Complete Symmetry Research Articles

AFLOW-SYM: platform for the complete, automatic and self-consistent symmetry analysis of crystals.

Determination of the symmetry profile of structures is a persistent challenge in materials science. Results often vary amongst standard packages, hindering autonomous materials development by requiring continuous user attention and educated guesses. This article presents a robust procedure for evaluating the complete suite of symmetry properties, featuring various representations for the point, factor and space groups, site symmetries and Wyckoff positions. The protocol determines a system-specific mapping tolerance that yields symmetry operations entirely commensurate with fundamental crystallographic principles. The self-consistent tolerance characterizes the effective spatial resolution of the reported atomic positions. The approach is compared with the most used programs and is successfully validated against the space-group information provided for over 54 000 entries in the Inorganic Crystal Structure Database (ICSD). Subsequently, a complete symmetry analysis is applied to all 1.7+ million entries of the AFLOW data repository. The AFLOW-SYM package has been implemented in, and made available for, public use through the automated ab initio framework AFLOW.

Equivalence and symmetries for variable coefficient linear heat type equations. I

A systematic and unified approach to transformations and symmetries of a class of variable coefficient heat type linear partial differential equations (PDEs) is presented. The complete symmetry group classification is re-performed in the current context. A useful criterion which is necessary and sufficient for being reducible to the standard heat equation by point transformations is established. A similar criterion is also valid for the equations to have a four- or six-dimensional symmetry group (nontrivial symmetry groups). In this situation, the basis elements are listed in terms of coefficients. A number of illustrative examples are given. In particular, some applications from the recent literature are re-examined in our new approach. Multidimensional parabolic PDEs of heat and Schrödinger type are also considered.

Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

This review is devoted to search for Lie and Q-conditional (nonclassical) symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

Gait symmetry measures: A review of current and prospective methods

Abstract Gait symmetry is important in measuring gait pattern alterations for establishing the level of functional limitation due to pathology, observing its changes over time and evaluating rehabilitative intervention effects. The aim of this topical review is twofold: 1) to present used symmetry measures and summarize their application to a diverse range of gait data and to demonstrate their capabilities in their utilization in research and practice, 2) to expose newly developed symmetry measures and highlight their perspectives. We divided symmetry measures into four subgroups: symmetry indices, complete gait cycle symmetry measures, statistically-based measures and approaches, and nonlinear measures. For each, we will discuss their advantages and limitations and raise new questions and recommendations about their development and clinical use.

An approach to the instanton effect in B system

We discuss the constraint on the size of QCD instanton effects in low-energy effective theory. Among various instanton effects in meson mass spectrum and dynamics, we concentrate on the instanton-induced masses of light quarks. The famous instanton-induced six-quark interaction, so-called ’t Hooft vertex, could give nonperturbative quantum corrections to light quark masses. Many works have already been achieved to constrain the mass corrections in light meson system, or the system of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], and now we know for a fact that the instanton-induced mass of up-quark is too small to realize the solution of the strong CP problem by vanishing current mass of up-quark. In this work, we give a constraint on the instanton-induced mass correction to light quarks from the mass spectrum of heavy mesons, [Formula: see text], [Formula: see text], [Formula: see text] and their antiparticles. To accomplish this, the complete second-order chiral symmetry breaking terms are identified in heavy meson effective theory. We find that the strength of the constraint from heavy meson masses is at the same level of that from light mesons, and it would be made even stronger by more precise data from future [Formula: see text] factories and lattice calculations.

Implementation of the FDTD method in cylindrical coordinates for dispersive materials: Modal study of C-shaped nano-waveguides

The objective of this work is to develop a code based on the finite difference time domain method in cylindrical coordinates (CC-FDTD) that integrates the Drude Critical Points model (DCP) and to apply it in the study of a metallic C-shaped waveguide (CSWG). The integrated dispersion model allows an accurate description of noble metals in the optical range and working in cylindrical coordinates is necessary to bypass the staircase effect induced by a Cartesian mesh especially in the case of curved geometrical forms. The CC-FDTD code developed as a part of this work is more general than the Body-Of-Revolution-FDTD algorithm that can only handle structures exhibiting a complete cylindrical symmetry. A N-order CC-FDTD code is then derived and used to perform a parametric study of an infinitly-long CSWG for nano-optic applications. Propagation losses and dispersion diagrams are given for different geometrical parameters.

Coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry: Symmetries and conservation laws

A complete symmetry group classification of a coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry is carried out. This system is a natural two-components generalization of the Klein–Gordon–Fock system with central symmetry. Moreover, conservation laws for the system are obtained. Some interesting physical conclusions related to the derived conserved vectors are discussed.

The minimal flavour violating axion

The solution to the Strong CP problem is analysed within the Minimal Flavour Violation (MFV) context. An Abelian factor of the complete flavour symmetry of the fermionic kinetic terms may play the role of the Peccei-Quinn symmetry in traditional axion models. Its spontaneous breaking, due to the addition of a complex scalar field to the Standard Model scalar spectrum, generates the MFV axion, which may redefine away the QCD theta parameter. It differs from the traditional QCD axion for its couplings that are governed by the fermion charges under the axial Abelian symmetry. It is also distinct from the so-called Axiflavon, as the MFV axion does not describe flavour violation, while it does induce flavour non-universality effects. The MFV axion phenomenology is discussed considering astrophysical, collider and flavour data.

Complete random matrix classification of SYK models with mathcal{N} = 0, 1 and 2 supersymmetry

We present a complete symmetry classification of the Sachdev-Ye-Kitaev (SYK) model with mathcal{N} = 0, 1 and 2 supersymmetry (SUSY) on the basis of the Altland-Zirnbauer scheme in random matrix theory (RMT). For mathcal{N} = 0 and 1 we consider generic q-body interactions in the Hamiltonian and find RMT classes that were not present in earlier classifications of the same model with q = 4. We numerically establish quantitative agreement between the distributions of the smallest energy levels in the mathcal{N} = 1 SYK model and RMT. Furthermore, we delineate the distinctive structure of the mathcal{N} = 2 SYK model and provide its complete symmetry classification based on RMT for all eigenspaces of the fermion number operator. We corroborate our classification by detailed numerical comparisons with RMT and thus establish the presence of quantum chaotic dynamics in the mathcal{N} =2 SYK model. We also introduce a new SYK-like model without SUSY that exhibits hybrid properties of the mathcal{N} = 1 and mathcal{N} = 2 SYK models and uncover its rich structure both analytically and numerically.

Lie Symmetry Classification of the Generalized Nonlinear Beam Equation

In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group theory for the equation under consideration. Lie symmetry reductions of a nonlinear beam-like equation which are singled out from the classification results are investigated. Some classes of exact solutions, including solitary wave solutions, triangular periodic wave solutions and rational solutions of the nonlinear beam-like equations are constructed by means of the reductions and symbolic computation.

The male abdominal, genital and pregenital sclerites and musculature in Neria commutata (Czerny, 1930) (Diptera, Micropezidae)

The muscles of the male abdomen and genitalia of Micropezidae were studied for the first time by the example of Neria commutata (Czerny, 1930). Based on analysis of the sclerites and musculature of the male genitalia of Micropezidae as compared to those of the previously studied Acalyptratae and Aschiza, we revealed several apomorphies of this group. The hypandrial complex is characterized by the presence of the phallic retractors and protractors M1 and M2, and the epandrial complex, by the presence of muscles M3 of the subepandrial sclerite, muscles M4 of the surstyli, muscles M7 of the cerci, and also the tergosternal muscles M5; all these muscles correspond to the ground plan of Cyclorrhapha. The following characters are considered apomorphic: the splitting of intersegmental sternal muscles ISM5–6 into 4 pairs that ensure the functioning of the forcipate appendages of sternite V; development of syntergosternite VII and reduction of muscles ISM6–7; the splitting of muscles M3 of the subepandrial sclerite into 4 pairs, enhancing the function of this sclerite; the appearance of pregonites with the associated muscles M42, which probably occurred independently several times in the evolution of different groups of Cyclorrhapha; asymmetry of syntergosternites VII and VIII and their muscles. The sclerites and muscles of the epandrium and hypandrium are characterized by complete symmetry.

Attribute-Level Satisfaction, Overall Customer Satisfaction, and Performance Outcomes in Business-to-Business Firms

Scholars have used the attribute-based model of overall satisfaction extensively in consumer markets. Yet, business-to-business (B2B) firms also strive to improve overall satisfaction and financial performance by improving satisfaction on key attributes. We develop an attribute-based model to link attribute-level satisfaction to overall customer satisfaction and its downstream outcomes, specifically loyalty intentions and financial performance in B2B firms. The key contributions of this research are to identify and validate four key strategic attributes used in B2B markets (i.e., quality, pricing, safety, corporate social responsibility), and to empirically test the attribute-based model of satisfaction. While extant research has primarily focused on negative asymmetry (i.e., losses loom larger than gains) in how the attributes are associated with overall satisfaction, our results also demonstrate complete symmetry and positive asymmetry. Moreover, our results offer insights into the role of safety and corporate social responsibility, two key attributes in B2B settings. Finally, we show that overall customer satisfaction not only affects behavioral intentions (repurchase intention, recommend intention, and positive word-of-mouth), but also affects short- and long-term financial outcomes (sales revenue, gross margin, Tobin’s q), which has implications for resource allocation across key attributes.

Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries

In this article, we will construct the additional perturbative quantum torus symmetry of the dispersionless BKP hierarchy basing on the $W_{\infty}$ infinite dimensional Lie symmetry. These results show that the complete quantum torus symmetry is broken from the BKP hierarchy to its dispersionless hierarchy. Further a series of additional flows of the multicomponent BKP hierarchy will be defined and these flows constitute an $N$-folds direct product of the positive half of the quantum torus symmetries.

Group invariant transformations for the Klein–Gordon equation in three dimensional flat spaces

We perform the complete symmetry classification of the Klein-Gordon equation in maximal symmetric spacetimes. The central idea is to find all possible potential functions $V(t,x,y)$ that admit Lie and Noether symmetries. This is done by using the relation between the symmetry vectors of the differential equations and the elements of the conformal algebra of the underlying geometry. For some of the potentials, we use the admitted Lie algebras to determine corresponding invariant solutions to the Klein-Gordon equation. An integral part of this analysis is the problem of the classification of Lie and Noether point symmetries of the wave equation.

Ultraviolet divergences in non-renormalizable supersymmetric theories

We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang–Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.

Nasal Base Retraction: A Treatment Algorithm.

Nasal base retraction results from cephalic malposition of the alar base in the vertical plane, which causes disharmony of the alar base with the rest of the nose structures. Correcting nasal base retraction is very important for improved aesthetic outcomes; however, there is a limited body of literature about this deformity and its treatment. Create a nasal base retraction treatment algorithm based on a severity classification system. This is a retrospective case review study of 53 patients who underwent rhinoplasty with correction of alar base retraction by the senior author (S.T.). The minimum follow-up time was 6 months. Levator labii alaque nasi muscle dissection or alar base release with or without a rim graft on the effected side were performed based on the severity of the alar base retraction. Aesthetic results were assessed with objective grading of preoperative and postoperative patient photographs by two independent plastic surgeons. Functional improvement was assessed with patient self-evaluations of nasal patency. Also, a rhinoplasty outcomes evaluation (ROE) questionnaire was distributed to patients. Comparison of preoperative and postoperative photographs demonstrated that nasal base asymmetry was significantly improved in all cases, and 85% of the patients had complete symmetry. Nasal obstruction was also significantly reduced after surgery (P < 0.001). The majority of patients reported satisfaction (92.5%), with an ROE total score greater than or equal to 20. New techniques and a treatment algorithm for correcting nasal base retraction deformities that will help rhinoplasty surgeons obtain aesthetically and functionally pleasing outcomes for patients.

Lie Symmetries and Conservation Laws of the Generalised Foam-Drainage Equation

Abstract We perform a complete Lie point symmetry classification of the generalised foam-drainage equation and then construct an optimal system of one-dimensional subalgebra of the admitted symmetry operators and use them to reduce the equations under study. A power series solution of the reduced equation is constructed. Moreover, we find all multipliers of the equations and apply them to construct conservation laws.

Pattern-Reconfigurable Cylindrical Dielectric Resonator Antenna Based on Parasitic Elements

A novel pattern-reconfigurable cylindrical dielectric resonator antenna is presented. By the incorporation of four p-i-n diode switches and four parasitic elements, the mode of dielectric resonator excited by the probe changed. The antenna’s radiation patterns can be shaped to concentrate energy in four specific directions, while minimizing the gain in other unwanted directions without affecting the impedance bandwidth of the antenna for its complete symmetry in structure. The antenna switches its radiation patterns among four reconfigurable modes with orthogonal directions at azimuth plane covering a bandwidth of several 870 MHz and exhibiting a high maximum gain of 9.74 dBi. A fully functional prototype has been designed, fabricated, and tested. The measured results of the reflection coefficient, radiation patterns, and realized gain verify the effectiveness of the proposed pattern switching concept for cylindrical dielectric resonator antenna. These capabilities make the antenna suitable for smart wireless devices in next generation communication systems as it can enhance the radio frequency front-end flexibility and performance by adding pattern diversity, especially for muti-input-muti-output systems in multipath environments.

SYMMETRY PROPERTIES OF A NOVEL RICCATI SEQUENCE

Ponte Academic JournalNov 2017, Volume 73, Issue 11 SYMMETRY PROPERTIES OF A NOVEL RICCATI SEQUENCEAuthor(s): Adhir Maharaj ,DB Lortan, M. GovenderJ. Ponte - Nov 2017 - Volume 73 - Issue 11 doi: 10.21506/j.ponte.2017.11.35 Abstract:Recursion operators and hierarchies of evolution partial differential equations have been well-established for the past forty years. An algorithm to calculate recursion operators may be found in \cite{Bluman a}. Recently sequences of ordinary differential equations were introduced which were investigated in terms of it's symmetry and singularity properties. We analyse the sequence in this paper in terms of it's Lie point symmetries and the possession of a complete symmetry group. Download full text:Check if you have access through your login credentials or your institution Username Password

A Differential Sequence Generated By A Second-Order Recursion Operator

Ponte Academic JournalOct 2017, Volume 73, Issue 10 A Differential Sequence Generated By A Second-Order Recursion OperatorAuthor(s): Adhir MaharajJ. Ponte - Oct 2017 - Volume 73 - Issue 10 doi: 10.21506/j.ponte.2017.10.3 Abstract:The motivation of our investigation is the paper by Petersson {\it et al} \cite{Petersson a} where recursion operators were obtained for a class of semilinear and quasilinear evolution equations. We consider the class of semilinear evolution equations as the basis of our investigation. By setting $a=0, b=0, c=0$ and $u_t=0$ we obtain an ordinary differential equation. We analyse the resulting differential sequence in terms of it's symmetry properties. We also obtain the complete symmetry group for each element of the sequence. Download full text:Check if you have access through your login credentials or your institution Username Password