Non-symmetric Configurations Research Articles

Multiplicity of solutions of lifted jet edge flames: Symmetrical and non-symmetrical configurations

A numerical investigation of the combustion process taking place after fuel and oxidizer are injected separately into a planar channel from an end-wall porous plug is presented. A fuel stream injected in the middle of the channel is surrounded on both sides by oxidizer streams and two edge flames are formed after contact of reactants and ignition. The formulation of the problem is symmetrical with respect to the middle of the channel. The study is based on the coupled Navier-Stokes and transport equations with one-step Arrhenius-type combustion kinetics. The main focus is on the influence of the fuel Lewis number, the flow rate and the Damköhler number on the flame structure. It is shown that symmetrical and non-symmetrical configurations of edge flames are possible for the same set of parameters, and that these solutions can be simultaneously stable. At the same time, the areas of existence of symmetric and non-symmetric flame configurations turn out to be different. Further, it is demonstrated that there can be at least seven different (but not all stable) steady-state solutions for the same set of parameters, although the evidence for the absence of other solutions, in addition to those found, cannot be achieved within the framework of the methods used in the study. These results may be critical for flames with low fuel Lewis number (e.g. hydrogen flames) and highlight the importance of taking into account the possibility of non-symmetrical flame configurations in the design and operation of combustion devices based on diffusion flames.

Using phase relationships in non-symmetric ToFD configurations

In conventional ToFD, operators are taught that diffracted echoes from the top and bottom of a planar defect have opposite phase and such defects can thus be discriminated from a pair of slag lines. This phase-inversion test is therefore used as a tool for characterizing an indication. When using non-symmetric probe arrangements and less-conventional beam angles, the situation becomes less clear-cut. Early in the development of the ToFD technique in the 1980s and 1990s, theoretical models enabled calculation of the amplitude and phase of diffracted signals from a crack edge for any incident and diffracted angle. Experimental studies at the time gave results that supported the theoretical predictions in idealized situations, but showed that for finite pulses and finite probe dimensions, it was more difficult to confirm the predictions for phase. In an inspection of a weld in a high-integrity component for the Hinkley Point C power station an asymmetric ToFD design was adopted as a solution to an access restriction. Comparison of top/bottom phase of indications was used as part of the procedure for characterization of indications. An analysis is made of the reasons why certain asymmetric configurations could not be used to identify planar defects using top-bottom phase inversion. The resulting re-design of the ToFD inspection configurations for a non-symmetrical inspection surface is presented, in which phase inversion remains a robust tool for defect characterization.

Design method of imaging optical systems using confocal flat phase elements.

Imaging systems consisting of flat phase element such as diffractive optical element, holographic optical element, and metasurface have important applications in many fields. However, there is still a lack of generalized and efficient design methods of these systems, especially for systems with nonsymmetric configurations. We proposed a design method of imaging system consisting of flat phase elements based on confocal properties. The description of the generalized phase function for realizing point-to-point stigmatic imaging is derived. Given the focal length or magnification as well as the locations of the elements based on the design requirements, the phase functions can be calculated very fast and stigmatic imaging of the central field is realized. The systems can be taken as good starting points for further optimization, during which the rotationally symmetric or freeform phase terms can be added. Several design examples are demonstrated to validate the feasibility of the method. The proposed method increases design efficiency while decreasing the dependence on existing systems and skills significantly, and can be easily integrated into optical design software.

Successive rotation approach based novel game puzzles for higher shade dispersion of PV array systems under non-uniform irradiations

Obstructed irradiation negatively impacts solar PV performance and raises issues of power loss (PL). In the partial shading conditions (PSCs), each row in the PV system has a distinct current production capability under the adverse shadowing effects, which is caused to introduce multiple power peaks known as GMPP and LMPP on the power-voltage (P-V) curves. The MPP tracking device is misleading during adverse irradiation circumstances due to numerous power maxima points. The array system adopted a realignment strategy to boost the PV system's resiliency under the shading mentioned earlier. In this paper, a novelphysical relocationapproach depends onthe 'Successive Rotation Approach' (SRA) based novel game puzzle, which illustrates high GMPP better performanceunder PSCs. The present study suggests that the SRA puzzle-based PVmodule restructuring methodology has a more significant shade dispersion factor (SDF) capability compared to traditional arrangements such as SP, TCT, SDK, and I-SDK, thus reducing PL and optimizing positions of GMPP. An experimental system is developed to validate the MATLAB/Simulink-based results, which proves the close agreement under similar realistic shading situations. In addition to this, the temperature effect due to shading is ivestigated and non-symmetric (6 × 9) PV array configurations are considered for performance evaluation through experimental work.

Polytopic Robust Stability for a Dual-Capacitor Boost Converter in Symmetric and Non-Symmetric Configurations

The step-up power electronic converter, which is easily implemented with two symmetric parallel-boost stages, has recently been proposed in the literature, showing considerable voltage gains with no excessive duty cycle, thus minimizing heat and other adverse effects. Its other advantages are floating-output voltage and increased power density because of the diminution of the capacitors’ voltage rating. In this paper, the Lyapunov-based robust stability of a converter operating in both closed- and open-loop is proved, showing its versatility even during the variation of parameters, which nullifies the symmetry of the converter. Simulation and experimental data allow the corroboration of the analysis.

Evaluation of the interlaminar fracture toughness on composite materials using DCB test on symmetric and unsymmetric configurations

A procedure to measure the interlaminar fracture toughness of a composite material is proposed in this work. This property is evaluated using the DCB test, the new formulation developed being applicable to small thicknesses and nonsymmetric configurations. The GC evaluation proposed in this paper does not require to know the evolution of the crack length with the load. This fact facilitates the performance of the test and allows complex situations (crack jumps, tests at high temperature,…) to be taken under consideration. An experimental campaign has been carried out on four different configurations, three symmetric (2 + 2, 4 + 4 and 8 + 8 layers) and one nonsymmetric (4 + 8 layers). The results show that, when they are appropriately treated, the values obtained are independent of the number of layers of the adherents and even of the symmetry of the joint, validating the use of the DCB test on nonstandardized coupons.

Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two

We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem.

Equilibrium of bi-stable flexural-tensegrity segmental beams

One dimensional discrete systems composed of a simple chain of bi-stable springs, with nearest neighbor interaction, have been used to interpret the complex equilibrium states of materials supporting multiple crystallographic phases, foldable macromolecules and biological structures. A discrete system is here proposed for bending within the broad class of flexural-tensegrity beams, which consist of segments in unilateral contact, with tailored-shaped contact surfaces, pre-stressed by an unbonded tendon. Any contact joint shows a bi-stable response to its relative rotation such as a snap-spring hinge, thanks to the internal carving of the segments that increases the mobility of the tendon within them. The constitutive response is nonlocal, because the tendon is free to slide within well lubricated sheaths. The case of pure bending, representing the counterpart of uniaxial tension in the one-dimensional lattice chain, shows that the system can support stable and metastable configurations, possibly containing one snap-spring hinge in the spinodal part of the energy landscape. Remarkably, not only the maximum hysteresis paths, but also the Maxwell paths, are strain-hardening in type. This is due to the nonlocal effect from the unbonded tendon: the rotation of any contact joint stiffens all the other joints, so that the orderly snaps of the spring-hinges occur at an increasing bending moment. An experimental program has been conducted on 3D printed physical models either in a hard or soft device. Symmetric and non-symmetric equilibrium configurations are obtained that are in perfect agreement with the theoretical predictions. Possible applications are envisaged, but they are yet to be fully appreciated.

Analysis and verification of the degree of bending isotropy of thin laminated composites manufactured using non-crimp fabric

Laminated composites generally provide anisotropic stiffness properties depending on their stacking sequences. These anisotropic properties are not desired for certain applications that are subjected to multi-directional loadings requiring optimal stiffness properties in all directions. As a result, this paper aims to present a formulation for assessing the degree of isotropy of thin laminated composites. The starting laminate configuration chosen is a quasi-isotropic laminate in which extensional isotropy is inherently satisfied. As for the degree of bending isotropy, it can be quantified from a generalized eigenvalue problem of the bending stiffness tensor. A new lay-up strategy is proposed for thin-ply non-crimp fabric (NCF), and a parametric design study was conducted on quasi-isotropic NCF to maximize the degree of bending isotropy. Using mid-plane symmetric and non-symmetric laminate configurations, the maximum degree of bending isotropy is achieved for non-symmetric ones. A fully isotropic laminate (FIL) can be obtained when both in-plane and bending stiffness tensors are equivalent to the isotropic stiffness counterpart with null coupling stiffness. Starting with a quasi-isotropic 3-ply NCF as the building block, a non-symmetric fully isotropic laminate with 18 plies was obtained. Two laminate designs composed of NCFs with different degrees of bending isotropy were manufactured for experimental verification using three-point bending testing, and the results validate a direct relation between the degree of bending isotropy and the flexural stiffnesses at multiple directions.

Thermal buckling of porous symmetric and non-symmetric sandwich plate with homogenous core and S-FGM face sheets resting on Pasternak foundation

The effect of porosity and thermal environment on buckling responses for the sandwich plates with different boundary conditions is analyzed and discussed in the present study. The author’s recently developed sandwich plate using a new modified sigmoid function based functionally graded material (S-FGM) plate of different symmetric and asymmetric configurations is considered. A new temperature distribution through the thickness based on modified sigmoid law is proposed in which temperature is assumed to be conducted in the thickness direction. Three different types of porosity are considered viz. even, uneven but symmetric and uneven but non-symmetric. A new uneven non-symmetric porosity model is used in which micro-voids are varied in accordance with material property variation in the thickness direction to capture the accurate distribution of voids on the plate. The principle of virtual work is employed to derive equilibrium equations. An exact solution is obtained using the assumed solution with shape functions satisfying the edge boundary conditions. This is implemented using Galerkin Vlasov’s method. The analysis has been performed to study the effect of porosity, geometric configurations, inhomogeneity parameter, and foundation parameter. It is observed that the elastic foundation parameters have the least effect on non-symmetric plate configuration subjected to nonlinear temperature distribution in comparison to other symmetric and non-symmetric plate configurations and temperature distribution. Besides, the non-symmetric plate configuration possesses maximum thermal buckling temperature in comparison to a symmetric configuration. The volume fraction exponent with value 2 is observed as a changeover point where the effect of porosity distribution is null and void for 2-1-1 plate configuration irrespective of boundary conditions. The calculated outcomes and interpretations can be useful as a validation study for the imminent investigation of sandwich S-FGM plates having porosities in the thermal environment.

The influence of symmetric and non-symmetric charge configurations on the possibility of sprite inception: Numerical experiments with a 3D electrostatic model

We present a simple, efficient, and flexible three-dimensional electrostatic model for calculating the magnitude and direction of the electric field from the ground to the base of the ionosphere for a given thunderstorm charge configuration, with the aim of evaluating the possibility for sprite inception. The model is based on a method-of-images solution to Poisson's equation, assuming near vacuum conditions and with perfectly conducting upper and lower boundaries. A dipole electrical structure within each thundercloud is assumed, with a screening (shielding) charge above the cloud. The charge centers (main positive, main negative, and screening charge) are modeled with average structural characteristics of summer and winter thunderstorms. To simulate a positive or negative cloud-to-ground lightning discharge, the main positive or main negative charge center, respectively, is removed from the domain. The computed electric potential at each grid point is converted to the electric field and is compared against the value of the conventional breakdown field to obtain an indication of the possibility of electrical breakdown and hence the possibility of sprite inception. This simple model is particularly useful for performing a sensitivity study with respect to variation in thunderstorm cell charge configuration, with no assumption of symmetry in the horizontal or vertical directions. Implications of the presence of neighboring clouds at different relative stages of development on the possibility of sprite inception and on the displacement of sprites from the location of the parent thunderstorm are also examined, as well as clouds with inverted dipole charge configuration.

Observation of Local Symmetry in a Photonic System

AbstractThe concept of local symmetry has been shown to be a powerful tool in predicting and designing complex transport phenomena in stationary scattering off aperiodic media, in terms of symmetry‐adapted nonlocal currents. For time‐evolving wavepackets, the spatiotemporal correlations caused by local symmetries are more challenging to reveal. A recent formalism‐based nonlocal continuity equation shows how local symmetries are encoded into the dynamics of light propagation in discrete waveguide arrays governed by a Schrödinger equation. However, the experimental demonstration is elusive so far. Representative examples of locally symmetric, globally symmetric, and fully nonsymmetric configurations are fabricated in fs laser‐written photonic arrays and their dynamics are probed. The approach allows to distinguish all three types of structures.

Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method: A semi-analytical approach

abstract In the present paper, for the first time, an attempt has been made to obtain the solution for bending and stress under the thermal environment using Galerkin Vlasov's method. A non-polynomial based higher-order shear deformation theory with inverse tangent hyperbolic shape function is used to define the displacement field. The formulation is performed for the author's recently developed sandwich plate using a new modified sigmoid function-based functionally graded material (S-FGM) plate of different symmetric and non-symmetric configurations. Using a one-dimensional steady-state heat conduction equation, a new temperature distribution through the thickness based on modified sigmoid law is proposed. Three different types of porosity are considered viz. even, uneven but symmetric and uneven but non-symmetric. A new uneven non-symmetric porosity model is used in which micro-voids are varied in accordance with material property variation in the thickness direction in order to capture the accurate distribution of voids on the plate. The principle of virtual work is employed to derive equilibrium equations. An exact solution is obtained using the assumed solution with shape functions satisfying the edge boundary conditions. From the present study on static analysis, it is deduced that more refined and accurate results for plate in thermal environment, it is necessary to include the thermal effect on the stiffness of the plate in addition to the initial deflection of the plate. The effect of boundary conditions on stress and deflection distribution along the surface of the porous plate is studied, and it is observed that the distribution is prominently affected by the type of symmetric or asymmetric boundary conditions. The considerable increase in deflection and stress can be seen for even porosity distribution (P-1) in comparison to uneven symmetric (P-2) or uneven non-symmetric (P-3) porosity distribution. In addition, the maximum transverse shear stresses are offset more from the center of the sandwich plate with an increase in temperature differences with a maximum offset at ΔT = 300 K and minimum offset at ΔT = 0 K. Different examples are considered to check the accuracy and validation of the present formulation. The calculated outcomes and interpretations can be useful as a validation study for the imminent investigation of sandwich S-FGM plates having porosities in the thermal environment.

Eight-Port Metamaterial Loaded UWB-MIMO Antenna System for 3D System-in-Package Applications

In this article, an eight-element ultra-wideband (UWB) Multiple-Input-Multiple Output (MIMO) antenna system is proposed for 3D non-planar applications. The proposed UWB-MIMO antenna is installed around a polystyrene block in the 3D-octagonal arrangement. The eight radiating elements are placed on the sides of the octagonal polystyrene block with top and bottom surfaces left open. The single antenna element consists of a modified Y-shaped radiating patch, epsilon-negative (ENG) metamaterial, and a partial ground plane. A modified pie-shaped decoupling structure is deployed at the back-side of the radiating patch to improve the isolation among array elements. Each antenna element is printed on a low-cost FR-4 substrate with dimensions of 28 mm $\times23$ mm with coverage of the whole UWB spectrum from 3.1 to 10.6 GHz frequency band. The eight-port UWB-MIMO antenna system consists of symmetric and non-symmetric array configurations. Simulated and measured MIMO performance parameters i.e. Channel Capacity Loss (CCL) < 0.35, Envelope Correlation Coefficient (ECC) < 0.0025 and Total Active Reflection Coefficient (TARC) < −11 dB are in acceptable limits for both symmetric and non-symmetric configurations. The proposed MIMO antenna system is suitable for 3D system-in-package, indoor localization systems, and wireless personal area network applications in industries where multiple machines are connected to a central server wirelessly through such kinds of antennas in a rich scattering environment.

The Optimal Pair of Rydberg Alkali-Metal Atoms in the Nonsymmetric Penning Ionization Processes

Features of Penning ionization in cold gaseous media of Rydberg alkali-metal atoms have been investigated. In contrast to the hydrogen atom, the corresponding autoionization widths exhibit a strong (by orders of magnitude) dependence on the orbital quantum numbers of the atoms involved in the long-range dipole–dipole interaction. An important feature of Penning ionization is the nontrivial dependence of its efficiency on the Rydberg particle size. For all types of alkali-metal atoms, the optimal highly nonsymmetric configurations of Rydberg pairs have been found that lead to the explosive (by several orders of magnitude) intensification of the free electron formation by means of the Penning ionization processes. This property makes Penning ionization an important means of forming primary charged particles during the cold Rydberg plasma formation. The numerical data for pairs of potassium atoms are reported that demonstrate a significant effect of the Forster resonance on the values of the Penning ionization rate constants.

On using load-axial shortening plots to determine the approximate buckling load of short, real angle columns under compression

In the present paper, a methodology for determination of an approximate value of the lowest buckling load of the thin-walled column under compression and with an arbitrary cross-section, affected by initial imperfections, whose amplitude does not exceed half the thickness of the wall, using a load-axial shortening plot, is presented. It has been shown that the load corresponding to an alternation in rigidity of the real structure on the load-axial shortening plot determines the buckling load with high accuracy. The attained results have been compared to the values corresponding to the bifurcation load and the lowest buckling loads determined with commonly used methods based on post-buckling equilibrium paths (i.e., P-w method, P-w2 method, inflection point method).The formulated problem of nonlinear buckling has been solved with the analytical-numerical method and the FEM. An influence of the imperfection amplitude on an approximate value of the lowest buckling load of laminated thin-walled structures has been analysed on the determined post-buckling equilibrium paths and the load-axial shortening plot. Non-symmetric configurations of laminate layers that additionally exhibit various types of the membrane and bending state coupling have been selected. Detailed computations have been conducted for short angle sections (i.e. angle columns) under uniform compression.

Freeform imaging spectrometer design using a point-by-point design method.

In this paper, we present a novel design method of freeform imaging spectrometers. All the freeform surfaces including the grating surface are generated point-by-point. The rays coming from multiple wavelengths, multiple fields, and different pupil coordinates are all used, and the refraction/reflection as well as the diffraction of the grating are considered simultaneously in the design process. In addition, this method can be easily used in the design of special nonsymmetric configurations. The system designed by this method can be taken as a good starting point for further optimization. To demonstrate the feasibility of the proposed method, we successfully designed a compact freeform reflective imaging spectrometer working under the visible and near infrared band. High performance and small distortion have been achieved.

On the anisotropic velocity distribution of fast ions in NBI-heated toroidal plasmas

A method to calculate the flux-surface-averaged anisotropy (the second Legendre order) in the slowing down velocity distribution of the fast ions generated by tangentially injected neutral beams is shown. This component is required for (1) perpendicular and parallel currents in MHD equilibrium calculations including the fast ions' pressure, (2) the anisotropic heating analyses on the thermalized target plasma species, and (3) the classical and the Pfirsch-Schlüter radial transport of both the thermalized target plasma species and the fast ions themselves. For including the parallel guiding center motion effect in non-symmetric toroidal configurations such as stellarators and heliotrons, the adjoint equation and the eigenfunctions are applied. In contrast to the previously investigated configuration dependence of the first Legendre order as the momentum input to the target plasma species, a quite different dependence of the second Legendre order on the magnetic field strength modulation B(θ,ζ) on the magnetic flux-surfaces is found. Even in a low energy range of the slowing down velocity distribution, the deviation (reduction) of the anisotropy from a result neglecting the orbit effect is proportional to 1−〈B〉/Bmax.

Numerical and experimental evaluation of ice storages with ice on capillary mat heat exchangers for solar-ice systems

Four capillary mat heat exchangers set-ups have been experimentally evaluated using two volume flow rates and several testing sequences, i.e. sensible and cooling, icing and melting. An ice storage model with capillary mat heat exchangers able to consider the solidification of ice for asymmetric tube configurations has been developed and validated with the experiments. The model showed good results with root mean square (RMS) energy differences around 2% for sensible heating and cooling and was able to predict the solidification of ice well for both symmetric and non-symmetric configurations with energy RMS differences of 6%. Differences in sensible heating and cooling, and in the solidification process, were in general in the same order of magnitude for varying volume flow rate and tube spacing in the two dimensions. Differences of the melting process were found to be more dependent on the tube spacing and volume flow rates.

Are nonsymmetric balanced configurations of four equal masses virtual or real?

Balanced configurations of N point masses are the configurations which, in a Euclidean space of high enough dimension, i. e., up to 2(N − 1), admit a relative equilibrium motion under the Newtonian (or similar) attraction. Central configurations are balanced and it has been proved by Alain Albouy that central configurations of four equal masses necessarily possess a symmetry axis, from which followed a proof that the number of such configurations up to similarity is finite and explicitly describable. It is known that balanced configurations of three equal masses are exactly the isosceles triangles, but it is not known whether balanced configurations of four equal masses must have some symmetry. As balanced configurations come in families, it makes sense to look for possible branches of nonsymmetric balanced configurations bifurcating from the subset of symmetric ones. In the simpler case of a logarithmic potential, the subset of symmetric balanced configurations of four equal masses is easy to describe as well as the bifurcation locus, but there is a grain of salt: expressed in terms of the squared mutual distances, this locus lies almost completely outside the set of true configurations (i. e., generalizations of triangular inequalities are not satisfied) and hence could lead most of the time only to the bifurcation of a branch of virtual nonsymmetric balanced configurations. Nevertheless, a tiny piece of the bifurcation locus lies within the subset of real balanced configurations symmetric with respect to a line and hence has a chance to lead to the bifurcation of real nonsymmetric balanced configurations. This raises the question of the title, a question which, thanks to the explicit description given here, should be solvable by computer experts even in the Newtonian case. Another interesting question is about the possibility for a bifurcating branch of virtual nonsymmetric balanced configurations to come back to the domain of true configurations.