi-modal pushover analysis and dominant modes

Pushover analysis is an incremental quasi-static procedure for evaluating the seismic behavior of buildings accounting for their non-linear behaviour. The simplest and classical version of this method is based on the following assumptions: (i) the structure has a vertical plane of symmetry; (ii) there is a single horizontal earthquake component, parallel to the plane of symmetry; (iii) the structural dynamic behavior in this plane is governed by a dominant mode of vibration. These assumptions prevent asymmetric buildings to be accurately analyzed accounting for torsion effects. Moreover, even for symmetric structures and single component earthquakes, the effect of higher modes is not taken into account. In order to overcome these limitations, several multi-modal generalizations of the basic pushover analysis method have been proposed in the past years. In this paper, a new multi-modal approach is presented. Inspired by the Direct Vectorial Addition (DVA) method, the load pattern for the pushover analysis is defined as a linear combination of modal load patterns. The novel approach improves the original DVA by introducing an operative procedure for the calculation of modal combination factors (called “α-factors”). This Enhanced DVA (E-DVA) method is based on the notion of elliptical response envelopes and allows several earthquake components to be taken into account simultaneously. In addition, an approach is proposed for the identification of dominant modes and for their use into the definition of the pushover load pattern. Furthermore, this paper describes a method to obtain the equivalent Single-Degree-of-Freedom (SDoF) oscillator properties in the general multi-modal case under multi-component earthquake, with the corresponding factors for the capacity curve normalization. The defnition of response spectrum for multi-component earthquakes is also given. For illustrative purposes, the E-DVA method is applied to a non-symmetric structure (SPEAR building), and the main results are presented and discussed.

Hydrodynamic surfaces with midsection in the form of Lame curve

General representation of ship geometry is given by the method of slicing the ship hull by three mutually perpendicular planes: vertical symmetry plane which runs along the middle of hull width, horizontal plane which divides the hull into underwater and abovewater parts, and vertical plane perpendicular to the other two which coincides with midsection. By taking the same three predefined sections of the theoretical hull shape, it is possible to obtain three algebraic surfaces of different order, which are called hydrodynamic in this article. By introducing alphabetic parameters to signify orders of ship skeleton main curves and then by giving them various numerical values, it is possible to consider a large number of hull shapes, having only three explicit surface equations. Method of deriving the equations, obtained by other authors, using only three explicit algebraic equations is demonstrated. The proposed technique is illustrated on six new ship hull shapes.

Symmetry Detection and Analysis of Chinese Paifang Using 3D Point Clouds

The Chinese paifang is an essential constituent element for Chinese or many other oriental architectures. In this paper, a new method for detection and analysis of the reflection symmetry of the paifang based on 3D point clouds is proposed. The method invokes a new model to simultaneously fit two vertical planes of symmetry to the 3D point cloud of a paifang to support further symmetry analysis. Several simulated datasets were used to verify the proposed method. The results indicated that the proposed method was able to quantity the symmetry of a paifang in terms of the RMSE obtained from the ICP algorithm, with resistance to the presence of some random noise added to the simulated measurements. For real datasets, three old Chinese paifangs (with ages from 90 to 500 years) were scanned as point clouds to input into the proposed method. The method quantified the degree of symmetry for the three Chinese paifangs in terms of the RMSE, which ranged from 20 to 61 mm. One of the paifangs with apparent asymmetry had the highest RMSE (61 mm). Other than the quantification of the symmetry of the paifangs, the proposed method could also locate which portion of the paifang was relatively more symmetric. The proposed method can potentially be used for structural health inspection and cultural studies of the Chinese paifangs and some other similar architecture.

Group-Theoretic Buckling Analysis of Symmetric Plane Frames

This paper presents a computationally efficient formulation based on group theory, for the buckling analysis of symmetric plane frames. Numerical examples ranging from simple frames with one vertical plane of symmetry to more complex configurations with multiple symmetry planes are considered. In contrast to conventional procedures for accounting for symmetry, group theory uses the full symmetry of the configuration, resulting in higher reductions of computational effort. Typically, the n-dimensional problem is decomposed into smaller problems that are independent of each other, permitting the buckling loads and mode shapes to be computed through the solution of problems of much smaller dimension. The approach also yields insights on the character of the buckling modes before detailed computations are carried out.

A New Thermal-Solar Field Configuration: The Rotatory Fresnel Collector or Sundial

A new type of Fresnel array has been devised and constructed as an answer to the need to reduce the investment costs of solar thermal collectors, without jeopardizing their efficiency in capturing solar radiation at high temperatures. The array of mirror bands is fixed onto a horizontal platform, which rotates around a virtual vertical axis, so that the sun is in the extrapolated vertical plane of symmetry of the array. The receptor central line is also placed in said plane, and it is physically made of at least one tube at each side of the plane. The geometrical relation between the mirrors and the receptor is therefore fixed. The platform rotates with the same speed as that of the sunlight’s azimuthal component. On the contrary, the angle of incidence of the sunlight on the mirrors changes as the sun rises and declines in its daily apparent motion, but this effect does not disturb the radiation concentration kinematics, although it induces a shift along the receptor. This is a new configuration based on the use of simple and cheap flat mirrors to obtain circular cylindrical mirrors. These mirrors are made of originally flat mirrors that are bent by applying an inexpensive and simple bending technique patented by our research group. The radius of curvature of each mirror is tuned to the distance from the mirror to the receiver central line. The integration of different scientific domains (such as structural analysis) and elementary technologies (such as 3D printing) in this innovative solar radiation concentrator and receiver can lead to a large reduction in costs. Nevertheless, the first experimental campaign has shown additional problems in the receiver configuration, which should be addressed in a next stage of research. This paper explains the methodology used and procedures in the development of the first prototype of the Sundial.

Dynamic interaction of the piggyback platform And semi-trailer truck

The article presents a mathematical model of joint oscillations of the car-platform for piggyback transportations and semi-trailer truck. Considered forced oscillations of the investigated object in the vertical plane of symmetry. Built a design scheme of the platform with mounted on it with a tractor and trailer system are presented in the form of a mechanical system, all bodies which, in addition platform, accept hard. The supporting structure of the platform is presented in the form of elastic massless beams carries seven lumped masses. A railway track is considered inertial with elastic-dissipative properties. In the simulation work for suspension updated power characteristic of the friction damper. As disturbances acting on the wheelset of the platform, considered butt roughness of the track. According to the results of computer simulation obtained measurements of vertical dynamics, piggyback platforms depending on the stiffness and characteristics of the oscillations damping. The obtained data dynamic calculations allowed us to estimate the schemes of fastening of a semi-trailer truck and to determine the influence on the dynamic indexes of changes in the stiffness of the spring suspension and the coefficient of friction relative to wedge the damper through adjustment of a spring set. Proved the feasibility of the decision on the free installation of the train on the platform, allowing automotive suspension gets the opportunity to actively damping the perturbations transmitted to the wheels of the road train from the platform.

Exact and approximate reflection/transmission responses from a layer containing vertical fractures

SUMMARYAnalyses of vertical fractures are of great interest in characterizing the fluid flow and minimum in situ stress direction in reservoirs. Long-wavelength equivalent orthorhombic (ORT) media typically characterize the anisotropy induced by a set of vertical parallel fractures or two sets of vertical and mutually orthogonal fractures embedded into a transversely isotropic medium with a vertical symmetry axis (VTI). Reflection and transmission (R/T) responses quantify wave amplitude variations in 1-D media and help to reveal the model property enclosing the heterogeneity. Conventionally, the R/T responses are analysed for an interface bounded by two half-spaces. However, for a plane wave travelling through a subsurface layer, the wave scattering effects at the top and bottom of the layer interact with each other. For a continuous infinite ORT space cut in two halves along the horizontal symmetry plane, we focus on the plane wave R/T responses from an ORT layer that is placed between the two halves, where the azimuths of the vertical symmetry plane in the layer and in the upper and lower half-spaces are identical. The R/T coefficient modelling method can be found in many publications for the ORT layer with an arbitrary finite thickness. We decompose the exact R/T coefficients into series expansions that correspond to different orders of intrabed multiples in the ORT layer. Under the weak-contrast assumption for the ORT half-spaces and the ORT layer, we use the anisotropic background medium to obtain the first-order R/T coefficient approximations and second-order reflectivity approximations. There is no constraint for the middle layer thickness in the obtained first-order reflectivity approximations. In the proposed first-order transmissivity approximations and second-order reflectivity approximations, the layer thickness is assumed to be thin to obtain appropriate approximations for a few wave modes. The isotropic background medium is also considered for weakly anisotropic models to obtain simpler approximations that facilitate parametric analyses. For the ORT layer with its thickness much smaller than the propagating wave's wavelength, the influences of the layer thickness on R/T coefficients can be inspected conveniently from the derived approximations. Particularly, the R/T coefficients are analysed for the model which would be a homogeneous VTI medium, if the vertical parallel fractures were absent from the middle layer. Numerical tests demonstrate that the proposed R/T coefficient approximations perform well for the thin ORT layer. The approximation accuracy decreases when the thin layer thickness increases.

The E-DVA method: A new approach for multi-modal pushover analysis under multi-component earthquakes

Pushover analysis is an incremental quasi-static procedure for evaluating the seismic behavior of buildings accounting for their non-linear behavior. The simplest and classical version of this method is based on the following assumptions: (i) the structure has a vertical plane of symmetry; (ii) there is a single horizontal earthquake component, parallel to the plane of symmetry; (iii) the structural dynamic behavior in this plane is governed by a dominant mode of vibration. These assumptions prevent asymmetric buildings to be accurately analyzed accounting for torsion effects. Moreover, even for symmetric structures and single component earthquakes, the effect of higher modes is not taken into account. In order to overcome these limitations, several multi-modal generalizations of the basic pushover analysis method have been proposed in the past years. In this paper, a new multi-modal approach is presented. Inspired by the Direct Vectorial Addition (DVA) method, the load pattern for the pushover analysis is defined as a linear combination of modal load patterns. The novel approach improves the original DVA by introducing an operative procedure for the calculation of modal combination factors (called “α-factors”). This Enhanced DVA (E-DVA) method is based on the notion of elliptical response envelopes and allows several earthquake components to be taken into account simultaneously. In addition, an approach is proposed for the identification of dominant modes and for their use into the definition of the pushover load pattern. Furthermore, this paper describes a method to obtain the equivalent Single-Degree-of-Freedom (SDoF) oscillator properties in the general multi-modal case under multi-component earthquake, with the corresponding factors for the capacity curve normalization. The definition of response spectrum for multi-component earthquakes is also given. For illustrative purposes, the E-DVA method is applied to a non-symmetric structure (SPEAR building), and the main results are presented and discussed.

Reflection and transmission approximations for weak contrast orthorhombic media

Subsurface media are in general anisotropic, and this fact should be taken into account for analyzing reflection and transmission (R/T) coefficients. Orthorhombic (ORT) media are commonly regarded as a practical symmetry system to account for polar anisotropy and azimuthal anisotropy. We have focused on the model made up of two welded ORT half-spaces to analyze the R/T coefficients normalized by vertical energy flux. The two half-spaces have azimuthally nonaligned vertical symmetry planes and are parameterized in two local 3D Cartesian coordinate frames, respectively. The vertical coordinate planes in each local frame coincide with the vertical symmetry planes for the corresponding ORT half-spaces. Under the weak contrast assumption for the two half-spaces, this model is taken as the perturbed model in R/T approximations with the perturbation theory. The unperturbed model is also composed of two unperturbed ORT half-spaces with their different vertical symmetry plane orientations inheriting the counterparts for the perturbed half-spaces above and below the interface, respectively. The unperturbed ORT half-spaces above and below the interface have the same model parameters defined in the two local coordinate frames, respectively. With the perturbations respectively evaluated in the local coordinate frames above and below the interface, the azimuth angle that indicates the local frames’ azimuthal difference is decoupled from the model parameter contrasts. Compared with the traditional approximation method with the perturbation theory in a global coordinate frame, the proposed R/T approximations depend on fewer model parameter discontinuities. We also consider the isotropic background medium under the weak anisotropy assumption. Influences of S-wave singularity points are mitigated by introducing pseudowaves for approximations. Numerical tests are implemented to demonstrate the accuracy.

The analytical solution of Newton’s aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary

The method of Hessian measures is used to find the differential equation that defines the optimal shape of nonrotationally symmetric bodies with minimal resistance moving in a rare medium. The synthesis of optimal solutions is described. A theorem on the optimality of the obtained solutions is proved.

An alternative procedure to obtain the ABCD matrix of multiphase transmission lines: Validation and applications

This paper presents an alternative procedure for obtaining the ABCD matrix of a generic multiphase transmission line. The ABCD matrix is obtained from the open and short-circuit responses of the line calculated in the frequency domain. The proposed procedure was used to obtain the ABCD matrix of a typical 440 kV overhead three-phase transmission line. To ensure that the proposed procedure was developed correctly, the ABCD matrix was used to represent the transmission line in simulations of electromagnetic transients resulting from switching and lightning. These simulations were also carried out with two known models that yielded identical results. The comparisons showed that the proposed methodology was developed correctly and that its main advantage is that it can be applied to generic multiphase transmission lines, whereas the existing methodology in the literature is restricted to three-phase lines with vertical planes of symmetry.

Low-frequency layer-induced kinematic parameters in transversely isotropic media and orthorhombic media

SUMMARY We develop a method to compute frequency-dependent kinematic parameters for an effective orthorhombic (ORT) medium. In order to investigate the influence of fracture weaknesses on the kinematic parameters, the effective ORT medium is composed based on the linear slip theory and derived by applying the limited Baker–Campbell–Hausdorff series. The frequency-dependent kinematic parameters including vertical velocity, two normal moveout velocities defined in vertical symmetry planes, and three anelliptic parameters (two of them are defined in vertical symmetry plane and one parameter is the cross-term one). We also investigate the influence of volume fraction, frequency, velocity ratio and fracture weaknesses on the effective kinematic parameters.