SYMBOLIC OPERATOR SOLUTIONS OF LAPLACE'S AND STOKES’ EQUATIONS PART I LAPLACE'S EQUATION

Symbolic operator techniques are employed to derive a general solution of Laplace's equation in the infinite space external to a sphere. This is done for the case where the function vanishes on the sphere surface and arbitrary continuous asymptotic boundary data are imposed at infinity, such data being prescribed in the form of a solution of Laplace's equation that is analytic at the origin. In contrast with other standard methods for solving Laplace's equation, e.g., Green's functions, eigenfunction expansions, etc., the novelty of the proposed method lies in the fact that the solution can be expressed in a completely explicit form, directly in terms of (radial derivatives of)the given “undisturbed” field at infinity

A reciprocal theorem is derived and used to demonstrate that certain integral properties of the field can be obtained directly from the prescribed data at infinity, without recourse to a detailed solution of the relevant boundary-value problem. This global symbolic operator technique is illustrated for ellipsoidal as well as spherical particles

The elementary scalar harmonic analysis of the present paper serves as an entré to a companion paper (Part II), concerned with the application of similar symbolic techniques to the solution of more difficult vector biharmonic boundary-value problems, relevant to hydrodynamic Stokes flows in the infinite region external to a particle.     

Time lag in diffusion

Adsorption and desorption diffusion time lags are given for some homogeneous hollow cylinder and spherical shell membrane systems. The treatment relates to a constant diffusion coefficient with solution or sorption obeying Henry's law. Time lags for both “forward” and “reverse” flow have been determined and identities between them derived. For the hollow cylinder and spherical shell membrane systems considered here, there are only three distinguishable time lags.     

Challenge 2005 and beyond: Recognition,Transformation, and profitable use of innovative thinking

In the opening years of the new millennium, we are witnessing the creation of a “cult of innovation”. The word is on everyone's lips, and nowhere more so than in board rooms and executive offices of the world's great business enterprises. Innovation is something that every business values and wishes to create; yet it is a concept that often defies definition. It is not uncommon for a group of knowledgeable individuals to disagree not only about the value of innovation, but also about the meaning of innovation. One person's “innovation” can be another's “product or process improvement” (e.g., Gillette's new M3 Power^TM vibrating blade razor—innovation or product improvement?) and the ensuing dialogue frequently raises questions not only about the nature and definition of innovation, but also about the way in which innovation is used to create something useful and market-friendly. The perceived value of new concepts and inventions quite often colors whether they are seen as innovations, or whether they are seen as intellectual and/or laboratory curiosities. Moreover, concepts and inventions that might be deemed to be “innovative” (i.e., having value) at “Point Y” in history may not have been seen that way at “Point X” 20 years earlier. Innovations, consequently, are often declared retrospectively—many years may pass between the initial cognitive output and the recognition that it either represented, or was transformed into, an innovation. There are periods of time, however, when the process of “innovative thinking” is much more important than the actual creation of true innovations, and we are in such a period. It is this broad concept—the recognition, transformation, and profitable use of innovative thinking—which is discussed in this article.     

Three‐dimensional solution for the vibration analysis of functionally graded multiwalled carbon nanotubes/phenolic nanocomposite cylindrical panels on elastic foundation

In this study, based on the three‐dimensional theory of elasticity, free vibration characteristics of nanocomposite cylindrical panels reinforced by multiwalled carbon nanotubes (MWCNT) are considered. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin–Tasi equation was used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin–Tsai equation from expressing a straight line to a nonlinear one in the MWNTs wt% range considered. Symmetric and asymmetric volume fraction profiles are provided in this article for comparison. It is shown that using only few grid points, accurate results are obtained which demonstrate the efficiency and convenience of the generalized differential quadrature method for the problem under consideration. The validity of the Young's modulus and frequency response were assessed by a comparison with available literature data, providing a good agreement. POLYM. COMPOS., 34:2040–2048, 2013. © 2013 Society of Plastics Engineers     

On a sustainability interval index and its computation through global optimization

Prior sustainability models have taken exact basic indicator (BI) values of an entity's sustainability and computed an exact value of the entity's sustainability index. However, BI values are either uncertain or difficult to obtain. In this work, we propose a novel approach that transforms BI data in the form of intervals containing all possible BI values to an interval containing all possible values of the sustainability index. This interval is termed the “sustainability index interval” (SII). Computation of the SII is achieved through solution of a minimization and a maximization problem using global optimization techniques. Although the underlying global optimization problems are nonconvex, they are shown to possess a number of properties that can be utilized to reduce the burden associated with SII's computation. Based on these properties, a branch‐and‐bound algorithm is developed, which exactly quantifies the SII in a finite number of iterations. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Use of basic color terms by red–green dichromats: 1. General description

Abstract: In this article we present data comparing red–green dichromats' use of “Basic Color Terms” (BCTs) with that of standard trichromats. In a complementary article (Color Res Appl 2013) we use these data to evaluate two models of the mechanisms underlying dichromats' use of BCTs. There were three groups of observers—trichromats, protanopes, and deuteranopes—that each performed two tasks: “mapping” (which of these are exemplars of X?) and “best exemplar” (which is the best instance of X?), where X took the value of each Spanish BCT. The mapping task results were subjected to multidimensional scaling that revealed that dichromats differ from trichromats in the number and nature of the dimensions needed for describing BCTs' use. Trichromats required three dimensions closely related to the opponent color mechanisms (red–green, yellow–blue) and the light‐dark channel. In contrast, tridimensional solution for dichromats was difficult to interpret, whereas the fit for the bidimensional solution was very good and revealed a chromatic dimension, which did not match any of the trichromatic dimensions, and an achromatic one. There were also some error‐asymmetries (sometimes “A” was the predominant error when choosing exemplars of “B”, but not vice versa) and the groups differed in the frequency of use of some BCTs (e.g., protanopes chose more stimuli as orange than trichromats and deuteranopes). As expected, the best exemplar task produced more correct responses than the mapping task, and for both tasks, “primary” BCTs (black, white, red, green, yellow, and blue) produced better results than “derived” ones (brown, purple, orange, pink, and grey). © 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 360–371, 2014     

Micromechanics of ITZ–Aggregate Interaction in Concrete Part I: Stress Concentration

At the macroscopic scale, concrete appears as a composite made of a cement paste matrix with embedded aggregates. The latter are covered by interfacial transition zones (ITZs) of reduced stiffness and strength. Cracking in the ITZs is probably the key to the nonlinear stress–strain behavior in the prepeak regime. For a deeper understanding of this effect triggered by tensile microstress peaks, we here employ and extend the framework of continuum micromechanics, as to develop analytical solutions relating the macroscopic stresses acting on a piece of concrete, to microtractions at the aggregates' surfaces and to three‐dimensional stress states within the ITZs. In the latter context, a new aggregate‐to‐ITZ stress concentration tensor is derived based on the separation‐of‐scale principle, which implies that ITZs may be modeled as two‐dimensional interfaces at the concrete scale, but as three‐dimensional bulk phases at the scale of a few micrometers. Microtensile peaks occur both under uniaxial macroscopic tension and compression. To describe the respective microtraction and microstress fields, it is suitable to define aggregate's “poles” and “equator” by an “axis” through the aggregate center, directed in the uniaxial macroscopic loading direction. Accordingly, tensile microtraction peaks, induced by macro‐tension and macro‐compression, respectively, occur at the “poles” and at the “equator”, respectively. The largest tensile ITZ‐microstresses occur at an offset of about π/8 from the “poles” and the “equator”, respectively. These fields of microtractions and ITZ microstresses are prerequisites for upscaling ITZ‐related strength to the macroscopic concrete level, as presented in the companion paper (Part II).     

Modified Wilson's Model for Correlating Solubilities in Supercritical Fluids of Some Polycyclic Aromatic Solutes

Since developing mathematical models is extremely useful to determine solubilities of various solutes in supercritical fluids (SCFs); in this work, the “expanded liquid” approach is adopted to predict the solubility of some polycyclic aromatic solutes (with different size, functionality, and polarity) in diverse SCFs. A modified form of the Wilson's model is proposed for predicting the solubilities of the considered binary systems by computation of the activity coefficient based on the local composition concept. Effect of high operating conditions is considered via the variation of the molar volume of the solute. The proposed correlation achieves an overall and average AARD of 9.2% and 7.8%, respectively, on a range of 1.14% to 19.9%, these results show that the predicted solubility data are in good agreement with the experimental ones. Moreover, dependence of binary parameters on density and some solute's characteristics is discussed on the base of their course versus solvent reduced density.     

A modified “inside-out” algorithm for simulation of multistage multicomponent separation processes using the UNIFAC group-contribution method

A computational procedure using a modification of Boston and Sullivan's “inside-out” multistage multicomponent separation algorithm (1974) is developed. In order to improve convergence behavior for problems involving mixtures with highly nonideal liquid phases, a two-parameter model is used to describe liquid-phase compositional effects upon the K-factor. The quasi-Newton methods of Mehra et al. (1983) and Nghiem (1983) are applied to solving various sets of solution variables in the proposed algorithm. Activity coefficients are calculated using the UNIQUAC activity-coefficient model (1975) with parameters obtained from the UNIFAC group-contribution method (1975). The computational procedure is applicable to distillation, absorption and reboiled-absorption configurations. The proposed algorithm was implemented in a FORTRAN 77 program and tested on the Honeywell DPS 8/70M computer at the University of Calgary. Inclusion of the liquid-phase model resulted in improved convergence behavior for nonideal systems in which the original “inside-out” method failed to converge.     

Selective Clathration of Aliphatic Alcohols by Dianin's Compound

Abstract

Dianin's Compound (4-p-hydroxyphenyl-2,2,4-trimethylchroman) has been shown to demonstrate a marked selectivity when it forms clathrates from binary alcohol solutions. The relationship between solvent composition in solution and in the crystalline adduct was found to be linear in all but one case. The degree of selectivity was expressed quantitatively as the “preference index.” Results obtained indicated that the molecular shape of a potential guest plays a dominant role in the formation of Dianin's Compound adducts.     

Composition of liver fats of mature and embryo sharks (galeocerdo tigrinus)

1. Two liver fats, one from the “mother” and the other from the “embryo” shark (Galeocerdo tigrinus), have been studied. Their component fatty acids are reported.
2. The mixed fatty acids from each of the fats were first resolved into groups of acids of varying unsaturation by the lithium salt acetone and/or lead salt alcohol methods. The methyl esters of each of these groups of acids were fractionated through the Longenecker's E.H.P. column.
3. The two fats are found to belong to the fourth group of Tsujimoto's classification of the Elasmobranch fish liver fats. The “mother” shark liver fat contains 43.3% saturated and 56.7% unsaturated acids. The “embryo” shark liver fat contains 39.1% saturated and 60.9% unsaturated acids. Palmitic acid was about 25% in both of the fats.
4. A possible explanation for the less unsaturation and the absence of higher polyethenoids in the “embryo” liver fat is given.

     

A STATISTICAL ANALYSIS OF A PACKED TOWER DEHUMIDIFIER

ABSTRACT

A dehumidifier is the heart of a liquid desiccant cooling system. In these systems, air is dehumidified using liquid desiccants and cooled with heat exchangers and/or evaporative coolers [I]. A Statistical Analysis Software (SAS) regression analysis was performed on experimental data from a packed tower desiccant dehumidifier tested at Texas Tech. The purpose of this analysis was to determine simple functional relationships for the liquid desiccant dehumidifier for use in computer models of liquid desiccant space cooling systems.

Six factors and four dependent variables were defined and four regression models were determined. These regression models were reduced to three factor models. The packed tower regression analysis showed Texas Tech's “Cost Effective Liquid Desiccant” (CELD) to be a well behaved stable desiccant solution.     

Bibliometrics in glass and other sciences: A Plea for reason

We show a scientometric analysis for glass researchers and compare it with those for researchers in two fashionable research topics, representing the science-push area “graphene” and the market-pull area “lithium ion battery (LIB)”. We also present similar statistics for two widely different macro fields, “materials science” (which contains the other three) and “mathematics”. While productivity (number of published articles) of a researcher and his/her H-index are found to be correlated, these correlations are very different for different research fields, depending on their size, fragmentation, interdisciplinarity, and on the community's publication and citation culture. We also explore the correlation between citation statistics and scientific quality and find it to be elusive. While certain bibliometric indexes indeed indicate how active, prolific, and visible a researcher (or a research group) is, we argue that quality—evaluated by the originality, strength, reproducibility and relevance of the findings of a researcher's publications (as judged by peer review)—is much more important than the number of published articles and citations, and this is where efforts must be concentrated by researchers and evaluating bodies.     

Dispersion state and hyperelastic behavior of tire tread compounds reinforced with nanoclay: Uniaxial tensile and compression studies

Tire-tread compounds based on natural rubber, butadiene rubber, and styrene-butadiene rubber (65/20/15) were reinforced with Cloisite 15A. Clay state-of-dispersion in the ternary matrix (clay aspect ratio and clay/matrix interface yield strength) was estimated using Halpin–Tsai, Guth, and Leidner–Woodhams–Pukanszky micro-mechanical models. The aspect ratio suggested by Halpin–Tsai (9.7) and Guth (16) models both propounded partially intercalated microstructure. Transmission electron microscopy micrographs indicated higher reliability of Halpin–Tsai theory. Wetting parameter values indicated the affinity of Cloisite 15A to disperse in butadiene rubber. However, it seems that clay particles were not provided with proper compounding conditions to further stabilize their thermodynamic state. The poor matrix/clay adhesion was responsible for the decrease in matrix/clay interface strength and thickness upon increasing clay content according to Leidner–Woodhams–Pukanszky. Hyperelastic modeling was conducted using Abaqus software (five strain energy potential forms) on the basis of large deformation uniaxial tension/compression measurements. Effect of nanoclay on the crosslink-density of samples was justified by C₁₀ (Mooney–Rivlin) and locking-stretch (Van der Waals) values. The sample containing 1 phr nanoclay presented the best fit to the hyperelastic models among the rest conforming to its small value of global interaction parameter “a”(Van der Waals model) calculated explaining minimum deviations. Overall, Marlow and Ogden provided the best consistency with the experimental stress–strain results.     

A comprehensive approach to chemical engineering computational problems

A general programme for the solution of large sparse systems of non-linear equations is presented that allows to afford in a general way most computational problems in chemical engineering.Equipments and plants can, in fact, be represented as networks of “unit cells” to which material and energy balance equations are applied in finite form.The lay-out of the network and the assessment of the equations is a matter of the engineer's judgment and depends upon the aims of the computation and the complexity and importance of the phenomena involved.The solution of the equations then becomes a straightforward procedure that may be committed to the computer.Examples of application to a variety of chemical equipments and to process computation are given.     

Research on color optimization of tricolor product considering color harmony and users' emotion

There are few studies on the tricolor design optimization, and the influence of color-area ratio on users' emotion has been ignored. This article aims to achieve multiobjective optimization of tricolor product color design. Two modes of color-area ratio are put forward. Using the proposed method of generating tricolor schemes, 368 tricolor schemes of the representative baby carriage are designed. Through questionnaire survey, color images are screened, and combined with correlation analysis and factor analysis, five perceptual features of color design are determined as “Order,” “Excitement,” “Temperature,” “Color harmony,” and “Users' emotional preference.” From two perspectives of color information processing, radial basis function neural networks are used to construct two emotional evaluation models. By integrating the radial basis function neural networks and a genetic algorithm, this study achieves multiobjective optimization of tricolor product color design for two optimization objectives of color harmony and users' emotional preference. Verification results show that the optimization schemes are significantly better than other schemes. Due to similar product characteristics, children's electric car is utilized to verify the generalization capability of the optimization method proposed in this article. It has been demonstrated that the optimization schemes achieve higher scores than randomly selected color schemes and the actual subjective scores match with the predicted scores computed by the color optimization method.     

The Mechanism of “Active Monomer” Polymerization of α-Amino Acid N-Carboxyanhydrides. Temperature Effects and the Significance of the Proton-Transfer Reaction

The temperature dependence of the polymerization rate is investigated using the NCA's of β-benzyl L-aspartate and γ -benzyl L-glutamate. Activation energies for polymerizing the above NCA's are 13 and 9 Kcal per mole, respectively. Entropies of activation and Arrhenius constants, A, are also calculated and discussed in terms of the polymerization mechanism. The significance of the proton-transfer reaction in the “active monomer” mechanism is recognized through a kinetic isotope effect and also by comparing the polymerization rates of L-alanine NCA and its structural analog L-alanine N-thiocarboxyanydride. It is theorized that a changing position of equilibrium of the neutralization step decreases the concentration of “active monomer”, thereby slowing the polymerization rate.     

Reinforced polystyrene via solvent‐exfoliated graphene

Solvent‐exfoliated graphene (SEG)‐reinforced polystyrene (PS) composites were prepared using a straightforward solution‐casting method. SEG sheets, obtained by sonication‐assisted solvent direct exfoliation from natural graphite, were well dispersed in the PS matrix as evidenced from scanning electron microscopy and transmission electron microscopy observations. Addition of 0.5 wt% SEG resulted in a 6% increase in tensile strength and a 77% improvement in Young's modulus over pure PS due to the effective load transfer between SEG and PS matrix. The Young's moduli of the PS/SEG composites were obtained from both tensile experiments and calculations using the well‐established Halpin–Tsai model. Results from dynamic mechanical analysis indicated that the storage modulus of the PS/SEG composites was significantly improved relative to neat PS. The glass transition temperatures of the composites were found to increase substantially upon addition of SEG, consistent with differential scanning calorimetry analysis. © 2017 Society of Chemical Industry     

Mechanical properties of surface‐treated banana fiber/polylactic acid biocomposites: A comparative study of theoretical and experimental values

Current study evaluates the effect of fiber surface treatments on the mechanical properties of banana fiber (BF) reinforced polylactic acid (PLA) biocomposites. Experimental results indicate increase in tensile modulus and strength upon surface treatments of BF with various silanes (APS and Si69) and NaOH. Approximately, an increase of 136% in tensile strength and 49% in impact strength was obtained in case of biocomposites with Si69‐treated BF compared with the untreated BF biocomposites. Also, experimentally determined mechanical modulus of untreated and surface‐treated BF biocomposite has been compared with the mechanical modulus calculated using various micromechanical models. Models such as Hirsch's, modified Bawyer and Bader's, and Brodnyan model showed good agreement with the experimentally determined results. Similarly, other models like Halpin‐Tsai, Nielson modified Halpin‐Tsai, and Cox's model also have been tried for the comparative study with the experimental data. Surface modification of BF showed increased interfacial adhesion between the fiber and the matrix which was evident from lowered difference between the experimentally and theoretically derived mechanical modulus. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013