Type Of Symmetry Research Articles

Enhancing Photoluminescence: Photonic Bound States in the Continuum in Si Structures with the Self‐Assembled Ge Nanoislands (Laser Photonics Rev. 15(7)/2021)

The cover image illustrates the photonic crystal slab's eigenmode as demonstrated in article number 2000242 by Sergey Dyakov and co-workers. The cones represent the rotation of the electric vector during one period of electromagnetic oscillations. From this figure, one can determine the symmetry type of this mode and predict the features of the far-field emissivity of quantum emitters at the corresponding frequency.

In English

The symmetry conditions have been derived for the occurrence of the ratchet effect in Brownian photomotors. To this end, spatiotemporal symmetry operations in vector transformations, coordinate and time shifts, and in the overdamped regime were applied to the average photomotor velocity taken as a functional of the coordinate- and time-dependent potential energy. As established, individual Brownian particles (molecules) can move directionally only provided a symmetrically distributed charge fluctuates in them and they are placed on the substrates with an antisymmetric charge distribution or, vice versa, they are characterized by antisymmetrically distributed charge fluctuations and are placed on symmetric substrates. The collective directed motion of orientation-averaged particles is possible only in the former case. If a particle charge distribution is described by a time dependence with the universal type of symmetry (i.e., simultaneously symmetric, antisymmetric, and shift-symmetric), an additional symmetry constraint on the ratchet functioning arises: the ratchet effect is ruled out in the overdamped regime but allowed for inertial moving particles if the charge distributions in both the particle and the substrate are neither symmetric nor antisymmetric. The effect of the universal type of symmetry is exemplified by dipole photomotors derived from donor-acceptor conjugated organic molecules. With a specific type of molecular photoexcitation and a specific relationship of the dipole moments in the ground and excited states, the ratchet effect becomes symmetry-forbidden. The forbiddenness can be removed by molecular polarization effects, which in this case become the predominant factor governing the direction of the motion and average velocity of photomotors. The estimated velocities of polarization photomotors are an order of magnitude larger than for known motor proteins and dipole Brownian photomotors. These results can be helpful in the purposeful molecular design of dipole photomotors.

On Some Continued Fractions and Series

We exhibit some explicit continued fraction expansions and their representation series in different fields. Some of these continued fractions have a type of symmetry, known as folding symmetry. We will extracted those whose are specialized.

Compact explicit matrix representations of the flexoelectric tensor and a graphic method for identifying all of its rotation and reflection symmetries

Flexoelectricity is an electromechanical phenomenon produced in a dielectric material, with or without centrosymmetric microstructure, undergoing a non-uniform strain. It is characterized by the fourth-order flexoelectric tensor, which links the electric polarization vector with the gradient of the second-order strain tensor. Our previous work [H. Le Quang and Q.-C. He, Proc. R. Soc. A 467, 2369 (2011)] solved the fundamental theoretical problem of determining the number and types of all rotational symmetries that the flexoelectric tensor can exhibit. In the present study, compact explicit matrix representations of the flexoelectric tensor are provided so as to facilitate the use of it with any possible rotational symmetry. The number and types of all reflection symmetries that the flexoelectric tensor can have are also determined. To identify the rotational symmetry and reflection symmetry of a given flexoelectric tensor, a simple and efficient graphic method based on the concept of pole figures is presented and illustrated.

Infinitely many multipulse solitons of different symmetry types in the nonlinear Schrödinger equation with quartic dispersion

We show that the generalized nonlinear Schr\"odinger equation (GNLSE) with quartic dispersion supports infinitely many multipulse solitons for a wide parameter range of the dispersion terms. These solitons exist through the balance between the quartic and quadratic dispersions with the Kerr nonlinearity, and they come in infinite families with different signatures. A traveling wave ansatz, where the optical pulse does not undergo a change in shape while propagating, allows us to transform the GNLSE into a fourth-order nonlinear Hamiltonian ordinary differential equation with two reversibilities. Studying families of connecting orbits with different symmetry properties of this reduced system, connecting equilibria to themselves or to periodic solutions, provides the key to understanding the overall structure of solitons of the GNLSE. Integrating a perturbation of them as solutions of the GNLSE suggests that some of these solitons may be observable experimentally in photonic crystal waveguides over several dispersion lengths.

Generalized quantum process discrimination problems

We study a broad class of quantum process discrimination problems that can handle many optimization strategies such as the Bayes, Neyman-Pearson, and unambiguous strategies, where each process can consist of multiple time steps and can have an internal memory. Given a collection of candidate processes, our task is to find a discrimination strategy, which may be adaptive and/or entanglement-assisted, that maximizes a given objective function subject to given constraints. Our problem can be formulated as a convex problem. Its Lagrange dual problem with no duality gap and necessary and sufficient conditions for an optimal solution are derived. We also show that if a problem has a certain symmetry and at least one optimal solution exists, then there also exists an optimal solution with the same type of symmetry. A minimax strategy for a process discrimination problem is also discussed. As applications of our results, we provide some problems in which an adaptive strategy is not necessary for optimal discrimination. We also present an example of single-shot channel discrimination for which an analytical solution can be obtained.

DTM-Based Morphometric Analysis of Scoria Cones of the Chaîne des Puys (France)—The Classic and a New Approach

Scoria cones are favorite targets of morphometric research. However, in-depth, DTM-based studies have appeared only recently, and new methods are being developed. This study provides a classic evaluation of the cones of Chaîne des Puys (Auvergne, France) as well as introduces a more detailed and statistics-based set of properties. Beside the classic parameters, a sectorial approach is applied to the slope distributions calculated from high resolution DTMs for 25 cones of different lithologies, in order to study the various (a)symmetries of the cones. DTM-based morphometric characteristics have been found to be different from classic descriptors, whereas the sectorial approach describes correctly the more and the less regular shapes. The distribution of interquartile ranges of the sectorial slope distributions is skewed. Sectorization discriminates various types of symmetries: there are almost circular cones, but the majority are elongated and have some asymmetry. The relationship between size parameters reflects the lithology, rather than the age of the cone. The attempt to relate morphometric parameters to age data is only partially successful: although there is a certain trend, within the same lithological group, subtle but possibly systematic trends can be detected for decreasing morphometric values (e.g., slope) with the age. The regression models indicate various outcomes. Further work is needed to understand all the diverse parameters, especially the lithology–shape relationship, and how symmetry is connected to different factors.

Reduction of plane-radial freezing - thawing problems to plane-parallel ones

Construction in northern conditions is complicated by the processes of seasonal freezing and thawing of soils. This factor is of particular importance in the area of permafrost distribution. The paper deals with the problems that arise when laying communication networks. Any engineering solution must be justified by a heat engineering calculation. In one case, it is necessary to exclude the thawing of water or sewer networks, in the other case – to prevent the destructive effect of the heating main on the permafrost soil. The most common mathematical model of the heat transfer process in the presence of phase transitions is the Stefan problem. When calculating the processes of freezing-thawing near the pipes of communications, it is rational to set the problem in cylindrical coordinates, using the property of plane-radial symmetry. But the Stefan problem has an exact solution only in Cartesian coordinates, for the case of plane-parallel symmetry. For this case, many approximate dependencies are also obtained. The paper presents a method that allows using the results of solving the plane-parallel Stefan problem to solve the plane-radial problem with the same values of the input parameters. Approximate values of the coordinate of the phase transition front as a function of time for the plane-parallel and plane-radial areas are obtained using the method of sequential change of stationary states. A one-to-one relationship is established between the obtained values. If there is a solution obtained by any method for a plane-parallel area, and then using this dependence, it can be applied to a plane-radial area. This technique is suitable not only for the Stefan problem, but also for many nonlinear heat conduction problems. The results given in the paper are of practical importance: using the above method, almost any solution obtained for one type of symmetry directly extends to other types of symmetry.

Symmetry type graphs on 4-orbit maps

It is well known that there exist 22 symmetry type graphs associated to [Formula: see text]-orbit maps. For this one, we give the feasible values taken by the degree of the vertices and the number appropriate of edges in the boundary of each face of the map, by introducing the concepts of vertex type graph, face type graph and characteristic system.

New refined model for curved linear anisotropic rods with circular cross section

An asymptotic reduction method is introduced to construct a curved rod theory for a general anisotropic linearized elastic material. For the sake of simplicity, the cross section is assumed to be circular. The starting point is Taylor expansions about the mean-line in curvilinear coordinates, and the goal is to eliminate the two spatial variables in the cross section in a pointwise manner in order to obtain a closed system for the displacement coefficients. We achieve this by using a Fourier series for the lateral traction condition together with the use of cylindrical coordinates in the cross section and by considering exact tridimensional equilibrium equation. We get a closed differential system of ten vector unknowns, and after a reduction process we obtain a differential system of the vector of the mean line displacement and twist angle. Six boundary conditions at each edge are obtained from the edge term in the tridimensional virtual work principle, and a unidimensional virtual work principle is also deduced from the weak forms of the rod equations. Through one example, we show that our theory gives more accurate results than the ones of both classical Euler-Bernoulli rod theory and Timoshenko rod theory. The displacement field is computed for two types of material symmetry : isotropy and transverse isotropy.

Classification and Effects of Symmetry of Mechanical Structure and Its Application in Design

Symmetry widely exists in natural objects and man-made objects. Mechanical structures, as man-made objects, have the property of symmetry without exception. The existence of symmetry affects the function and performance of mechanical products. Therefore, on the basis of analyzing a large number of examples and referring to the Schoenflies symbol of crystal, the symmetry of mechanical structures is divided into point group symmetry and space group symmetry, and these two types are further subdivided according to the types and spatial positions of the symmetry elements. Then, the general effects of symmetry are summarized according to symmetry types and functions, and several symmetry rules for design are further refined. Finally, after defining the requirements of speed change and technology background, a multispeed device for bicycle shaft drive is proposed by applying symmetry knowledge comprehensively.

Cool white light emanation and photo physical features of combustion derived Dy3+ doped ternary yttrate oxide based nanophosphors for down converted WLEDs

Novel orthorhombic symmetry type BaSrY4(1-x)Dy4xO8 (x = 1, 3, 5, 7, 10 mol %) cool white light emitting nanocrystals was synthesized by low temperature based solution combustion approach. Information related to crystallographic analysis was made by utilizing X-ray diffraction and Rietveld-refinement technique. The manufactured nanoparticles exhibit cool white emission corresponding to 4F9/2 → 6H15/2 (at 480 nm, blue color), 4F9/2 → 6H13/2 (at 572 nm, yellow color) and 4F9/2 → 6H11/2 (at 673 nm, a weak red color emission). CIE coordinates and CCT values of optimized nanocrystals were found resemblance with white-coordinates of commercial LEDs and NTSC which prove them a potential candidate for outdoor lightning purpose i.e. in WLEDs.

Entropic order parameters for the phases of QFT

We propose entropic order parameters that capture the physics of generalized symmetries and phases in QFT’s. We do it through an analysis of simple properties (additivity and Haag duality) of the net of operator algebras attached to space-time regions. We observe that different types of symmetries are associated with the breaking of these properties in regions of different non-trivial topologies. When such topologies are connected, we show that the non locally generated operators generate an Abelian symmetry group, and their commutation relations are fixed. The existence of order parameters with area law, like the Wilson loop for the confinement phase, or the ’t Hooft loop for the dual Higgs phase, is shown to imply the existence of more than one possible choice of algebras for the same underlying theory. A natural entropic order parameter arises by this non-uniqueness. We display aspects of the phases of theories with generalized symmetries in terms of these entropic order parameters. In particular, the connection between constant and area laws for dual order and disorder parameters is transparent in this approach, new constraints arising from conformal symmetry are revealed, and the algebraic origin of the Dirac quantization condition (and generalizations thereof) is described. A novel tool in this approach is the entropic certainty relation satisfied by dual relative entropies associated with complementary regions, which quantitatively relates the statistics of order and disorder parameters.

W algebras, cosets and VOAs for 4d mathcal{N} = 2 SCFTs from M5 branes

We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general mathcal{N} = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.

Vibration of general symmetric systems using group theory

This work presents group-theory-based vibration analysis to determine the highly structured, symmetry-related modal properties of symmetric systems and classify them into specific types. No eigenvalue problem solutions are required. In fact, the properties are obtained without a mathematical model. They derive only from symmetry and the degrees of freedom chosen to describe the deformation. Dynamic or static response is similarly decomposed into the sum of multiple response components associated with the mode types. One knows a priori, without any numerical computation, which mode types can or can not be excited by a given input excitation. Group theory divides the full system equations of motion and eigenvalue problem into multiple, smaller, decoupled problems associated with each mode type, which is computationally efficient. The method applies for general three-dimensional systems having any type of symmetry where components of the system are modeled using any mixture of lumped-parameter (including finite element) and elastic continuum models. Only basic elements of group theory are required, and they are introduced. Among three examples of the method, one derives the modal properties for general cyclically symmetric systems having any number of central components and substructures that can be modeled as any of rigid bodies, finite element meshes, and elastic continua.

Quasi-exact solution of the Dirac equation on curved space-time with Coulomb scalar and vector potentials and Mie-type tensor potential with pseudo-spin and spin symmetries

In this paper we solve the Dirac equation with the Coulomb scalar U(r) and vector V(r) potentials and type-Mie tensor potential in curved space-time whose metric is of type with spherical symmetry. For this we consider two types of symmetry in the system, first spin symmetry with V(r) = U(r) and then with pseudo-spin symmetry V(r) = − U(r). In both cases we have a tensor potential A(r) that coupling through the electromagnetic field A μ = (V(r), cA(r), 0, 0). We find, quasi-exactly, the Dirac spinor and the energy spectrum of the system, and we sketch the probability densities and some energy spectra.

Symmetry properties of a Brownian motor with a sawtooth potential perturbed by harmonic fluctuations

We present a study of general symmetry properties of a Brownian ratchet model. The study is based both on constructing chains of symmetry transformations reflecting explicit and hidden symmetries of the average ratchet velocity as a functional of the spatially periodic potential energy of a nanoparticle and on taking into account the symmetry types of periodic functions that are components of the potential energy of an additive-multiplicative form. A ratchet with a sawtooth stationary potential profile, dichotomously perturbed by a spatially harmonic signal, is investigated. Conclusions are made on both the possibility of occurrence of the ratchet effect and its direction for given values of the asymmetry parameter of the sawtooth profile, phase shifts of the control component, and frequencies of temporal fluctuations. These conclusions have been obtained only on the basis of symmetry transformations; that demonstrates the predictive value of the approach presented. The results of the symmetry analysis are confirmed by numerical simulation of the functioning of a ratchet with dichotomous stochastic spatially periodic fluctuations of the nanoparticle potential energy.

Multi-resonator metamaterials as multi-band metastructures

Introducing multi-resonator microstructure into phononic metamaterials provides more flexibility in bandgap manipulation. In this work, 3D-acoustic metamaterials of the body- and face-centered cubic lattice systems encompassing nodal isotropic multivibrators are investigated. Our main results are: (1) the number of bandgaps equals the number, n, of internal masses as each bandgap is a result of the classical analog of the quantum level-repulsion mechanism between internal and external oscillations, and (2) the upper boundary frequencies, ωupper2i, i = 1, 2, ⋯, n, of the gaps formed coincide with eigen-frequencies, ωint;i2 ≠ 0, of the isolated multivibrator, ωupper2;i = ωint; i2, and the lower boundary frequencies, ωlower2,i2, are in good agreement with estimations as ωlower,i2≈ω^int;i2 (ωlower,i2<ω^int;i2), where ω^int;i2 represent the eigen-frequencies of the multivibrator when its external shell is motionless.The morphologies of the set of dispersion surfaces, ωm2(k), m = 1, 2, …, 6, in the corresponding passbands are similar to each other and to that of the set of dispersion surfaces, ωext; m2(k), obtained through the exclusion of internal masses. Thus, the problem of analyzing the acoustic properties of the complicated system is reduced to the study of two simple sets {ωint; i2} and ω^int;i2, along with {ωext; m2(k)}, the morphology of which depends only on the type of lattice symmetry. This splitting renders controlled phononic bandgaps formation in homogeneous multi-resonator metamaterials feasible.

Symmetry Transformations in Metazoan Evolution and Development

In this review, we consider transformations of axial symmetry in metazoan evolution and development, the genetic basis, and phenotypic expressions of different axial body plans. In addition to the main symmetry types in metazoan body plans, such as rotation (radial symmetry), reflection (mirror and glide reflection symmetry), and translation (metamerism), many biological objects show scale (fractal) symmetry as well as some symmetry-type combinations. Some genetic mechanisms of axial pattern establishment, creating a coordinate system of a metazoan body plan, bilaterian segmentation, and left–right symmetry/asymmetry, are analysed. Data on the crucial contribution of coupled functions of the Wnt, BMP, Notch, and Hedgehog signaling pathways (all pathways are designated according to the abbreviated or full names of genes or their protein products; for details, see below) and the axial Hox-code in the formation and maintenance of metazoan body plans are necessary for an understanding of the evolutionary diversification and phenotypic expression of various types of axial symmetry. The lost body plans of some extinct Ediacaran and early Cambrian metazoans are also considered in comparison with axial body plans and posterior growth in living animals.

Thermofield double states in group field theory

Group field theories are higher-rank generalizations of matrix/tensor models, and encode the simplicial geometries of quantum gravity. In this paper, we study the thermofield double states in group field theories. The starting point is the equilibrium Gibbs states in group field theory recently found by Kotecha and Oriti, based on which we construct the thermofield double state as a “thermal” vacuum respecting the Kubo–Martin–Schwinger condition. We work with the Weyl [Formula: see text]-algebra of group fields, and a particular type of thermofield double states with single type of symmetry is obtained from the squeezed states on this Weyl algebra. The thermofield double states, when viewed as states on the group field theory Fock vacuum, are condensate states at finite flow parameter [Formula: see text]. We suggest that the equilibrium flow parameters [Formula: see text] of this type of thermofield double states in the group field theory condensate pictures of black hole horizon and quantum cosmology are related to the inverse temperatures in gravitational thermodynamics.