Smooth Topology Research Articles

Combined Topology and Shape Optimization of Structures using Nodal Density as Design Parameter

In this study, a new nodal–based distribution method of material properties is proposed for material topology optimization in linear elastostatic structures. It is based on a design domain concept of a density distribution method (Bendsøe, 1989). Nodal densities of material properties are considered as optimization design variables. Geometric boundaries are represented by fixed grids, thus an Eulerian type of formulation is used for optimal interfaces. The objective is to obtain both optimal smooth shapes and topologies based on the design domain concept avoiding an excessive number of finite elements. This approach allows us to perform a nodal–based topology and shape optimization, which can be easily implemented in existing gradient–based optimization codes. Numerical examples demonstrate the efficiency of the present method.

3-D topology optimization of single-pole-type head by using design sensitivity analysis

It is necessary to develop a write head having a large recording field and small stray field in adjacent tracks and adjacent bits in perpendicular magnetic recording systems. In this paper, a practical three-dimensional topology optimization technique combined with the edge-based finite-element method is proposed. A technique for obtaining a smooth topology is also shown. The optimization of single-pole-type head having a magnetic shield is performed by using the topology optimization technique so that the leakage flux in the adjacent bit can be reduced. A useful shape of the magnetic shield obtained by the proposed technique is illustrated

L-fuzzifying topology

A new topology in terms of order on fuzzy sets, revealing better the relationship between smooth topology and Chang's fuzzy topology, is presented in the paper. Some basic properties are discussed.

Constructing integrable high-pressure full-current free-boundary stellarator magnetohydrodynamic equilibrium solutions

For the (non-axisymmetric) stellarator class of plasma confinement devices to be feasible candidates for fusion power stations it is essential that, to a good approximation, the magnetic field lines lie on nested flux surfaces; however, the inherent lack of a continuous symmetry implies that magnetic islands responsible for breaking the smooth topology of the flux surfaces are guaranteed to exist. Thus, the suppression of magnetic islands is a critical issue for stellarator design, particularly for small aspect ratio devices. Pfirsch–Schlüter currents, diamagnetic currents and resonant coil fields contribute to the formation of magnetic islands, and the challenge is to design the plasma and coils such that these effects cancel.Magnetic islands in free-boundary high-pressure full-current stellarator magnetohydrodynamic equilibria are suppressed using a procedure based on the Princeton Iterative Equilibrium Solver (Reiman and Greenside 1986 Comput. Phys. Commun. 43 157) which iterates the equilibrium equations to obtain the plasma equilibrium. At each iteration, changes to a Fourier representation of the coil geometry are made to cancel resonant fields produced by the plasma. The changes are constrained to preserve certain measures of engineering acceptability and to preserve the stability of ideal kink modes. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible, the plasma is stable to ideal kink modes, and the coils satisfy engineering constraints. The method is applied to a candidate plasma and coil design for the National Compact Stellarator eXperiment (Reiman et al 2001 Phys. Plasma 8 2083).

Determinants of Laplacians and isopolar metrics on surfaces of infinite area

We construct a determinant of the Laplacian for infinite-area surfaces that are hyperbolic near $\infty$ and without cusps. In the case of a convex cocompact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order 2 with zeros at the eigenvalues and resonances of the Laplacian. In the hyperbolic near $\infty$ case, the determinant is analyzed through the zeta-regularized relative determinant for a conformal metric perturbation. We establish that this relative determinant is a ratio of entire functions of order 2 with divisor corresponding to eigenvalues and resonances of the perturbed and unperturbed metrics. These results are applied to the problem of compactness in the smooth topology for the class of metrics with a given set of eigenvalues and resonances.

Smooth neighborhood structures

In this paper, we introduce the notion of smooth neighborhoods in smooth topological spaces and investigate some of their properties. In particular, we can obtain some smooth topologies from a smooth neighborhood system.

The complete lattice [formula omitted] of smooth fuzzy topologies

Smooth fuzzy topologies are an extension of both crisp topologies and fuzzy topologies, in the sense that not only the objects are fuzzified, but also the axiomatics. In this article, we will complete the proof of the result given in (Chattopadhyay et al., Fuzzy Sets and Systems 49 (1992) 237), stating that the collection of smooth fuzzy topologies, equipped with the pointwise order, is a complete lattice. To this end, we will establish a subbase and base lemma for these by proving that any valuation function can be modified to construct a gradation of openness.

On smooth topological spaces IV

We introduce the concept of convergence of nets in the framework of smooth topology and establish their fundamental properties.

Subspaces of smooth fuzzy topologies and initial smooth fuzzy structures

Smooth fuzzy topologies are an extension of both crisp topologies and fuzzy topologies, in the sense that not only the objects are fuzzified, but also the axiomatics. In [9], Ramadan gave a description of a subspace of a smooth fuzzy topology. Although we do not doubt the results, with all due respect, some of the proofs involve interchangements of suprema and infima that are generally not allowed. We would like to give a corrected proof, and also study initial structures in the category of smooth fuzzy topological spaces in general. The main result will be that the subspaces as described below are indeed the categorically correct ones, i.e. in initial structures with respect to the canonical injection.

The Surface Film Formed on a Lithium Metal Electrode in a New Imide Electrolyte, Lithium Bis(perfluoroethylsulfonylimide) [ LiN ( C 2 F 5 SO 2 ) 2

A newly developed imide electrolyte salt, (LiBETI) was found to give very uniform, thin, and stable surface films on a lithium metal electrode in the propylene carbonate (PC) solution. LiBETI/PC was studied and compared to determine its ability to form such a stable surface film, with conventional electrolyte systems such as , , and (LiTFSI/PC). The surface film formed in LiBETI/PC system was a hemispherical, and the composition of the film consisted mainly of LiF, which is similar to that in a system. Quartz crystal microbalance (QCM) and cyclic voltammetry (after the tenth cycle) indicated that the surface film formed in LiBETI/PC (ca. 50 nm) was thinner than those in (ca. 90 nm), LiTFSI/PC (ca. 140 nm), or (ca. 255 nm). The variation of the resonance resistance (ΔR) obtained from in situ CV/QCM measurement, which has been demonstrated to be a good measure of the surface roughness, also suggested that LiBETI/PC system gave a compact and smooth surface topology during lithium deposition‐dissolution cycles. Impedance spectroscopy together with preliminary cycling tests showed that the LiBETI/PC system provides the highest cycling efficiency and improved cycleability among existing electrolyte salt systems in rechargeable battery systems employing lithium metal anodes. © 1999 The Electrochemical Society. All rights reserved.

Examples of 4-manifolds Without Gompf Nuclei

A problem of Kirby (Problem 4.98 in [9]) will be answered in the negative. We show that the 4-manifold X2,2,2 defined below does not contain the Gompf nucleus N2. More generally, we also show the existence of 4-manifolds without Gompf nuclei Nn. The proofs rely on the connection between the smooth topology and the Seiberg-Witten basic classes of a given 4-dimensional manifold M.

D-brane topology changing transitions

We study D-branes on three-dimensional orbifold backgrounds that admit topologically distinct resolutions differing by flop transitions. We show that these distinct phases are part of the vacuum moduli space of the super Yang-Mills gauge theory describing the D-brane dynamics. In this way we establish that D-branes—like fundamental strings—allow for physically smooth topology changing transitions.

On several types of compactness in smooth topological spaces

The smooth closure and smooth interior of a fuzzy set w.r.t. a smooth topology were defined by Gayyar et al. (1994), and some relations between a few types of compactness were established in the presence of strong restrictions. In this paper, by constructing new definitions of smooth closure and smooth interior which have more desirable properties than those of Gayyar et al. (1994), we prove that several hypothesis in the results of Gayyar et al. (1994) can be weakened and show that the relations which hold between various types of compactness in fuzzy topological spaces in Chang's sense (CFTS for short) (Di Concilio and Gerla, 1984; Haydar Es, 1987) can be extended to smooth topological spaces.

Social choice and the closed convergence topology

This paper revisits the aggregation theorem of Chichilnisky (1980), replacing the original smooth topology by the closed convergence topology and responding to several comments (N. Baigent (1984, 1985, 1987, 1989), N. Baigent and P. Huang (1990) and M. LeBreton and J. Uriarte (1990a, b). Theorems 1 and 2 establish the contractibility of three spaces of preferences: the space of strictly quasiconcave preferences P SCO, its subspace of smooth preferences P infSCO supS , and a space P 1 of smooth (not necessarily convex) preferences with a unique interior critical point (a maximum). The results are proven using both the closed convergence topology and the smooth topology. Because of their contractibility, these spaces satisfy the necessary and sufficient conditions of Chichilnisky and Heal (1983) for aggregation rules satisfying my axioms, which are valid in all topologies. Theorem 4 constructs a family of aggregation rules satisfying my axioms for these three spaces. What these spaces have in common is a unique maximum (or peak). This rather special property makes them contractible, and thus amenable to aggregation. However, these aggregation rules cannot be extended to the whole space of preferences P which is not contractible and therefore does not admit continuous aggregation rules satisfying anonymity and unanimity, Chichilnisky (1980, 1982). The results presented here clarify an erroneous example in LeBreton and Uriarte (1990a, b) and respond to Baigent (1984, 1985, 1987) and Baigent and Huang (1990) on the relative advantages of continuous and discrete approaches to Social Choice.

The T-Cell nature of the lymphocytes in two human epithelial thymomas: A comparative immunologic, scanning and transmission electron microscopic study

The lymphocytes in two human epithelial thymomas have been examined by techniques which help to discriminate between T and B cells. Most of the lymphocytes had a smooth surface topology as revealed by both scanning and transmission electron microscopy and 98% of the lymphocytes in each of the thymomas formed spontaneous sheep red blood cell rosettes. Anti-T sera killed over 98% of the lymphocytes in one case. The lymphocytes lacked the surface receptors that characterize monocytes and B cells and contained no surface immunoglobulins. It was concluded that the great majority of these lymphocytes were T cells and their possible role in epithelial thymomas is discussed.

ALGEBRAIC CONSTRUCTION AND PROPERTIES OF HERMITIAN ANALOGS OF $ K$-THEORY OVER RINGS WITH INVOLUTION FROM THE VIEWPOINT OF HAMILTONIAN FORMALISM. APPLICATIONS TO DIFFERENTIAL TOPOLOGY AND THE THEORY OF CHARACTERISTIC CLASSES. II

The complicated and intricate algebraic material in smooth topology (the theory of surgery) does not fit into the already existing concepts of stable algebra. It turns out that the systematization of this material is most naturally carried through from the point of view of an algebraic version of the hamiltonian formalism over rings with involution. The present article is devoted to this task. The first part contains a development of the algebraic concepts.