Diffusion, sedimentation, and rheology of concentrated suspensions of core-shell particles

Short-time dynamic properties of concentrated suspensions of colloidal core-shell particles are studied using a precise force multipole method which accounts for many-particle hydrodynamic interactions. A core-shell particle is composed of a rigid, spherical dry core of radius a surrounded by a uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ(-1). The solvent flow inside the permeable shell is described by the Brinkman-Debye-Bueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact non-hydrodynamically by a hard-sphere no-overlap potential of radius b. Numerical results are presented for the high-frequency shear viscosity, η(∞), sedimentation coefficient, K, and the short-time translational and rotational self-diffusion coefficients, D(t) and D(r). The simulation results cover the full three-parametric fluid-phase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Many-particle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Our simulation results show that for thin or hardly permeable shells, the core-shell systems can be approximated neither by no-shell nor by no-core models. However, one of our findings is that for κ(b - a) ? 5, the core is practically not sensed any more by the weakly penetrating fluid. This result is explained using an asymptotic analysis of the scattering coefficients entering into the multipole method of solving the Stokes equations. We show that in most cases, the influence of the core grows only weakly with increasing concentration.     

A study of cyclohexane diffusion in hybrid (organic/inorganic) gels monitored by an oscillating balance reactor

Hybrid (organic/inorganic) gels are studied in terms of cyclohexane diffusion transients with an oscillating balance reactor (OBR) which, unlike conventional microbalances, has the well-defined gas flow profile characteristics of packed beds (PB's). The OBR-based flow-through adsorption system, when properly designed, has very good time resolution and is particularly useful in modeling adsorption processes under more realistic PB geometries. With the test sample adopted in this study, the "semirigid" nature of hybrid gels becomes apparent when simple relaxation models are chosen to fit experimental data.     

High school students' emotional experiences in mathematics classes

The aim of this qualitative research is to identify Mexican high school students' emotional experiences in mathematics classes. In order to obtain the data, focus group interviews were carried out with 22 students. The data analysis is based on the theory of the cognitive structure of emotions, which specifies the eliciting conditions for each emotion and the variables that affect the intensity of each emotion. The participant students' emotional experiences in mathematics classes are composed of: (1) satisfaction and disappointment while solving a problem; (2) joy or distress when taking a test; (3) fear and relief during classes; (4) pride and self-reproach during classes; and (5) boredom and interest during classes. Finally, we discuss how the theory of the cognitive structure of emotions and our analysis contribute to emotion research in mathematics education.     

A posteriori estimate and asymptotic partial domain decomposition

The method of asymptotic partial decomposition of a domain aims at replacing a 3D or 2D problem by a hybrid problem 3D???1D; or 2D???1D, where the dimension of the problem decreases in part of the domain. The location of the junction between the heterogeneous problems is asymptotically estimated in certain circumstances, but for numerical simulations it is important to be able to determine the location of the junction accurately. In this article, by reformulating the problem in a mixed formulation context and by using an a posteriori error estimate, we propose an indicator of the error due to a wrong position of the junction. Minimizing this indicator allows us to determine accurately the location of the junction. Some numerical results are presented for a toy problem.     

Additivity properties of operator ranges

In the present paper we study different conditions regarding the sum of operator ranges. In particular, we find conditions on operators A, B   which imply that R(A+B)=R(A)+R(B)$R(A+B)=R(A)+R(B)$ and derive some results concerning projections.     

Mexican high school students' social representations of mathematics,its teaching and learning

This paper reports a qualitative research that identifies Mexican high school students’ social representations of mathematics. For this purpose, the social representations of ‘mathematics’, ‘learning mathematics’ and ‘teaching mathematics’ were identified in a group of 50 students. Focus group interviews were carried out in order to obtain the data. The constant comparative style was the strategy used for the data analysis because it allowed the categories to emerge from the data. The students’ social representations are: (A) Mathematics is…(1) important for daily life, (2) important for careers and for life, (3) important because it is in everything that surrounds us, (4) a way to solve problems of daily life, (5) calculations and operations with numbers, (6) complex and difficult, (7) exact and (6) a subject that develops thinking skills; (B) To learn mathematics is…(1) to possess knowledge to solve problems, (2) to be able to solve everyday problems, (3) to be able to make calculations and operations, and (4) to think logically to be able to solve problems; and (C) To teach mathematics is…(1) to transmit knowledge, (2) to know to share it, (3) to transmit the reasoning ability, and (4) to show how to solve problems.     

Entropy,Information, and the Updating of Probabilities

This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes pragmatic elements in the derivation. An epistemic notion of information is defined in terms of its relation to the Bayesian beliefs of ideally rational agents. The method of updating from a prior to posterior probability distribution is designed through an eliminative induction process. The logarithmic relative entropy is singled out as a unique tool for updating (a) that is of universal applicability, (b) that recognizes the value of prior information, and (c) that recognizes the privileged role played by the notion of independence in science. The resulting framework—the ME method—can handle arbitrary priors and arbitrary constraints. It includes the MaxEnt and Bayes’ rules as special cases and, therefore, unifies entropic and Bayesian methods into a single general inference scheme. The ME method goes beyond the mere selection of a single posterior, and also addresses the question of how much less probable other distributions might be, which provides a direct bridge to the theories of fluctuations and large deviations.     

Spatial cues alone produce inaccurate sound segregation: the effect of interaural time differences

To clarify the role of spatial cues in sound segregation, this study explored whether interaural time differences (ITDs) are sufficient to allow listeners to identify a novel sound source from a mixture of sources. Listeners heard mixtures of two synthetic sounds, a target and distractor, each of which possessed naturalistic spectrotemporal correlations but otherwise lacked strong grouping cues, and which contained either the same or different ITDs. When the task was to judge whether a probe sound matched a source in the preceding mixture, performance improved greatly when the same target was presented repeatedly across distinct distractors, consistent with previous results. In contrast, performance improved only slightly with ITD separation of target and distractor, even when spectrotemporal overlap between target and distractor was reduced. However, when subjects localized, rather than identified, the sources in the mixture, sources with different ITDs were reported as two sources at distinct and accurately identified locations. ITDs alone thus enable listeners to perceptually segregate mixtures of sources, but the perceived content of these sources is inaccurate when other segregation cues, such as harmonicity and common onsets and offsets, do not also promote proper source separation.     

Bounded and unbounded polynomials and multilinear forms: Characterizing continuity

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question as to whether a polynomial is continuous if and only if it transforms connected sets into connected sets. These results motivate the natural question as to how many non-continuous polynomials there are on an infinite dimensional normed space. A problem on the lineability of the sets of non-continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered.