Construction of a Generalized Algorithm for Calculating Diffuse Radiation Configuration Factors

A hybrid Cartesian grid and gridless method for compressible flows

Heat exchangers with small-diameter multi-path tubes have been recently used to improve the efficiency of air conditioners. The difficulty in using tubes with small diameters and multi-paths is the nonuniformity of refrigerant distribution in refrigerant distributors, which results in lower heat-exchange efficiency. Grid methods, such as the volume of fluid method, are now widely used to simulate detailed motions of gas–liquid interfaces. A weak point of grid methods is the numerical diffusion of interfaces that occurs if the scale of interfaces becomes close to the computational grid sizes. We previously developed a particle/grid hybrid method for simulating multi-scale free surfaces. For this study, we modified the hybrid method and applied it to gas–liquid flow simulations in a distributor. The liquid film behaviors in both the distributor and a bend pipe placed in the upstream of the distributor were simulated mainly using the particle method, and gas flows were simulated using the grid method. The predicted liquid film near the outer circumference of the curvature in the bend pipe was thicker than that of near inner circumference of the curvature, which qualitatively agreed with the measurement. The simulated distribution ratio under a steady-flow condition agreed well with the measurement; the predicted distribution ratio was 0.63 and the measured distribution ratio was 0.6.

Optimal design of selective catalyst reduction denitrification system using numerical simulation

Bead encoding is a key problem central to all multiplexed bead-based microarrays. Most existing bead-based microarrays require complicated and costly bead fabrication and/or sophisticated bead decoding hardware to achieve high multiplexing. Recently, the development of spatial bead encoding techniques have opened up the possibility of using pattern matching and image processing to develop highly multiplexed, high-throughput bead-based arrays. In this thesis, we improve the existing spatial bead encoding scheme, and develop a pipeline of computational methods, which allows for automated spatial bead encoding. Six novel computational methods, that automate the proposed bead encoding scheme, are developed in this thesis. The proposed scheme improves the previously reported spatial encoding schemes by making them better suited for use in real world scenarios. In the spatial bead encoding scheme, a sequential bead deposition method is used to capture the identities of the beads in bright or dark field images of the array. While, a second fluorescence image of the array is used to quantify the target analyte concentrations associated with the beads. By aligning the two images using the patterns formed by the beads, both the bead identities (i.e. the target analyte associate with the bead) and the analyte concentrations are decoded. The six computational methods developed in this thesis, are grouped into three categories: bright and dark field image processing, fluorescence image processing, and bead pattern matching. These methods are developed such that they require minimal parameter tuning, and are able to deal with noisy images acquired in uncontrolled environments As part of the bright and dark field image processing we have developed two novel methods: a fully automatic method for detecting the underlying micro-well grid structure in the images, and an unsupervised learning based method to classify the micro-wells as either empty or containing a bead. We show the ability of the proposed methods to deal with extreme amounts of noise and distortions using multiple datasets. While, microarray image gridding is a well-studied problem in the context of fluorescence images of planar microarrays, to the best of our knowledge no methods have yet been developed for processing either bright or dark field images of bead-based microarrays. Unlike in bright field images, where all the beads are visible, in fluorescence images only those beads that are expressed in the sample are visible. Therefore, in fluorescence image analysis the first step is to detect the beads in the image. To this end, we have developed an unsupervised, simultaneous bead detection and segmentation method which uses the coherence in shape and size of the beads to circumvent the need for parameter optimization. The main challenge in this segmentation is the large dynamic range across which the beads are expressed. We have also developed a probabilistic non-linear gridding method that attempts to establish the micro-well grid structure from the detected beads. While similar gridding techniques have been developed in the past, we make two contributions in this regard: first, we put the gridding method in a probabilistic framework, and second, we show that in certain cases it is impossible to ascertain if the correct grid has been detected without using additional information about the physical properties of the array. The final step in the proposed bead encoding scheme is to establishing one-to-one correspondences between the beads detected in the bright field and fluorescence images. We have developed two methods for this matching. When the micro-well grid structure in the fluorescence image is successfully established, the grid information can be used to reduce the matching problem to a binary grid alignment problem. A grid matching method that is very fast and can handle a large number of beads (>50,000) has been developed for this purpose. Finally, to perform matching when the fluorescence image grid is not available, a novel point pattern matching method that is affine invariant and robust to small non-linear distortions has been developed. The point pattern matching method addresses the problem of matching large point sets in the presence of large amounts of outliers and occlusion. The proposed method is evaluated using several real and simulated datasets.

CFD-DEM simulation of fluorination reaction in fluidized beds with local grid and time refinement method

Sensitivity and uncertainty analysis is becoming increasingly widespread in many fields of engineering and sciences, encompassing practically all of the experimental data-processing activities and many computational modeling and process simulation activities. There are many methods, based either on deterministic or statistical concepts, for performing sensitivity and uncertainty analysis. However, a precise, unified terminology across all methods does not seem to exist, yet often, identical words (e.g., “sensitivity”) may not necessarily describe identical quantities, particularly when stemming from conceptually distinct (statistical versus deterministic) methods. Furthermore, the relative strengths and weaknesses of the various methods do not seem to have been reviewed comparatively in the literature published thus far.This paper is the first part of a comparative review, written in two parts, that focuses on the salient features of the statistical and deterministic methods currently used for local and global sensitivity and uncertainty analysis of both large-scale computational models and indirect experimental measurements. Deterministic methods are analyzed in Part I, while statistical methods are highlighted in Part II.Part I of this review commences by highlighting the deterministic methods for computing local sensitivities, namely, the so-called Brute-Force Method (based on recalculations), the Direct Method (including the Decoupled Direct Method), the Green’s Function Method, the Forward Sensitivity Analysis Procedure (FSAP), and the Adjoint Sensitivity Analysis Procedure (ASAP). Except for the Brute-Force Method, it is emphasized that local sensitivities can be computed exactly and exhaustively only by using deterministic methods. Furthermore, it is noted that the Direct Method and the FSAP require at least as many model evaluations as there are parameters, while the ASAP requires a single model evaluation of an appropriate adjoint model whose source term is related to the response under investigation. If this adjoint model is developed simultaneously with the original model, then the adjoint model requires relatively modest additional resources to develop and implement. If, however, the adjoint model is constructed a posteriori, considerable skills may be required for its successful development and implementation. Nevertheless, the ASAP is the most efficient method to use for computing local sensitivities of large-scale systems, where the number of parameters, and parameter variations, exceeds the number of responses of interest.The Global ASAP (GASAP) is also highlighted as it appears to be the only deterministic method published thus far for performing genuinely global analysis of nonlinear systems. The GASAP uses both the forward and the adjoint sensitivity systems to explore, exhaustively and efficiently, the entire phase-space of system parameters and dependent variables in order to obtain complete information about the important global features of the physical system, namely, the critical points of the response and the bifurcation branches and/or turning points of the system’s state variables.

Statistical and experimental methods in sensitivity analysis

Factors that influence the non-uniform gas-liquid distribution in refrigerant distributors in air conditioners were studied. Gas-liquid flows in two-pass and multi-pass distributors were numerically simulated with a particle/grid hybrid method; droplets and liquid films were mainly simulated using a particle method, and gas flows were simulated using a grid method. Complex behaviors of multi-scale gas-liquid interfaces in the multi-pass distributor were simulated because droplets that were smaller than the grid size could be simulated without numerical diffusion through the gas-liquid interfaces. The effect of the connecting angle of the bend pipe was studied in the two-pass distributor, whereas the effects of the tube’s position relative the distributor inflow and the effect of gravity were investigated in the multi-pass distributor. The model was validated against multiple experimental data taken from an at-scale physical model. We found that keeping the liquid at the inlets of the multi-pass tubes was important for ensuring a uniform distribution.

<p class="zhengwen">This paper proposes a hybrid genetic algorithm method for optimizing constrained black box functions utilizing shrinking box and exterior penalty function methods (SBPGA). The constraints of the problem were incorporated in the fitness function of the genetic algorithm through the penalty function. The hybrid method used the proposed Variance-based crossover (VBC) and Arithmetic-based mutation (ABM) operators; moreover, immigration operator was also used. The box constraints constituted a hyperrectangle that kept shrinking adaptively in the light of the revealed information from the genetic algorithm about the optimal solution. The performance of the proposed algorithm was assessed using 11 problems which are used as benchmark problems in constrained optimization literatures. ANOVA along with a success rate performance index were used to analyze the model.</p>Based on the results, we believe that the proposed method is fairly robust and efficient global optimization method for Constrained Optimization Problems whether they are continuous or discrete.

Summary A sparse grid approach to orbit uncertainty propagation is presented. Efficient and accurate uncertainty propagation methods for nonlinear dynamic systems have been of enormous interest to space object tracking. Recent methods include those based on the time evolution of the probability density function, the statistical moments, the random samples, or a sum of Gaussian components. The idea of the sparse grid method for orbit uncertainty propagation is to represent the initial uncertainty by a sparse grid, propagate the sparse grid points individually through the nonlinear orbit dynamics, and compute the statistical moments from the propagated sparse grid points. The Smolyak rule is used to generate the sparse grid through linear combinations of low-level tensor products; the number of the resultant sparse grid points is polynomial in the dimension of the state. The sparse grid based uncertainty propagation may be considered a generalization of the Unscented Transformation (UT) of the well-known Unscented Kalman Filter but can achieve much higher accuracy levels than UT. Two examples of orbit propagation in different dynamic environments are used to show the efficacy of the sparse grid approach.

Development and implementation of high-tech and energy-efficient methods of feed production is important and ap¬propriate due to the fact that enterprises are not able to provide the market of feed consumers with high quality products at affordable prices. To solve this problem, an alternative technology for the production of protein green concentrate (PGC) from the cormophyte mass of high protein plants was developed. The most energy-intensive process of obtaining PGC is spray drying. At the same time the problems of energy saving, and the product quality are solved by modeling. The drying model developed in this study is based on the falling edge of evaporation, which is used in many studies of drops drying. The problem of obtaining the basic equations of heat and mass transfer during the periods of constant and decreasing drying rate was to be solved. It is also supposed that the drying takes place during the periods of constant and decreasing drying rate. Basic equations of heat and mass transfer for both periods of drying were obtained. Changing of thermophysical characteristics were determined by statistical methods in the range of PGC humidity of 10 ... 75% and a temperature of 20 ... 100%. The model is solved by finite difference method with an accuracy of modeling results of 12%. Method of finite differences is a numerical method for solving differential equations based on the replacement of derivative differences schemes and is the grid method. Identification of model parameters to experimental data obtained in the experimental spray dryer was carried out. The solution allows the mathematical model to determine the change in moisture content (DS concentration ) and drop radial temperature in the spray drying of the PGC concentrate that is necessary both to select the geometrical sizes of the dryer and the drying process parameters controlling.

The paper suggests that the only feasible method for implementing adequate nearshore wave dynamics models under conditions of extreme complexity is numerical methods with computational experiments on powerful computers. When the fundamental laws of continuum mechanics are roughly written for a finite element (FE) with an emphasis on the ensuing numerical solution, the finite element method (FEM) offers great opportunities in this regard. The FEM has the benefit of allowing for the well-approximation of coastal water areas by a collection of irregular triangles, and their boundaries can typically be curvilinear. The FEM has the advantage that its grid equations typically are independent of the type of grid and its topology, setting it apart from other grid methods. The generalized solutions to the original problems are divided into grid-like equations for the FEM, which are derived on the basis of integral relations. The fundamental integral laws are thus automatically maintained for grid equations. For the study of the coastal wave regime in a non-stationary three-dimensional formulation, grid equations of the FEM are constructed in this work. The generalized solutions to the original problems are divided into grid-like equations for the FEM, which are derived on the basis of integral relations. The fundamental integral laws are thus automatically maintained for grid equations. For the study of the coastal wave regime in a non-stationary three-dimensional formulation, grid equations of the FEM are constructed in this work.

ABSTRACTHybrid approaches combine computational methods with experimental data. The information contained in the experimental data can be leveraged to probe the structure of proteins otherwise elusive to computational methods. Compared with computational methods, the structures produced by hybrid methods exhibit some degree of experimental validation. In spite of these advantages, most hybrid methods have not yet been validated in blind tests, hampering their development. Here, we describe the first blind test of a specific cross‐link based hybrid method in CASP. This blind test was coordinated by the CASP organizers and utilized a novel, high‐density cross‐linking/mass‐spectrometry (CLMS) approach that is able to collect high‐density CLMS data in a matter of days. This experimental protocol was developed in the Rappsilber laboratory. This approach exploits the chemistry of a highly reactive, photoactivatable cross‐linker to produce an order of magnitude more cross‐links than homobifunctional cross‐linkers. The Rappsilber laboratory generated experimental CLMS data based on this protocol, submitted the data to the CASP organizers which then released this data to the CASP11 prediction groups in a separate, CLMS assisted modeling experiment. We did not observe a clear improvement of assisted models, presumably because the properties of the CLMS data—uncertainty in cross‐link identification and residue‐residue assignment, and uneven distribution over the protein—were largely unknown to the prediction groups and their approaches were not yet tailored to this kind of data. We also suggest modifications to the CLMS‐CASP experiment and discuss the importance of rigorous blind testing in the development of hybrid methods. Proteins 2016; 84(Suppl 1):152–163. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

A method for constructing a solution for some systems of first-order quasilinear partial differential equations is presented. The type of equations can either be hyperbolic or elliptic. The method is based on the application of the generalized hodograph method, which allows us to write the solution in an implicit form. There is a system of first-order linear partial differential equations that is used for commuting flows in the generalized hodograph method. We discover an analogy between the commuting flows and divided differences for the Hermite polynomial. This analogy allows us to obtain an explicit representation for commuting flows. The introduction of new (Lagrangian) variables, which are conserved on the characteristics of the original system, suggests a way to transform the solution of the Cauchy problem for first-order quasilinear partial differential equations to the solution of the Cauchy problem for ordinary differential equations. Numerical, and in some cases analytical, integration of the Cauchy problem makes it possible to construct explicit solutions of the problem on the level lines (isochrons) of the implicit solution. The method proposed is significantly different from the grid method, finite element method, finite volume method, and, in fact, is more precise. The error of the solution can arise only at the last stage in the numerical integration of the Cauchy problem for ordinary differential equations. Moreover, the method allows us to obtain multivalued solutions, in particular, to study the process of wave breaking in hyperbolic systems. Particular cases of the equations considered here describe diffusion-free approximation in a wide range of mass transport processes in multicomponent mixtures, such as electrophoresis, chromatography, centrifugation. As a simple example, the solution of the electrophoresis problem (separation multicomponent mixture to individual component) is presented.KeywordsGeneralized hodograph methodCommuting flowsDivided differenceMathematical Subject Classification (2000)35L4535L4035L65

In this paper, recursive extensions to the standard equidistant grid method are proposed whereby the gridding is adapted locally such that a prescribed distance is achieved between neighbouring points in the computed value set (template). Also presented is the Prune algorithm, which finds the outer border of a value set defined by a set of points whose nearest neighbour lies within a prescribed distance. The Prune algorithm is part of the recursive grid methods, but can also be used independently with other methods to compute value sets. As an alternative to analytical or search algorithms, a recursive grid algorithm is presented to compute Horowitz–Sidi bounds (QFT bounds, or boundaries). Isaac Horowitz's contribution to computational methods for QFT is outlined in the perspective of the presented algorithms. Copyright © 2006 John Wiley & Sons, Ltd.