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Point Group (PG) symmetries play a fundamental role in many aspects of theoretical chemistry and computational materials science. With the objective to automatize the search of PG symmetry operations of generic atomic clusters, we present a new algorithm called Symmetry Operation FInder (SOFI). SOFI addresses the problem of identifying PG symmetry by framing it as a degenerate shape-matching problem, where the multiple solutions correspond to distinct symmetry operations. The developed algorithm is compared against three other algorithms dedicated to PG identification on a large set of atomic clusters. The results, along with some illustrative use cases, showcase the effectiveness of SOFI. The SOFI algorithm is released as part of the iterative rotations and assignments library, accessible at https://github.com/mammasmias/IterativeRotationsAssignments. [ABSTRACT FROM AUTHOR]

A consideration of the point group symmetry of molecules is often advantageous from a computational efficiency standpoint and sometimes necessary for the correct treatment of chemical physics problems. Many modern electronic structure software packages include a treatment of symmetry, but these are sometimes incomplete or unusable outside of that program's environment. Therefore, we have developed the MolSym package for handling molecular symmetry and its associated functionalities to provide a platform for including symmetry in the implementation and development of other methods. Features include point group detection, molecule symmetrization, arbitrary generation of symmetry element sets and character tables, and symmetry adapted linear combinations of real spherical harmonic basis functions, Cartesian displacement coordinates, and internal coordinates. We present some of the advantages of using molecular symmetry as achieved by MolSym, particularly with respect to Hartree–Fock theory, and the reduction of finite difference displacements in gradient/Hessian computations. This package is designed to be easily integrated into other software development efforts and may be extended to further symmetry applications. [ABSTRACT FROM AUTHOR]

Single crystal Cr1.27Te2 samples were synthesized by using the chemical vapor transport method. Single crystal x-ray diffraction studies show a trigonal crystal structure with a P 3 ̄ m 1 symmetry space group. We then systematically investigate magnetic properties and critical behaviors of single crystal Cr1.27Te2 around its paramagnetic-to-ferromagnetic phase transition. The Arrott plot indicates a second-order magnetic phase transition. We estimate critical exponents β = 0.2631 ± 0.002, γ = 1.2314 ± 0.007, and TC = 168.48 ± 0.031 K by using the Kouvel–Fisher method. We also estimate other critical exponents δ = 5.31 ± 0.004 by analyzing the critical isotherm at TC = 168.5 K. We further verify the accuracy of our estimated critical exponents by the scaling analysis. Further analysis suggests that Cr1.27Te2 can be best described as a quasi-2D Ising magnetic system. [ABSTRACT FROM AUTHOR]

Single crystal Cr1.27Te2 samples were synthesized by using the chemical vapor transport method. Single crystal x-ray diffraction studies show a trigonal crystal structure with a P 3 ̄ m 1 symmetry space group. We then systematically investigate magnetic properties and critical behaviors of single crystal Cr1.27Te2 around its paramagnetic-to-ferromagnetic phase transition. The Arrott plot indicates a second-order magnetic phase transition. We estimate critical exponents β = 0.2631 ± 0.002, γ = 1.2314 ± 0.007, and TC = 168.48 ± 0.031 K by using the Kouvel–Fisher method. We also estimate other critical exponents δ = 5.31 ± 0.004 by analyzing the critical isotherm at TC = 168.5 K. We further verify the accuracy of our estimated critical exponents by the scaling analysis. Further analysis suggests that Cr1.27Te2 can be best described as a quasi-2D Ising magnetic system. [ABSTRACT FROM AUTHOR]

Body-centered-cubic–face-centered-cubic (bcc–fcc) multi-metallic nanoparticles (NPs) associating a single-crystal core (Fe, FeCo alloys, etc.) with a polycrystalline noble metal shell (Au, AuAg alloys, etc.) are perfectly symmetrical or more irregular, even dramatically dissymmetrical, yet presenting a good crystalline organization. Here, a combination of experimental analysis and theoretical symmetry analysis is proposed, in order to provide a unified description of the observed morphologies (Fe–Au and Fe–AuAg systems), whatever their symmetry, and predict some morphology variability in a population of NPs. First, the central role of the crystal lattice accommodation is comprehensively analyzed from the experimental Fe–AuAg system. The two possible bcc–fcc epitaxial relationships generate a core–shell interface in the shape of a truncated rhombic dodecahedron. This results in two different types of grains in the shell, which are elastically accommodated between them by an equal distribution of twins and low-angle grain boundaries, however, at the cost of internal stresses. At the same time, symmetry breaking results from two possible growth variants originating from the Nishiyama–Wasserman epitaxial relationships. The shell grains fit together in a nanopuzzle-like organization, resulting in a large number of possible arrangements distributed in 13 different point groups of symmetry, all of lower order than the core symmetry (highest order of cubic symmetry). If the variants are randomly distributed, the probability for the NP to be asymmetric (group 1) is 80%. The dissymmetrical development of the NPs is then discussed. Extending this approach to other core shapes succeeds in predicting dissymmetrical or dramatically off-centered morphologies experimentally observed in Fe–Au NPs. [ABSTRACT FROM AUTHOR]

We study various aspects of global symmetries in five-dimensional superconformal field theories. Whenever a supersymmetry-preserving relevant deformation is available, the infrared gauge theory description might exhibit a finite order mixed 't Hooft anomaly between a 1-form symmetry and the instantonic symmetry. This anomaly constrains the flavor symmetry group acting faithfully on the SCFT and the consistency of certain RG flows. As an additional example, we consider the instructive case of three-dimensional N = 4 SQED. Finally, we discuss the compatibility between conformal invariance and the presence of 1-form and 2-group global symmetries. [ABSTRACT FROM AUTHOR]

The problem of describing invariant extensions of the 3D Schrödinger operator H with finite number of point interactions leads to the need for studying matrices of a special type, the permutation matrices. A large class of such extensions considered in a certain boundary triplet is in one-to-one correspondence with a set of the so-called boundary operators (matrices). The extension of H with point interactions concentrated on X = {x1,... , xm} ⊂ R 3 is invariant under the symmetry group of X (or its subgroup) if and only if the corresponding boundary matrix commutes with the set of m-by-m permutation matrices induced by the symmetry group, i.e., belongs to its commutant. The bicommutant theorem for such a set of matrices is proven for an arbitrary finite point set. For the special cases of regular polygon, tetrahedron, and cube, the basis of the bicommutant, considered as a vector space, is specified explicitly. [ABSTRACT FROM AUTHOR]

In the present work the atomic, electronic and optical properties of two-dimensional graphene, borophene, and boron carbide heterojunction bilayer systems (Graphene–BC3, Graphene–Borophene and Graphene–B4C3) as well as their constituent monolayers are investigated on the basis of first-principles calculations using the HSE06 hybrid functional. Our calculations show that while borophene is metallic, both monolayer BC3 and B4C3 are indirect semiconductors, with band-gaps of 1.822 eV and 2.381 eV as obtained using HSE06. The Graphene–BC3 and Graphene–B4C3 bilayer heterojunction systems maintain the Dirac point-like character of graphene at the K-point with the opening of a very small gap (20–50 meV) and are essentially semi-metals, while Graphene–Borophene is metallic. All bilayer heterostructure systems possess absorbance in the visible region where the resonance frequency and resonance absorption peak intensity vary between structures. Remarkably, all heterojunctions support plasmons within the range 16.5–18.5 eV, while Graphene–B4C3 and Graphene–Borophene exhibit a π -type plasmon within the region 4–6 eV, with the latter possessing an additional plasmon at the lower energy of 1.5–3 eV. The dielectric tensor for Graphene–B4C3 exhibits complex off-diagonal elements due to the lower P3 space group symmetry indicating it has anisotropic dielectric properties and could exhibit optically active (chiral) effects. Our study shows that the two-dimensional heterostructures have desirable optical properties broadening the potential applications of the constituent monolayers. [ABSTRACT FROM AUTHOR]

In the classical model, ferroelectricity is associated with small ion displacements from paraelectric phases with high symmetry, and ferroelectric crystals must adopt one of the ten polar point groups with low symmetry according to Neumann's principle. In this work, it is proposed that this conclusion is based on perfect bulk crystals without taking the boundaries into account. First‐principles evidence shows that ferroelectric polarizations may also be formed in some non‐polar point groups as the edges generally break the crystal symmetry. Meanwhile, such polarizations can be maintained at macroscale and are switchable when the transition between multiple equivalent states with high symmetry can be realized via long ion displacements， essentially akin to ion conductors. For example, the switching barriers can be much reduced in sliding ferroelectric bilayer systems or ionic compounds with covalent‐like directionality. Such unconventional ferroelectricity can be attributed to the boundaries and long ion displacements, and its existence in several systems like CuCrS2 is supported by experimental observations. It may explain a series of unclarified phenomena reported previously as well as significantly expand the scope of ferroelectrics, especially those with high polarizations induced by long ion displacements. [ABSTRACT FROM AUTHOR]

Since the discovery of quantum mechanics, the fact that the wavefunction is defined on the 3 n -dimensional configuration space rather than on the 3-dimensional space has seemed uncanny to many, including Schrödinger, Lorentz, and Einstein. Even today, this continues to be seen as a significant issue in the foundations of quantum mechanics. In this article, it will be shown that the wavefunction is, in fact, a genuine object on space. While this may seem surprising, the wavefunction does not possess qualitatively new features that were not previously encountered in objects known from Euclidean geometry and classical physics. The methodology used involves finding equivalent reinterpretations of the wavefunction exclusively in terms of objects from the geometry of space. The result is that we will find the wavefunction to be equivalent to geometric objects on space in the same way as was always the case in geometry and physics. This will be demonstrated to hold true from the perspective of Euclidean geometry, but also within Felix Klein's Erlangen Program, which naturally fits into the classification of quantum particles by the representations of spacetime isometries, as realized by Wigner and Bargmann, adding another layer of confirmation. These results lead to clarifications in the debates about the ontology of the wavefunction. From an empirical perspective, we already take for granted that all quantum experiments take place in space. I suggest that the reason why this works is that they can be interpreted naturally and consistently with the results presented here, showing that the wavefunction is an object on space. [ABSTRACT FROM AUTHOR]

For all integers n ≥ 1 and k ≥ 2 , the Hadamard product v 1 ★ ⋯ ★ v k of k elements of K n + 1 (with K being the complex numbers or real numbers) is the element v ∈ K n + 1 which is the coordinate-wise product of v 1 , ... , v k (introduced by Cueto, Morton, and Sturmfels for a model in Algebraic Statistics). This product induces a rational map h : P n (K) k ⤏ P n (K) . When K = C , k = 2 and X i (C) ⊂ P n (C) , i = 1 , 2 are irreducible, we prove four theorems for the case dim X 2 (C) = 1 , three of them with X 2 (C) as a line. We discuss the existence (non-existence) of a cancellation law for ★-products and use the symmetry group of the Hadamard product. In the second part, we work over R. Under mild assumptions, we prove that by knowing X 1 (R) ★ ⋯ ★ X k (R) , we know X 1 (C) ★ ⋯ ★ X k (C) . The opposite, i.e., taking and multiplying a set of complex entries that are invariant for the complex conjugation and then seeing what appears in the screen P n (R) , very often provides real ghosts, i.e., images that do not come from a point of X 1 (R) × ⋯ × X k (R) . We discuss a case in which we certify the existence of real ghosts as well as a few cases in which we certify the non-existence of these ghosts, and ask several open questions. We also provide a scenario in which ghosts are not a problem, where the Hadamard data are used to test whether the images cover the full screen. [ABSTRACT FROM AUTHOR]

A regular map is an abstract generalization of a Platonic solid. It describes a group, a topological cell decomposition of a 2-manifold of type { p ,   q } with only p-gons, such that q of them meet at each vertex in a circular manner, and we have maximal combinatorial symmetry, expressed by the flag transitivity of the symmetry group. On the one hand, we have articles on topological surface embeddings of regular maps by F. Razafindrazaka and K. Polthier, C. Séquin, and J. J. van Wijk.On the other hand, we have articles with polyhedral embeddings of regular maps by J. Bokowski and M. Cuntz, A. Boole Stott, U. Brehm, H. S. M. Coxeter, B. Grünbaum, E. Schulte, and J. M. Wills. The main concern of this partial survey article is to emphasize that all these articles should be seen as contributing to the common body of knowledge in the area of regular map embeddings. This article additionally provides a method for finding symmetrical equivelar polyhedral embeddings of type { 3 ,   7 } based on symmetrical graph embeddings on convex surfaces. [ABSTRACT FROM AUTHOR]

An exhaustive search for missing symmetry was performed for 223076 entries in the ICSD (2023‐2 release). Approximately 0.65% of them can be described with higher symmetry than reported. Out of the identified noncentrosymmetric entries, ∼74% can be described by centrosymmetric space groups; this has implications for compatible physical properties. It is proposed that the information on the correct space group is included in the ICSD. [ABSTRACT FROM AUTHOR]

In recent decades, sustained theoretical and software developments have clearly established that representation analysis and magnetic symmetry groups are complementary concepts that should be used together in the investigation and description of magnetic structures. Historically, they were considered alternative approaches, but currently, magnetic space groups and magnetic superspace groups can be routinely used together with representation analysis, aided by state‐of‐the‐art software tools. After exploring the historical antagonism between these two approaches, we emphasize the significant advancements made in understanding and formally describing magnetic structures by embracing their combined use. [ABSTRACT FROM AUTHOR]

Synthesis experiments were conducted in the quaternary system K2O–Na2O–CaO–SiO2, resulting in the formation of a previously unknown compound with the composition K0.72Na1.71Ca5.79Si6O19. Single crystals of sufficient size and quality were recovered from a starting mixture with a K2O:Na2O:CaO:SiO2 molar ratio of 1.5:0.5:2:3. The mixture was confined in a closed platinum tube and slowly cooled from 1150°C at a rate of 0.1°C min−1 to 700°C before being finally quenched in air. The structure has tetragonal symmetry and belongs to space group P4122 (No. 91), with a = 7.3659 (2), c = 32.2318 (18) Å, V = 1748.78 (12) Å3, and Z = 4. The silicate anion consists of highly puckered, unbranched six‐membered oligomers with the composition [Si6O19] and point group symmetry 2 (C2). Although several thousands of natural and synthetic oxosilicates have been structurally characterized, this compound is the first representative of a catena‐hexasilicate anion, to the best of our knowledge. Structural investigations were completed using Raman spectroscopy. The spectroscopic data was interpreted and the bands were assigned to certain vibrational species with the support of density functional theory at the HSEsol level of theory. To determine the stability properties of the novel oligosilicate compared to those of the chemically and structurally similar cyclosilicate combeite, we calculated the electronegativity of the respective structures using the electronegativity equalization method. The results showed that the molecular electronegativity of the cyclosilicate was significantly higher than that of the oligostructure due to the different connectivities of the oxygen atoms within the molecular units. [ABSTRACT FROM AUTHOR]

The study focused on the nitrilo‐tris‐(methylene phosphonate) [K2ntpH4]2 and [(K1−yTly)2ntpH4]2 complexes, which are a series of isovalent substitutions. The crystals of [K2ntpH4]2 are monoclinic and belong to the space group of symmetry P21/c with Z=4. When thallium substitutes potassium, the molecular structure remains the same, but the symmetry of the crystal packing changes to a triclinic system, space group of symmetry P1‾ ${\bar{1}}$ , with Z=2. One coordination polyhedra maintains an isometric configuration, while the other undergoes significant distortions. Polarization‐selective coordination is observed, where the thallium(I) ion, which is easily polarizable, populates the highly distorted polyhedron. The low polarizable potassium ion populates the weakly distorted one. The crystal is formed with an average thallium fraction higher than the initial aqueous solution. This suggests that replacing potassium ions in the complex with thallium ions is energetically favourable. It could explain why thallium is toxic to intracellular enzymes and carriers of genetic information. The isovalent substitution of potassium made it possible to observe the step‐by‐step formation of a super‐strong hydrogen bond, a phenomenon that is rarely detected under normal conditions. The O...O interatomic distance in the hydrogen bond decreases gradually from 2.55 Å for [K2ntpH4]2 to 2.474 Å for [Tl2ntpH4]2. [ABSTRACT FROM AUTHOR]

This paper describes the synthesis of a cerium(IV)‐based molecular gear composed of a thioether functionalized phthalocyanine anchoring ligand, and a helical naphthalocyanine rotating cogwheel functionalized with four carbazoles. The naphthalocyanine ligand 9 was obtained after eleven steps (overall yield of 0.2 %) as a mixture of three geometrical isomers, two of which are chiral and exhibit high levels of steric hindrance, as shown by DFT calculations. Their attributions have been made using 1H‐NMR based on their different symmetry groups. The ratio of isomers was also determined and the prochiral C4h naphthalocyanine shown to be the major compound (55 %). Its heteroleptic complexation with cerium (IV) and the anchoring phthalocyanine ligand 10 gave the targeted molecular gear in a 16 % yield. [ABSTRACT FROM AUTHOR]

Recently a large variety of non‐collinear spin textures have been revealed in various crystals with different symmetry groups. Of particular interest are crystals with D2d symmetry that exhibit a complex variety of stable and metastable spin textures that includes antiskyrmions, elliptical Bloch‐skyrmions, fractional‐antiskyrmions, fractional Bloch‐skyrmions, and type‐II trivial‐bubbles. The observation of these structures necessitates their stabilization via magnetic field and temperature protocols which demands a thorough understanding of their creation, transformation, and collapse dynamics. Utilizing the real‐space imaging capabilities of Lorentz transmission electron microscopy, the generation and annihilation of diverse spin textures in a single D2d Heusler compound are demonstrated. It is showed that antiskyrmions and elliptical Bloch‐skyrmions can be deformed into more elaborate elongated magnetic nano‐objects through a collapse mechanism. Their elongation is governed by the intrinsic antisymmetric Dzyaloshinskii‐Moriya vector exchange interaction and dipolar energy present in the system. Furthermore, antiskyrmions are found to be metastable at all temperatures on field‐cooling, while a topological phase transformation from elliptical Bloch‐skyrmions to antiskyrmions rather takes places on field‐heating. These results are corroborated by micromagnetic simulations and demonstrate the efficient manipulation of different spin textures in a D2d compound by varying field and temperature protocols and represents a critical step toward the application of magnetic skyrmions. [ABSTRACT FROM AUTHOR]

We proceed to obtain an exact analytical solution of the Brans–Dicke (BD) equations for the spatially flat (k = 0) Friedmann–Lamaître–Robertson–Walker (FLRW) cosmological model in both cases of the absence and presence of the cosmological constant. The solution method that we use to solve the field equations of the BD equations is called the "invariants of symmetry groups method" (ISG method). This method is based on the extended Prelle–Singer (PS) method and it employs the Lie point symmetries, λ -symmetries, and Darboux polynomials (DPs). Indeed, the ISG method tries to provide two independent first-order invariants associated to the one-parameter Lie groups of transformations keeping the ordinary differential equations (ODEs) invariant, as solutions. It should be noted for integrable ODEs that the ISG method guarantees the extraction of these two invariants. In this work, for the BD equations in FLRW cosmological model, we find the Lie point symmetries, λ -symmetries, and DPs, and obtain the basic quantities of the extended PS method (which are the null forms and the integrating factors). By making use of the extended PS method we find two independent first-order invariants in such a way that appropriate cosmological solutions from solving these invariants as a system of algebraic equations are simultaneously obtained. These solutions are wealthy in that they include many known special solutions, such as the O'Hanlon–Tupper vacuum solutions, Nariai's solutions, Brans–Dicke dust solutions, inflationary solutions, etc. [ABSTRACT FROM AUTHOR]

The proposition that photon is a topological object [S. C. Tiwari, J. Math. Phys. 49, 032303 (2008)] is given rigorous foundation based on pure vector field theory independent of the electromagnetic fields. Holomorphy of 4-dimensional spacetime and the nature of topological obstructions are investigated to articulate singular vortex model for photon. The utility of the Euclidean symmetry group is discussed in detail for the proposed photon model. [ABSTRACT FROM AUTHOR]

The anhydrous alkaline earth metal carbonate Be(CO3) was synthesized in a laser-heated diamond anvil cell at moderate pressures and temperatures (20(2) GPa and 1500(200) K) by a reaction of BeO with CO2. It crystallizes in the acentric, trigonal space group P3121 with Z = 3. The crystal structure was obtained from synchrotron single crystal X-ray diffraction data and confirmed by density functional theory-based calculations in combination with Raman spectroscopy. Second harmonic generation measurements were employed to verify the acentric space group symmetry. The crystal structure of Be(CO3) is characterized by the presence of isolated [CO3]2−-groups and BeO4-tetrahedra. This is a new structure type and such a topology has not been observed in carbonates before. Be(CO3) can be recovered to ambient conditions and is not undergoing a phase transition during decompression. [ABSTRACT FROM AUTHOR]

In this paper, we use the Lie symmetry analysis to obtain the closed-form solutions of the (3+1)-dimensional generalized Kadomtsev–Petviashvili Benjamin–Bona–Mahony (gKP-BBM) equation. We obtain the infinitesimal generators, commutator table of Lie algebra, adjoint representation of subalgebras, symmetry group, and similarity reduction for the gKP-BBM equation. Also, we evaluated the interactions of soliton solutions of the gKP-BBM equation. It is observed that multi-soliton complexes are self-localized in state wherein, several fundamental solitons including bright solitons and dark solitons are nonlinearly superimposed. A notable observation is the existence of topological defects in soliton interactions, where two solitons appear to be separated, with the adjoining structure being “out of phase” with each other. The kink, acting as a twist in the soliton’s value, overcomes topological defects, leading to a transition from one phase to another. This comprehensive analysis contributes to a deeper understanding of the dynamics and interactions of solitons in the (3+1)-dimensional gKP-BBM equation. [ABSTRACT FROM AUTHOR]

The anhydrous alkaline earth metal carbonate Be(CO3) was synthesized in a laser-heated diamond anvil cell at moderate pressures and temperatures (20(2) GPa and 1500(200) K) by a reaction of BeO with CO2. It crystallizes in the acentric, trigonal space group P3121 with Z = 3. The crystal structure was obtained from synchrotron single crystal X-ray diffraction data and confirmed by density functional theory-based calculations in combination with Raman spectroscopy. Second harmonic generation measurements were employed to verify the acentric space group symmetry. The crystal structure of Be(CO3) is characterized by the presence of isolated [CO3]2−-groups and BeO4-tetrahedra. This is a new structure type and such a topology has not been observed in carbonates before. Be(CO3) can be recovered to ambient conditions and is not undergoing a phase transition during decompression. [ABSTRACT FROM AUTHOR]

Recent developments have introduced a groundbreaking form of collinear magnetism known as “altermagnetism”. This emerging magnetic phase is characterized by robust time‐reversal symmetry breaking, antiparallel magnetic order, and alternating spin‐splitting band structures, yet it exhibits vanishing net magnetization constrained by symmetry. Altermagnetism uniquely integrates traits previously considered mutually exclusive to conventional collinear ferromagnetism and antiferromagnetism, thereby facilitating phenomena and functionalities previously not achievable within these traditional categories of magnetism. Initially proposed theoretically, the existence of the altermagnetic phase has since been corroborated by a range of experimental studies, which have confirmed its unique properties and potential for applications. This review explores the rapidly expanding research on altermagnets, emphasizing the novel physical phenomena they manifest, methodologies for inducing altermagnetism, and promising altermagnetic materials. The goal of this review is to furnish readers with a comprehensive overview of altermagnetism and to inspire further innovative studies on altermagnetic materials which can potentially revolutionize applications in technology and materials science. [ABSTRACT FROM AUTHOR]

In this work, a new method to determine and to describe the evolution of physical systems (in classical or quantum regimes) is proposed. The main idea is based in the observation that the complete determination of dynamics of the system is connected to the nonlinear realization (NLR) of the symmetry group associated with the symmetry of the Hamiltonian H (t) of the system. The Maurer–Cartan forms, when they are parametrically associated to the projection on the hypersurface induced by the group in question via pullback, of the Hamiltonian components (based on the generators of the symmetry group by which it is defined) give rise to a fundamental system of equations by which the precise evolution can be determined. Such a system of equations under certain conditions that we will specify in this paper coincides with the system obtained through the Wei–Norman method, thus showing explicitly that our proposal is more general due the universal character of equations from the NLRs approach. As example, the important problem of the Caldirola–Kanai inverted Hamiltonian is completely solved, showing at the same time a new interpretation of what NLRs refer to. [ABSTRACT FROM AUTHOR]

A novel interpretation of Symmetry Topological Field Theories (SymTFTs) as theories of gravity is explored by proposing a holographic duality where the bulk SymTFT (with the gauging of a suitable Lagrangian algebra) is dual to the universal effective field theory (EFT) that describes spontaneous symmetry breaking on the boundary. The authors tested this conjecture in various dimensions and with many examples involving different continuous symmetry structures, including non‐Abelian and non‐invertible symmetries, as well as higher groups. For instance, many Abelian SymTFTs are found to be dual to free theories of Goldstone bosons or generalized Maxwell fields, while non‐Abelian SymTFTs relate to non‐linear sigma models with target spaces defined by the symmetry groups. The analysis is also extended to include the non‐invertible Q/Z$\mathbb {Q}/\mathbb {Z}$ axial symmetry, which is shown to be dual to axion‐Maxwell theory, and a non‐Abelian 2‐group structure in four dimensions, deriving a new parity‐violating interaction that has implications for the low‐energy dynamics of U(N)$U(N)$ QCD. [ABSTRACT FROM AUTHOR]

Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group symmetries and arranging the gauge fields in a 2D lattice, the local symmetries become the stabilizer of the XZZX-code for any Abelian group. By twisting the gauging map, we obtain codes that explicitly confine anyons, whose local creating operators violate an odd number of plaquettes. Their fusion results in either mobile dipole excitations twisting only half of the plaquette terms, or complete immobile Sierpiński-like excitations if we twist all the terms. Our construction naturally realizes any gapped boundary by taking different quantum phases of the initial (1+1)D globally symmetric system. In addition, our method also establishes a promising route to obtain higherdimensional topological codes from lower ones and to identify their gapped boundaries and their tensor network representations. Here, it is shown how two-dimensional physics can emerge from its one-dimensional boundary. The 2D topological order comes from the concatenation of gauging maps of 1D global symmetries. [ABSTRACT FROM AUTHOR]

Many deployable structures in nature, as well as human-made mechanisms, preserve symmetry as their configurations evolve. Examples in nature include blooming flowers, dilation of the iris within the human eye, viral capsid maturation and molecular and bacterial motors. Engineered examples include opening umbrellas, elongating scissor jacks, variable apertures in cameras, expanding Hoberman spheres and some kinds of morphing origami structures. In these cases, the structures either preserve a discrete symmetry group or are described as an evolution from one discrete symmetry group to another of the same type as the structure deploys. Likewise, elastic metamaterials built from lattice structures can also preserve symmetry type while passively deforming and changing lattice parameters. A mathematical formulation of such transitions/deployments is articulated here. It is shown that if X is Euclidean space, G is a continuous group of motions of Euclidean space and Γ is the type of the discrete subgroup of G describing the symmetries of the deploying structure, then the symmetry of the evolving structure can be described by time-dependent subgroups of G of the form Γαt:=αtΓαt−1 , where αt is a time-dependent affine transformation. Then, instead of considering the whole structure in X , a 'sector' of it that lives in the orbit space Γαt\X can be considered at each instant in time, and instead of considering all motions in G , only representatives from right cosets in the space Γαt\G need to be considered. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'. [ABSTRACT FROM AUTHOR]

The Edelstein effect is the origin of the spin-orbit torque: a current-induced torque that is used for the electrical control of ferromagnetic and antiferromagnetic materials. This effect originates from the relativistic spin-orbit coupling, which necessitates utilizing materials with heavy elements. Here, we show that in magnetic materials with non-collinear magnetic order, the Edelstein effect and, consequently, a current-induced torque can exist even in the absence of the spin-orbit coupling. Using group symmetry analysis, model calculations, and realistic simulations on selected compounds, we identify large classes of non-collinear magnet candidates and demonstrate that the current-driven torque is of similar magnitude as the celebrated spin-orbit torque in conventional transition metal structures. We also show that this torque can exist in an insulating material, which could allow for highly efficient electrical control of magnetic order. A major goal of spintronics is to manipulate magnetic order with electric fields. The typical approach is to use a material with spin-orbit coupling, and the resulting Edelstein effect. Here, González-Hernández et al. show theoretically that non-collinear magnets can also host an Edelstein effect, even in the absence of spin-orbit coupling. [ABSTRACT FROM AUTHOR]

Background: The proximity of the rectum to the prostate in radiation therapy (RT) for prostate cancer presents a significant dosimetric challenge, leading to high rectal doses and resulting in detrimental side effects. Perirectal tissue spacing reduces rectal dose and gastrointestinal toxicities by mechanically separating these organs. A variety of materials have been explored for use as rectal spacers, most recently, a stabilized hyaluronic acid (HA) gel, which can be formed into deliberate a shape, and retains the definition of that shape, while remaining flexible, unlike polyethylene glycol (PEG) hydrogels. Purpose: This study evaluates the dosimetric impact of the spacer, including shape symmetry, the degree of separation at different locations, and the temporal stability of the space. Our goal is to provide physics‐informed guidance on the optimal use of this sculptable spacer. Methods: A secondary analysis was performed on data from a 13‐center prospective randomized trial (NCT 04189913), involving 136 patients with centrally‐reviewed treatment plans conducted on CT/MR simulation scans before and after receiving HA spacer implants. Patients were treated with 60 Gy in 20 fractions to the prostate. For this study, python software was utilized for automated processing of DICOM RTstruct and RTdose files, facilitating detailed analysis of the spacer's impact on anatomical displacement and dosimetric outcomes. Complete dose‐volume histograms (DVHs) were reconstructed, and combined into composite population DVHs before and after implant, verified against trial‐reported dose points. Patients were divided into similar groups of separation and symmetry, and differences in their composite DVHs were tested for significance. Stability of the spacer was studied by comparing serial MRI images and by computing the distance between contours at four axial planes, at simulation and 3‐month follow‐up, post RT. Results: The introduction of the HA spacer significantly enhanced rectal sparing, as evidenced by a reduction in the mean rectal integral dose by over 6 Gy. High rates of implant symmetry (>95%) were observed, indicating nearly optimal lateral spacer placement. In superior–inferior coverage, this study like many others, saw the spacing largest at the superior extent but becoming more variable inferiorly at the level of the prostate apex. This allowed study of the apex as a specific area for dosimetric concern. Stability assessments confirmed that the spacer maintained its position and dimensions between the simulation and the 3‐month post‐RT, implying stable geometry during treatment, with only minimal separation changes observed. Statistical analysis using the Kruskal–Wallis test revealed significant correlations of larger separations at the inferior and apical planes with improved dosimetric outcomes, including rV30Gy. Conclusion: The use of a stabilized HA spacer in prostate RT effectively enhances prostate–rectum separation, leading to significant rectal sparing without undesirable dose compromises. This study underscores the role of strategic placement and shape, specifically including > 1 cm separation from the base down to the prostate apex. When combined with the treatment planning techniques used in the trial to create a steep dosimetric gradient across the spacer, these findings elucidate the dosimetric outcomes that can be expected in the clinical implementation of HA spacer. This is particularly relevant in the evolution of hypofractionated treatment regimens for prostate cancer therapy. [ABSTRACT FROM AUTHOR]

We extend two KdVSKR models to fractional KdVSKR models with the Caputo derivative. The KdVSKR equation in (2+1)-dimension, which is a recent extension of the KdVSKR equation in (1+1)-dimension, can model the soliton resonances in shallow water. Applying the Hirota bilinear method, finite symmetry group method, and consistent Riccati expansion method, many new interaction solutions have been derived. Soliton and elliptical function interplaying solution for the fractional KdVSKR model in (1+1)-dimension has been derived for the first time. For the fractional KdVSKR model in (2+1)-dimension, two-wave interaction solutions and three-wave interaction solutions, including dark-soliton-sine interaction solution, bright-soliton-elliptic interaction solution, and lump-hyperbolic-sine interaction solution, have been derived. The effect of the order γ on the dynamical behaviors of the solutions has been illustrated by figures. The three-wave interaction solution has not been studied in the current references. The novelty of this paper is that the finite symmetry group method is adopted to construct interaction solutions of fractional nonlinear systems. This research idea can be applied to other fractional differential equations. [ABSTRACT FROM AUTHOR]

The study delves into the relationship between symmetry groups and automorphism groups in polyhedral graphs, emphasizing their interconnected nature and their significance in understanding the symmetries and structural properties of fullerenes. It highlights the visual importance of symmetry and its applications in architecture, as well as the mathematical structure of the automorphism group, which captures all of the symmetries of a graph. The paper also discusses the significance of groups in Abstract Algebra and their relevance to understanding the behavior of mathematical systems. Overall, the findings offer an inclusive understanding of the relationship between symmetry groups and automorphism groups, paving the way for further research in this area. [ABSTRACT FROM AUTHOR]

Context: Li2VMgO6, Li2NbMgO6, and Li2TaMgO6 double perovskite compounds were energetically the most stable in the FM phase. The lattice constants were 7.63 Å, 7.94 Å, and 7.95 Å, and the Curie temperatures were 910.451 K, 930.739 K, and 1258.821 K, respectively. The wide bandgap semiconductor characters were provided in the GGA-PBE methods as 2.139 eV, 4.209 eV, and 5.007 eV, respectively. This wide band gap semiconductor state in the majority carriers and the metallic state in the minority states made these double perovskites true half-metallic ferromagnetics. The bulk modulus obtained in the ground state calculations and the values obtained from thermodynamic calculations were relatively close. Debye temperatures in the initial state conditions were 747 K, 685.13 K, and 587.77 K, respectively. The total magnetic moment values were calculated as 3.00 µB/f.u. The most significant contribution to this value came from oxygen atoms. Methods: The theoretical calculations of Li2VMgO6, Li2NbMgO6, and Li2TaMgO6 double perovskite alloys were performed using the WIEN2k program developed by Blaha et al. The electronic calculations were made with GGA-PBE, GGA + mBJ, and GGA + U approximations in the space number 225 and the Fm-3 m symmetry group. The thermodynamic calculations were performed using Gibbs2. In thermodynamic calculations, temperature increases were determined as 100 K and temperature values were increased from 0 to 1200 K. [ABSTRACT FROM AUTHOR]

An elastic map T associates stress with strain in some material. A symmetry of T is a rotation of the material that leaves T unchanged, and the symmetry group of T consists of all such rotations. The symmetry class of T describes the symmetry group but without the orientation information. With an eye toward geophysical applications, Browaeys & Chevrot developed a theory which, for any elastic map T and for each of six symmetry classes Σ , computes the " Σ -percentage" of T . The theory also finds a "hexagonal approximation"—an approximation to T whose symmetry class is at least transverse isotropic. We reexamine their theory and recommend that the Σ -percentages be abandoned. We also recommend that the hexagonal approximations to T be replaced with the closest transverse isotropic maps to T . [ABSTRACT FROM AUTHOR]

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A new species and genus of colonial coral, Lindaphylon solovjevi, from the Upper Ordovician of Estonia is described in detail. The colony has a zonation similar to the zonation structure of the mesogleal skeleton of octocorals, since it consists of a narrow axis and a surrounding wide cortex of small calcite sclerites and a system of large solenia. Corallites present 12 sclerosepta in a wide shallow cup. A new family Lindaphylonidae and an order Lyndaphylonaceae are based on these features, and a new order placed in the subphylum Anthozoa as incertae sedis. A comparative study of skeleton formation and mesenteric apparatus symmetry in different groups of coral polyps is considered in detail. [ABSTRACT FROM AUTHOR]

A new polymorph of tert-butyl (2-aminophenyl)carbamate was identified using single crystal X-ray diffraction. The compound crystallised in the centrosymmetric, monoclinic space group P21/n with an asymmetric unit comprising two crystallographically-independent molecules (Zʹ = 2). This new structure was compared to that of the known polymorph with the differences between the two being attributed to a combination of space group symmetry, conformational variation, hydrogen bonding network dimensionality and crystal packing. A new polymorph of tert-butyl (2-aminophenyl)carbamate exhibits π···H interactions that precipitate conformational variations and an asymmetric unit with two crystallographically-independent molecules. [ABSTRACT FROM AUTHOR]

Here, we report a successful synthesis of single crystals of a topological semimetal (TSM) candidate, PdSn4, using a self-flux route. The synthesized crystal is well characterized through x-ray diffraction (XRD), field emission scanning electron microscopy, and x-ray photoelectron spectroscopy. A detailed Rietveld analysis of the powder XRD pattern of PdSn4 confirmed the same to crystallize in an Aea2 space group instead of reported Ccce. A large magnetoresistance (MR) along with Shubnikov–de Haas (SdH) oscillations have been observed in magneto-transport measurements at 2 K. The presence of weak antilocalization (WAL) effect in the synthesized PdSn4 crystal is confirmed and analyzed using Hikami Larkin Nagaoka formalism, being applied on magnetoconductivity of the same at a low magnetic field. An extended Kohler's rule is implemented on MR data to determine the role of scattering processes and temperature-dependent carrier density on the transport phenomenon in PdSn4. Furthermore, the non-trivial band topology and the presence of edge states are shown through density functional theory-based theoretical calculations. All calculations are performed considering the Aea2 space group symmetry. The calculated Z2 invariants (0; 0 1 0) suggest the presence of weak topological insulating properties in PdSn4. A clear evidence of topological edge states at Γ point is visible in calculated edge states spectra. This is the first report on PdSn4, showing the presence of SdH oscillation in magneto-transport measurements. Also, the presence of a weak insulating phase in PdSn4 is described for the first time on the basis of calculated Z2 invariants. [ABSTRACT FROM AUTHOR]

Here, we report a successful synthesis of single crystals of a topological semimetal (TSM) candidate, PdSn4, using a self-flux route. The synthesized crystal is well characterized through x-ray diffraction (XRD), field emission scanning electron microscopy, and x-ray photoelectron spectroscopy. A detailed Rietveld analysis of the powder XRD pattern of PdSn4 confirmed the same to crystallize in an Aea2 space group instead of reported Ccce. A large magnetoresistance (MR) along with Shubnikov–de Haas (SdH) oscillations have been observed in magneto-transport measurements at 2 K. The presence of weak antilocalization (WAL) effect in the synthesized PdSn4 crystal is confirmed and analyzed using Hikami Larkin Nagaoka formalism, being applied on magnetoconductivity of the same at a low magnetic field. An extended Kohler's rule is implemented on MR data to determine the role of scattering processes and temperature-dependent carrier density on the transport phenomenon in PdSn4. Furthermore, the non-trivial band topology and the presence of edge states are shown through density functional theory-based theoretical calculations. All calculations are performed considering the Aea2 space group symmetry. The calculated Z2 invariants (0; 0 1 0) suggest the presence of weak topological insulating properties in PdSn4. A clear evidence of topological edge states at Γ point is visible in calculated edge states spectra. This is the first report on PdSn4, showing the presence of SdH oscillation in magneto-transport measurements. Also, the presence of a weak insulating phase in PdSn4 is described for the first time on the basis of calculated Z2 invariants. [ABSTRACT FROM AUTHOR]

We give a complete classification of topological field theories with reflection structure and spin-statistics in one and two spacetime dimensions. Our answers can be naturally expressed in terms of an internal fermionic symmetry group G, which is different from the spacetime structure group. Fermionic groups encode symmetries of systems with fermions and time-reversing symmetries. We show that 1-dimensional topological field theories with reflection structure and spin-statistics are classified by finite-dimensional Hermitian representations of G. In spacetime dimension 2 we give a classification in terms of strongly G-graded stellar Frobenius algebras. Our proofs are based on the cobordism hypothesis. Along the way, we develop some useful tools for the computation of homotopy fixed points of 2-group actions on bicategories. [ABSTRACT FROM AUTHOR]

In this paper, we study the phenomenological implications of two minor zeros in neutrino mass matrix using trimaximal mixing matrix. In this context, we analyzed 15 possible cases of two minor zeros in neutrino mass matrix and found only two cases, namely, class A 1 and class A 2 , that are compatible with the present neutrino oscillation data. We present correlations of several neutrino oscillation parameters and give prediction of the total neutrino mass, the values of effective Majorana mass, the effective electron anti-neutrino mass and CP violating Majorana phases for these two classes. We also explore the degree of fine tuning in the elements of neutrino mass matrix for the allowed classes. Moreover, we propose a flavor model within the seesaw model along with Z 8 symmetry group that can generate such classes. [ABSTRACT FROM AUTHOR]

In Liu et al. [On the generalized time fractional diffusion equation: Symmetry analysis, conservation laws, optimal system and exact solutions, Int. J. Geom. Methods Mod. Phys. 17(01) (2020) 2050013], the generalized time-fractional diffusion equation Dtαu = aupu xx + buqu x2 is studied by the symmetry analysis method. Liu et al. obtained two group generators X1 = ∂ ∂x, X2 = 2t α ∂ ∂t + x ∂ ∂x and only one trivial solution u(t,x) = f(t) = C0 Γ(α)tα−1 for the equation. In this paper, we classify the Lie symmetry group admitted by the equation, and for the case p = q + 1, we obtain a richer set of group generators and some nontrivial solutions, including unprecedented exact solutions and power series solutions. In addition, we construct the one-dimensional optimal system of the Lie symmetry group admitted by the time-fractional diffusion-type equation by Olver’s method, and obtain the conservation laws for all the obtained Lie symmetries using the general method developed by Ibragimov. For the novel exact solutions and power series solutions, we analyze their dynamic behavior graphically. [ABSTRACT FROM AUTHOR]

In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. However, in practice, the process of determining equivalence of two spacetimes relies on determining if a set of equations has a solution. Depending on the form of the equations this may be undecideable. Furthemore, if a solution does exist the equations may still be unsolvable in some way. In the case that spacetimes admit Killing vector fields with non-trivial orbits, we propose a new set of invariant quantities, called Killing invariants. These invariants will allow for the sub-classification of spacetimes admitting the same group of symmetries and will, in principle, be substantially less complicated than other sets of invariants. We apply this approach to the class of static spherically symmetric geometries as an illustrative example. [ABSTRACT FROM AUTHOR]

We show that dynamical gluon and quark solutions possess inherent color symmetry with respect to Weyl group of . Such a symmetry manifests itself in the space of physical solutions after removing all pure gauge degrees of freedom, and it leads to existence of invariant non-degenerate vacuum and one-particle quantum states for gluons and quarks. Some physical implications are discussed. [ABSTRACT FROM AUTHOR]

We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. We want to know which vector-valued finite element spaces have bases invariant under permutation of vertex indices. The permutations of vertex indices correspond to the symmetry group of the simplex. That symmetry group is represented on simplicial finite element spaces by the pullback action. We determine a natural notion of invariance and sufficient conditions on the dimension and polynomial degree for the existence of invariant bases. We conjecture that these conditions are necessary too. We utilize Djoković and Malzan's classification of monomial irreducible representations of the symmetric group and show new symmetries of the geometric decomposition and canonical isomorphisms of the finite element spaces. Explicit invariant bases with complex coefficients are constructed in dimensions two and three for different spaces of finite element differential forms. [ABSTRACT FROM AUTHOR]

A certain type of defectivity applicable to binary mixtures of uniform solids and liquid crystals is identified as arising from the possible lack of uniformity of the composite as a result of a misalignment between the structures of the underlying constituents. Various local measures of misalignment are derived for the case of a smectic-A combined with solids with discrete or continuous symmetry groups. [ABSTRACT FROM AUTHOR]

The grand antiprism A is an outlier among the uniform 4-polytopes, since it is not obtainable from Wythoff's construction. Its symmetry group G (A) has been incorrectly described as [ [ 10 , 2 + , 10 ] ] or even as an 'ionic diminished Coxeter group'. In fact, G (A) is another group of order 400, namely the group ± [ D 10 × D 10 ] · 2 , in the notation of Conway and Smith. We explain all this and so correct a persistent error in the literature. This fresh look at the beautiful geometry of the polytope A is also a fine opportunity to introduce the reader to the elegance of Wythoff's construction and to the less familiar use of quaternions to classify the finite 4-dimensional isometry groups. [ABSTRACT FROM AUTHOR]