Point Symmetry Research Articles

Physics-augmented neural networks for constitutive modeling of hyperelastic geometrically exact beams

We present neural network-based constitutive models for hyperelastic geometrically exact beams. The proposed models are physics-augmented, i.e., formulated to fulfill important mechanical conditions by construction, which improves accuracy and generalization. Strains and curvatures of the beam are used as input for feed-forward neural networks that represent the effective hyperelastic beam potential. Forces and moments are received as the gradients of the beam potential, ensuring thermodynamic consistency. Normalization conditions are considered via additional projection terms. Symmetry conditions are implemented by an invariant-based approach for transverse isotropy and a more flexible point symmetry constraint, which is included in transverse isotropy but poses fewer restrictions on the constitutive response. Furthermore, a data augmentation approach is proposed to improve the scaling behavior of the models for varying cross-section radii. Additionally, we introduce a parameterization with a scalar parameter to represent ring-shaped cross-sections with different ratios between the inner and outer radii. Formulating the beam potential as a neural network provides a highly flexible model. This enables efficient constitutive surrogate modeling for geometrically exact beams with nonlinear material behavior and cross-sectional deformation, which otherwise would require computationally much more expensive methods. The models are calibrated and tested with data generated for beams with circular and ring-shaped hyperelastic deformable cross-sections at varying inner and outer radii, showing excellent accuracy and generalization. The applicability of the proposed point symmetric model is further demonstrated by applying it in beam simulations. In all studied cases, the proposed model shows excellent performance.

A hybrid linear Diophantine fuzzy group decision approach for enterprise digital transformation maturity evaluation

PurposeThe main goal of this paper is to present a synthetic multiple criteria group decision-making (MCGDM) methodology for assessing the enterprise digital maturity with linear Diophantine fuzzy (LDF) setting.Design/methodology/approachThis paper utilizes the presented LDF generalized Dombi operator to aggregate assessment information of experts. The developed combined weight model through merging the rank sum (RS) model and symmetry point of criterion (SPC) method is used to ascertain the comprehensive importance of criterion. The evaluation based on distance from average solution (EDAS) approach based upon regret theory (RT) is presented to achieve the sorting of candidate enterprises.FindingsFirstly, the proposed method has strong stability. Secondly, the proposed method takes into consideration the psychological behavior of experts during the decision-making process which further enhances the rationality of the decision results. Finally, the proposed method integrates expert and criterion weight determination models which provides a practical evaluation framework for assessing the digital maturity of enterprises. The research outcomes confirm that the proposed approach fails to resolve the decision problems with unknown weight information flexibly, but also reflect the psychological behavior of expert in decision process. The presented weight approach also provides a rational algorithm to ascertain the weight more accurate.Originality/valueA composite LDF group decision-making approach is presented by aggregating the proposed generalized Dombi operator, combined weight model and the EDAS model, which make the outcome more reasonable. Sensitivity analysis and comparison study are conducted to reflect the superiority of the proposed approach.

Phase Portraits and Abundant Soliton Solutions of a Hirota Equation with Higher-Order Dispersion

The Hirota equation, an advanced variant of the nonlinear Schrödinger equation with cubic nonlinearity, incorporates time-delay adjustments and higher-order dispersion terms, offering an enhanced approximation for wave propagation in optical fibers and oceanic systems. By utilizing the traveling wave transformation generated from Lie point symmetry analysis with the combination of generalized exponential differential rational function and modified Bernoulli sub-ODE techniques, several traveling wave solutions, such as periodic, singular-periodic, and kink solitons, emerge. To examine the solutions visually, parametric values are adjusted to create 3D, contour, and 2D illustrations. Additionally, the dynamic properties of the model are explored through bifurcation analysis. The exact results demonstrate that both techniques are practical and robust.

Observation of higher-order gyrotropic modes and energy transfer in cylindrical ferromagnetic nanodots-based square lattices

We investigated and reported on a wide variety of gyrotropic modes in both isolated thick cylindrical magnetic vortices and lattices of such magnetic vortices arranged in square-lattice structures. In significantly thicker magnetic vortices, we see a higher-order flexure modes in addition to the uniform gyrotropic modes. We thoroughly examined the variation of the frequency and intensity of these modes with the thickness of the magnetic nanodots forming a vortex. We specifically looked at how the thickness, diameter, and aspect ratio of a single magnetic vortex and magnetic vortex lattice in various configurations affect the mode frequencies. When the magnetic vortex at the center is excited by an a.c. spin-polarized current with an excitation frequency equal to the collective gyrotropic frequencies of the lattice, we discuss the dynamics of the transfer of magnetic energy at three high symmetry points of the three-dimensional lattice of Permalloy nanodots with a vortex structure. The energy transmission in these lattice systems is estimated using the power and phase distributions for such configurations. Lattice configurations with substantially thicker nanodots consisting of uniform modes and higher-order flexure modes in the Eigen spectrum have transmission with uniform modes in specific directions and suppression in others, acting as a magnonic filter, and no transmission at all with higher-order modes. Such magnonic vortex lattice structures seek to improve the future prospects of technology and provide emerging applications in information processing devices, magnonic filters, three-dimensional waveguides, and magnonic crystals.

Fermatean fuzzy distance and Sugeno–Weber operators-based SPC-MARCOS approach for sustainable supplier evaluation in the healthcare supply chain

The present work proposes a new decision support tool for assessing the sustainable suppliers in the healthcare supply chain. For this purpose, the classical Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) model is integrated with the Sugeno–Weber weighted averaging operators, modified symmetry point of criterion (SPC) model, rank sum (RS) tool and Fermatean fuzzy sets (FFSs), and named as the ‘FF-SPC-RS-MARCOS’ framework. The developed model firstly determines the decision experts’ weights through RS model. Second, novel Sugeno–Weber weighted operators are introduced to combine the experts’ opinions. Third, a unified weighting procedure is presented based on the combination of modified SPC approach for objective weight and RS method for subjective weight of attributes. To this aim, a novel distance measure is introduced for FFSs and further applied to compute the distance between aggregated Fermatean fuzzy numbers and symmetry point value of an attribute in the modified SPC approach. Further, a hybrid FF-SPC-RS-MARCOS approach is proposed to tackle the decision-making problems on FFSs setting. To elucidate the efficacy of the developed method, it is applied to a case study of sustainable supplier selection problem in the healthcare supply chain. The paper further conducts sensitivity investigation and comparison with existent approaches to test the stability and robustness of the ranking outcomes. This study shows how the proposed MARCOS method in combination with SPC and RS models can be used to prioritize the alternative suppliers in the healthcare supply chain. The introduced work provides a new methodology, which can help the practitioners and academics to evaluate suppliers with uncertain information and can also be employed to other areas facing similar types of decision-making problems.

Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution

Various mathematical frameworks have been developed to study dynamics of the fluid flow in stretching films. In this work, a three–dimensional flow induced by an unsteady stretching of an infinite flat sheet is analyzed through the Lie symmetry approach. Twelve Lie point symmetries for the nonlinear partial differential equations describing the considered flow and heat transfer phenomena are derived. Invariants for these Lie symmetries are obtained to construct a new class of similarity transformations. With the deduced similarity transformations, the flow equations are converted to ordinary differential equations which are solved using the Homotopy analysis method. The deduced analytic solution enables an exploration of the effects of various parameters on the flow and heat transfer, which have not been revealed previously using the Lie method as per the authors’ knowledge. The influences of the stretching rate, parameters that maintain the non-uniformity and unsteadiness of sheet temperature, and the Prandtl number, are demonstrated with the help of graphs and tables. These results show that for certain values of the system parameters, heat transfer reverses its direction and occurs from the fluid to the sheet. At these values, maximum heat transfer does not occur at the sheet but rather slightly above it.

Residual symmetry and interactions between solitons and periodic waves of the Drinfeld–Sokolov–Satsuma–Hirota system

In this paper, the Drinfeld–Sokolov–Satsuma–Hirota (DSSH) system is studied by using residual symmetry and the consistent Riccati expansion (CRE) method, respectively. The residual symmetry of the DSSH system is localized to Lie point symmetry in a properly prolonged system, based on which we get a new Bäcklund transformation for this system. New symmetry reduction solutions of the DSSH system are obtained by applying the classical Lie group approach on the prolonged system. Moreover, the DSSH system proves to be CRE integrable and new interesting interaction solutions between solitons and periodic waves are generated and analyzed.

Topological material in the III–V family: Heteroepitaxial InBi on InAs

InBi(001) is formed epitaxially on InAs(111)-A by depositing Bi onto an In-rich surface. Angle-resolved photoemission measurements reveal topological electronic surface states, close to the M¯ high symmetry point. This demonstrates a heteroepitaxial system entirely in the III–V family with topological electronic properties. InBi shows coexistence of Bi and In surface terminations, in contradiction with other III–V materials. For the Bi termination, the study gives a consistent physical picture of the topological surface electronic structure of InBi(001) terminated by a Bi bilayer rather than a surface formed by splitting to a Bi monolayer termination. Theoretical calculations based on relativistic density functional theory and the one-step model of photoemission clarify the relationship between the InBi(001) surface termination and the topological surface states, supporting a predominant role of the Bi bilayer termination. Furthermore, a tight-binding model based on this Bi bilayer termination with only Bi–Bi hopping terms, and no Bi–In interaction, gives a deeper insight into the spin texture. Published by the American Physical Society 2024

Dynamic phase transition region in electrically injected PT-symmetric lasers

Research on parity-time (PT) symmetry and exceptional points in non-Hermitian laser systems has been extensively conducted. However, in practical electrically injected PT-symmetric lasers, the frequency detuning and linewidth enhancement factor of the laser can influence the symmetry breaking of the system in another dimension. We find that the previous exceptional point now transforms into a dynamic phase transition region, where the states are temporally unstable, indicating the occurrence of multimode oscillation. The relative phase and field amplitude ratio in this region also exhibit many novel phenomena indicating its instability. This region can be manipulated by adjusting the coupling strength between adjacent waveguides and the pumping intensity in the loss waveguide. Experimentally, we characterize the near-field, far-field, and spectrum of several structures, and the results validate our theoretical model. This work elucidates the dynamic process and phase transition process of electrically injected PT-symmetric lasers, providing support for the practical application of PT-symmetric lasers.

(2+1)-dimensional Burgers equation with a Caputo fractional derivative: Lie symmetry analysis, optimal system, exact solutions and conservation laws

In this paper, the Lie group method is applied to analyze the (2+1)-dimensional Burgers equation with Caputo fractional derivative. The infinitesimal generators of the equation are investigated. Then, using the Lie point symmetry of the equation, a one-dimensional optimal system is constructed. Subsequently, within the framework of the optimal system, the equation is symmetrically simplified and the exact solutions of the original equation are determined using the invariant subspace method and the homogeneous balance method. In the process of simplifying the equation to a (1+1)-dimensional fractional differential equation, it is deliberately avoided to use complex Erdélyi-Kober fractional derivative operator. Instead, a simple transformation is utilized to obtain a low-dimensional fractional differential equation. Finally, based on the concept of nonlinear self-adjointness, the conservation laws of the fractional differential equation are obtained.

Shock wave propagation in a real gas with or without gravitational field in the presence of magnetic field and monochromatic radiation via group invariance method

PurposeThis article aims to find the similarity solutions for the one-dimensional motion of spherical symmetric shock wave in non-ideal gas influenced by the azimuthal magnetic field and monochromatic radiation in the presence or absence of gravitational field. This paper also aims to study the effects of physical parameters on the strength of shock wave, and on the flow variables in the flow-field region behind the shock front.Design/methodology/approachThe Roche model is used to describe the gravitational field effects due to a massive nucleus at the point of symmetry. To derive the similarity solutions, the Lie group symmetry method has been used. Also, the numerical solutions to the present problem are obtained by using Rung–Kutta method of the fourth order with the use of Mathematica software. The effects of variation in the parameter of non-idealness of the gas, the gravitation parameter, the strength of the ambient magnetic field and the adiabatic index of the gas on the shock wave, and on the flow variables is discussed. A comparative study between with and without gravitational field is also, made.FindingsFor different choices of the arbitrary constants that appeared in the solution of infinitesimal generators, we have obtained seven distinct cases of similarity solutions. In the absence of the gravitational field, the similarity solution exists to the power and exponential law shock paths, but in the presence of gravitational field, the similarity solution exists to the power law shock path case only. In the absence of gravitational field, the shock strength is enhanced in the exponential law shock path case in comparison to the power law shock path case. It is found that the shock wave decays with an increase in the value of the adiabatic exponent, the strength of magnetic field, non-idealness of the gas or gravitational parameter.Research limitations/implicationsThe consideration of medium under the influence of gravitational field due to a heavy nucleus at the center and presence of magnetic field decrease the shock strength. This result may be helpful in designing space vehicle and jet engine.Practical implicationsThe result of the present study may be used in the analysis of data from the measurements by space craft in the solar wind and in neighborhood of the Earth’s magnetosphere.Social implicationsThe obtained results may be used for mankind.Originality/valueThe study of spherical shock wave propagation influenced by monochromatic radiation and azimuthal magnetic field in a non-ideal gas with or without gravitational field has yet to be discussed by any authors by using the Lie group symmetry method. In this article, we have discussed all possible cases of similarity solutions using the Lie group symmetry method, which is not studied by anyone as known to us.

First principle study of structural and optoelectronic properties of ZnLiX3 (X = Cl or F) perovskites

The zinc-based perovskites ZnLiX3 (X = Cl or F) were investigated for their structural, electronic, and optical properties using the WIEN2k package within density functional theory (DFT). Structural properties were calculated using the generalized gradient approximation (GGA), while the modified Becke-Johnson (mBJ) potential was applied for a more accurate description of the optical and electronic properties. Both compounds are confirmed to be stable, crystallizing in the cubic Pm-3 m (No. 221) space group. ZnLiCl3 has an indirect band gap of 0.30 eV between the Γ and M symmetry points, indicating semiconducting behaviour, while ZnLiF3 exhibits an indirect band gap of 5.45 eV, typical of an insulating material. The electronic states contributing to the band structure were analyzed using the total density of states (TDOS) and partial density of states (PDOS). Optical properties, evaluated in the energy range of 0–14 eV, reveal strong optical conductivity and absorption at higher energies, while both materials show transparency to lower-energy photons. These findings suggest that ZnLiCl3 and ZnLiF3 are suitable candidates for high-frequency UV optoelectronic device applications.

Symmetry Reductions of the (1 + 1)-Dimensional Broer–Kaup System Using the Generalized Double Reduction Method

The generalized theory of the double reduction of systems of partial differential equations (PDEs) based on the association of conservation laws with Lie–Bäcklund symmetries is one of the most effective algorithms for performing symmetry reductions of PDEs. In this article, we apply the theory to a (1 + 1)-dimensional Broer–Kaup (BK) system, which is a pair of nonlinear PDEs that arise in the modeling of the propagation of long waves in shallow water. We find symmetries and construct six local conservation laws of the BK system arising from low-order multipliers. We establish associations between the Lie point symmetries and conservation laws and exploit the association to perform double reductions of the system, reducing it to first-order ordinary differential equations or algebraic equations. Our paper contributes to the broader understanding and application of the generalized double reduction method in the analysis of nonlinear PDEs.

Harnessing Flex Point Symmetry to Estimate Logistic Tumor Population Growth.

The observed time evolution of a population is well approximated by a logistic growth function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential, then decelerates as the population approaches its limit size, i.e., the carrying capacity. In mathematical oncology, the tumor carrying capacity has been postulated to be dynamically evolving as the tumor overcomes several evolutionary bottlenecks and, thus, to be patient specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic function's rotation symmetry can help estimate the population's growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against published pan-cancer animal and human breast cancer data, achieving a 30% to 40% reduction in the time at which subsequent data collection is necessary to estimate the logistic growth rate and carrying capacity correctly. These results could improve tumor dynamics forecasting and augment the clinical decision-making process.

Topologically protected bound modes in non-neighboring hexagonal lattices

In the last decade, the study of wave localization and guiding has gained a renewed interest thanks to the introduction of the concept of topological protection. Originally developed in the field of quantum mechanics, topological protection has successively inspired the search for its analogue in other physical domains, including elasticity. In this context, periodic hexagonal lattices have been proposed as ideal candidates to realize these concepts. In this work, we explore the dynamic behavior of discrete hexagonal lattices with third nearest neighbor connections. First, the formation and transition of multiple Dirac cones above a critical value of the relative stiffness between the first and third nearest neighbor connections is derived. Then, the formation of extremely localized modes (i.e., bound modes) at the interface between regions formed by lattices which are inverted copies of each other is demonstrated. Our results show that this localization derives from a type of interface satisfying a point reflection symmetry for which the considered chain decouples into two identical copies at the high symmetry point of the Brillouin zone. Our findings open novel avenues for topological waveguiding and confinement with potential applications in surface acoustic wave devices.

Exact solution of a mathematical model for human muscular motion

An ordinary differential equation (ODE) which models human muscular movement is considered. A functional form of the model parameter is specified through the Lie symmetry approach, yielding a different expression from the one derived in the previous study (Kosugi et al., 2019). The Lie point symmetries corresponding to the model parameter are employed for derivation of exact solution.

Band structure engineering to improve the optical and thermoelectric properties of Rb2AgXBr6 (X=Al, In, Ga) for energy applications within DFT framework

In the current study, we have employed density functional theory to evaluate thermoelectric, optical and electronic properties of rubidium bromide based double perovskites. It has been found that all three compounds i.e. Rb2AgAlBr6, Rb2AgGaBr6 and Rb2AgInBr6 have a direct band gap and the band gap appears at Γ symmetry point. The band gap of Rb2AgAlBr6 = 0.92 eV and of Rb2AgInBr6 = 0.29 eV whereas for Rb2AgGaBr6 has shown bands overlapping. The merged band gap of Ga-substituted material imparts in it excellent conductivity which makes it a potential candidate for application in conducting materials. Among all Rb2AgAlBr6 composition showed efficient TE properties with power factor of around 3.0 x 1011 W/msK2 and ZT value of 0.3. The optical properties found consist of high absorption coefficients (about 106 cm−1), low reflectivity (around 1–15 %), and high optical conductivity (approximately 1015sec−1).

Ab-initio investigation of structural, electronic, thermoelectric and optical properties of Full-Heusler X2MnB (X = Ti, Zr) for energy harvesting applications

In this manuscript comprehensive first-principles calculations have been presented for Full-Heusler X2MnB (X = Ti, Zr) compounds. This work includes detailed observations of the structural stability, origin of the transport phenomenon, optical properties, and electronic response. Structural parameters support the previous findings by confirming structural stability in the non-magnetic phase. Ti2MnB (Zr2MnB) valence band maxima and conduction band minima have bandgaps of 0.217 (0.301) eV and 0.181 (0.209) eV for PBE-GGA (mBJ) approximations which lie between L-L symmetry points. Due to the comparative measurements of the two states, the DOS results show that the Ti1/Zr1, Ti2/Zr2 Mn eg, and t2g states mainly contribute to the valence band region for Ti2MnB and Zr2MnB alloys, confirming their ionic nature. The computation of the overall electronic parameters’ reveals semiconducting nature. Thermoelectric properties have been calculated as a function of temperature in the 100–1200 K range. The positive values of Seebeck coefficients specify p-type character of X2MnB While at 300 K, Zr2MnB and Ti2MnB showed the highest Seebeck coefficients, measuring roughly values of 268 (µK/V) and 243 (µK/V), respectively. These values suggest that the material exhibits high thermoelectric performance. Though high optical absorption coefficient and low reflectivity in the visible and ultra violet regions, confirms use of these materials in solar cell applications. These findings suggest that material holds great potential for use in thermoelectrical applications which can support in upcoming experimental considerations.

Effect of Ag2O nanoparticles on the excited state dipole moment of a novel BMNFC molecules through solvatochromic shift method

We experimentally determined the ground and excited state dipole moments of BMNFC (5-bromo-N’-[(Z)-(4-methoxyphenyl)methylidene]naptho[2,1-b]furan-2-carbohydrazide) dye using the solvatochromic shift method and various solvatochromic correlations, including Lippert’s, Bakhshiev’s, Kawski-Chamma-Viallet’s, and solvent polarity equations. We employed the B3LYP/6-311G (d) level of theory to calculate the HOMO, LUMO, and MESP. In this study, we synthesized Ag2O nanoparticles using a quick and cost-effective chemical reduction method. Then, we used carboxymethylcellulose (CMC) as a capping agent. We studied the size, shape, and composition of these nanoparticles using a variety of analytical techniques. Transmission electron microscopy (TEM) analysis revealed a spherical morphology with an average diameter of 17 nm. The results show that adding Ag2O nanoparticles to BMNFC molecules changes their symmetric charge distribution, which in turn enhances their dipole moment. Molecules of enhanced dipole moment have attractive features in biomedical applications. Each molecule’s symmetry point group determines the extent to which nanoparticles affect the BMNFC molecule.

Evaluating cranial landmarks for yaw orientation in natural head position: a 3D study.

To assess the symmetry of various cranial anthropometric points used as references for yaw orientation in the natural head position (NHP), relative to the mid-sagittal plane. A prospective analysis using tomography data from 55 patients was conducted. Radiopaque markers, placed on patients in NHP, facilitated head position recording in three planes, with subsequent digital transfer for orientation analysis. Symmetry of eight points (zygomaxillare, zygion, ectoconchion, frontozygomatic suture, stephanion, porion, mastoidale, condylion laterale) was measured against the mid-sagittal plane. Significant asymmetry was observed in the stephanion, frontozygomatic suture, and ectoconchion points (p < 0.05). No significant differences were found in the symmetry of other points (p > 0.05). Findings suggest that stephanion, frontozygomatic suture, and ectoconchion are unreliable for yaw orientation in NHP. Other points, combined with clinical measurements, may offer better reliability.