Computational modeling of optical trapping of vaterite microspheres

The ability to grow microscopic spherical birefringent crystals of vaterite, a calcium carbonate mineral, has allowed the development of an optical microrheometer based on optical tweezers. However, since these crystals are birefringent, and worse, are expected to have non-uniform birefringence, computational modeling of the microrheometer is a highly challenging task. Modeling the microrheometer - and optical tweezers in general - typically requires large numbers of repeated calculations for the same trapped particle. This places strong demands on the efficiency of computational methods used. While our usual method of choice for computational modelling of optical tweezers - the T-matrix method - meets this requirement of efficiency, it is restricted to homogeneous isotropic particles. General methods that can model complex structures such as the vaterite particles, such as finite-difference time-domain (FDTD) or finite-difference frequency-domain (FDFD) methods, are inefficient. Therefore, we have developed a hybrid FDFD/T-matrix method that combines the generality of volume-discretisation methods such as FDFD with the efficiency of the T-matrix method. We have used this hybrid method to calculate optical forces and torques on model vaterite spheres in optical traps. We present and compare the results of computational modelling and experimental measurements.

Forces from highly focused laser beams: Modeling, measurement and application to refractive index measurements

The optical forces in optical tweezers can be robustly modeled over a broad range of parameters using generalsed Lorenz–Mie theory. We describe the procedure, and show how the combination of experimental measurement of properties of the trap coupled with computational modeling, can allow unknown parameters of the particle—in this case, the refractive index—to be determined.

H-ras, K-ras, and inner plasma membrane raft proteins operate in nanoclusters with differential dependence on the actin cytoskeleton

Plasma membrane compartmentalization imposes lateral segregation on membrane proteins that is important for regulating signal transduction. We use computational modeling of immunogold spatial point patterns on intact plasma membrane sheets to test different models of inner plasma membrane organization. We find compartmentalization at the nanoscale level but show that a classical raft model of preexisting stable domains into which lipid raft proteins partition is incompatible with the spatial point patterns generated by the immunogold labeling of a palmitoylated raft marker protein. Rather, approximate to 30% of the raft protein exists in cholesterol-dependent nanoclusters, with approximate to 70% distributed as monomers. The cluster/monomer ratio (number of proteins in clusters/number of proteins outside clusters) is independent of expression level. H-rasG12V and K-rasG12V proteins also operate in nanoclusters with fixed cluster/monomer ratios that are independent of expression level. Detailed calibration of the immunogold imaging protocol suggests that radii of raft and RasG12V protein nanoclusters may be as small as 11 and 6 nm, respectively, and shows that the nanoclusters contain small numbers (6.0-7.7) of proteins. Raft nanoclusters do not form if the actin cytoskeleton is disassembled. The formation of K-rasG12V but not H-rasG12V nanoclusters also is actin-dependent. K-rasG12V but not H-rasG12V signaling is abrogated by actin cytoskeleton disassembly, which shows that nanoclustering is critical for Ras function. These findings argue against stable preexisting domains on the inner plasma membrane in favor of dynamic actively regulated nanoclusters similar to those proposed for the outer plasma membrane. RasG12V nanoclusters may facilitate the assembly of essential signal transduction complexes.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

Computational properties of min/max autocorrelation factors

Minimum/maximum autocorrelation factor (MAF) is a suitable algorithm for orthogonalization of a vector random field. Orthogonalization avoids the use of multivariate geostatistics during joint stochastic modeling of geological attributes. This manuscript demonstrates in a practical way that computation of MAF is the same as discriminant analysis of the nested structures. Mathematica software is used to illustrate MAF calculations from a linear model of coregionalization (LMC) model. The limitation of two nested structures in the LMC for MAF is also discussed and linked to the effects of anisotropy and support. The analysis elucidates the matrix properties behind the approach and clarifies relationships that may be useful for model-based approaches. (C) 2003 Elsevier Science Ltd. All rights reserved.

A review of flow modeling for dense medium cyclones

A critical assessment is presented for the existing fluid flow models used for dense medium cyclones (DMCs) and hydrocyclones. As the present discussion indicates, the understanding of dense medium cyclone flow is still far from the complete. However, its similarity to the hydrocyclone provides a basis for improved understanding of fluid flow in DMCs. The complexity of fluid flow in DMCs is basically due to the existence of medium as well as the dominance of turbulent particle size and density effects on separation. Both the theoretical and experimental analysis is done with respect to two-phase motions and solid phase flow in hydrocyclones or DMCs. A detailed discussion is presented on the empirical, semiempirical, and the numerical models based upon both the vorticity-stream function approach and Navier-Stokes equations in their primitive variables and in cylindrical coordinates available in literature. The existing equations describing turbulence and multiphase flows in cyclone are also critically reviewed.

Ecological-economic modeling for biodiversity management: Potential, pitfalls, and prospects

Ecologists and economists both use models to help develop strategies for biodiversity management. The practical use of disciplinary models, however, can be limited because ecological models tend not to address the socioeconomic dimension of biodiversity management, whereas economic models tend to neglect the ecological dimension. Given these shortcomings of disciplinary models, there is a necessity to combine ecological and economic knowledge into ecological-economic models. It is insufficient if scientists work separately in their own disciplines and combine their knowledge only when it comes to formulating management recommendations. Such an approach does not capture feedback loops between the ecological and the socioeconomic systems. Furthermore, each discipline poses the management problem in its own way and comes up with its own most appropriate solution. These disciplinary solutions, however are likely to be so different that a combined solution considering aspects of both disciplines cannot be found. Preconditions for a successful model-based integration of ecology and economics include (1) an in-depth knowledge of the two disciplines, (2) the adequate identification and framing of the problem to be investigated, and (3) a common understanding between economists and ecologists of modeling and scale. To further advance ecological-economic modeling the development of common benchmarks, quality controls, and refereeing standards for ecological-economic models is desirable.

Patterns in complex systems modeling

The design, development, and use of complex systems models raises a unique class of challenges and potential pitfalls, many of which are commonly recurring problems. Over time, researchers gain experience in this form of modeling, choosing algorithms, techniques, and frameworks that improve the quality, confidence level, and speed of development of their models. This increasing collective experience of complex systems modellers is a resource that should be captured. Fields such as software engineering and architecture have benefited from the development of generic solutions to recurring problems, called patterns. Using pattern development techniques from these fields, insights from communities such as learning and information processing, data mining, bioinformatics, and agent-based modeling can be identified and captured. Collections of such 'pattern languages' would allow knowledge gained through experience to be readily accessible to less-experienced practitioners and to other domains. This paper proposes a methodology for capturing the wisdom of computational modelers by introducing example visualization patterns, and a pattern classification system for analyzing the relationship between micro and macro behaviour in complex systems models. We anticipate that a new field of complex systems patterns will provide an invaluable resource for both practicing and future generations of modelers.

Towards a Modeling Environment for Earth Systems Simulations

The developments of models in Earth Sciences, e.g. for earthquake prediction and for the simulation of mantel convection, are fare from being finalized. Therefore there is a need for a modelling environment that allows scientist to implement and test new models in an easy but flexible way. After been verified, the models should be easy to apply within its scope, typically by setting input parameters through a GUI or web services. It should be possible to link certain parameters to external data sources, such as databases and other simulation codes. Moreover, as typically large-scale meshes have to be used to achieve appropriate resolutions, the computational efficiency of the underlying numerical methods is important. Conceptional this leads to a software system with three major layers: the application layer, the mathematical layer, and the numerical algorithm layer. The latter is implemented as a C/C++ library to solve a basic, computational intensive linear problem, such as a linear partial differential equation. The mathematical layer allows the model developer to define his model and to implement high level solution algorithms (e.g. Newton-Raphson scheme, Crank-Nicholson scheme) or choose these algorithms form an algorithm library. The kernels of the model are generic, typically linear, solvers provided through the numerical algorithm layer. Finally, to provide an easy-to-use application environment, a web interface is (semi-automatically) built to edit the XML input file for the modelling code. In the talk, we will discuss the advantages and disadvantages of this concept in more details. We will also present the modelling environment escript which is a prototype implementation toward such a software system in Python (see www.python.org). Key components of escript are the Data class and the PDE class. Objects of the Data class allow generating, holding, accessing, and manipulating data, in such a way that the actual, in the particular context best, representation is transparent to the user. They are also the key to establish connections with external data sources. PDE class objects are describing (linear) partial differential equation objects to be solved by a numerical library. The current implementation of escript has been linked to the finite element code Finley to solve general linear partial differential equations. We will give a few simple examples which will illustrate the usage escript. Moreover, we show the usage of escript together with Finley for the modelling of interacting fault systems and for the simulation of mantel convection.

A Computational Framework for Institutional Agency

This paper provides a computational framework, based on Defeasible Logic, to capture some aspects of institutional agency. Our background is Kanger-Lindahl-P\"orn account of organised interaction, which describes this interaction within a multi-modal logical setting. This work focuses in particular on the notions of counts-as link and on those of attempt and of personal and direct action to realise states of affairs. We show how standard Defeasible Logic can be extended to represent these concepts: the resulting system preserves some basic properties commonly attributed to them. In addition, the framework enjoys nice computational properties, as it turns out that the extension of any theory can be computed in time linear to the size of the theory itself.

Modeling control objectives for business process compliance

Business process design is primarily driven by process improvement objectives. However, the role of control objectives stemming from regulations and standards is becoming increasingly important for businesses in light of recent events that led to some of the largest scandals in corporate history. As organizations strive to meet compliance agendas, there is an evident need to provide systematic approaches that assist in the understanding of the interplay between (often conflicting) business and control objectives during business process design. In this paper, our objective is twofold. We will firstly present a research agenda in the space of business process compliance, identifying major technical and organizational challenges. We then tackle a part of the overall problem space, which deals with the effective modeling of control objectives and subsequently their propagation onto business process models. Control objective modeling is proposed through a specialized modal logic based on normative systems theory, and the visualization of control objectives on business process models is achieved procedurally. The proposed approach is demonstrated in the context of a purchase-to-pay scenario.

Two dimensional computational fluid dynamic models for waste stabilisation ponds

Traditional waste stabilisation pond (WSP) models encounter problems predicting pond performance because they cannot account for the influence of pond features, such as inlet structure or pond geometry, on fluid hydrodynamics. In this study, two dimensional (2-D) computational fluid dynamics (CFD) models were compared to experimental residence time distributions (RTD) from literature. In one of the-three geometries simulated, the 2-D CFD model successfully predicted the experimental RTD. However, flow patterns in the other two geometries were not well described due to the difficulty of representing the three dimensional (3-D) experimental inlet in the 2-D CFD model, and the sensitivity of the model results to the assumptions used to characterise the inlet. Neither a velocity similarity nor geometric similarity approach to inlet representation in 2-D gave results correlating with experimental data. However. it was shown that 2-D CFD models were not affected by changes in values of model parameters which are difficult to predict, particularly the turbulent inlet conditions. This work suggests that 2-D CFD models cannot be used a priori to give an adequate description of the hydrodynamic patterns in WSP. (C) 1998 Elsevier Science Ltd. All rights reserved.

A computational study of shock speeds in high-performance shock tubes

This paper describes U2DE, a finite-volume code that numerically solves the Euler equations. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm in a shock tube. From the simulations, the speed of the developing shock wave was recorded and compared with other estimates. The ability of U2DE to compute shock speed was confirmed by comparing numerical results with the analytic solution for an ideal shock tube. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one-dimensional models. The shock speeds computed with the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and, thus, were closer to the experimental measurements. This indicates that multi-dimensional flow effects were partly responsible for the relatively high shock speeds measured in the experiments.

Modeling ex vivo hematopoiesis using chemical engineering metaphors

Ex vivo hematopoiesis is increasingly used for clinical applications. Models of ex vivo hematopoiesis are required to better understand the complex dynamics and to optimize hematopoietic culture processes. A general mathematical modeling framework is developed which uses traditional chemical engineering metaphors to describe the complex hematopoietic dynamics. Tanks and tubular reactors are used to describe the (pseudo-) stochastic and deterministic elements of hematopoiesis, respectively. Cells at any point in the differentiation process can belong to either an immobilized, inert phase (quiescent cells) or a mobile, active phase (cycling cells). The model describes five processes: (1) flow (differentiation), (2) autocatalytic formation (growth),(3) degradation (death), (4) phase transition from immobilized to mobile phase (quiescent to cycling transition), and (5) phase transition from mobile to immobilized phase (cycling to quiescent transition). The modeling framework is illustrated with an example concerning the effect of TGF-beta 1 on erythropoiesis. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

Reactivity of chars and carbons: New insights through molecular modeling

A new model proposed for the gasification of chars and carbons incorporates features of the turbostratic nanoscale structure that exists in such materials. The model also considers the effect of initial surface chemistry and different reactivities perpendicular to the edges and to the faces of the underlying crystallite planes comprising the turbostratic structure. It may be more realistic than earlier models based on pore or grain structure idealizations when the carbon contains large amounts of crystallite matter. Shrinkage of the carbon particles in the chemically controlled regime is also possible due to the random complete gasification of crystallitic planes. This mechanism can explain observations in the literature of particle size reduction. Based on the model predictions, both initial surface chemistry and the number of stacked planes in the crystallites strongly influence the reactivity and particle shrinkage. Its test results agree well with literature data on the air-oxidation of Spherocarb and show that it accurately predicts the variation of particle size with conversion. Model parameters are determined entirely from rate measurements.