Self-diffusion in two-dimensional hard ellipsoid suspensions

We studied the self-diffusion of colloidal ellipsoids in a monolayer near a flat wall by video microscopy. The image processing algorithm can track the positions and orientations of ellipsoids with sub-pixel resolution. The translational and rotational diffusions were measured in both the lab frame and the body frame along the long and short axes. The long-time and short-time diffusion coefficients of translational and rotational motions were measured as functions of the particle concentration. We observed sub-diffusive behavior in the intermediate time regime due to the caging of neighboring particles. Both the beginning and the ending times of the intermediate regime exhibit power-law dependence on concentration. The long-time and short-time diffusion anisotropies change non-monotonically with concentration and reach minima in the semi-dilute regime because the motions along long axes are caged at lower concentrations than the motions along short axes. The effective diffusion coefficients change with time t as a linear function of (lnt)/t for the translational and rotational diffusions at various particle densities. This indicates that their relaxation functions decay according to 1/t which provides new challenges in theory. The effects of coupling between rotational and translational Brownian motions were demonstrated and the two time scales corresponding to anisotropic particle shape and anisotropic neighboring environment were measured

Scale space analysis by stabilized inverse diffusion equations

Caption title.Includes bibliographical references (p. 11).Supported by AFSOR. F49620-95-1-0083 Supported by ONR. N00014-91-J-1004 Supported in part by Boston University under the AFOSR Multidisciplinary Research Program on Reduced Signature Target Recognition. GC123919NGDIlya Pollak, Alan S. Willsky, Hamid Krim

Experimental analysis and numerical simulation of sintered micro-fluidic

This paper investigates the use of numerical simulations to describe solid state diffusion of a sintering stage during a Powder Hot Embossing (PHE) process for micro-fluidic components. Finite element analysis based on a thermo-elasto-viscoplastic model was established to describe the densification process of a PHE stainless steel porous component during sintering. The corresponding parameters such as the bulk viscosity, shearing viscosity and sintering stress are identified from dilatometer experimental data. The numerical analyses, which were performed on a 3D micro-structured component, allowed comparison between the numerical predictions and experimental results of during a sintering stage. This comparison demonstrates that the FE simulation results are in better agreement with the experimental results at high temperatures

Dynamics Of Anisotropic Gold Nanopartilces In Synthetic And Biopolymer Solutions

Soft matter is a subfield of condensed matter physics including systems such as polymers, colloids, amphiphiles and liquid crystals. Understanding their interaction and dynamics is essential for many interdisciplinary fields of study as well as important for technological advancements. We used gold nanorods (AuNRs) to investigate the length-scale dependent dynamics in semidilute polymer solutions, their conjugation and interaction with a protein bovine serum albumin (BSA), and the effect of shape anisotropy on the dynamics within a crowded solution of spheres. Multiphoton fluctuation correlation spectroscopy (MP-FCS) technique was used to investigate the translation and rotational diffusion of AuNRs. For polymer solutions, we determined the nanoviscosity experienced by the rods from the measured diffusion coefficient. Our results showed the importance of microscopic friction in determing the particle dynamics. In BSA solutions, we observed a submonolayer formation at the AuNRs surface, which indicates loss of protein native conformation. For rod – sphere mixture, our results indicated significant diffusional anisotropy for translational motion, whereas the rotation of the rods closely followed the ‘caging theory’

Image segmentation and edge enhancement with stabilized inverse diffusion equations

Caption title.Includes bibliographical references (p. 24-25).Supported by AFSOR. F49620-95-1-0083 Supported by ONR. N00014-91-J-1004 Supported in part by Boston University under the AFOSR Multidisciplinary Research Program on Reduced Signature Target Recognition. GC123919NGDIlya Pollak, Alan S. Willsky, Hamid Krim

Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization

In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it depends on a shock detector. Further, the resulting method is linearity preserving. The same shock detector is used to gradually lump the mass matrix. The resulting method is LED, positivity preserving, and also satisfies a global DMP. Lipschitz continuity has also been proved. However, the resulting scheme is highly nonlinear, leading to very poor nonlinear convergence rates. We propose a smooth version of the scheme, which leads to twice differentiable nonlinear stabilization schemes. It allows one to straightforwardly use Newton’s method and obtain quadratic convergence. In the numerical experiments, steady and transient linear transport, and transient Burgers’ equation have been considered in 2D. Using the Newton method with a smooth version of the scheme we can reduce 10 to 20 times the number of iterations of Anderson acceleration with the original non-smooth scheme. In any case, these properties are only true for the converged solution, but not for iterates. In this sense, we have also proposed the concept of projected nonlinear solvers, where a projection step is performed at the end of every nonlinear iterations onto a FE space of admissible solutions. The space of admissible solutions is the one that satisfies the desired monotonic properties (maximum principle or positivity).Peer ReviewedPostprint (author's final draft

Analysis of anisotropic subgrid-scale stress for coarse large-eddy simulation

This study discusses the necessity of anisotropic subgrid-scale (SGS) stress in large-eddy simulations (LESs) of turbulent shear flows using a coarse grid resolution. We decompose the SGS stress into two parts to observe the role of SGS stress in turbulent shear flows in addition to the energy transfer between grid-scale (GS or resolved scale) and SGS. One is the isotropic eddy-viscosity term, which contributes to energy transfer, and the other is the residual anisotropic term, which is separated from the energy transfer. We investigate the budget equation for GS Reynolds stress in turbulent channel flows accompanied by the SGS stress decomposition. In addition, we examine the medium and coarse filter length cases; the conventional eddy-viscosity models can fairly predict the mean velocity profile for the medium filter case and fails for the coarse filter case. The budget for GS turbulent kinetic energy shows that the anisotropic SGS stress has a negligible contribution to energy transfer. In contrast, the anisotropic stress has a large and non-dissipative contribution to the streamwise and spanwise components of GS Reynolds stress when the filter size is large. Even for the medium-size filter case, the anisotropic stress contributes positively to the budget for the spanwise GS Reynolds stress. Spectral analysis of the budget reveals that the positive contribution is prominent at a scale consistent with the spacing of streaks in the near-wall region. Therefore, we infer that anisotropic stress contributes to the generation mechanism of coherent structures. Predicting the positive contribution of the anisotropic stress to the budget is key to further improving SGS models.Comment: 40 pages, 17 figure

An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems

Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral angles are now measured in a metric depending on the diffusion matrix of the underlying problem. Several variants of the new condition are obtained. Based on one of them, two metric tensors for use in anisotropic mesh generation are developed to account for DMP satisfaction and the combination of DMP satisfaction and mesh adaptivity. Numerical examples are given to demonstrate the features of the linear finite element method for anisotropic meshes generated with the metric tensors.Comment: 34 page