Stress-resultant plasticity theories for composite laminated plates

Constitutive laws are presented for the inelastic analysis of laminated composite plates. The implications of using an elastoplastic theory, applied in a stress-resultant formulation, are discussed and investigated. Two different stress-resultant plasticity theories are proposed, both of which overlook the matrix and fiber inelastic behavior and describe the inelastic response of the laminate as a function of overall laminate properties. Results from numerical experiments with the proposed models are compared with results obtained using a micromechanical elastoplastic composite constitutive model.     

Analysis of KrF excimer laser beam modification resulting from ablation under closed thick film flowing filtered water

The application of a closed thick film flowing filtered water to immerse the ablation etching mechanism of an excimer laser poses interesting possibilities concerning debris control, modification of machined feature topography and modification of the ablation rate. Furthermore, these parameters have been shown to be dependent on flow velocity; hence, offering further user control of machining characteristics. However, the impact of this technique requires investigation. This contribution offers comparison of the calculated ablation pressure and the effect on feature surface characteristics given for laser ablation of bisphenol A polycarbonate using KrF excimer laser radiation in ambient air against laser ablation of the same substrate under closed thick film flowing filtered water immersion. Also, an impact of such immersion equipment on the optical performance of the micromachining centre used is quantified and reviewed. The pressure is calculated to have risen by a magnitude of 48, when using the liquid immersed ablation technique. This increase in pressure is proposed to have an increased surface roughness, promoting the number of asperities with a surface area lower than 16 μm²; resulting in a diffuse reflection of light and an apparent darkening of features. The focal length of the optical system was accurately predicted to increase by 2.958 mm, when using the closed flowing liquid immersion equipment. This equipment is predicted to have increased the optical depth of focus via reduction in the angle of convergence of the two defining image rays; yet the perceived focus, measured discretely by mean feature wall angle, was found to be 25% smaller when using the closed thick film flowing filtered water immersion technique instead of similar laser ablation in ambient air. A compressed plume interaction is proposed as a contributing factor in this change.     

A nonlinear PSE method for two-fluid shear flows with complex interfacial topology

A nonlinear stability method is developed for laminar two-fluid shear flows which undergo changes in the interface topology. The method is based on the nonlinear parabolized stability equations (PSE) and incorporates a scalar-based interface capturing (IC) scheme in order to track complex deformations of the fluid interface. In doing so, the formulation retains the flexibility and physical insight of instability-wave based methods, while providing hydrodynamic modeling capabilities similar to direct numerical calculations: the new formulation, referred to as the IC-PSE, can capture the nonlinear physical mechanisms responsible for generating large-scale, two-fluid structures, without incurring heavy computational costs. This approach is valid for spatially developing, laminar two-fluid shear flows which are convectively unstable, and can naturally account for the growth of finite amplitude interfacial waves, along with changes to the interfacial topology. We demonstrate the accuracy of the IC-PSE against direct Navier–Stokes calculations for two-fluid mixing layers with density and viscosity stratification. The comparisons show that the IC-PSE can predict the dynamics of the instability waves and capture the formation of Kelvin–Helmholtz vortex rolls and large scale liquid structures, at an order of magnitude less computational cost than direct calculations. The role of surface tension in the IC-PSE formulation is shown to be valid for flows in which Re/We ? 1, and the method accurately predicts the formation and non-linear evolution of flow structures in this limit. This is demonstrated for spatially developing mixing layers which lead to vortex roll-up and ligaments, prior to droplet formation. The pinch-off process itself is a high surface tension phenomenon and in not considered herein. The method also accurately captures the effect of interfacial waves on the mean flow, and the topology changes during the non-linear evolution of the two-fluid structures.     

Fast fat-suppressed reduced field-of-view temperature mapping using 2DRF excitation pulses

The purpose of this study is to develop a fast and accurate temperature mapping method capable of both fat suppression and reduced field-of-view (rFOV) imaging, using a two-dimensional spatially-selective RF (2DRF) pulse. Temperature measurement errors caused by fat signals were assessed, through simulations. An 11×1140μs echo-planar 2DRF pulse was developed and incorporated into a gradient-echo sequence. Temperature measurements were obtained during focused ultrasound (FUS) heating of a fat-water phantom. Experiments both with and without the use of a 2DRF pulse were performed at 3T, and the accuracy of the resulting temperature measurements were compared over a range of TE values. Significant inconsistencies in terms of measured temperature values were observed when using a regular slice-selective RF excitation pulse. In contrast, the proposed 2DRF excitation pulse suppressed fat signals by more than 90%, allowing good temperature consistency regardless of TE settings. Temporal resolution was also improved, from 12 frames per minute (fpm) with the regular pulse to 28 frames per minute with the rFOV excitation. This technique appears promising toward the MR monitoring of temperature in moving adipose organs, during thermal therapies.     

Scheduling networks of queues: Heavy traffic analysis of a simple open network

We consider a queueing network with two single-server stations and two types of customers. Customers of type A require service only at station 1 and customers of type B require service first at station 1 and then at station 2. Each server has a different general service time distribution, and each customer type has a different general interarrival time distribution. The problem is to find a dynamic sequencing policy at station 1 that minimizes the long-run average expected number of customers in the system.The scheduling problem is approximated by a dynamic control problem involving Brownian motion. A reformulation of this control problem is solved, and the solution is interpreted in terms of the queueing system in order to obtain an effective sequencing policy. Also, a pathwise lower bound (for any sequencing policy) is obtained for the total number of customers in the network. We show via simulation that the relative difference between the performance of the proposed policy and the pathwise lower bound becomes small as the load on the network is increased toward the heavy traffic limit.     

A proof of Markov's theorem for polynomials on Banach spaces

Our object is to present an independent proof of the extension of V.A. Markov's theorem to Gâteaux derivatives of arbitrary order for continuous polynomials on any real normed linear space. The statement of this theorem differs little from the classical case for the real line except that absolute values are replaced by norms. Our proof depends only on elementary computations and explicit formulas and gives a new proof of the classical theorem as a special case. Our approach makes no use of the classical polynomial inequalities usually associated with Markov's theorem. Instead, the essential ingredients are a Lagrange interpolation formula for the Chebyshev nodes and a Christoffel-Darboux identity for the corresponding bivariate Lagrange polynomials. We use these tools to extend a single variable inequality of Rogosinski to the case of two real variables. The general Markov theorem is an easy consequence of this.     

Locally compact abelian groups with trivial multiplier group

LCA groups with trivial multiplier group are characterized. It is found that every LCA group with nontrivial multiplier group has an “irreducible” quotient with the same property, and the irreducible groups are described.     

Efficiency in integral facility design problems

An example of design might be a warehouse floor (represented by a setS) of areaA, with unspecified shape. Givenm warehouse users, we suppose that useri has a known disutility functionf _isuch thatH _i(S), the integral off _iover the setS (for example, total travel distance), defines the disutility of the designS to useri. For the vectorH(S) with entriesH _i(S), we study the vector minimization problem over the set {H(S) :S a design} and call a design efficient if and only if it solves this problem. Assuming a mild regularity condition, we give necessary and sufficient conditions for a design to be efficient, as well as verifiable conditions for the regularity condition to hold. For the case wheref _iis thel _p-distance from warehouse docki, with 1<p<, a design is efficient if and only if it is essentially the same as a contour set of some Steiner-Weber functionf =₁ f ₁++ _m f _m ,when the _i are nonnegative constants, not all zero.This research was supported in part by the Interuniversity College for PhD Studies in Management Sciences (CIM), Brussels, Belgium; by the Army Research Office, Triangle Park, North Carolina; by a National Academy of Sciences-National Research Council Postdoctorate Associateship; and by the Operations Research Division, National Bureau of Standards, Washington, D.C. The authors would like to thank R. E. Wendell for calling Ref. 16 to their attention.     

Comments on the evolving field of sonochemistry by a cavitation physicist

Sonochemistry is an evolving field that has shown recent rapid growth and increasing interest. Although this field concentrates on chemistry and uses acoustics principally as a tool, the basic mechanism that gives rise to sonochemistry — acoustic cavitation — is often ignored or given little attention. This paper addresses some of the relevant aspects of cavitation and physical acoustics that apply to sonochemistry.