Статті в журналах: "Topological discontinuity"

1

YILDIZ, IZZET BURAK. "Discontinuity of topological entropy for Lozi maps." Ergodic Theory and Dynamical Systems 32, no. 5 (September 16, 2011): 1783–800. http://dx.doi.org/10.1017/s0143385711000411.

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AbstractRecently, Buzzi [Maximal entropy measures for piecewise affine surface homeomorphisms. Ergod. Th. & Dynam. Sys.29 (2009), 1723–1763] showed in the compact case that the entropy map f→htop(f) is lower semi-continuous for all piecewise affine surface homeomorphisms. We prove that topological entropy for Lozi maps can jump from zero to a value above 0.1203 as one crosses a particular parameter and hence it is not upper semi-continuous in general. Moreover, our results can be extended to a small neighborhood of this parameter showing the jump in the entropy occurs along a line segment in the parameter space.

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2

Janse, Å. M., B. C. Low, and E. N. Parker. "Topological complexity and tangential discontinuity in magnetic fields." Physics of Plasmas 17, no. 9 (September 2010): 092901. http://dx.doi.org/10.1063/1.3474943.

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3

Maslyuchenko, Oleksandr V. "The discontinuity point sets of quasi-continuous functions." Bulletin of the Australian Mathematical Society 75, no. 3 (June 2007): 373–79. http://dx.doi.org/10.1017/s0004972700039307.

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It is proved that a subsetEof a hereditarily normal topological spaceXis a discontinuity point set of some quasi-continuous functionf:X→ ℝ if and only ifEis a countable union of setsEn=Ān⋂Bdash abovenwhereĀn⋂Bn=An⋂Bdash aboven= φ

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4

NOGUEIRA, A., and D. RUDOLPH. "Topological weak-mixing of interval exchange maps." Ergodic Theory and Dynamical Systems 17, no. 5 (October 1997): 1183–209. http://dx.doi.org/10.1017/s0143385797086276.

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An interval map with only one discontinuity is isomorphic to a rotation of the circle, and has continuous eigenfunctions. What we show here is that for almost every choice of lengths of the intervals, this is the only way an irreducible interval exchange can have a somewhere continuous eigenfunction. We show slightly more, considering certain towers over the interval exchange, showing that outside of a set of choices for interval lengths of measure zero these have a somewhere continuous eigenfunction only if they are isomorphic to either a rotation, or a tower of constant height over an interval exchange.

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5

Fan, Jun. "Computer Data Structure for Geological Entities Modelling Based on OO-Solid Model." Advanced Materials Research 383-390 (November 2011): 2484–91. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.2484.

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In the long evolution of the earth formation often form a complex geological structure, modeling for these complex geological entities (such as thinning-out, bifurcation, reverse, etc.) still require in-depth 3D modeling study. Because of discontinuity, complexity and uncertainty of distribution of 3D geo-objects, some models only are suitable for regular, continuous and relatively simple spatial objects, and some are suitable for discontinue, complex and uncertain geo-objects, but some improvements on these models, such as, updating of model, maintenance of topological and seamless integration between models, are still to be made. OO-Solid model, put forward by writer in 2002, is an object- oriented topological model based on sections. The OO-Solid Model is an object-oriented 3D topologic data model based on component for geology modeling with fully considering the topological relations between geological objects and its geometric primitives, Comparatively, it accords with the actual requirements of three-dimensional geological modeling . The key issue of 3D geology modeling is the 3D data model. Some data models are suitable for discontinue, complex and uncertain geo-objects, but the OO-Solid model is an object-oriented 3D topologic data model based on component for geology modeling with fully considering the topological relations between geological objects and its geometric primitives. OO-Solid model and data structure are designed. At last, 3D complex geological entities modeling based on OO-Solid are studied in this paper. These study is important and one of the core techniques for the 3DGM.

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6

PANTAZOPOULOS, IOANNIS A., and SPYROS G. TZAFESTAS. "OPTIMIZING THE SUBDIVISION OF ELEMENTS IN DISCONTINUITY MESHING FOR HIERARCHICAL RADIOSITY." International Journal on Artificial Intelligence Tools 12, no. 04 (December 2003): 395–411. http://dx.doi.org/10.1142/s0218213003001290.

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This paper presents a new topological structure for use in the context of hierarchical radiosity combined with discontinuity meshing. This is most useful for a new strategy adopted for subdividing the elements of a scene consisting of convex polygons. The subdivision is done in a local optimization manner keeping the aspect ratios of produced polygons low. The generated meshes give high visual accuracy.

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7

KRASNENKER, A. "DISCONTINUITY OF FOURIER TRANSFORMS OF POISSONIAN TYPE COUNTABLY ADDITIVE MEASURES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 01 (March 2013): 1350002. http://dx.doi.org/10.1142/s0219025713500021.

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It is proved in the paper that different natural Fourier transforms (FTs) of the measure mentioned in the title are not continuous with respect to such sufficient topologies as Sazonov and Gross–Sazonov (introduced by Smolyanov [Gross–Sazonov theorem for alternating cylindrical measures, Vestnik Moskov. Univ. (4) (1983) 4–12]) topologies. The motivation of the result is the fact that the FT of the standard Wiener measure is discontinuous in a known sufficient topologies as stated by Smolyanov and Fomin (see e.g., [Measures on Topological Linear Spaces, Uspekhi Mat. Nauk31(4) (1976) 3–56]).

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8

Ohshika, Ken'ichi. "Strong convergence of Kleinian groups and Carathéodory convergence of domains of discontinuity." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 2 (September 1992): 297–307. http://dx.doi.org/10.1017/s0305004100070985.

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In the theory of Kleinian groups, important examples of Kleinian groups are frequently constructed as algebraic limits of known sequences of Kleinian groups, for example quasi-conformal deformations of a Kleinian group. It is an important problem to determine the properties of the limit Kleinian group from information on the sequence converging to the limit. The topological properties of the domain of discontinuity and the limit set of a Kleinian group provide valuable pieces of information about the Kleinian group. It is reasonable to expect that in a good situation, the domain of discontinuity of the limit Kleinian group is the Carathéodory limit of the domains of discontinuity of the sequence, or, equivalently, the limit set of the limit Kleinian group is the Hausdorif limit of the limit sets of the sequence. Our main theorem (Theorem 5) shows that this is true when the sequence strongly converges to the limit, and the Kleinian groups of the sequence and the limit preserve the parabolicity in both directions and satisfy the condition (*) introduced by Bonahon.

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9

Kuznetsov, Yu A., S. Rinaldi, and A. Gragnani. "One-Parameter Bifurcations in Planar Filippov Systems." International Journal of Bifurcation and Chaos 13, no. 08 (August 2003): 2157–88. http://dx.doi.org/10.1142/s0218127403007874.

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We give an overview of all codim 1 bifurcations in generic planar discontinuous piecewise smooth autonomous systems, here called Filippov systems. Bifurcations are defined using the classical approach of topological equivalence. This allows the development of a simple geometric criterion for classifying sliding bifurcations, i.e. bifurcations in which some sliding on the discontinuity boundary is critically involved. The full catalog of local and global bifurcations is given, together with explicit topological normal forms for the local ones. Moreover, for each bifurcation, a defining system is proposed that can be used to numerically compute the corresponding bifurcation curve with standard continuation techniques. A problem of exploitation of a predator–prey community is analyzed with the proposed methods.

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10

Razani, Abdolrahman. "Chapman-Jouguet detonation profile for a qualitative model." Bulletin of the Australian Mathematical Society 66, no. 3 (December 2002): 393–403. http://dx.doi.org/10.1017/s0004972700040259.

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In this article, the existence of traveling wave fronts for a one step chemical reaction with a natural discontinuous reaction rate function is studied. This discontinuity occurs because of the cold boundary difficulty and implies a discontinuous system of ordinary differential equations. By some general topological arguments in ordinary differential equations, the Chapman-Jouguet detonation for exothermic reactions is shown to exist. In addition, the uniqueness of this wave is considered.

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11

Hartley, John P. "Effective discontinuity and a characterisation of the superjump." Journal of Symbolic Logic 50, no. 2 (June 1985): 349–58. http://dx.doi.org/10.2307/2274221.

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One of the most fundamental results of higher-type recursion theory was first proved by Thomas Grilliot [3]. He showed that the functional embodying number quantification, 2E, is computable from a type-2 object F if and only if F has an effective discontinuity. For the background to this work we recommend Normann's book [9] or his summary [10], and for an example of its many applications Normann-Wainer [11].The purpose of §1 of this paper is to give an effective proof of the “only if” part of this result: i.e. a construction of a discontinuity of F from the information 2E = {e}F. This contrasts with Grilliot's argument which is topological and nonconstructive, and shows that “Grilliot's trick” for computing 2E from a discontinuity of F is essentially the only method.We then apply the method to two more general situations in which it gives new results. In §2 we treat type-3 objects in which 3E is computable (assuming AC and CH), and obtain a strengthening of the result of Hartley [5, §5]. In §3 we consider the superjump and characterise it as the least among a class of functionals with a particular sort of family of discontinuities.

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12

Ding, Changlin, Yibao Dong, Yuanbo Wang, Jianbing Shi, Shilong Zhai, and Xiaopeng Zhao. "Acoustic metamaterials and metasurfaces composed of meta-atoms and meta-molecules." Journal of Physics D: Applied Physics 55, no. 25 (February 25, 2022): 253002. http://dx.doi.org/10.1088/1361-6463/ac4b72.

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Abstract Acoustic metamaterials (AMMs) and acoustic metasurfaces (AMSs) are artificially structured materials with unique properties not found in natural materials. We review herein the properties of AMMs and AMSs that have been designed using different kinds of meta-atoms or meta-molecules with local resonance. AMMs composed of meta-atoms display a transmission dip with a negative modulus or a negative mass density. AMMs composed of two kinds of meta-atoms present a transparent transmission, indicating that they simultaneously have a negative modulus and a negative mass density. Furthermore, meta-molecule AMMs also exhibit double-negative properties. Moreover, acoustic meta-atoms or meta-molecules can be used to fabricate acoustic topological metamaterials with topologically protected edge state propagation. These meta-atoms and meta-molecules can also attain phase discontinuity near the resonant frequency, and thus they can be used to design AMSs with anomalous manipulation for acoustic waves. The tunability of meta-molecules provides a feasible path to achieve broadband AMS.

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13

Liu, Xia. "Regularization of the Boundary-Saddle-Node Bifurcation." Advances in Mathematical Physics 2018 (2018): 1–10. http://dx.doi.org/10.1155/2018/5094878.

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In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is transversal to the boundary. The boundary-saddle-node (BSN) bifurcation occurs at a critical value when the saddle-node point is located on the discontinuity boundary. We derive a local topological normal form for the BSN bifurcation and study its local dynamics by applying the classical Filippov’s convex method and a novel regularization approach. In fact, by the regularization approach a given Filippov system is approximated by a piecewise-smooth continuous system. Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.

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14

Cha, Yun Ju, Hyun Woo Kim, Sun Ho Ko, Lee Ku Kwac, and Hong Gun Kim. "Mechanical and Thermal Analysis of Topological Optimization for Load Bearing Skate." Advanced Materials Research 785-786 (September 2013): 1305–8. http://dx.doi.org/10.4028/www.scientific.net/amr.785-786.1305.

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Load bearing skate for the current weight is heavy and requires its own weight, but persist without improvement in the lack of capital and technology, but it is a reality. In this study, carried out phase optimal design to remove unwanted elements that do not have a stress to reduce the weight of skating that is being used for cargo transportation for, it reduces the weight of the objective function, we examined the safety associated with it.Using the FEM analysis Let's examine the effect on the failure strength by extreme temperatures that are used in the field of stress concentration due to discontinuity in the analysis at the time, structure - was carried out thermal analysis.Further, while ensuring safety through safety factor 2.1 and 20% weight reduction by the phase volume of for weight reduction.

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15

Corob Cook, Ged. "Eilenberg–Mac Lane Spaces for Topological Groups." Axioms 8, no. 3 (July 27, 2019): 90. http://dx.doi.org/10.3390/axioms8030090.

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In this paper, we establish a topological version of the notion of an Eilenberg–Mac Lane space. If X is a pointed topological space, π 1 ( X ) has a natural topology coming from the compact-open topology on the space of maps S 1 → X . In general, the construction does not produce a topological group because it is possible to create examples where the group multiplication π 1 ( X ) × π 1 ( X ) → π 1 ( X ) is discontinuous. This discontinuity has been noticed by others, for example Fabel. However, if we work in the category of compactly generated, weakly Hausdorff spaces, we may retopologise both the space of maps S 1 → X and the product π 1 ( X ) × π 1 ( X ) with compactly generated topologies to see that π 1 ( X ) is a group object in this category. Such group objects are known as k-groups. Next we construct the Eilenberg–Mac Lane space K ( G , 1 ) for any totally path-disconnected k-group G. The main point of this paper is to show that, for such a G, π 1 ( K ( G , 1 ) ) is isomorphic to G in the category of k-groups. All totally disconnected locally compact groups are k-groups and so our results apply in particular to profinite groups, answering a question of Sauer’s. We also show that analogues of the Mayer–Vietoris sequence and Seifert–van Kampen theorem hold in this context. The theory requires a careful analysis using model structures and other homotopical structures on cartesian closed categories as we shall see that no theory can be comfortably developed in the classical world.

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16

Shi, Peng, Luping Du, and Xiaocong Yuan. "Strong spin–orbit interaction of photonic skyrmions at the general optical interface." Nanophotonics 9, no. 15 (September 17, 2020): 4619–28. http://dx.doi.org/10.1515/nanoph-2020-0430.

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AbstractPhotonic skyrmions have applications in many areas, including the vectorial and chiral optics, optical manipulation, deep-subwavelength imaging and nanometrology. Much effort has been focused on the experimental characterization of photonic skyrmions. Here, we give an insight into the spin and orbital features of photonic skyrmions constructed by the p-polarized and s-polarized surface waves at an interface with various electric and magnetic properties by analyzing the continuity of chirality, energy flow and momentum densities through the electric and magnetic interface. The continuity of chirality density indicates that the photonic skyrmion has a property of the optical transverse spin. Most importantly, the continuity of energy flow and momentum densities results in four spin–orbit interaction quantities, which indicate the gradient of electric polarizability or permeability governs the spin–orbit interaction of photonic skyrmions and leads to the discontinuity and even the reversal of spin orientation through the optical interface. Our investigations on the spin–orbit properties of photonic skyrmions, which can give rise to the spin-dependent force and topological unidirectional transportation, is thorough and can be extended to other classical wave, such as acoustic and fluid waves. The findings help in understanding the spin–orbit feature of photonic topological texture and in constructing further optical manipulation, sensing, quantum and topological techniques.

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17

FU, GUOYANG, LEI HE, and GUOWEI MA. "3D ROCK MASS GEOMETRICAL MODELING WITH ARBITRARY DISCONTINUITIES." International Journal of Applied Mechanics 02, no. 04 (December 2010): 871–87. http://dx.doi.org/10.1142/s1758825110000809.

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This paper describes an algorithm to generate the realistic numerical representation of three-dimensional rock masses. The discontinuities can be treated as infinite or finite planes with or without thickness. A finite plane is represented by a polygon and defined using centroid of the polygon, orientation, geometry in 2D plane, the angle between strike line and reference line and other properties including cohesion, friction angle, tensile strength and aperture. Through 3D discontinuity network simulation, the information of discontinuities is obtained as the input data for block generation. The block generation process includes boundary planes cutting, discontinuities cutting and block integration. The results are also verified by graphical check, topological and geometrical properties of a polyhedron. The algorithm we adopt is convenient to be developed into a computer program. The generated model, in which the blocks and loops of blocks could be convex or concave, can be used for single block stability analysis or block model codes like discrete element method (DEM) and discontinuous deformation analysis (DDA).

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18

Saraoui, Selma, Azeddine Belakehal, Abdelghani Attar, and Amar Bennadji. "The Topological Reading of Ambiances in the Built Environment: The New Methodology for the Analysis of the Luminous Ambiance in the Museum Space." SHS Web of Conferences 64 (2019): 03004. http://dx.doi.org/10.1051/shsconf/20196403004.

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Daylight is currently at the centre of discourse on architectural space. The definition of architectural space takes essence from Euclidean geometry related to metric dimensions. The present study is an attempt to shed light on topology which is a non-Euclidean geometry. It can support non-metric components of space such as light to define architectural space. A corpus of six European museums has been chosen to study the immaterial or material relationships between form and daylight, since light is an essential element for the success of the exhibition. It also seeks to highlight discontinuity reports, and to confirm their existence through their software visualizations Therefore, the current study has taken into account an analysis model based on the notions of "route" and "sequence". The contemporary architectural project focused on taking into account human postures, both physical and psychological, within the architectural space. The results obtained show that light can release other spatial features for the museum space that can be highlighted by visualization with sequential analysis.

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19

Li, Zhao Kun, Hua Mei Bian, Li Juan Shi, and Xiao Tie Niu. "Multiobjective Topology Extraction of the Compliant Mechanisms." Advanced Materials Research 971-973 (June 2014): 1941–48. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.1941.

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Homogenization or material distribution method based topology optimization will create final topologies in grey level image and saw tooth jump discontinuity boundaries that are not suitable for direct engineering practice, so it is necessary to extract the topological diagram. And a new topology extraction method for compliant mechanisms is presented. In the fist stage, the grey image is transferred into the black-and white finite element topology optimization results. The threshold value meeting to objective function is obtained so that each element is either empty or solid; in the second stage, the density contour approach is used by redistributing nodal densities to generate the smooth boundaries; in the third stage, Smooth boundaries are represented by parameterized B-spline curves whose control points selected from the viewpoint of stiffness and flexibility constitute the parameters ready to undergo shape optimization; Then shape optimization is executed to improve stress-based local performance, The parameters that present the outer shape of the compliant mechanism are used as design variables; In the final stage, simulations of numerical examples are presented to show the validity of the proposed method.

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20

Shee, Saraswati, Raisa Fabiha, Marc Cahay, and Supriyo Bandyopadhyay. "Reflection and Refraction of a Spin at the Edge of a Quasi-Two-Dimensional Semiconductor Layer (Quantum Well) and a Topological Insulator." Magnetism 2, no. 2 (April 18, 2022): 117–29. http://dx.doi.org/10.3390/magnetism2020009.

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We derive the reflection and refraction laws for an electron spin incident from a quasi-two-dimensional semiconductor region (with no spin–orbit interaction) on the metallic surface of a topological insulator (TI) when the two media are in contact edge to edge. For a given incident angle, there can generally be two different refraction angles for refraction into the two spin eigenstates in the TI surface, resulting in two different ‘spin refractive indices’ (birefringence) and the possibility of two different critical angles for total internal reflection. We derive expressions for the spin refractive indices and the critical angles, which depend on the incident electron’s energy for given effective masses in the two regions and a given potential discontinuity at the TI/semiconductor interface. For some incident electron energies, there is only one critical angle, in which case 100% spin polarized injection can occur into the TI surface from the semiconductor if the angle of incidence exceeds that critical angle. The amplitudes of reflection of the incident spin with and without spin flip at the interface, as well as the refraction (transmission) amplitudes into the two spin eigenstates in the TI, are derived as functions of the angle of incidence.

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21

Park, Keunhong, Utkarsh Sinha, Peter Hedman, Jonathan T. Barron, Sofien Bouaziz, Dan B. Goldman, Ricardo Martin-Brualla, and Steven M. Seitz. "HyperNeRF." ACM Transactions on Graphics 40, no. 6 (December 2021): 1–12. http://dx.doi.org/10.1145/3478513.3480487.

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Neural Radiance Fields (NeRF) are able to reconstruct scenes with unprecedented fidelity, and various recent works have extended NeRF to handle dynamic scenes. A common approach to reconstruct such non-rigid scenes is through the use of a learned deformation field mapping from coordinates in each input image into a canonical template coordinate space. However, these deformation-based approaches struggle to model changes in topology, as topological changes require a discontinuity in the deformation field, but these deformation fields are necessarily continuous. We address this limitation by lifting NeRFs into a higher dimensional space, and by representing the 5D radiance field corresponding to each individual input image as a slice through this "hyper-space". Our method is inspired by level set methods, which model the evolution of surfaces as slices through a higher dimensional surface. We evaluate our method on two tasks: (i) interpolating smoothly between "moments", i.e., configurations of the scene, seen in the input images while maintaining visual plausibility, and (ii) novel-view synthesis at fixed moments. We show that our method, which we dub HyperNeRF , outperforms existing methods on both tasks. Compared to Nerfies, HyperNeRF reduces average error rates by 4.1% for interpolation and 8.6% for novel-view synthesis, as measured by LPIPS. Additional videos, results, and visualizations are available at hypernerf.github.io.

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22

Hwang, Jinah, Suyeon Shin, Myoungin Shin, and Woonjae Hwang. "Four-Quadrant Riemann Problem for a 2×2 System Involving Delta Shock." Mathematics 9, no. 2 (January 10, 2021): 138. http://dx.doi.org/10.3390/math9020138.

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In this paper, a four-quadrant Riemann problem for a 2×2 system of hyperbolic conservation laws is considered in the case of delta shock appearing at the initial discontinuity. We also remove the restriction in that there is only one planar wave at each initial discontinuity. We include the existence of two elementary waves at each initial discontinuity and classify 14 topologically distinct solutions. For each case, we construct an analytic solution and compute the numerical solution.

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23

Hwang, Jinah, Suyeon Shin, Myoungin Shin, and Woonjae Hwang. "Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock." Mathematics 9, no. 2 (January 10, 2021): 138. http://dx.doi.org/10.3390/math9020138.

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In this paper, a four-quadrant Riemann problem for a 2×2 system of hyperbolic conservation laws is considered in the case of delta shock appearing at the initial discontinuity. We also remove the restriction in that there is only one planar wave at each initial discontinuity. We include the existence of two elementary waves at each initial discontinuity and classify 14 topologically distinct solutions. For each case, we construct an analytic solution and compute the numerical solution.

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24

Hwang, Jinah, Suyeon Shin, Myoungin Shin, and Woonjae Hwang. "Four-Quadrant Riemann Problem for a 2×2 System II." Mathematics 9, no. 6 (March 10, 2021): 592. http://dx.doi.org/10.3390/math9060592.

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In previous work, we considered a four-quadrant Riemann problem for a 2×2 hyperbolic system in which delta shock appears at the initial discontinuity without assuming that each jump of the initial data projects exactly one plane elementary wave. In this paper, we consider the case that does not involve a delta shock at the initial discontinuity. We classified 18 topologically distinct solutions and constructed analytic and numerical solutions for each case. The constructed analytic solutions show the rich structure of wave interactions in the Riemann problem, which coincide with the computed numerical solutions.

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25

ALONSO RODRÍGUEZ, ANA, and MIRCO RAFFETTO. "UNIQUE SOLVABILITY FOR ELECTROMAGNETIC BOUNDARY VALUE PROBLEMS IN THE PRESENCE OF PARTLY LOSSY INHOMOGENEOUS ANISOTROPIC MEDIA AND MIXED BOUNDARY CONDITIONS." Mathematical Models and Methods in Applied Sciences 13, no. 04 (April 2003): 597–611. http://dx.doi.org/10.1142/s0218202503002672.

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A result on the existence and uniqueness of the solutions of electromagnetic boundary value problems is presented. It is a generalization of the results already available in the open literature which holds true in all cases of practical interest. As a matter of fact, it holds true even in the presence of general inhomogeneous anisotropic media, surfaces of discontinuity, topologically complicated domains and mixed boundary conditions.

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26

Eldracher, Martin, Alexander Staller, and René Pompl. "Adaptive Encoding Strongly Improves Function Approximation with CMAC." Neural Computation 9, no. 2 (February 1, 1997): 403–17. http://dx.doi.org/10.1162/neco.1997.9.2.403.

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The Cerebellar Model Arithmetic Computer (CMAC) (Albus 1981) is well known as a good function approximator with local generalization abilities. Depending on the smoothness of the function to be approximated, the resolution as the smallest distinguishable part of the input domain plays a crucial role. If the binary quantizing functions in CMAC are dropped in favor of more general, continuous-valued functions, much better results in function approximation for smooth functions are obtained in shorter training time with less memory consumption. For functions with discontinuities, we obtain a further improvement by adapting the continuous encoding proposed in Eldracher and Geiger (1994) for difficult-to-approximate areas. Based on the already far better function approximation capability on continuous functions with a fixed topologically distributed encoding scheme in CMAC (Eldracher et al. 1994), we present the better results in learning a two-valued function with discontinuity using this adaptive topologically distributed encoding scheme in CMAC.

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27

Ryu, S., H. Zhou, T. R. Paudel, N. Campbell, J. Podkaminer, C. W. Bark, T. Hernandez, et al. "Electronic reconstruction at the polar (111)-oriented oxide interface." APL Materials 10, no. 3 (March 1, 2022): 031115. http://dx.doi.org/10.1063/5.0067445.

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Atomically flat (111) interfaces between insulating perovskite oxides provide a landscape for new electronic phenomena. For example, the graphene-like coordination between interfacial metallic ion layer pairs can lead to topologically protected states [Xiao et al., Nat. Commun. 2, 596 (2011) and A. Rüegg and G. A. Fiete, Phys. Rev. B 84, 201103 (2011)]. The metallic ion/metal oxide bilayers that comprise the unit cell of the perovskite (111) heterostructures require the interface to be polar, generating an intrinsic polar discontinuity [Chakhalian et al., Nat. Mater. 11, 92 (2012)]. Here, we investigate epitaxial heterostructures of (111)-oriented LaAlO3/SrTiO3 (LAO/STO). We find that during heterostructure growth, the LAO overlayer eliminates the structural reconstruction of the STO (111) surface with an electronic reconstruction, which determines the properties of the resulting two-dimensional conducting gas. This is confirmed by transport measurements, direct determination of the structure and atomic charge from coherent Bragg rod analysis, and theoretical calculations of electronic and structural characteristics. Interfacial behaviors of the kind discussed here may lead to new growth control parameters useful for electronic devices.

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Ugai, M. "Magnetic field structure of large-scale plasmoid generated by the fast reconnection mechanism in a sheared current sheet." Annales Geophysicae 28, no. 8 (August 11, 2010): 1511–21. http://dx.doi.org/10.5194/angeo-28-1511-2010.

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Abstract. On the basis of the spontaneous fast reconnection model, three-dimensional magnetic field profiles associated with a large-scale plasmoid propagating along the antiparallel magnetic fields are studied in the general sheared current sheet system. The plasmoid is generated ahead of the fast reconnection jet as a result of distinct compression of the magnetized plasma. Inside the plasmoid, the sheared (east-west) field component has the peak value at the plasmoid center located at x=XC, where the north-south field component changes its sign. The plasmoid center corresponds to the so-called contact discontinuity that bounds the reconnected field lines in x<XC and the field lines without reconnection in x>XC. Hence, contray to the conventional prediction, the reconnected sheared field lines in x<XC are not spiral or helical, since they cannot be topologically connected to the field lines in x>XC. It is demonstrated that the resulting profiles of magnetic field components inside the plasmoid are, in principle, consistent with satellite observations. In the ambient magnetic field region outside the plasmoid too, the magnetic field profiles are in good agreement with the well-known observations of traveling compression regions (TCRs).

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Li, Shenhong, Xiongwu Xiao, Bingxuan Guo, and Lin Zhang. "A Novel OpenMVS-Based Texture Reconstruction Method Based on the Fully Automatic Plane Segmentation for 3D Mesh Models." Remote Sensing 12, no. 23 (November 28, 2020): 3908. http://dx.doi.org/10.3390/rs12233908.

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The Markov Random Field (MRF) energy function, constructed by existing OpenMVS-based 3D texture reconstruction algorithms, considers only the image label of the adjacent triangle face for the smoothness term and ignores the planar-structure information of the model. As a result, the generated texture charts results have too many fragments, leading to a serious local miscut and color discontinuity between texture charts. This paper fully utilizes the planar structure information of the mesh model and the visual information of the 3D triangle face on the image and proposes an improved, faster, and high-quality texture chart generation method based on the texture chart generation algorithm of the OpenMVS. This methodology of the proposed approach is as follows: (1) The visual quality on different visual images of each triangle face is scored using the visual information of the triangle face on each image in the mesh model. (2) A fully automatic Variational Shape Approximation (VSA) plane segmentation algorithm is used to segment the blocked 3D mesh models. The proposed fully automatic VSA-based plane segmentation algorithm is suitable for multi-threaded parallel processing, which solves the VSA framework needed to manually set the number of planes and the low computational efficiency in a large scene model. (3) The visual quality of the triangle face on different visual images is used as the data term, and the image label of adjective triangle and result of plane segmentation are utilized as the smoothness term to construct the MRF energy function. (4) An image label is assigned to each triangle by the minimizing energy function. A texture chart is generated by clustering the topologically-adjacent triangle faces with the same image label, and the jagged boundaries of the texture chart are smoothed. Three sets of data of different types were used for quantitative and qualitative evaluation. Compared with the original OpenMVS texture chart generation method, the experiments show that the proposed approach significantly reduces the number of texture charts, significantly improves miscuts and color differences between texture charts, and highly boosts the efficiency of VSA plane segmentation algorithm and OpenMVS texture reconstruction.

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Karlova, Olena, and Volodymyr Mykhaylyuk. "A Characterization of the discontinuity point set of strongly separately continuous functions on products." Mathematica Slovaca 66, no. 6 (January 1, 2016). http://dx.doi.org/10.1515/ms-2016-0237.

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AbstractWe study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a strongly separately continuous mapping to be continuous on a product of an arbitrary family of topological spaces. Moreover, we characterize the discontinuity point set of strongly separately continuous function defined on a subset of countable product of finite-dimensional normed spaces.

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31

Huang, Shiu-Ming, Pin-Cing Wang, Hao-Lun Jian, and Mitch M. C. Chou. "The Magnetic Susceptibility Bifurcation in the Ni-Doped Sb2Te3 Topological Insulator with Antiferromagnetic Order Accompanied by Weak Ferromagnetic Alignment." Nanoscale Research Letters 16, no. 1 (December 2021). http://dx.doi.org/10.1186/s11671-021-03637-5.

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AbstractThe magnetic susceptibility reveals a discontinuity at Néel temperature and a hysteresis loop with low coercive field was observed below Néel temperature. The magnetic susceptibility of zero field cool and field cool processes coincide at a temperature above the discontinuity, and they split at temperature blow the discontinuity. The magnetic susceptibility splitting is larger at lower external magnetic fields. No more magnetic susceptibility splitting was observed at a magnetic field above 7000 Oe which is consistent with the magnetic anisotropy energy. Our study supports that these magnetic susceptibility characteristics originate from an antiferromagnetic order accompanied by weak ferromagnetism.

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Marić, Vanja, Salvatore Marco Giampaolo, and Fabio Franchini. "Quantum phase transition induced by topological frustration." Communications Physics 3, no. 1 (December 2020). http://dx.doi.org/10.1038/s42005-020-00486-z.

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AbstractIn quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems. Here we show an example of the opposite. We consider a spin chain with two competing interactions, set on a ring with an odd number of sites. When only the dominant interaction is antiferromagnetic, and thus induces topological frustration, the standard antiferromagnetic order (expressed by the magnetization) is destroyed. When also the second interaction turns from ferro to antiferro, an antiferromagnetic order characterized by a site-dependent magnetization which varies in space with an incommensurate pattern, emerges. This modulation results from a ground state degeneracy, which allows to break the translational invariance. The transition between the two cases is signaled by a discontinuity in the first derivative of the ground state energy and represents a quantum phase transition induced by a special choice of boundary conditions.

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33

Taylor, James V. "Separated Flow Topology in Compressors." Journal of Turbomachinery 141, no. 9 (September 1, 2019). http://dx.doi.org/10.1115/1.4044132.

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Abstract When a multistage high-speed compressor is operated away from its design point, extreme incidence is caused in some blade rows. This results in large, localized separations that are three dimensional in nature. In this paper, topological reasoning is used to describe the behavior of these three-dimensional separations. It is shown that two classes of separation exist: one in which the flow progresses from attached to separate in a smooth way and another where there is a discontinuity in the response of the flow topology. It is shown that the global structure of the flow depends on the type of topological response that occurs. When the response is discontinuous, nonaxisymmetric cells of separated blades are formed. When the response is smooth, the resultant separated flow is axisymmetric. The paper is split into two broad sections: The first section presents examples of the two different classes of topological response that can occur in a single blade row, and it also shows how an engineer can achieve a different response by altering the blade design. The second section covers the analysis of a multistage high-speed compressor. The compressor initially presents the discontinuous behavior with rotating cells of separations. It is then redesigned to reduce the severity of the cell behavior or remove it entirely.

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Rickards, Silas Edwin, Teertho Bhattacharya, Grace Cheng, Josh Valan, and Zachary Webb. "Knot the Usual Suspects: Finding the Diagrammatic Representations of Physical Knots." UF Journal of Undergraduate Research 23 (October 13, 2021). http://dx.doi.org/10.32473/ufjur.v23i.128717.

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In the last few hundred years, mathematicians have been attempting to describe the topological and algebraic properties of mathematical knots. Regarding the study of knots, there exists a disconnect between examining a knot’s mathematical and physical definitions. This is due to the inherent difference in the topology of an open-ended physical knot and a closed mathematical knot. By closing the ends of a physical knot, this paper presents a method to break this discontinuity by establishing a clear relation between physical and mathematical knots. By joining the ends and applying Reidemeister moves, this paper will calculate the equivalent mathematical prime or composite knots for several commonly used physical knots. In the future, it will be possible to study the physical properties of these knots and their potential to expand the field of mathematical knot theory.

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