Anisotropic Interpolation on Graphs: The Combinatorial Dirichlet Problem

The combinatorial Dirichlet problem is formulated, and an algorithm for solving it is presented. This provides an effective method for interpolating missing data on weighted graphs of arbitrary connectivity. Image processing examples are shown, and the relation to anistropic diffusion is discussed.

Moisture Effects on the Reliability of Anisotropic Conductive Film Interconnection for Flip Chip on Flex Applications

Anisotropic conductive film (ACF) which consists of an adhesive epoxy matrix and randomly distributed conductive particles are widely used as the connection material for electronic devices with high I/O counts. However, for the semiconductor industry the reliability of the ACF is still a major concern due to a lack of experimental reliability data. This paper reports the investigations into the moisture-induced failures in Flip-Chip-on-Flex interconnections with Anisotropic Conductive Films (ACFs). Both experimental and modeling methods were applied. In the experiments, the contact resistance was used as a quality indicator and was measured continuously during the accelerated tests (autoclave tests). The temperature, relative humidity and the pressure were set at 121°C, 100%RH, and 2atm respectively. The contact resistance of the ACF joints increased during the tests and nearly 25% of the joints were found to be open after 168 hours’ testing time. Visible conduction gaps between the adhesive and substrate pads were observed. Cracks at the adhesive/flex interface were also found. For a better understanding of the experimental results, 3-D Finite Element (FE) models were built and a macro-micro modeling method was used to determine the moisture diffusion and moisture-induced stresses inside the ACF joints. Modeling results are consistent with the findings in the experimental work.

Experimental and Modelling Analysis on the Moisture Induced Failures in Flip Chip on Flex Interconnections with Anisotropic Conductive Film

This paper reports the investigations into the moisture induced failures in flip-chip-on-flex interconnections with anisotropic conductive films (ACF). Both experimental and modeling methods were applied. In the experiments, the contact resistance was used as a quality indicator and was measured continuously during the accelerated tests (autoclave tests). The temperature, relative humidity and the pressure were set at 121°C, 100%RH, 1atm respectively. The contact resistance of the ACF joints increased during the tests and nearly 25% of the joints were found to be open after 168 hours' testing time. Visible conduction gaps between the adhesive and substrate pads were observed. Cracks at the adhesive/flex interface were also found. It is believed that the swelling effect of the adhesive and the water penetration along the adhesive/flex interface are the main causes of this contact degradation. Another finding from the experimental work was that the ACF interconnections that had undergone the reflow treatment were more sensitive to the moisture and showed worse reliability during the tests. For a better understanding of the experimental results, 3D finite element (FE) models were built and a macro-micro modeling method was used to determine the moisture diffusion and moisture-induced stresses inside the ACF joints. Modeling results are consistent with the findings in the experimental work.

Anisotropic dispersion, space competition, and the slowdown of the Neolithic transition

The front speed of the Neolithic (farmer) spread in Europe decreased as it reached Northern latitudes, where the Mesolithic (huntergatherer) population density was higher. Here, we describe a reaction diffusion model with (i) an anisotropic dispersion kernel depending on the Mesolithic population density gradient and (ii) a modified population growth equation. Both effects are related to the space available for the Neolithic population. The model is able to explain the slowdown of the Neolithic front as observed from archaeological data

Modal analysis of anisotropic diffused-channel waveguide by a scalar finite element method

A procedure to model optical diffused-channel waveguides is presented in this work. The dielectric waveguides present anisotropic refractive indexes which are calculated from the proton concentration. The proton concentration inside the channel is calculated by the anisotropic 2D-linear diffusion equation and converted to the refractive indexes using mathematical relations obtained from experimental data, the arbitrary refractive index profile is modeled by a. nodal expansion in the base functions. The TE and TM-like propagation properties (effective index) and the electromagnetic fields for well-annealed proton-exchanged (APE) LiNbO3 waveguides are computed by the finite element method.

Anisotropic Brownian motion in ordered phases of DNA fragments

Using Fluorescence Recovery After Photobleaching, we investigate the Brownian motion of DNA rod-like fragments in two distinct anisotropic phases with a local nematic symmetry. The height of the measurement volume ensures the averaging of the anisotropy of the in-plane diffusive motion parallel or perpendicular to the local nematic director in aligned domains. Still, as shown in using a model specifically designed to handle such a situation and predicting a non-Gaussian shape for the bleached spot as fluorescence recovery proceeds, the two distinct diffusion coefficients of the DNA particles can be retrieved from data analysis. In the first system investigated (a ternary DNA-lipid lamellar complex), the magnitude and anisotropy of the diffusion coefficient of the DNA fragments confined by the lipid bilayers are obtained for the first time. In the second, binary DNA-solvent system, the magnitude of the diffusion coefficient is found to decrease markedly as DNA concentration is increased from isotropic to cholesteric phase. In addition, the diffusion coefficient anisotropy measured within cholesteric domains in the phase coexistence region increases with concentration, and eventually reaches a high value in the cholesteric phase.

Rotational diffusion membrane and fluorescence anisotropy.

Structural properties of model membranes, such as lipid vesicles, may be investigated through the addition of fluorescent probes. After incorporation, the fluorescent molecules are excited with linearly polarized light and the fluorescence emission is depolarized due to translational as well as rotational diffusion during the lifetime of the excited state. The monitoring of emitted light is undertaken through the technique of time-resolved fluorescence: the intensity of the emitted light informs on fluorescence decay times, and the decay of the components of the emitted light yield rotational correlation times which inform on the fluidity of the medium. The fluorescent molecule DPH, of uniaxial symmetry, is rather hydrophobic and has collinear transition and emission moments. It has been used frequently as a probe for the monitoring of the fluidity of the lipid bilayer along the phase transition of the chains. The interpretation of experimental data requires models for localization of fluorescent molecules as well as for possible restrictions on their movement. In this study, we develop calculations for two models for uniaxial diffusion of fluorescent molecules, such as DPH, suggested in several articles in the literature. A zeroth order test model consists of a free randomly rotating dipole in a homogeneous solution, and serves as the basis for the study of the diffusion of models in anisotropic media. In the second model, we consider random rotations of emitting dipoles distributed within cones with their axes perpendicular to the vesicle spherical geometry. In the third model, the dipole rotates in the plane of the of bilayer spherical geometry, within a movement that might occur between the monolayers forming the bilayer. For each of the models analysed, two methods are used by us in order to analyse the rotational diffusion: (I) solution of the corresponding rotational diffusion equation for a single molecule, taking into account the boundary conditions imposed by the models, for the probability of the fluorescent molecule to be found with a given configuration at time t. Considering the distribution of molecules in the geometry proposed, we obtain the analytical expression for the fluorescence anisotropy, except for the cone geometry, for which the solution is obtained numerically; (II) numerical simulations of a restricted rotational random walk in the two geometries corresponding to the two models. The latter method may be very useful in the cases of low-symmetry geometries or of composed geometries.

Modeling and simulations of some anisotropic soft-matter systems: from biaxial to chiral materials

We have modeled various soft-matter systems with molecular dynamics (MD) simulations. The first topic concerns liquid crystal (LC) biaxial nematic (Nb) phases, that can be possibly used in fast displays. We have investigated the phase organization of biaxial Gay-Berne (GB) mesogens, considering the effects of the orientation, strength and position of a molecular dipole. We have observed that for systems with a central dipole, nematic biaxial phases disappear when increasing dipole strength, while for systems characterized by an offset dipole, the Nb phase is stabilized at very low temperatures. In a second project, in view of their increasing importance as nanomaterials in LC phases, we are developing a DNA coarse-grained (CG) model, in which sugar and phosphate groups are represented with Lennard-Jones spheres, while bases with GB ellipsoids. We have obtained shape, position and orientation parameters for each bead, to best reproduce the atomistic structure of a B-DNA helix. Starting from atomistic simulations results, we have completed a first parametrization of the force field terms, accounting for bonded (bonds, angles and dihedrals) and non-bonded interactions (H-bond and stacking). We are currently validating the model, by investigating stability and melting temperature of various sequences. Finally, in a third project, we aim to explain the mechanism of enantiomeric discrimination due to the presence of a chiral helix of poly(gamma-benzyl L-glutamate) (PBLG), in solution of dimethylformamide (DMF), interacting with chiral or pro-chiral molecules (in our case heptyl butyrate, HEP), after tuning properly an atomistic force field (AMBER). We have observed that DMF and HEP molecules solvate uniformly the PBLG helix, but the pro-chiral solute is on average found closer to the helix with respect to the DMF. The solvent presents a faster isotropic diffusion, twice as HEP, also indicating a stronger interaction of the solute with the helix.

Proton diffusion tensor spectroscopy of metabolites in human muscle in vivo

PURPOSE To study the apparent diffusivity and its directionality for metabolites of skeletal muscle in humans in vivo by (1) H magnetic resonance spectroscopy. METHODS The diffusion tensors were determined on a 3 Tesla MR system using optimized acquisition and processing methods including an adapted STEAM sequence with orientation-dependent diffusion weighting, pulse-triggering with individually adapted delays, eddy-current correction schemes, median filtering, and simultaneous prior-knowledge fitting of all related spectra. RESULTS The average apparent diffusivities, as well as the fractional anisotropies of taurine (ADCav  = 0.74 × 10(-3) s/mm(2) , FA = 0.46), creatine (ADCav  = 0.41 × 10(-3)  s/mm(2) , FA = 0.33), trimethylammonium compounds (ADCav  = 0.48 × 10(-3)  s/mm(2) , FA = 0.34), carnosine (ADCav  = 0.46 × 10(-3)  s/mm(2) , FA = 0.47), and water (ADCav  = 1.5 × 10(-3)  s/mm(2) , FA = 0.36) were estimated. The diffusivities of most metabolites and water were significantly different from each other. Diffusion was found to be anisotropic and the diffusion tensors showed tensor correlation coefficients close to 1 and were hence found to be essentially coaligned. The magnitudes of apparent metabolite diffusivities were largely ordered according to molecular weight, with taurine as the smallest molecule diffusing fastest, both along and across the fiber direction. CONCLUSION Diffusivities, directional dependence of diffusion and fractional anisotropies of (1) H MRS-visible muscle metabolites were presented. It was shown that metabolites share diffusion directionality with water and have similar fractional anisotropies, hinting at similar diffusion barriers. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.

TILTED COLUMNAR THIN FILM COATINGS WITH ANISOTROPIC LIGHT SCATTERING PROPERTIES FOR SOLAR ENERGY APPLICATIONS

The main goal of this thesis is to show the versatility of glancing angle deposition (GLAD) thin films in applications. This research is first focused on studying the effect of select deposition variables in GLAD thin films and secondly, to demonstrate the flexibility of GLAD films to be incorporated in two different applications: (1) as a reflective coating in low-level concentration photovoltaic systems, and (2) as an anode structure in dye-sensitized solar cells (DSSC). A particular type of microstructure composed of tilted micro-columns of titanium is fabricated by GLAD. The microstructures form elongated and fan-like tilted micro-columns that demonstrate anisotropic scattering. The thin films texture changes from fiber texture to tilted fiber texture by increasing the vapor incidence angle. At very large deposition angles, biaxial texture forms. The morphology of the thin films deposited under extreme shadowing condition and at high temperature (below recrystallization zone) shows a porous and inclined micro-columnar morphology, resulting from the dominance of shadowing over adatom surface diffusion. The anisotropic scattering behavior of the tilted Ti thin film coatings is quantified by bidirectional reflectance distribution function (BRDF) measurements and is found to be consistent with reflectance from the microstructure acting as an array of inclined micro-mirrors that redirect the incident light in a non-specular reflection. A silver-coating of the surface of the tilted-Ti micro-columns is performed to enhance the total reflectance of the Ti-thin films while keeping the anisotropic scattering behavior. By using such coating is as a booster reflector in a laboratory-scale low-level concentration photovoltaic system, the short-circuit current of the reference silicon solar cell by 25%. Finally, based on the scattering properties of the tilted microcolumnar microstructure, its scattering effect is studied as a part of titanium dioxide microstructure for the anode in DSSCs. GLAD-fabricated TiO2 microstructures for the anode in a DSSC, consisting of vertical micro-columns, and combined vertical topped with tilted micro-columns are compared. The solar cell with the two-part microstructure shows the highest monochromatic incident photon to current efficiency with 20% improvement compared to the vertical microstructure, and the efficiency of the cell increases from 1.5% to 2% due to employing the scattering layer.

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement. The theoretical results are illustrated by a series of numerical experiments.

A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems

We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal-oriented a posteriori error indicators are presented. The examples presented clearly demonstrate the capabilities and the benefits of combining our pre-processing mesh movement algorithm with both uniform, as well as, adaptive isotropic and anisotropic mesh refinement.

Synthesis of Anisotropic Magnetic Nanoobjects Designed for Locomotion in External Magnetic Fields

The subject of the present work is the synthesis of novel nanoscale objects, designed for self-propulsion under external actuation. The synthesized objects present asymmetric hybrid particles, consisting of a magnetic core and polymer flagella and their hydrodynamic properties under the actuation by external magnetic fields are investigated. The single-domain ferromagnetic cobalt ferrite nanoparticles are prepared by thermal decomposition of a mixture of metalorganic complexes based on iron (III) cobalt (II) in non-polar solvents. Further modification of the particles includes the growth of the silver particle on the surface of the cobalt ferrite particle to form a dumbbell-shaped heterodimer. Different possible mechanisms of dumbbell formation are discussed. A polyelectrolyte tail with ability to adjust the persistence length of the polymer, and thus the stiffness of the tail, by variation of pH is attached to the particles. A polymer tail consisting of a polyacrylic acid chain is synthesized by hydrolysis of poly(tert-butyl acrylate) obtained by atom transfer radical polymerization (ATRP). A functional thiol end-group enables selective attachment of the tail to the silver part of the dumbbell, resulting in an asymmetric functionalization of the dumbbells. The calculations on the propulsion force and the sperm number for the resulting particles reveal a theoretical possibility for the propelled motion. Under the actuation of the particles with flagella by alternating magnetic field an increase in the diffusion coefficient compared to non-actuated or non-functionalized particles is observed. Further development of such systems for application as nanomotors or in drug delivery is promising.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.