A new framework for solution of multidimensional population balance equations

A new framework is proposed in this work to solve multidimensional population balance equations (PBEs) using the method of discretization. A continuous PBE is considered as a statement of evolution of one evolving property of particles and conservation of their n internal attributes. Discretization must therefore preserve n + I properties of particles. Continuously distributed population is represented on discrete fixed pivots as in the fixed pivot technique of Kumar and Ramkrishna [1996a. On the solution of population balance equation by discretization-I A fixed pivot technique. Chemical Engineering Science 51(8), 1311-1332] for 1-d PBEs, but instead of the earlier extensions of this technique proposed in the literature which preserve 2(n) properties of non-pivot particles, the new framework requires n + I properties to be preserved. This opens up the use of triangular and tetrahedral elements to solve 2-d and 3-d PBEs, instead of the rectangles and cuboids that are suggested in the literature. Capabilities of computational fluid dynamics and other packages available for generating complex meshes can also be harnessed. The numerical results obtained indeed show the effectiveness of the new framework. It also brings out the hitherto unknown role of directionality of the grid in controlling the accuracy of the numerical solution of multidimensional PBEs. The numerical results obtained show that the quality of the numerical solution can be improved significantly just by altering the directionality of the grid, which does not require any increase in the number of points, or any refinement of the grid, or even redistribution of pivots in space. Directionality of a grid can be altered simply by regrouping of pivots.

Is the mental wellbeing of young Australians best represented by a single, multidimensional or bifactor model?

Internationally there is a growing interest in the mental wellbeing of young people. However, it is unclear whether mental wellbeing is best conceptualized as a general wellbeing factor or a multidimensional construct. This paper investigated whether mental wellbeing, measured by the Mental Health Continuum-Short Form (MHC-SF), is best represented by: (1) a single-factor general model; (2) a three-factor multidimensional model or (3) a combination of both (bifactor model). 2,220 young Australians aged between 16 and 25 years completed an online survey including the MHC-SF and a range of other wellbeing and mental ill-health measures. Exploratory factor analysis supported a bifactor solution, comprised of a general wellbeing factor, and specific group factors of psychological, social and emotional wellbeing. Confirmatory factor analysis indicated that the bifactor model had a better fit than competing single and three-factor models. The MHC-SF total score was more strongly associated with other wellbeing and mental ill-health measures than the social, emotional or psychological subscale scores. Findings indicate that the mental wellbeing of young people is best conceptualized as an overarching latent construct (general wellbeing) to which emotional, social and psychological domains contribute. The MHC-SF total score is a valid and reliable measure of this general wellbeing factor.

Comprehending adverbs of doubt and certainty in health communication: A multidimensional scaling approach

This research explored the feasibility of using multidimensional scaling (MDS) analysis in novel combination with other techniques to study comprehension of epistemic adverbs expressing doubt and certainty (e.g., evidently, obviously, probably) as they relate to health communication in clinical settings. In Study 1, Australian English speakers performed a dissimilarity-rating task with sentence pairs containing the target stimuli, presented as "doctors' opinions". Ratings were analyzed using a combination of cultural consensus analysis (factor analysis across participants), weighted-data classical-MDS, and cluster analysis. Analyses revealed strong within-community consistency for a 3-dimensional semantic space solution that took into account individual differences, strong statistical acceptability of the MDS results in terms of stress and explained variance, and semantic configurations that were interpretable in terms of linguistic analyses of the target adverbs. The results confirmed the feasibility of using MDS in this context. Study 2 replicated the results with Canadian English speakers on the same task. Semantic analyses and stress decomposition analysis were performed on the Australian and Canadian data sets, revealing similarities and differences between the two groups. Overall, the results support using MDS to study comprehension of words critical for health communication, including in future studies, for example, second language speaking patients and/or practitioners. More broadly, the results indicate that the techniques described should be promising for comprehension studies in many communicative domains, in both clinical settings and beyond, and including those targeting other aspects of language and focusing on comparisons across different speech communities.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Bounded-input/bounded-output stability of linear multidimensional time- varying systems

The present study of the stability of systems governed by a linear multidimensional time-varying equation, which are encountered in spacecraft dynamics, economics, demographics, and biological systems, gives attention the lemma dealing with L(inf) stability of an integral equation that results from the differential equation of the system under consideration. Using the proof of this lemma, the main result on L(inf) stability is derived according; a corollary of the theorem deals with constant coefficient systems perturbed by small periodic terms. (O.C.)

A Multidimensional Kinetic Upwind Method for Euler Equations

The study of directional derivative lead to the development of a rotationally invariant kinetic upwind method (KUMARI)3 which avoids dimension by dimension splitting. The method is upwind and rotationally invariant and hence truly multidimensional or multidirectional upwind scheme. The extension of KUMARI to second order is as well presented.

Performance Modeling based on Multidimensional Surface Learning for Performance Predictions of Parallel Applications in Non-Dedicated Environments

Modeling the performance behavior of parallel applications to predict the execution times of the applications for larger problem sizes and number of processors has been an active area of research for several years. The existing curve fitting strategies for performance modeling utilize data from experiments that are conducted under uniform loading conditions. Hence the accuracy of these models degrade when the load conditions on the machines and network change. In this paper, we analyze a curve fitting model that attempts to predict execution times for any load conditions that may exist on the systems during application execution. Based on the experiments conducted with the model for a parallel eigenvalue problem, we propose a multi-dimensional curve-fitting model based on rational polynomials for performance predictions of parallel applications in non-dedicated environments. We used the rational polynomial based model to predict execution times for 2 other parallel applications on systems with large load dynamics. In all the cases, the model gave good predictions of execution times with average percentage prediction errors of less than 20%

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Multidimensional data reconstruction for two color fluorescence microscopy

We propose an iterative data reconstruction technique specifically designed for multi-dimensional multi-color fluorescence imaging. Markov random field is employed (for modeling the multi-color image field) in conjunction with the classical maximum likelihood method. It is noted that, ill-posed nature of the inverse problem associated with multi-color fluorescence imaging forces iterative data reconstruction. Reconstruction of three-dimensional (3D) two-color images (obtained from nanobeads and cultured cell samples) show significant reduction in the background noise (improved signal-to-noise ratio) with an impressive overall improvement in the spatial resolution (approximate to 250 nm) of the imaging system. Proposed data reconstruction technique may find immediate application in 3D in vivo and in vitro multi-color fluorescence imaging of biological specimens. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4769058]

Taylor series expansion based multidimensional image reconstruction for confocal and 4pi microscopy

We propose and experimentally demonstrate a three-dimensional (3D) image reconstruction methodology based on Taylor series approximation (TSA) in a Bayesian image reconstruction formulation. TSA incorporates the requirement of analyticity in the image domain, and acts as a finite impulse response filter. This technique is validated on images obtained from widefield, confocal laser scanning fluorescence microscopy and two-photon excited 4pi (2PE-4pi) fluorescence microscopy. Studies on simulated 3D objects, mitochondria-tagged yeast cells (labeled with Mitotracker Orange) and mitochondrial networks (tagged with Green fluorescent protein) show a signal-to-background improvement of 40% and resolution enhancement from 360 to 240 nm. This technique can easily be extended to other imaging modalities (single plane illumination microscopy (SPIM), individual molecule localization SPIM, stimulated emission depletion microscopy and its variants).

Multidimensional free energy surface of unfolding of HP-36: Microscopic origin of ruggedness

The protein folding funnel paradigm suggests that folding and unfolding proceed as directed diffusion in a multidimensional free energy surface where a multitude of pathways can be traversed during the protein's sojourn from initial to final state. However, finding even a single pathway, with the detail chronicling of intermediates, is an arduous task. In this work we explore the free energy surface of unfolding pathway through umbrella sampling, for a small globular a-helical protein chicken-villin headpiece (HP-36) when the melting of secondary structures is induced by adding DMSO in aqueous solution. We find that the unfolding proceeds through the initial separation or melting of aggregated hydrophobic core that comprises of three phenylalanine residues (Phe7, Phe11, and Phe18). This separation is accompanied by simultaneous melting of the second helix. Unfolding is found to be a multistage process involving crossing of three consecutive minima and two barriers at the initial stage. At a molecular level, Phe18 is observed to reorient itself towards other hydrophobic grooves to stabilize the intermediate states. We identify the configuration of the intermediates and correlate the intermediates with those obtained in our previous works. We also give an estimate of the barriers for different transition states and observe the softening of the barriers with increasing DMSO concentration. We show that higher concentration of DMSO tunes the unfolding pathway by destabilizing the third minimum and stabilizing the second one, indicating the development of a solvent modified, less rugged pathway. The prime outcome of this work is the demonstration that mixed solvents can profoundly transform the nature of the energy landscape and induce unfolding via a modified route. A successful application of Kramer's rate equation correlating the free energy simulation results shows faster rate of unfolding with increasing DMSO concentration. This work perhaps presents the first systematic theoretical study of the effect of a chemical denaturant on the microscopic free energy surface and rates of unfolding of HP-36. (C) 2014 AIP Publishing LLC.

Coherent (photon) vs incoherent (current) detection of multidimensional optical signals from single molecules in open junctions

The nonlinear optical response of a current-carrying single molecule coupled to two metal leads and driven by a sequence of impulsive optical pulses with controllable phases and time delays is calculated. Coherent (stimulated, heterodyne) detection of photons and incoherent detection of the optically induced current are compared. Using a diagrammatic Liouville space superoperator formalism, the signals are recast in terms of molecular correlation functions which are then expanded in the many-body molecular states. Two dimensional signals in benzene-1,4-dithiol molecule show cross peaks involving charged states. The correlation between optical and charge current signal is also observed. (C) 2015 AIP Publishing LLC.

Controlled material transport and multidimensional patterning at small length scales using electromigration

Electromigration, mostly known for its damaging effects in microelectronic devices, is basically a material transport phenomenon driven by the electric field and kinetically controlled by diffusion. In this work, we show how controlled electromigration can be used to create scientifically interesting and technologically useful micro-/nano-scale patterns, which are otherwise extremely difficult to fabricate using conventional cleanroom practices, and present a few examples of such patterns. In a solid thin-film structure, electromigration is used to generate pores at preset locations for enhancing the sensitivity of a MEMS sensor. In addition to electromigration in solids, the flow instability associated with the electromigration-induced long-range flow of liquid metals is shown to form numerous structures with high surface area to volume ratio. In very thin solid films on non-conductive substrates, solidification of flow-affected region results in the formation of several features, such as nano-/micro-sized discrete metallic beads, 3D structures consisting of nano-stepped stairs, etc.

A Bayesian wavelet-based multidimensional deconvolution with sub-band emphasis

This paper proposes a new algorithm for waveletbased multidimensional image deconvolution which employs subband-dependent minimization and the dual-tree complex wavelet transform in an iterative Bayesian framework. In addition, this algorithm employs a new prior instead of the popular ℓ1 norm, and is thus able to embed a learning scheme during the iteration which helps it to achieve better deconvolution results and faster convergence. © 2008 IEEE.