Fast algorithms for Brownian dynamics simulation with hydrodynamic interactions

In the Brownian dynamics simulation with hydrodynamic interactions, one needs to generate the total displacement vectors of Brownian particles consisting of two parts: a deterministic part which is proportional to the product of the Rotne-Prager-Yamakawa (RPY) tensor D [1, 2] and the given external forces F; and a hydrodynamically correlated random part whose covariance is proportional to the RPY tensor. To be more precise, one needs to calculate Du for a given vector u and compute √Dv for a normally distributed random vector v. For an arbitrary N-particle configuration, D is a 3N x 3N matrix and u, v are vectors of length 3N. Thus, classical algorithms require O(N2) operations for computing Du and O(N3) operations for computing √Dv, which are prohibitively expensive and render large scale simulations impossible since one needs to carry out these calculations many times in a Brownian dynamics simulation. In this dissertation, we first present two fast multipole methods (FMM) for computing Du. The first FMM is a simple application of the kernel independent FMM (KIFMM) developed by Ying, Biros, and Zorin [3], which requires 9 scalar FMM calls. The second FMM, similar to the FMM for Stokeslet developed by Tornberg and Greengard [4], decomposes the RPY tensor into harmonic potentials and its derivatives, and thus requires only four harmonic FMM calls. Both FMMs reduce the computational cost of Du from O(N2) to O(N) for an arbitrary N-particle configuration. We then discuss several methods of computing √Dv, which are all based on the Krylov subspace approximations, that is, replacing √Dv by p(D)v with p(D) a low degree polynomial in D. We first show rigorously that the popular Chebyshev spectral approximation method (see, for example, [5, 6]) requires √κ log 1/ε terms for a desired precision E, where K is the condition number of the RPY tensor D. In the Chebyshev spectral approximation method, one also needs to estimate the extreme eigenvalues of D. We have considered several methods: the classical Lanczos method, the Chebyshev-Davidson method, and the safeguarded Lanczos method proposed by Zhou and Li [7]. Our numerical experiments indicate that K is usually very small when the particles are distributed uniformly with low density, and that the safeguarded Lanczos method is most effective for our cases with very little additional computational cost. Thus, when combined with the FMMs we described earlier, the Chebyshev approximation method with safeguarded Lanczos method as eigenvalue estimators essentially reduces the cost of computing √Dv from O(N3) to O(N) for most practical particle configurations. Finally, we propose to combine the so-called spectral Lanczos decomposition method (SLDM) (see, for example, [8]) and the FMMs to compute √Dv. Our numerical experiments show that the SLDM is generally more efficient than the popular Chebyshev spectral approximation method. The fast algorithms developed in this dissertation will be useful for the study of diffusion limited reactions, polymer dynamics, protein folding, and particle coagulation as it enables large scale Brownian dynamics simulations. Moreover, the algorithms can be extended to speed up the computation involving the matrix square root for many other matrices, which has potential applications in areas such as statistical analysis with certain spatial correlations and model reduction in dynamic control theory

Physically Based Mesh-free Deformation Framework and Techniques for Computer Graphics

In this thesis, we introduce a mesh-free deformation framework. Four different applications are presented based on it. Among them, a technique of mesh-free deformations and a technique ofreusable deformations are to model the deformations in two different ways, while the hyper-twist and the force mapping are applied to other graphic purposes related to deformations.Existing physicanv-based deformation techniques, such as the finite element method and the massspring systems, require the deformed object to be properly meshed. The proposed mesh-free deformations are constructed with unconnected points and no mesh is required in the computation.This process strict~1' follows the principles of classic mechanics and a deformation is defined as a combination of fundamental solutions. Because no mesh is involved, deforming a complex shape is as straightforw'ard as deforming a simple one and the trade-off between efficiency and accuracy is easy to achieve by redistributing the points concerned. Experiments show that this method is fast and offers similar accuracy to the finite element methods.Reducing both computational cost and amount of unnecessary human intervention remains a pressing issue in the animation production. To provide a faster and more user-friendly tool, we extend the above mesh-free deformations technique and develop another technique. A key feature is thereusability of deformations. Existing deformations can be simply extracted and reapplied physicallyusing the 'copy' and 'paste' operations. it relieves the modelling efforts. In this way, the visual realism is combined with the modelling efficiency and the user-friendliness for animators.The mesh-free deformation framework is capable to describe the deformations in an infinite body which is in line with the distortion of a 3D space. The twist of an infinite body, hyper-twist, is investigated to show how a 3D space and the object embedded can be radically deformed. Abstract shapes with aesthetic effects can be created in this process as well as their animations. Following the idea of mesh-free computation, we apply forces on a surface to create the fine details of the surface. A force map records the applied forces and their distributions. We call this technique force mapping, which can be used for surface modeling, compression, reconstruction and editing. As an alternative to displacement mapping, force mapping benefits from the fact that the physical property, force, is integrated into a geometric surface explicitly

Application of Sensitive API-Based Indicators and Numerical Simulation Tools to Advance Hot-Melt Extrusion Process Understanding

This dissertation explored the use of active pharmaceutical ingredients (APIs) as indicator substances as well as numerical process simulation to enhance process understanding of hot-melt extrusion (HME) in the pharmaceutical field. Two APIs, torasemide and telmisartan, were identified which, when combined with the appropriate matrix and processed at appropriate conditions, behaved like highly sensitive indicator substances. With these indicator substances, two relevant critical quality attributes (CQAs) for the HME process, degradation and residual crystallinity, enabled analysis of process performance, evaluation of scaling and were correlated with both empirical and simulated process performance. Customized formulations were developed for both APIs in order to target the relevant process and CQA design spaces. Formulations were developed to minimize the impact of the API dissolution into the polymeric matrix on melt viscosity or thermal properties by minimizing the difference between the Tg of the API and that of the matrix. Both APIs were processed below their single-component melting points as well as below their solubility temperatures in the matrix system. By doing so, the APIs were forced to dissolve into the surrounding matrix rather than first melt and then disperse and distribute. As a result, for the given drug loading, dissolution was never complete and residually crystalline API material was always present after extrusion. In the case of torasemide, the amount of residually crystalline API material present was correlated to both melt temperature and residence time. For the telmisartan formulations, it was highly correlated with melt temperature. Due to a dissolve-then-degrade mechanism, torasemide degradation was dependent on the amount of API dissolved in the Soluplus®-PEG 1500 matrix. Numerical simulation with the commercially available software Ludovic® enabled correlation of the CQAs with simulation-derived results. For torasemide, the empirical relationship between the sum of degradants and the residual crystallinity was found to correlate with the simulated integral of the time that the material spent above the dissolution temperature of torasemide in the polymeric matrix. For telmisartan, in the samples which exhibited almost no residual crystallinity, the simulated maximum melt temperature was equivalent to the solubility temperature of the API in the copovidone-based matrix, irrespective of processing conditions or the plasticizing polysorbate 80 content. The telmisartan system and process simulation were further used to study scaling of the HME process. Simulation was utilized to select the most processable formulation as well as to identify processing conditions which would yield a scaled quasi-adiabatic process while residual crystallinity was used to assess the success of scaling

A Molecular-Level View of the Physical Stability of Amorphous Solid Dispersions

Many pharmaceutical compounds being developed in recent years are poorly soluble in water. This has led to insufficient oral bioavailability of many compounds in vitro. The amorphous formulation is one of the promising techniques to increase the oral bioavailability of these poorly water-soluble compounds. However, an amorphous drug substance is inherently unstable because it is a high energy form. In order to increase the physical stability, the amorphous drug is often formulated with a suitable polymer to form an amorphous solid dispersion. Previous research has suggested that the formation of an intimately mixed drug-polymer mixture contributes to the stabilization of the amorphous drug compound. The goal of this research is to better understand the role of miscibility, molecular interactions and mobility on the physical stability of amorphous solid dispersions. Methods were developed to detect different degrees of miscibility on nanometer scale and to quantify the extent of hydrogen-bonding interactions between the drug and the polymer. Miscibility, hydrogen-bonding interactions and molecular mobility were correlated with physical stability during a six-month period using three model systems. Overall, this research provides molecular-level insights into many factors that govern the physical stability of amorphous solid dispersions which can lead to a more effective design of stable amorphous formulations

Physically based mesh-free deformation framework and techniques for computer graphics

In this thesis, we introduce a mesh-free deformation framework. Four different applications are presented based on it. Among them, a technique of mesh-free deformations and a technique ofreusable deformations are to model the deformations in two different ways, while the hyper-twist and the force mapping are applied to other graphic purposes related to deformations.Existing physicanv-based deformation techniques, such as the finite element method and the massspring systems, require the deformed object to be properly meshed. The proposed mesh-free deformations are constructed with unconnected points and no mesh is required in the computation.This process strict~1' follows the principles of classic mechanics and a deformation is defined as a combination of fundamental solutions. Because no mesh is involved, deforming a complex shape is as straightforw'ard as deforming a simple one and the trade-off between efficiency and accuracy is easy to achieve by redistributing the points concerned. Experiments show that this method is fast and offers similar accuracy to the finite element methods.Reducing both computational cost and amount of unnecessary human intervention remains a pressing issue in the animation production. To provide a faster and more user-friendly tool, we extend the above mesh-free deformations technique and develop another technique. A key feature is thereusability of deformations. Existing deformations can be simply extracted and reapplied physicallyusing the 'copy' and 'paste' operations. it relieves the modelling efforts. In this way, the visual realism is combined with the modelling efficiency and the user-friendliness for animators.The mesh-free deformation framework is capable to describe the deformations in an infinite body which is in line with the distortion of a 3D space. The twist of an infinite body, hyper-twist, is investigated to show how a 3D space and the object embedded can be radically deformed. Abstract shapes with aesthetic effects can be created in this process as well as their animations. Following the idea of mesh-free computation, we apply forces on a surface to create the fine details of the surface. A force map records the applied forces and their distributions. We call this technique force mapping, which can be used for surface modeling, compression, reconstruction and editing. As an alternative to displacement mapping, force mapping benefits from the fact that the physical property, force, is integrated into a geometric surface explicitly.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Transient behaviour of a 3-phase slip-ring induction motor with external impedance in the rotor circuit

An investigation is described into the effect of an external rotor circuit impedance on both the steady state and the transient behaviour of a 3-phase slip-ring induction motor. The external impedance took the form of a 3-phase resistor, capacitor, or saturistor and attention is directed towards the differences in the current, torques and speeds of the motor produced by the extra circuit components. [Continues.

Image and Evidence: The Study of Attention through the Combined Lenses of Neuroscience and Art

: Levy, EK 2012, ‘An artistic exploration of inattention blindness’, in Frontiers Hum Neurosci, vol. 5, ISSN=1662-5161.Full version unavailable due to 3rd party copyright restrictions.This study proposed that new insights about attention, including its phenomenon and pathology, would be provided by combining perspectives of the neurobiological discourse about attention with analyses of artworks that exploit the constraints of the attentional system. To advance the central argument that art offers a training ground for the attentional system, a wide range of contemporary art was analysed in light of specific tasks invoked. The kinds of cognitive tasks these works initiate with respect to the attentional system have been particularly critical to this research. Attention was explored within the context of transdisciplinary art practices, varied circumstances of viewing, new neuroscientific findings, and new approaches towards learning. Research for this dissertation required practical investigations in a gallery setting, and this original work was contextualised and correlated with pertinent neuroscientific approaches. It was also concluded that art can enhance public awareness of attention disorders and assist the public in discriminating between medical and social factors through questioning how norms of behaviour are defined and measured. This territory was examined through the comparative analysis of several diagnostic tests for attention deficit hyperactivity disorder (ADHD), through the adaptation of a methodology from economics involving patent citation in order to show market incentives, and through examples of data visualisation. The construction of an installation and collaborative animation allowed participants to experience first-hand the constraints on the attentional system, provoking awareness of our own “normal” physiological limitations. The embodied knowledge of images, emotion, and social context that are deeply embedded in art practices appeared to be capable of supplementing neuroscience’s understanding of attention and its disorders

Estudo da distorção harmônica em redes de distribuição de baixa tensão com sistemas fotovoltaicos e veículos elétricos

Estima-se um crescimento significativo na integração de fontes alternativas de energia e no aumento de cargas não lineares nas redes de distribuição de baixa tensão como, por exemplo, a geração fotovoltaica e a instalação de carregadores de veículos elétricos. Tais equipamentos necessitam de conversores eletrônicos para viabilizar sua conexão na rede e causam, portanto, distorção harmônica. Este trabalho propõe analisar a distorção harmônica causada por esses elementos por meio de simulações diárias, utilizando o OpenDSS, considerando cenários nos quais os equipamentos operam em condições distintas. É implementada uma metodologia de simulações que calcula os índices de distorção harmônica ao longo das 24h do dia para identificar os intervalos que apresentam variação e o que a motiva. De forma complementar, são calculados os índices regulamentados pelo PRODIST, que define os limites que não podem ser ultrapassados em mais de 5% das medições em uma semana. Constata-se que um alto nível de penetração de sistemas fotovoltaicos e carregadores de veículos elétricos causaria problemas de subtensão atingindo valores na faixa de tensão precária antes de serem verificados altos níveis de distorção harmônica. O deslocamento da recarga de veículos elétricos do horário de ponta para um período com menor carga apresenta melhoras tanto na tensão como nos índices de distorção. Nos cenários simulados não foram verificadas elevações alarmantes de distorção harmônica; portanto, esse indicador não seria um fator limitante na instalação dos equipamentos. Verifica-se, também, que a distorção harmônica depende fortemente dos ângulos de fase das componentes harmônicas individuais, pois isso define como os diferentes equipamentos irão interagir e isso pode aumentar ou reduzir a distorção total de tensão.Significant growth is expected for the integration of alternative sources of energy and nonlinear loads in low voltage distribution networks, e.g. photovoltaic generation and the installation of electric vehicle chargers. Such equipment requires electronic converters to enable their connection to the network, thus cause harmonic distortion. This paper proposes to analyse the harmonic distortion caused by these elements through daily simulations, using OpenDSS, in scenarios with the equipment operating under different conditions. A simulation methodology is implemented for calculating the harmonic distortion indices over 24h periods to identify daily time intervals that present variation and what is it driven by. In addition, the indices regulated by PRODIST are calculated. PRODIST defines the limits that cannot be exceeded in more than 5 % of the measurements made in one week. It is found that a significant insertion of photovoltaic systems and electric vehicle chargers would cause undervoltage problems before high levels of harmonic distortion are reached. Shifting the recharge of electric vehicles from the end of the day to a period with lower demand improves both voltage levels and distortion rates. In simulated scenarios no alarming elevations of harmonic distortion were observed; therefore, this indicator would not be a limiting factor in equipment installation. It is also verified that the harmonic flow strongly depends on the phase angles of the individual harmonic components, showing how the different equipment will interact, eventually increasing or reducing the voltage total harmonic distortion

The Impact of Mineral Dust Aerosol Particles on Cloud Formation

This investigation examines the role of selected mineral dust samples in heterogeneous ice nucleation. The experiments were done by seeding artificial clouds in the large aerosol chamber AIDA at temperatures between 273 and 190 K. Five different dust samples were collected for this purpose: Two airborne mineral dust samples (denoted Cairo dust 1:CD1 and Cairo dust 2: CD2) were collected during dust storm events at a location about 50 km North of Cairo city. The source regions of these dust samples were identified by altitude-resolved back-trajectory calculations using the FLEXTRA trajectory model and comparing with aerosol index data from the EP/TOMS, MODIS/Terra, and MODIS/Aqua satellite images. The third dust sample (denoted Egyptian Sahara mineral dust: SD) was collected from a hole of 1.5 m depth in the desert 70 km northeast of Cairo city. The fourth dust sample (denoted Asian dust sample: AD) was collected from the ground in the easterly part of the Takla Makan desert in northwest China. The fifth dust sample (denoted Arizona test dust sample: ATD) consists of crushed Arizona desert sand and was purchased from Powder technology Inc. (Minnesota, USA). It is used as a reference material for comparison. All dust samples were analysed on their elemental composition by X-ray fluorescence and on their water soluble ion contents by ion chromatography. The reported data reveals that the fraction of gypsum is the largest in CD1 and CD2, followed by SD. Furthermore, it could be shown that the airborne dust samples (CD1 & CD2) had accumulated soluble coatings during their transportation by interaction with air pollutants. In addition to the surface-chemical analysis, the mineral dust seed particles were collected during the experiments and analysed on their surface morphology by Scanning Electron Microscopy (SEM). It was found that spherical particles are slightly more efficient ice nuclei than non-spherical particles. The size distribution of the ice particles was measured by an optical particle counter (OPC, PCS-2000). The output of this instrument was successfully corrected for the evaporation of ice crystals or water droplets in the sampling line. The corrected count median diameters show a good agreement with the values determined from the optical particle counter Welas and FTIR measurements. The measured ice water content is in good agreement between the OPC-based and FTIR-retrieved. Generally, the observed ice water contents compare well with the results from upper tropospheric measurements that were obtained during the INCA campaign (Gayet et al., 2006), although both sets of measurements are totally different. In the temperature range between 273 and 240 K where mixed clouds form, all dust particles formed liquid water clouds for temperature between 273 and 255 K; very few ice crystals were formed either by condensation or immersion freezing. Between 255 and 240 K, SD and AD formed liquid water droplets, whereas ATD particles are already efficient ice nuclei by deposition freezing. The airborne Sahara dust samples CD1 and CD2 are also very efficient ice nuclei even in comparison with ATD in the temperature range from 255 to 240 K. Coating ATD particles with sulphuric acid had no significant influence on their ice nucleating ability. In the temperature range between 240 and 200 K where cirrus clouds form, ATD, SD, and AD show a reduction of the critical ice saturation ratio with decreasing temperature from 1.25 for ATD and 1.35 for SD and AD at 240 K to about 1.1 and less at the lower temperature of the cirrus cloud regime. This is in agreement with critical saturation ratios reported by Bailey and Hallett 2002 and the parameterisation line of cirrus cloud formation by Heymsfield and Miloshevich 1995. Coating ATD with sulphuric acid reduces its ice nucleation efficiency to values predicted for the freezing of haze particles after Koop et al., 2000. Coated SD, on the other hand, shows also reduced nucleation efficiencies, but the effect becomes less important at the lower temperatures. Finally, the measurements show that the nucleation rates for deposition freezing in the cirrus cloud regime increase as function of the saturation ratio, but decrease towards lower temperatures. The data reported by Archuleta et al. 2005 is in good agreement with our measurement. The results from this work can be used to improve the description of cirrus cloud formation in microphysical cloud models, but there still remain uncertainties about the ice formation in the mixed cloud regime