Nontrivial solutions of singular nonlinear m-point boundary value problems

In this paper, by using the method of topology degree, some existence theorems of nontrivial solutions for singular nonlinear m-point boundary value problems are established. Our nonlinearity may be singular in its dependent variable.     

An efficient sensitivity computation strategy for the evolutionary structural optimization (ESO) of continuum structures subjected to self-weight loads

This work presents a modified version of the evolutionary structural optimization procedure for topology optimization of continuum structures subjected to self-weight forces. Here we present an extension of this procedure to deal with maximum stiffness topology optimization of structures when different combinations of body forces and fixed loads are applied. Body forces depend on the density distribution over the design domain. Therefore, the value and direction of the loading are coupled to the shape of the structure and they change as the material layout of the structure is modified in the course of the optimization process. It will be shown that the traditional calculation of the sensitivity number used in the ESO procedure does not lead to the optimum solution. Therefore, it is necessary to correct the computation of the element sensitivity numbers in order to achieve the optimum design. This paper proposes an original correction factor to compute the sensitivities and enhance the convergence of the algorithm. The procedure has been implemented into a general optimization software and tested in several numerical applications and benchmark examples to illustrate and validate the approach, and satisfactorily applied to the solution of 2D, 3D and shell structures, considering self-weight load conditions. Solutions obtained with this method compare favourably with the results derived using the SIMP interpolation scheme.     

Topologies on totally ordered sets

A well-formed ordered space is a totally ordered set equipped with any topology which possesses a subbase consisting entirely of initial and final segments of the set. The well-formed ordered spaces are the structures obtained by repeatedly taking subspaces, quotient spaces and inverse limits, starting from a collection of totally ordered sets with the interval topology, and the paper studies their properties.     

关于Fuzzy格的若干注记—兼评直觉主义模糊集

对Ｆｕｚｚｙ格Ｌ的定义，演变及概括范围作了分析，指出所谓直觉主义模糊集只不过是一种特殊的Ｌ－模糊集。     

关于变分不等式的例外簇

给出了变分不等式的例外簇的一个新定义 ,十分简洁地证明它是Zhao ,Han和Qi( 1 999)所定义的例外簇的推广 ,并以此为基础 ,对张、韩和徐 ( 2 0 0 0 )的一般存在性定理给出一个新的证明 .     

A Topological Approach to the Problem of Ring Structures

In the mechanized documentation of chemical literature, the definition of structural concept is very important. The usual for definitions for ring structures are inadequate. Essential ring structures are sometimes not recognized on the basis of these definitions and are therefore missed in a literature search. This is particularly true of bridged ring systems. The ring concept and ring condensation types are now redefined on a topological basis in the closest possible analogy to the intuitive approach of the chemist. In complicated molecular structures, these “fundamental rings” can be easily determined, either manually or by means of a programmed computer. The concept of the “ring complex” is defined and suggested as a preliminary screen in literature searches for ring structures. This will save machine time, and so reduce the cost of searches.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Polystyrene with different topologies: Study of the glass transition temperature in confined geometry of thin films

The glass transition behaviour of polystyrene (PS) with systematically varied topologies (linear, star-like and hyperbranched) confined in nanoscalic films was studied by means of spectroscopic vis-ellipsometry. All applied PS samples showed no or only a marginal depression in glass transition temperature T_g in the order hyperbranched PS (5 K) > star-like PS (3 K) > linear PS (0 K) for the thinnest films analyzed. The T_g behaviour was accompanied by the observation of the film density in dependence of film thickness. A maximum decreased density of about 7% for hyperbranched PS and 5% for star-like PS and again no deviation in density of bulk was found for linear PS. Accordingly, we deduce from these results considering an experimental accuracy of about ± 2 K for T_g and up to ±3% for film density, that the polymer topology only barely influences T_g in the confinement of thin films.     

Filament-breaking length—a measure of elasticity in extension

A technique has been developed to assess elasticity in extension of fluids which are weakly elastic. The technique is based on stretching a fluid sample held between two small closely spaced co-axial disks until the fluid bridge or filament breaks. The distance between the disks on breakup, ‘the breaking length’, is measured. When the fluid is elastic, this length is greater than that of an equivalent inelastic fluid. An inelastic baseline was established by measuring the breaking lengths of a wide variety of Newtonian fluids. Measurements with weakly elastic fluids reveal that the extra breaking length increases with polymer type and concentration and with the rate of stretching, the expected behavior for elastic liquids. The breaking lengths of model paper coatings were measured and found to correlate with the degree of misting in a roll coating machine, indicating that droplet formation is related to extensional elasticity.     

Viscosity enhancement in non-Newtonian flow of dilute aqueous polymer solutions through crystallographic and random porous media

We report results on the flow of dilute aqueous solutions of hydrolysed poly(acrylamide) (HPAA) through beds of spheres packed in simple cubic and body-centred cubic crystallographic arrays. Pressure drop measurements made across the arrays as a function of the flow rate have been used to estimate the specific viscosities of the HPAA solutions as a function of the superficial strain rate. It is found that greater non-Newtonian increases in the specific viscosity occur in the body-centred cubic array, which is thought to be due to the presence of trailing stagnation points, which are not present in the simple cubic array. Experiments have been performed using HPAA solutions in the presence of mono- and divalent cations at various concentrations and, for validity, have been compared with results obtained from a traditional randomly packed porous medium. In addition, a study of mechanical degradation of the polymer in flow through the crystallographic arrays has been carried out and reveals a greater rate of degradation in the body-centred array and also a significant increase in degradation with salt concentration.