New and improved results for packing identical unitary radius circles within triangles, rectangles and strips

The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of non-linear equations systems through the Newton-Raphson method, the herein presented algorithm succeeds in improving the accuracy of previous results attained by continuous optimization approaches up to numerical machine precision. The computer implementation and the data sets are available at http://www.ime.usp.br/similar to egbirgin/packing/. (C) 2009 Elsevier Ltd, All rights reserved.

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions. (C) 2011 Elsevier Inc. All rights reserved.

Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D-1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D-3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D-1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2M unknowns are determined by 2M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2M x 2M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden`s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden`s algorithm is identified and recommended on the basis of its computer cost and reliability. (C) 2010 Elsevier B.V. All rights reserved.

Surface modification and crystallization of the BaO-B2O3-SiO2 glassy system using CO2 laser irradiation

The surface modification and crystallization process of BaO-B2O3-SiO2 glass compositions when exposed to CO2 laser irradiation was evaluated as a function of the laser power, irradiation time and surface condition. The glass surface was modified by the application of laser power exceeding 0.40 W and an irradiation time of more than 300 s. Micro-Raman and X-ray diffraction measurements revealed at high laser power the formation of beta-BaB2O4 (beta-BBO) crystalline phase. The crystallization of the irradiated region was enhanced when beta-BBO micrometer sized particles were dispersed on the surface of the glass sample. The intensity of the second harmonic generation observed in the crystallized region was found to depend mainly on the condition of the glassy surface prior to glass irradiation. (C) 2007 Elsevier B.V. All rights reserved.

Probing the dependence of the properties of cellulose acetates and their films on the degree of biopolymer substitution: use of solvatochromic indicators and thermal analysis

Although cellulose acetates, CAs, are extensively employed there is scant information about the systematic dependence of their properties on their degree of substitution, DS; this is the subject of the present work. Nine CAs samples, DS from 0.83 to 3.0 were synthesized; their films were prepared. The following solvatochromic probes have been employed in order to determine the empirical polarity, E (T)(33); ""acidity, alpha""; ""basicity, beta"", and ""dipolarity/polarizability, pi*"" of the casted films: 2,6-dichloro-4-(2,4,6-triphenyl-pyridinium-1-yl) phenolate, WB; 4-nitroaniline; 4-nitroanisole; 4-nitro-N,N-dimethylaniline; 2,6-diphenyl-4-(2,4,6-triphenyl-pyridinium-1-yl)phenolate, RB. Additionally, two systems, ethanol plus ethyl acetate (EtOH-EtAc), and cellulose plus cellulose triacetate, CTA, were employed as models for CAs of different DS. Regarding the model systems, the following was observed: (i) For EtOH-EtAc, the dependence of all solvatochromic parameters on the ""equivalent-DS"" of the binary mixture was non-linear because of preferential solvation; (ii) The dependence of E (T)(33) on equivalent DS of the cellulose-CTA films is linear, but the slope is smaller than that of the corresponding plot for CAs. This is attributed to the more efficient hydrogen bonding in the model system, a conclusion corroborated by IR measurements. The dependence of solvatochromic parameters of CAs on their DS is described by the simple equations; a consequence of the substitution of the OH by the ester group. The thermal properties of bulk CAs samples were investigated by DSC and TGA; their dependence on DS is described by simple equations. The relevance of these data to the processing and applications of CAs is briefly discussed.