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1
Brown, D. R. L., e D. M. Jackson. "A rooted map invariant, non-orientability and Jack symmetric functions". Journal of Combinatorial Theory, Series B 97, n.º 3 (maio de 2007): 430–52. http://dx.doi.org/10.1016/j.jctb.2006.07.007.
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RUSAKOV, B. YE. "LOOP AVERAGES AND PARTITION FUNCTIONS IN U(N) GAUGE THEORY ON TWO-DIMENSIONAL MANIFOLDS". Modern Physics Letters A 05, n.º 09 (10 de abril de 1990): 693–703. http://dx.doi.org/10.1142/s0217732390000780.
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Loop averages and partition functions in the U(N) gauge theory are calculated for loops without intersections on arbitrary two-dimensional manifolds including nonorientable ones. The physical quantities are directly expressed through geometrical characteristics of a manifold (areas enclosed by loops and the genus) and gauge group parameters (Casimir eigenvalues and dimensions of the irreducible representations). It is shown that, from the physical quantities’ point of view, non-orientability of the manifold is equivalent to its non-compactness.
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Aguirre, Pablo, Bernd Krauskopf e Hinke M. Osinga. "Global Invariant Manifolds Near Homoclinic Orbits to a Real Saddle: (Non)Orientability and Flip Bifurcation". SIAM Journal on Applied Dynamical Systems 12, n.º 4 (janeiro de 2013): 1803–46. http://dx.doi.org/10.1137/130912542.
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MAGNON, ANNE. "PT VIOLATION AND ORIENTABILITY IN THE EARLY UNIVERSE". International Journal of Modern Physics D 03, n.º 01 (março de 1994): 225–30. http://dx.doi.org/10.1142/s0218271894000344.
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We recall that the “Sagnac Effect” can be viewed as a clock converting rotation (torsion) into a lapse of time. It is shown that the two available helicities can be used to show that PT invariance can be experimentally confirmed within the framework of General Relativity. These clocks are rather similar to those proposed by de Broglie (the particle-clocks) to convert (right or left) rotation into a quantum of energy. The Quantum analogue of this PT invariance is analyzed for zero rest-mass fields and related Mass and Spin Casimir operators. We suggest that Quantum PT invariance could have been violated in the monopole phase, due to mixing of homotopy classes of the Lorentz Lie Group along a spacetime track, appearance of superselected Mass and Spin Casimir operators, and spontaneous breaking of their proportionality. We suggest that this could be viewed as an evidence of the asymmetric flow of time, (arrow of time) in the Early Universe. Existence (non existence) of spinor structure and orientability of space, is discussed.
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Singerman, David. "Orientable and non-orientable Klein surfaces with maximal symmetry". Glasgow Mathematical Journal 26, n.º 1 (janeiro de 1985): 31–34. http://dx.doi.org/10.1017/s0017089500005747.
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Let X be a bordered Klein surface, by which we mean a Klein surface with non-empty boundary. X is characterized topologically by its orientability, the number k of its boundary components and the genus p of the closed surface obtained by filling in all the holes. The algebraic genus g of X is defined by.If g≥2 it is known that if G is a group of automorphisms of X then |G|≤12(g-l) and that the upper bound is attained for infinitely many values of g ([4], [5]). A bordered Klein surface for which this upper bound is attained is said to have maximal symmetry. A group of 12(g-l) automorphisms of a bordered Klein surface of algebraic genus g is called an M*-group and it is known that a finite group G is an M*-group if and only if it is generated by 3 non-trivial elements T1, T2, T3 which obey the relations([4]).
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Costa, Antonio F., e Milagros Izquierdo. "On real trigonal Riemann surfaces". MATHEMATICA SCANDINAVICA 98, n.º 1 (1 de março de 2006): 53. http://dx.doi.org/10.7146/math.scand.a-14983.
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A closed Riemann surface $X$ which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering will be called a trigonal morphism. A trigonal Riemann surface $X$ is called real trigonal if there is an anticonformal involution (symmetry) $\sigma$ of $X$ commuting with the trigonal morphism. If the trigonal morphism is a cyclic regular covering the Riemann surface is called real cyclic trigonal. The species of the symmetry $\sigma $ is the number of connected components of the fixed point set $\mathrm{Fix}(\sigma)$ and the orientability of the Klein surface $X/\langle\sigma\rangle$. We characterize real trigonality by means of Fuchsian and NEC groups. Using this approach we obtain all possible species for the symmetry of real cyclic trigonal and real non-cyclic trigonal Riemann surfaces.
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LIENHARDT, PASCAL. "N-DIMENSIONAL GENERALIZED COMBINATORIAL MAPS AND CELLULAR QUASI-MANIFOLDS". International Journal of Computational Geometry & Applications 04, n.º 03 (setembro de 1994): 275–324. http://dx.doi.org/10.1142/s0218195994000173.
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The scope of this work is Geometric Modeling. We study the representation and the construction of subdivisions of quasi-manifolds, using a topology-based approach. Quasi-manifolds are here defined as a subset of pseudo-manifolds, which are well-known objects in Algebraic Topology. N-dimensional generalized maps (resp. n-dimensional maps) are combinatorial models defined for representing the topology of subdivisions of orientable or non-orientable quasi-manifolds with or without boundaries (resp. orientable quasi-manifolds without boundaries). In this paper, we define the models, main related notions and properties as cells, boundaries, duality, orientability, Euler characteristic. Basic operations are proposed for handling the models. We also show the correspondence between the combinatorial models and combinatorial cellular quasi-manifolds, here defined as combinatorial simplicial quasi-manifolds to which a structure into cells is added. This correspondence establishes that the models are rigorous and unambiguous ones. Moreover, the definitions of the models and the related notions and operations are quite simple, and they can be easily implemented and used in geometric modellers.
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Xu, Yun, Anja Winkler, Martin Helwig, Niels Modler, Maik Gude, Axel Dittes, Dominik Höhlich e Thomas Lampke. "Numerical Investigation of the Magnetic Alignment of Fe-Co-Coated Single Reinforcement Fibers". Journal of Physics: Conference Series 2526, n.º 1 (1 de junho de 2023): 012036. http://dx.doi.org/10.1088/1742-6596/2526/1/012036.
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Abstract Fiber-reinforced composites are progressively more used in a variety of industrial applications. In recent years, carbon fiber-reinforced plastics have become increasingly popular, particularly in the aerospace sector because they offer outstanding mechanical properties combined with low weight. However, the orientation and distribution of the fibers have a significant effect on the mechanical and physical properties of the composite materials. Using conventional manufacturing technologies, it is not always technologically possible to adjust the fiber orientation to the load direction. One possible approach to targeted fiber alignment is the combination of classical manufacturing processes with a superimposed alignment mechanism so that the fibers can be oriented according to the load during component manufacturing. In this context, the orientation and distribution of short and long fibers through an external magnetic field seem to be well-suited to be integrated into the conventional manufacturing process of fiber-reinforced composites. Therefore, the generally non-magnetic reinforcement fibers, e.g. carbon or glass fibers, need to be modified or coated with magnetic materials. In this paper, carbon fibers coated with an iron-cobalt alloy are prepared by electrodeposition for the validation of simulation models developed in previous studies. Furthermore, numerical studies are presented in regard to the orientation of such fibers in polymeric matrices. Thus, simulative investigations of the orientability of coated carbon fibers in polymeric materials are shown and the works provide an important reference for future studies of fiber orientation and alignment using magnetic fields.
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Winkler, Anja, Niels Modler, Maik Gude, Yun Xu, Martin Helwig, Eike Dohmen, Axel Dittes, Dominik Höhlich e Thomas Lampke. "Numerical Investigation of the Orientability of Single Reinforcement Fibers in Polymer Matrices". Polymers 14, n.º 3 (28 de janeiro de 2022): 534. http://dx.doi.org/10.3390/polym14030534.
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Fiber-reinforced polymers are increasingly being used, especially in lightweight structures. Here, the effective adaptation of mechanical or physical properties to the necessary application or manufacturing requirements plays an important role. In this context, the alignment of reinforcing fibers is often hindered by manufacturing aspects. To achieve graded or locally adjusted alignment of different fiber lengths, common manufacturing technologies such as injection molding or compression molding need to be supported by the external non-mechanical process. Magnetic or electrostatic fields seem to be particularly suitable for this purpose. The present work shows a first simulation study of the alignment of magnetic particles in polymer matrices as a function of different parameters. The parameters studied are the viscosity of the surrounding polymer as a function of the focused processing methods, the fiber length, the thickness and permeability of the magnetic fiber coatings, and the magnetic flux density. The novelty of the presented works is in the development of an advanced simulation model that allows the simulative representation and reveal of the fluid–structure interaction, the influences of these parameters on the inducible magnetic torque and fiber alignment of a single fiber. Accordingly, the greatest influence on fiber alignment is caused by the magnetic flux density and the coating material.
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Lemos, N. A., e M. J. Rebouças. "Inquiring electromagnetic quantum fluctuations about the orientability of space". European Physical Journal C 81, n.º 7 (julho de 2021). http://dx.doi.org/10.1140/epjc/s10052-021-09426-9.
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AbstractOrientability is an important global topological property of spacetime manifolds. It is often assumed that a test for spatial orientability requires a global journey across the whole 3-space to check for orientation-reversing paths. Since such a global expedition is not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are usually offered to support the choosing of time- and space-orientable spacetime manifolds. Another theoretical argument also offered to support this choice comes from the impossibility of having globally defined spinor fields on non-orientable spacetime manifolds. In this paper, we argue that it is possible to locally access spatial orientability of Minkowski empty spacetime through physical effects involving quantum vacuum electromagnetic fluctuations. We study the motions of a charged particle and a point electric dipole subject to these electromagnetic fluctuations in Minkowski spacetime with orientable and non-orientable spatial topologies. We derive analytic expressions for a statistical orientability indicator for both of these point-like particles in two inequivalent spatially flat topologies. For the charged particle, we show that it is possible to distinguish the orientable from the non-orientable topology by contrasting the time evolution of the orientability indicators. This result reveals that it is possible to access orientability through electromagnetic quantum vacuum fluctuations. However, the answer to the central question of the paper, namely how to locally probe the orientability of Minkowski 3-space intrinsically, comes about only in the study of the motions of an electric dipole. For this point-like particle, we find that a characteristic inversion pattern exhibited by the curves of the orientability statistical indicator is a signature of non-orientability. This result makes it clear that it is possible to locally unveil spatial non-orientability through the inversion pattern of curves of our orientability indicator for a point electric dipole under quantum vacuum electromagnetic fluctuations. Our findings might open the way to a conceivable experiment involving quantum vacuum electromagnetic fluctuations to locally probe the spatial orientability of Minkowski empty spacetime.
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Pincak, Richard, Alexander Pigazzini, Saeid Jafari, Cenap Özel e Andrew DeBenedictis. "A topological approach for emerging D-branes and its implications for gravity". International Journal of Geometric Methods in Modern Physics 18, n.º 14 (29 de setembro de 2021). http://dx.doi.org/10.1142/s0219887821502273.
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In this paper, we introduce a new geometric/topological approach to the emerging braneworld scenario in the context of D-branes using partially negative-dimensional product (PNDP) manifolds. The working hypothesis is based on the fact that the orientability of PNDP manifolds can be arbitrary, and starting from this, we propose that gravitational interaction can derive naturally from the non-orientability. According to this hypothesis, we show that topological defects can emerge from non-orientability and they can be identified as gravitational interaction at macroscopic level. In other words, the orientability of fundamental PNDPs can be related to the appearance of curvature at low-energy scales.
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Lemos, N. A., D. Müller e M. J. Rebouças. "Probing time orientability of spacetime". European Physical Journal C 83, n.º 6 (2 de junho de 2023). http://dx.doi.org/10.1140/epjc/s10052-023-11642-4.
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AbstractIn general relativity, cosmology and quantum field theory, spacetime is assumed to be an orientable manifold endowed with a Lorentz metric that makes it spatially and temporally orientable. The question as to whether the laws of physics require these orientability assumptions is ultimately of observational or experimental nature, or the answer might come from a fundamental theory of physics. The possibility that spacetime is time non-orientable lacks investigation, and so should not be dismissed straightaway. In this paper, we argue that it is possible to locally access a putative time non-orientability of Minkowski empty spacetime by physical effects involving quantum vacuum electromagnetic fluctuations. We set ourselves to study the influence of time non-orientability on the stochastic motions of a charged particle subject to these electromagnetic fluctuations in Minkowski spacetime equipped with a time non-orientable topology and with its time orientable counterpart. To this end, we introduce and derive analytic expressions for a statistical time orientability indicator. Then we show that it is possible to pinpoint the time non-orientable topology through an inversion pattern displayed by the corresponding orientability indicator, which is absent when the underlying manifold is time orientable.
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Czyżewska-Jankowska, Agnieszka, e Piotr Śniady. "Bijection Between Oriented Maps and Weighted Non-Oriented Maps". Electronic Journal of Combinatorics 24, n.º 3 (14 de julho de 2017). http://dx.doi.org/10.37236/6718.
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We consider bicolored maps, i.e. graphs which are drawn on surfaces, and construct a bijection between (i) oriented maps with arbitary face structure, and (ii) (weighted) non-oriented maps with exactly one face. Above, each non-oriented map is counted with a multiplicity which is based on the concept of the orientability generating series and the measure of orientability of a map. This bijection has the remarkable property of preserving the underlying bicolored graph. Our bijection shows equivalence between two explicit formulas for the top-degree of Jack characters, i.e. (suitably normalized) coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions.
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Liu, Guangxiu, Maocai Pi, Long Zhou, Zhehong Liu, Xudong Shen, Xubin Ye, Shijun Qin et al. "Physical realization of topological Roman surface by spin-induced ferroelectric polarization in cubic lattice". Nature Communications 13, n.º 1 (2 de maio de 2022). http://dx.doi.org/10.1038/s41467-022-29764-w.
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AbstractTopology, an important branch of mathematics, is an ideal theoretical tool to describe topological states and phase transitions. Many topological concepts have found their physical entities in real or reciprocal spaces identified by topological invariants, which are usually defined on orientable surfaces, such as torus and sphere. It is natural to investigate the possible physical realization of more intriguing non-orientable surfaces. Herein, we show that the set of spin-induced ferroelectric polarizations in cubic perovskite oxides AMn3Cr4O12 (A = La and Tb) reside on the topological Roman surface—a non-orientable two-dimensional manifold formed by sewing a Möbius strip edge to that of a disc. The induced polarization may travel in a loop along the non-orientable Möbius strip or orientable disc, depending on the spin evolution as controlled by an external magnetic field. Experimentally, the periodicity of polarization can be the same or twice that of the rotating magnetic field, which is consistent with the orientability of the disc and the Möbius strip, respectively. This path-dependent topological magnetoelectric effect presents a way to detect the global geometry of a surface and deepens our understanding of topology in both mathematics and physics.
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Bernardi, Olivier, e Guillaume Chapuy. "Counting unicellular maps on non-orientable surfaces". Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AN,..., Proceedings (1 de janeiro de 2010). http://dx.doi.org/10.46298/dmtcs.2859.
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International audience A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is a topological disk. In this paper we give a bijective operation that relates unicellular maps on a non-orientable surface to unicellular maps of a lower topological type, with distinguished vertices. From that we obtain a recurrence equation that leads to (new) explicit counting formulas for non-orientable precubic (all vertices of degree 1 or 3) unicellular maps of fixed topology. We also determine asymptotic formulas for the number of all unicellular maps of fixed topology, when the number of edges goes to infinity. Our strategy is inspired by recent results obtained for the orientable case [Chapuy, PTRF 2010], but significant novelties are introduced: in particular we construct an involution which, in some sense, ``averages'' the effects of non-orientability. \par Une carte unicellulaire est le plongement d'un graphe connexe dans une surface, tel que le complémentaire du graphe est un disque topologique. On décrit une opération bijective qui relie les cartes unicellulaires sur une surface non-orientable aux cartes unicellulaires de type topologique inférieur, avec des sommets marqués. On en déduit une récurrence qui conduit à de (nouvelles) formules closes d'énumération pour les cartes unicellulaires précubiques (sommets de degré 1 ou 3) de topologie fixée. On obtient aussi des formules asymptotiques pour le nombre total de cartes unicellulaires de topologie fixée, quand le nombre d'arêtes tend vers l'infini. Notre stratégie est motivée par de récents résultats dans le cas orientable [Chapuy, PTRF, 2010], mais d'importantes nouveautés sont introduites: en particulier, on construit une involution qui, en un certain sens, "moyenne'' les effets de la non-orientabilité.
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Chen, Z. Y., Shengyuan A. Yang e Y. X. Zhao. "Brillouin Klein bottle from artificial gauge fields". Nature Communications 13, n.º 1 (25 de abril de 2022). http://dx.doi.org/10.1038/s41467-022-29953-7.
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AbstractA Brillouin zone is the unit for the momentum space of a crystal. It is topologically a torus, and distinguishing whether a set of wave functions over the Brillouin torus can be smoothly deformed to another leads to the classification of various topological states of matter. Here, we show that under $${{\mathbb{Z}}}_{2}$$ Z 2 gauge fields, i.e., hopping amplitudes with phases ±1, the fundamental domain of momentum space can assume the topology of a Klein bottle. This drastic change of the Brillouin zone theory is due to the projective symmetry algebra enforced by the gauge field. Remarkably, the non-orientability of the Brillouin Klein bottle corresponds to the topological classification by a $${{\mathbb{Z}}}_{2}$$ Z 2 invariant, in contrast to the Chern number valued in $${\mathbb{Z}}$$ Z for the usual Brillouin torus. The result is a novel Klein bottle insulator featuring topological modes at two edges related by a nonlocal twist, radically distinct from all previous topological insulators. Our prediction can be readily achieved in various artificial crystals, and the discovery opens a new direction to explore topological physics by gauge-field-modified fundamental structures of physics.
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Holanda, Frederico de. "Brasília: Superblocks in perspective". Journal of Design for Resilience in Architecture and Planning, 31 de dezembro de 2021. http://dx.doi.org/10.47818/drarch.2021.v2si034.
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The design for the Superquadra Norte 109 [North Superblock 109] of the Brasília Pilot Plan, Brazil’s Federal Capital, has started from a critical appraisal of the existent superblocks and makes a proposal that intends to: 1) establish clear relations of the block with the surroundings, stressing the importance of elements as the entrance for vehicles, the bus stop and the connections with the local shopping and the club, through the dimension and form of places, the localization of facilities, public lighting and vegetation; 2) improve internal legibility of the block, by creating places clearly defined by the buildings, to which entrance doors open; 3) create a street system in rings, not in a tree-like one, which are common in the existing superblocks, to improve internal circulation; 4) locate facilities internal to the superblock accessible to its entrance, by recognising (against what was predicted) that non-locals use them; 5) establish a continuous system of sidewalks that privileges the pedestrian, not the vehicle, as is traditional; 6) use vegetation and illumination to reinforce the identities of places in the superblock; 7) implement a configuration that explores a clear variation in forms, dimensions and uses, which favour the identity and orientability of the block; 8) configure open spaces and localise facilities of the superblock to favour co-presence and co-awareness among the inhabitants and between the latter and those passing by.
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Dołęga, Maciej. "Top Degree Part in $b$-Conjecture for Unicellular Bipartite Maps". Electronic Journal of Combinatorics 24, n.º 3 (11 de agosto de 2017). http://dx.doi.org/10.37236/6130.
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Goulden and Jackson (1996) introduced, using Jack symmetric functions, some multivariate generating series $\psi(\boldsymbol{x}, \boldsymbol{y},\boldsymbol{z}; 1, 1+\beta)$ with an additional parameter $\beta$ that might be interpreted as a continuous deformation of the rooted bipartite maps generating series. Indeed, it has a property that for $\beta \in \{0,1\}$, it specializes to the rooted, orientable (general, i.e. orientable or not, respectively) bipartite maps generating series. They made the following conjecture: coefficients of $\psi$ are polynomials in $\beta$ with positive integer coefficients that can be written as a multivariate generating series of rooted, general bipartite maps, where the exponent of $\beta$ is an integer-valued statistics that in some sense "measures the non-orientability" of the corresponding bipartite map.We show that except two special values of $\beta = 0,1$ for which the combinatorial interpretation of the coefficients of $\psi$ is known, there exists a third special value $\beta = -1$ for which the coefficients of $\psi$ indexed by two partitions $\mu,\nu$, and one partition with only one part are given by rooted, orientable bipartite maps with arbitrary face degrees and black/white vertex degrees given by $\mu$/$\nu$, respectively. We show that this evaluation corresponds, up to a sign, to a top-degree part of the coefficients of $\psi$. As a consequence, we introduce a collection of integer-valued statistics of maps $(\eta)$ such that the top-degree of the multivariate generating series of rooted, bipartite maps with only one face (called unicellular) with respect to $\eta$ gives the top degree of the appropriate coefficients of $\psi$. Finally, we show that $b$ conjecture holds true for all rooted, unicellular bipartite maps of genus at most $2$.