Smooth Topology Research Articles

Energy Landscapes of Atomic Clusters as Black Box Optimization Benchmarks

We present the energy minimization of atomic clusters as a promising problem class for continuous black box optimization benchmarks. Finding the arrangement of atoms that minimizes a given potential energy is a specific instance of the more general class of geometry optimization or packing problems, which are generally NP-complete. Atomic clusters are a well-studied subject in physics and chemistry. From the large set of available cluster optimization problems, we propose two specific instances: Cohn-Kumar clusters and Lennard-Jones clusters. The potential energies of these clusters are governed by distance-dependent pairwise interaction potentials. The resulting collection of landscapes is composed of smooth and rugged single-funnel topologies, as well as tunable double-funnel topologies. In addition, all problems possess a feature that is not covered by the synthetic functions in current black box optimization test suites: isospectral symmetry. This property implies that any atomic arrangement is uniquely defined by the pairwise distance spectrum, rather than the absolute atomic positions. We hence suggest that the presented problem instances should be included in black box optimization benchmark suites.

Combined gradient‐stochastic optimization with negative circular masks for large deformation topologies

SUMMARYTopology optimization of large deformation two‐dimensional continua is presented using a combined gradient‐stochastic search with negative circular masks. The possibility of generating perfect black and white topologies is explored while attaining the efficiency of first‐order and second‐order search algorithms. The design region is modeled with honeycomb tessellation to thwart the known connectivity singularities such as the checkerboards and point flexures. Mask shrinkage is incorporated for ease in density transition between gradient and stochastic steps. Notches at continuum boundaries are moderated through multiple use of a simple boundary smoothing method. A neo‐Hookean elasticity model is employed to simulate the material nonlinearities in large displacement continua. With examples on stiff beams and large deformation compliant mechanisms, it is illustrated that perfectly binary, connected and smooth topologies can be obtained within a few hundred design evaluations.Copyright © 2012 John Wiley & Sons, Ltd.

Ordinary Smooth Topological Spaces

In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X. And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. Also we introduce the concepts of a base and a subbase in an ordinary smooth topological space and study their properties. Finally, we investigate some properties of an ordinary smooth subspace.

On the approximation of functions on a Hodge manifold

If f is a smooth function on a Hodge manifold, we construct a canonical sequence of real algebraic functions that converge to f in the smooth topology. The definition of of the approximants is inspired by Berezin-Toeplitz quantization. The proof follows quickly from known results of Fine, Liu and Ma.

THE LATTICE OF ORDINARY SMOOTH TOPOLOGIES

Lim et al. [5] introduce the notion of ordinary smooth topologies by considering the gradation of openness[resp. closedness] of ordinary subsets of X. In this paper, we study a collection of all ordinary smooth topologies on X, say OST(X), in the sense of a lattice. And we prove that OST(X) is a complete lattice.

On-substrate, self-standing Au-nanorod arrays showing morphology controlled properties

We use supported alumina templates and electrodeposition to fabricate self-standing Au-nanorods (Au-NR) arrays. Depending on electrolyte and deposition conditions two different NR morphologies with either corrugated or smooth topologies are fabricated. We show that the properties of the NR arrays, including amphiphilic and optical, very much depend on their morphology. Smooth NR arrays are hydrophobic while the corrugated ones are hydrophilic. Also the optical reflectance, though it shows plasmon resonances at very similar wave lengths, is much lower for the corrugated NR arrays. The activity of the NR arrays as substrates for molecular detection using Raman scattering, and Rhodamine 6G (R6G) as model dye, also strongly depends on their morphology. R6G concentrations down to 1 pM are detected on the corrugated arrays yielding an effective enhancement factor (EF) of approximately 1 × 109. In contrast an over-estimated (because of their hydrophobic character) EF of 6 × 106 is obtained for the smooth NR arrays.

퍼지 준-위상 공간에 관한 연구

본 논문에서는 smooth topology 와 Chang's fuzzy topology의 개념을 일반화시킨 fuzzy quasi topology의 개념을 소개한다. 그리고 퍼지 준-위상의 일반적인 위상적 성질들을 조사한다. In this paper, we introduce the concept of fuzzy quasi topologies which are generalizations of smooth topologies and Chang's fuzzy topologies, and obtain some basic properties of their structures.

Intuitionistic Smooth Topological Spaces

We introduce the concept of intuitionistic smooth topology in Lowen's sense and we prove that the family IST(X) of all intuitionistic smooth topologies on a set is a meet complete lattice with least element and the greatest element[Proposition 3.6]. Also we introduce the notion of level fuzzy topology on a set X with respect to an intuitionistic smooth topology and we obtain the relation between the intuitionistic smooth topology τ and the intuitionistic smooth topology ŋ generated by level fuzzy topologies with respect to τ [Theorem 3.10].

Toxicogenomics of nanoparticulate delivery of etoposide: potential impact on nanotechnology in retinoblastoma therapy.

To develop a suitable formulation with high entrapment efficiency, etoposide-loaded poly(lactide-co-glycolide) nanoparticles (NPs) were formulated by single emulsion-solvent evaporation method by changing different formulation parameters such as drug loading, choice of organic solvent and percentage of emulsifier polyvinyl alcohol. The NPs showed higher entrapment efficiency, ~86% (with 15% (w/w) drug loading). The physicochemical parameters revealed smooth topology with size range (240–320 nm), a negative zeta potential (~19 mV) and in vitro sustained-release activity (~60% drug release in 40 days). Greater anti-proliferative activity ~100 times was observed with NPs (IC50 = 0.002 μg/ml) than that of native etoposide (IC50 = 0.2 μg/ml) in retinoblastoma cell line (Y-79). These NPs demonstrated greater (G1/S) blocking and decreased mitochondrial membrane potential as measured by flow cytometry. There was upregulation of apoptotic gene activity in NPs than native etoposide, as revealed through microarray analysis. However, this is the first ever report demonstrating the intricate modulation of genetic network affected by NPs. Collectively, these results suggest that etoposide-loaded NPs could be potentially useful as a novel drug delivery system for retinoblastoma in the future.FigureNanoparticle-mediated etoposide delivery promotes apoptosis through upregulating several apoptotic inducer genesElectronic supplementary materialThe online version of this article (doi:10.1007/s12645-010-0010-4) contains supplementary material, which is available to authorized users.

Design of compliant mechanism using hyper radial basis function network and reanalysis formulation

The design of compliant mechanisms often involves multiple minima. Since non-gradient type global optimization techniques cannot handle as many design variables as the commonly used, gradient based SIMP method, a hyper radial basis function network is used in this paper for Particle Swarm Optimization. An exact reanalysis formulation is presented which computes the strain energy from the solution of the mutual energy problem. The design of motion inverter is presented to demonstrate the proposed approach. The use of hyper radial basis function network results in checkerboard-free, smooth topology using very crude finite element analysis mesh, whereas the reanalysis formulation cuts down the analysis time into half. Thus the design process is made computationally efficient and less dependent on human interpretation of the optimal topology.

A Low-Dropout Regulator With Smooth Peak Current Control Topology for Overcurrent Protection

The proposed low-dropout (LDO) regulator with a smooth peak current control (SPCC) circuit can be simultaneously controlled by using an error amplifier to regulate output voltage and a peak current controller as a means to limit its current level. The SPCC circuit can be switched smoothly between these two control mechanisms by detecting the information of load current and the dropout voltage. Measured results show that overcurrent protection can make the pass device operate as a current source while the load current exceed the peak current level. Moreover, the control mechanism can return to error amplifier control when load current becomes smaller than the limiting current, thus ensuring output voltage to be close to the rated value. Output voltage is stable and varies smaller than 15 mV when a 160 mA load current step or a 2 V supply voltage step is placed on this LDO regulator.

Customized Polynomial Contact Lenses via Wet Etching

Customized polynomial contact lenses are meant to correct high-order optical distortions in the human vision, beyond focus and astigmatism, but they are not yet a commercial solution mainly due to reproducibility and cost issues. Aiming at circumventing these obstacles to market, this paper investigates the possibility of fabrication of such lenses by wet etching of a silicon mould and subsequent casting of the lens polymer. The proposed technique to obtain the mould is based on ordinary anisotropic etching of c-Si with an aqueous KOH solution, where a subtle step ensures the achievement of an arbitrary smooth topology.

On the analyticity of the bivariant JLO cocycle

The goal of this note is to outline a proof that, for any l $\geq 0$, the JLO bivariant cocycle associated with a family of Dirac type operators along a smooth fibration $M\to B$ over the pair of algebras $(C^\infty (M), C^\infty(B))$, is entire when we endow $C^\infty(M)$ with the $C^{l+1}$ topology and $C^\infty(B)$ with the $C^{l}$ topology. As a corollary, we deduce that this cocycle is analytic when we consider the Frechet smooth topologies on $C^\infty(M)$ and $C^\infty(B)$.

퍼지 일반위상 공간에 관한 연구

In this paper, we introduce the concept of fuzzy generalized topologies which are generalizations of smooth topologies and Chang`s fuzzy topologies and obtain some basic properties of their structure. Also we introduce and study the concepts of fuzzy generalized continuity and weakly fuzzy generalized continuity.

Electrochemical Passivation of (100) Silicon in Alkyl Grignard Solutions

Surface modification of (100) silicon with methyl groups is analyzed using electrografting and thermal hydrosilation. The surface chemistry is investigated by Fourier transform infrared (FTIR), X-ray photoelectron spectroscopy (XPS), voltammetry and atomic force microscopy (AFM). Surfaces anodically electrografted in methyl Grignard solutions show a smooth topology and improved passivation relative to passivation via hydrosilation. Functionalized surfaces are stable and hinder the formation of oxides up to 45 days after the electrografting as shown in the XPS results.

Topology Optimization Using Hyper Radial Basis Function Network

In this paper we present the application of a hyper radial basis function network as a topology description function. A hyper radial basis function network is used to parameterize the material distribution (density) for topology optimization. The density of each finite element in the continuum topology optimization domain is governed by a single network of hyper radial function bases. Thus, the topology optimization problem is to determine the parameters governing the hyper radial basis function network to satisfy certain design criteria. Here we present the solution to a minimum compliance topology design. A hyper radial basis function network is used to parameterize the material density during the finite element analysis stage. An efficient optimization algorithm that makes use of perturbation and sequential linear programming is developed to obtain the hyper radial basis function network parameters. Examples are presented to demonstrate the proposed approach and to compare it with the traditional solid isotropic microstructures with penalization topology optimization. Some of the advantages of the proposed approach are that it can yield checkerboard-free, manufacturable topologies using coarse-mesh finite element analysis models as opposed to the traditional approach, which requires fine meshes. This results in a reduction in the solution time for finite element analysis while conserving the ability to yield a smooth topology.

Smooth Boundary Topology Optimization for Electrostatic Problems Through the Combination of Shape and Topological Design Sensitivities

This paper presents a new methodology for topology optimization in which the topology of the design domain considered may change during the shape optimization process, unlike the case of classical shape or topology optimization. To achieve this, the concept of the topological gradient is introduced to compute the sensitivity of an objective function when a small hole is drilled in the domain, and this is successfully connected to the shape sensitivity. A test problem consisting of an elliptic dielectric material with a circular hole has been selected to illustrate the validity of the proposed method.

Smooth boundary topology optimization for eigenvalue performance and its application to the design of a flexural stage

The new topology optimization method known as smooth boundary topology optimization (SBTO) is enhanced to deal with natural frequencies as a design characteristic. SBTO combines boundary representation using computer graphics with a selection criterion which determines the usefulness of generating a hole. Topological changes such as hole generation and hole merging are successfully implemented. SBTO is used to establish a systematic procedure for the design of a flexural stage is established. When designing flexural stages, it is necessary to be compliant in the actuating or moving direction and stiff in the parasitic direction, and the optimization related to maximizing the difference between the first and second natural frequency is formulated. SBTO has been shown to be a promising methodology for topology optimization with smooth boundaries in the design of a flexural stage.

Open–closed strings: Two-dimensional extended TQFTs and Frobenius algebras

We study a special sort of 2-dimensional extended Topological Quantum Field Theories (TQFTs). These are defined on open–closed cobordisms by which we mean smooth compact oriented 2-manifolds with corners that have a particular global structure in order to model the smooth topology of open and closed string worldsheets. We show that the category of open–closed TQFTs is equivalent to the category of knowledgeable Frobenius algebras. A knowledgeable Frobenius algebra ( A , C , ı , ı * ) consists of a symmetric Frobenius algebra A, a commutative Frobenius algebra C, and an algebra homomorphism ı : C → A with dual ı * : A → C , subject to some conditions. This result is achieved by providing a description of the category of open–closed cobordisms in terms of generators and the well-known Moore–Segal relations. In order to prove the sufficiency of our relations, we provide a normal form for such cobordisms which is characterized by topological invariants. Starting from an arbitrary such cobordism, we construct a sequence of moves (generalized handle slides and handle cancellations) which transforms the given cobordism into the normal form. Using the generators and relations description of the category of open–closed cobordisms, we show that it is equivalent to the symmetric monoidal category freely generated by a knowledgeable Frobenius algebra. Our formalism is then generalized to the context of open–closed cobordisms with labeled free boundary components, i.e. to open–closed string worldsheets with D-brane labels at their free boundaries.

Smooth boundary topology optimisation applied to an electrostatic actuator

Smooth boundary topology optimisation in conjunction with the continuum design sensitivity analysis avoids many of the problems encountered by conventional cell-based systems coupled with material homogenisation or the density method. Shape optimisation becomes part of topology optimisation. The effectiveness of the proposed method is demonstrated through the design of an electrostatic MEMS actuator to generate maximum torque for a predefined maximum size (area).