A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions

In this paper, we study a lattice Boltzmann method for the advection-diffusion equation with Neumann boundary conditions on general boundaries. A novel mass conservative scheme is introduced for implementing such boundary con- ditions, and is analyzed both theoretically and numerically. Second order convergence is predicted by the theoretical analysis, and numerical investigations show that the convergence is at or close to the predicted rate. The nu- merical investigations include time-dependent problems and a steady-state diffusion problem for computation of effective diffusion coefficients

The impact of interfaces in laminated packaging on transport of carboxylic acids

The permeability of oleic and acetic acid through low density polyethylene (LDPE) and ethylene acrylic acid (EAA) have been measured using diffusion cells. In addition, the permeability through combinations of LDPE and EAA in the form of laminates with different numbers of layers has been determined. Oleic acid shows an almost 30 times higher permeability compared to acetic acid, which was partly explained by the adsorption of oleic acid to the film surface during the permeability experiment. In addition, the permeability is lower for both oleic and acetic acid in the laminates compared to the pure films. The decreased permeability can be explained by the presence of crystalline domains close to the interface. This is supported by SAXS data which suggests an ordering of polymer chains in the EAA film close to the interface. In summary, the results show that it is possible to create barrier materials with decreased permeability, which is interesting for example in the packaging industry. (C) 2016 Elsevier B.V. All rights reserved

Edge detection in microscopy images using curvelets

BACKGROUND: Despite significant progress in imaging technologies, the efficient detection of edges and elongated features in images of intracellular and multicellular structures acquired using light or electron microscopy is a challenging and time consuming task in many laboratories. RESULTS: We present a novel method, based on the discrete curvelet transform, to extract a directional field from the image that indicates the location and direction of the edges. This directional field is then processed using the non-maximal suppression and thresholding steps of the Canny algorithm to trace along the edges and mark them. Optionally, the edges may then be extended along the directions given by the curvelets to provide a more connected edge map. We compare our scheme to the Canny edge detector and an edge detector based on Gabor filters, and show that our scheme performs better in detecting larger, elongated structures possibly composed of several step or ridge edges. CONCLUSION: The proposed curvelet based edge detection is a novel and competitive approach for imaging problems. We expect that the methodology and the accompanying software will facilitate and improve edge detection in images available using light or electron microscopy

On boundary value problems for intracellular subdiffusion and signaling pathways, and for geometric flows

The main part of this thesis concerns mathematical models for diffusion of proteins inside cells, including reactions between the proteins. Initially, such models are applied to describe signaling pathways in yeast cells, and the properties of the model are studied, especially in relation to models that do not include diffusion. The results show that it is sometimes necessary to include diffusion in the model to capture important aspects of the biological system. The thesis also contains work on the numerical methods used to compute solutions to the reaction-diffusion equations inside domains. Specifically, the Immersed Interface Method, which allows efficient numerical solution inside arbitrary domains using uniform rectangular grids, is applied on Boolean grids, which give the same accuracy as uniform grids while using fewer grid points. The third part of the thesis also concerns models for protein diffusion inside cells, but now describing the phenomenon subdiffusion (or anomalous diffusion), which has been observed inside cells and manifests itself as a qualitatively different, and slower, diffusion behaviour of proteins. The cause of this phenomenon is the crowdedness of the interior of the cell, where other proteins and larger structures interfere with the motion of the proteins. In the thesis, a new mathematical model for anomalous diffusion in the form of a parabolic pseudo-differential equation is proposed, and a proof of existence of solutions for boundary value problems representing anomalous diffusion inside a cell is given. Experiments using Fluorescence Correlation Spectroscopy which support the model have also been performed. Finally, the thesis contains a convergence result for a computational scheme for approximation of mean curvature flows inside a domain, that is the description of the motion of surfaces which move at each point with a velocity depending on the mean curvature at that point. The scheme allows a quite general dependence on the curvature and concerns the case when the moving surface is inside a domain and intersects the domain boundary at a right angle

Analytical Solutions for the Pencil-Beam Equation with Energy Loss and Straggling

In this article, we derive equations approximating the Boltzmann equation for charged particle transport under the continuous slowing down assumption. The objective is to obtain analytical expressions that approximate the solution to the Boltzmann equation. The analytical expressions found are based on the Fermi-Eyges solution, but include correction factors to account for energy loss and spread. Numerical tests are also performed to investigate the validity of the approximations

Computational modeling of Protein based super-absorbents from waste

Hydrogels are used for various applications, for example as transporters in drug delivery, incontrol lenses, and as superabsorbent material in diapers.[1] Most synthetic produced hydrogelsare based on synthetic polymers. Even though they are efficient and cheap, they are notbiodegradable and sometimes even toxic.To produce more environmental friendly and biodegradable superabsorbent polymers (Bio-SAPs), other building blocks can be used, such as polysaccharides[2] and various proteinstructures, for example fish shells[3], collagen[4], soy protein[5] and egg protein[6]. Experimentalstudies at the University of Boras show that it is possible to produce Bio-SAPs from by-productsof ethanol production from ligno-cellulose.[2, 6, 7]2. MethodWe have studied the absorption properties of protein structures in silico as a comparison toexperimental studies. The NPT Gibbs Ensemble Monte Carlo (GEMC) simulation scheme withtwo phases is used in order to calculate the absorption capacity of the protein. Pure water wassimulated in the first GEMC-phase and the peptide in the second phase. The simulations weremade with SPC/E water model [8] and the AMBER99 atomistic force field for the peptides [9].Furthermore, mesoscopic studies with coarse grained force fields have been done.To facilitate faster computations, we used cell lists for the atom-atom interactions,configurational bias algorithm to build the water molecules and the peptide side-chains, and thecavity bias algorithm [10] for molecule insertions.Model peptides have been studied with varying secondary structure, temperature andprotonation (pH). We also plan to study how cross-links affect the absorption. One of the peptideswe study is a 20 amino acid long peptide called SSP1.[11] This peptide is designed to form afibrous structure a hydrogel, and its structure is well defined. We have also studied a peptidewhich changes secondary structure when changing the pH, and concentration.[12] This makes itpossible to compare absorption properties with respect to the secondary structure.3. ConclusionWe have simulated peptides with the Gibbs Ensemble Monte Carlo scheme in order to studythe water absorption rate dependent of structure, charge, pH and temperature. This information isuseful when developing new biodegradable superabsorbent materials

Water absorption in polymers

In this work two different examples of water absorbtion in polymers are studied by MonteCarlo simulations. Both of them are of large technical and commercial impotance. The firstexample is the water absorption in polyethylene cables where the water absorption plays acrucial role in the degradation of the cable insulation and thus should be as low as possible.The second example is bio-based superabsorbents made from denatured protein where waterabsorption capability is the prime desired property.MethodsGibbs Ensemble Monte Carlo simulations [1] were used to study the hydration of polymers.All simulations are performed with two boxes, one of which is filled with water at the start ofthe simulation, whereas the other contains polymer molecules and possible ions. The polymermolecules are not allowed to swap boxes whereas the water molecules are allowed to do sothus constituting an osmotic Gibbs ensemble [2]. For the polyethylene a connectivity-alteringalgorithm was used whereas the protein molecules were simulated using a side-chainregrowth model in addition to traditional Monte Carlo moves. For the polyethylene, theTraPPE [3] force field was used and the protein molecules, the Amber force field [4] wasused. Water was modelled using simple point charge models [5]. Electrostatic interactions aretreated using Ewald summation methods. The protein molecules were of different amino acidcompositions and in different conformations, e.g., β-turns and random coils obtained usingthe amorphous cell method[6]. Studies were made with different degrees of charging on, e.g.,lysine side chains mimicking different ionization states.ResultsThe studies of polyethylene revealed the importance of ions left from the polymerisationcatalyst for the absorbtion of water and the concomitant degradation of polyethylene cableinsulation. Also the absorption properties of the protein molecules is strongly related to thepresence of charged groups and fully charged protein molecules absorb large amounts ofwater. However, neither native nor denatured protein molecules show superabsorbingproperties (i.e. absorbing hundreds of times their own mass) as they show in experimentalstudies and the reasons for this discrepancy will be discussed.References1. A.Z. Panagiotopoulos, Mol. Phys. 61, 813 (1987).2. E. Johansson, K. Bolton, D.N. Theodorou, P. Ahlström, J. Chem. Phys., 126, 224902 (2007).3. M.G. Martin, and J.I. Siepmann, J. Phys. Chem. B, 103, 4508-4517 (1999).4. W.D. Cornell, P. Cieplak, C.I. Bayly, I.R. Gould, K.M. Merz Jr, D.M. Ferguson, D.C. Spellmeyer, T. Fox,J.W. Caldwell, P.A. Kollman (1995). J. Am. Chem. Soc. 117, 5179–5197.5. H. J. C. Berendsen, J. P. M. Postma and W. F. van Gunsteren, in Intermolecular Forces, B. Pullman, ed.(Reidel, Dordrecht, 1981) p. 331; H. J. C. Berendsen, J. R. Grigera and T. P. Straatsma, J. Phys. Chem. 91,6269 (1987).6. D.N. Theodorou, U.W. Suter, Macromolecules, 18, 1467 (1985)

An overview of the transport of liquid molecules through structured polymer films, barriers and composites – Experiments correlated to structure-based simulations

Films engineered to control the transport of liquids are widely used through society. Examples include barriers in packaging, wound care products, and controlled release coatings in pharmaceutics. When observed at the macroscopic scale such films commonly appear homogeneous, however, a closer look reveals a complex nano- and microstructure that together with the chemical properties of the different domains control the transport properties. In this review we compare and discuss macroscopic transport properties, measured using the straightforward, yet highly powerful technique “modified Ussing chambers”, also denoted side-by-side diffusion cells, for a wide range of structured polymer films and composites. We also discuss and compare the macroscopic observations and conclusions on materials properties with that of lattice Boltzmann simulations of transport properties based on underlying material structure and chemistry. The survey of the field: (i) highlights the use and power of modified Ussing Chambers for determining liquid transport properties of polymer films, (ii) demonstrates the predictability in both directions between macroscopic observations of transport using modified Ussing chambers and structure-based simulations, and (iii) provides experimental and theoretical insights regarding the transport-determining properties of structured polymer films and composites

Interactions between the volume effects of hydroxyethyl starch 130/0.4 and Ringer´s acetate

INTRODUCTION: The turnover of Ringer´s solutions is greatly dependent on the physiological situation, such as the presence of dehydration or anaesthesia. The present study evaluates whether the kinetics is affected by previous infusion of colloid fluid. METHODS: Ten male volunteers with a mean age of 22 years underwent three infusion experiments, on separate days and in random order. The experiments included 10 mL/kg of 6% hydroxyethyl starch 130/0.4 (Voluven™), 20 mL/kg of Ringer's acetate, and a combination of both, where Ringer´s was administered 75 minutes after the starch infusion ended. The kinetics of the volume expansion was analysed by non-linear least- squares regression, based on urinary excretion and serial measurement of blood haemoglobin concentration for up to 420 minutes. RESULTS: The mean volume of distribution of the starch was 3.12 L which agreed well with the plasma volume (3.14 L) estimated by anthropometry. The volume expansion following the infusion of starch showed monoexponential elimination kinetics with a half-life of two hours. Two interaction effects were found when Ringer´s acetate was infused after the starch. First, there was a higher tendency for Ringer´s acetate to distribute to a peripheral compartment at the expense of the plasma volume expansion. The translocated amount of Ringer´s was 70% higher when HES had been infused earlier. Second, the elimination half-life of Ringer´s acetate was five times longer when administered after the starch (88 versus 497 minutes, P <0.02). CONCLUSIONS: Starch promoted peripheral accumulation of the later infused Ringer´s acetate solution and markedly prolonged the elimination half-life