ISSN Print: 1543-1649
ISSN Online: 1940-4352
Volume 17, 2019
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Volume 6, 2008
Volume 5, 2007
Volume 4, 2006
Volume 3, 2005
Volume 2, 2004
Volume 1, 2003
International Journal for Multiscale Computational Engineering
A THEORETICAL AND NUMERICAL MULTISCALE FRAMEWORK FOR THE ANALYSIS OF PATTERN FORMATION IN PROTEIN CRYSTAL ENGINEERING
CTC, Naples, Italy
The relevance of self-organization, pattern formation, nonlinear phenomena, and nonequilibrium behavior in a wide range of problems related to macromolecular crystal engineering calls for a concerted approach using the tools of statistical physics, thermodynamics, fluid dynamics, nonlinear dynamics, mathematical modeling, and numerical simulation in synergy with experimentally oriented work. The reason behind such a need is that in many instances of relevance in this field one witnesses an interplay between molecular and macroscopic-level entities and processes. Along these lines, two models are defined here and discussed in detail, one dealing with issues of complex behavior at the microscopic level and the other referring to the strong nonlinear nature of macroscopic evolution. Such models share a common fundamental feature, a group of equations strictly related from a mathematical point of view to the kinetic conditions used to model mass transfer at the crystal surface. Model diversification then occurs on the basis of the desired scale length; i.e., according to the level of detail required by the analysis (local or global). If the local evolution of the crystal surface is the subject of the investigation (distribution of the local growth rate along the crystal face, shape instabilities, onset of surface depressions due to diffusive and/or convective effects, etc.; i.e., all those factors dealing with the local history of the shape) the model is conceived to provide microscopic and morphological details. For this specific case a kinetic-coefficient-based moving boundary numerical (computational fluid dynamics) strategy is carefully developed on the basis of the volume-of-fluid methods (also known as the volume tracking methods) and level-set techniques, which have become popular in the last years as numerical techniques capable of modeling complex multiphase problems as well as for their capability to undertake a fixed-grid solution without resorting to mathematical manipulations and transformations. On the contrary, if the size of the crystals is negligible with respect to the size of the reactor (i.e., if they are small and undergo only small dimensional changes with respect to the overall dimensions of the cell containing the feeding solution), the shape of the crystals is ignored and the proposed approach relies directly on an algebraic formulation of the nucleation events and on the application of an integral form of the mass balance kinetics for each protein crystal. The applicability and the suitability of the different submodels are discussed according to some worked examples of practical interest. Pattern formation in these processes is described here with respect to crystal shapes, nuclei spatial discrete arrangements, and the convective multicellular structures arising as a consequence of buoyancy forces, thus enriching the discussions with some interdisciplinary flavor.
Adalsteinsson, D. and Sethian, J. A.,
The fast construction of extension velocities in level set methods.
Bennon, W. D. and Incropera, F. P.,
A continuum model for momentum, heat and species transport in binary solidâ€“liquid phase change systems. Part I. Model formulation.
Buki, A., Karpati-Smidroczki, E., and ZrÄ±nyi, M.,
Two-dimensional chemical pattern formation in gels. Experiments and computer simulation.
Burger, M., HauÃŸer, F., Stocker, C., and Voigt, A.,
A level set approach to anisotropic flows with curvature regularization.
Carotenuto, L., Piccolo, C., Castagnolo, D., Lappa, M., and GarcÄ±a-Ruiz, J. M.,
Experimental observations and numerical modeling of diffusion-driven crystallization processes.
Chang, Y. C., Hou, T. Y., Merriman, B., and Osher, S.,
A level set formulation of eulerian interface capturing methods for incompressible fluid flows.
Chen, S., Merriman, B., Osher, S., and Smereka, P.,
A simple level set method for solving Stefan problems.
Chen, Z., Chen, C., and Hao, L.,
Numerical simulation of facet dendrite growth.
Cherepanova, V. K., Cherepanov, A. N., Sharapov, V. N., and Plaksin, S. I.,
On the dynamics of the rhythmic crystallization of magmatic bodies during the directional solidification of cotectic melts.
Chernavskii, D. S., Polezhaev, A. A., and Muller, S. C.,
A model of pattern formation by precipitation.
Chou, K. C. and Shen, H. B.,
Review: Recent advances in developing web-servers for predicting protein attributes.
Coriell, S. R., Chernov, A. A., Murray, B. T., and McFadden, G. B.,
Step bunching: Generalized kinetics.
Eggleston, J., McFadden, G., and Voorhees, P.,
A phase-field model for highly anisotropic interfacial energy.
Galkin, O., and Vekilov, P. G.,
Direct determination of the nucleation rates of protein crystals.
George, J. and Varghese, G.,
Formation of periodic precipitation patterns: A moving boundary problem.
George, J. and Varghese, G.,
Intermediate colloidal formation and the varying width of periodic precipitation bands in reactionâ€“ diffusion systems.
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Volume of fluid interface tracking with smoothed surface stress methods for three-dimensional flows.
Gurtin, M. and Voorhees, P.,
On the effects of elastic stress on the motion of fully faceted interfaces.
Hebert, D. J.,
Simulations of stochastic reaction-diffusion systems.
Henisch, H. K.,
Periodic Precipitation: A Microcomputer Analysis of Transport and Reaction Processes in Diffusion Media with Software Development.
Henisch, H. K. and GarcÄ±a-Ruiz, J. M.,
Crystal growth in gels and Liesegang ring formation: Crystallization criteria and successive precipitation.
Hong, C. P., Zhu, M. F., and Lee, S. Y.,
Modeling of dendritic growth in alloy solidification with melt convection.
Izsak, F. and Lagzi, I.,
Simulation of Liesegang pattern formation using a discrete stochastic model.
Kazanyan, A., Wang, Y., Dregia, S. A., and Patton, B. P.,
Generalized phase-field model for computer simulation of grain growth in anisotropic systems.
Kim, Y. T., Goldenfeld, N., and Dantzig, J.,
Computation of dendritic microstructures using a level set method.
To the geometric selection of crystals.
Lagzi, I. and Ueyama, D.,
Pattern transition between periodic Liesegang pattern and crystal growth regime in reactionâ€“diffusion systems.
An â€˜attachment-kinetics-basedâ€™ volume of fraction method for organic crystallization: A fluid-dynamic approach to macromolecular crystal engineering.
Growth and mutual interference of protein seeds under reduced gravity conditions.
Fluids, Materials and Microgravity: Numerical Techniques and Insights into the Physics.
An â€˜attachment kinetics-basedâ€™ level-set method for protein crystallization under buoyancy-driven convective effects.
Discrete layers of interacting growing protein seeds: convective and morphological stages of evolution.
Coalescence and non-coalescence phenomena in multi-material problems and dispersed multiphase flows. Part 1: A critical review of theories.
Coalescence and non-coalescence phenomena in multi-material problems and dispersed multiphase flows. Part 2: A critical review of CFD approaches.
Single- and multi-droplet configurations out of thermodynamic equilibrium: Pulsating, traveling, and erratic fluiddynamic instabilities.
Thermal Convection: Patterns, Evolution and Stability.
Lappa, M. and Savino, R.,
3D analysis of crystal/melt interface shape and Marangoni flow instability in solidifying liquid bridges.
Lappa, M. and Carotenuto, L.,
Effect of convective disturbances induced by g-jitter on the periodic precipitation of lysozyme.
Lappa, M. and Castagnolo, D.,
Complex dynamics of rhythmic patterns and sedimentation of organic crystals: A new numerical approach.
Lappa, M., Castagnolo, D., and Carotenuto, L.,
Sensitivity of the non-linear dynamics of lysozyme â€˜Liesegang Ringsâ€™ to small asymmetries.
Lappa, M., Piccolo, C., and Carotenuto, L.,
Numerical and experimental analysis of periodic patterns and sedimentation of lysozyme.
Lin, H., Rosenberger, F., Alexander, J. I. D., and Nadarajah, A.,
Convectiveâ€“diffusive transport in protein crystal growth.
Loginova, I., Amberg, G., and AÂ° gren, J.,
Phase-field simulations of non-isothermal binary alloy solidification.
Ma, N., Chen, Q., and Wang, Y.,
Implementation of high interfacial energy anisotropy in phase field simulations.
Malladi, R., Sethian, J. A., and Vemuri, B. C.,
Shape modeling with front propagation: A level set approach.
McFadden, G. B., Wheeler, A. A., Braun, R., Coriel, S. R., and Sekerka, R. F.,
Phase-field models for anisotropic interfaces.
Current approaches to macromolecular crystallization.
Merriman, B., Bence, J., and Osher, S.,
Motion of multiple junctions: A level set approach.
Monaco, A. and Rosenberger, F.,
Growth and etching kinetics of tetragonal lysozyme.
Noh, D. S., Koh, Y., and Kang, I. S.,
Numerical solutions for shape evolution of a particle growing in axisymmetric flows of supersaturated solution.
Norris, S. and Watson, S.,
Geometric simulation and surface statistics of coarsening faceted surfaces.
Norris, S. A. and Watson, S. J.,
The kinematics of completely-faceted surfaces.
Osher, S. and Sethian, J. A.,
Fronts propagating with curvature-dependent speed: Algorithms based on Hamiltonâ€“Jacobi formulations.
Osher, S. and Merriman, B.,
The Wulff shape as the asymptotic limit of a growing crystalline interface.
Osher, S. and Fedkiw, R.,
Level set methods: An overview and some recent results.
Osher, S. and Fedkiw, R.,
The Level Set Method and Dynamic Implicit Surfaces.
Otalora, F. and Garcia-Ruiz, J. M.,
Crystal growth studies in microgravity with the APCF: Computer simulation and transport dynamics.
Otalora, F., Novella, M. L., Gavira, J. A., Thomas, B. R., and Garcia-Ruiz, J. M.,
Experimental evidence for the stability of the depletion zone around a growing protein crystal under microgravity.
Paritosh, F., Srolovitz, D. J., Battaile, C. C., Li, X., and Butler, J. E.,
Simulation of faceted film growth in two dimensions: Microstructure, morphology, and texture.
Peng, D., Osher, S., Merriman, B., and Zhao, H.,
The geometry of Wulff crystal shapes and its relations with Riemann problems.
Peng, D., Merriman, B., Osher, S., Zhao, H.-K., and Kang, M.,
A PDE-based fast local level set method.
Peng, D., Osher, S., Merriman, B., and Zhao, H.-K.,
The geometry ofWulff crystal shapes and its relations with Riemann problems.
Pfeiffer, L., Paine, S., Gilmer, G., van Saarloos, W., and West, K.,
Pattern formation resulting from faceted growth in zone-melted thin films.
Piccolo, C., Lappa, M., Tortora, A., and Carotenuto, L.,
Non-linear behavior of lysozyme crystallization.
Plapp, M. and Karma, A.,
Multiscale random-walk algorithm for simulating interfacial pattern formation.
Provatas, N., Goldenfeld, N., and Dantzig, J.,
Adaptive mesh refinement computation of solidification microstructures using dynamic data structures.
Pusey, M. L., Snyder, R. S., and Naumann, R.,
Protein crystal growth: Growth kinetics for tetragonal lysozyme crystals.
Formation of Liesegang patterns.
Inorganic and protein crystal growth: Similarities and differences.
Russo, G. and Smereka, P.,
A level-set method for the evolution of faceted crystals.
Shangguan, D. and Hunt, J.,
Dynamical study of the pattern formation of faceted cellular array growth.
Smereka, P., Li, X., Russo, G., and Srolovitz, D.,
Simulation of faceted film growth in three dimensions: Microstructure, morphology, and texture.
Generalized motion of a front propagating along its normal direction: A differential games approach.
Sussman, M. and Ohta, M.,
Improvements for calculating two-phase bubble and drop motion using an adaptive sharp interface method.
Taylor, J. E.,
Motion of curves by crystalline curvature, including triple junctions and boundary points.
Taylor, J. and Cahn, J.,
Linking anisotropic sharp and diffuse surface motion laws via gradient flows.
Taylor, J. and Cahn, J.,
Diffuse interfaces with sharp comers and facets: Phase field models with strongly anisotropic surfaces.
Taylor, J. E., Cahn, J., and Handwerker, C. A.,
Geometrical models of crystal growth.
Thijssen, J., Knops, H., and Dammers, A.,
Dynamic scaling in polycrystalline growth.
Uehara, T. and Sekerka, R. F.,
Phase field simulations of faceted growth for strong anisotropy of kinetic coefficient.
van der Drift, A.,
Evolutionary selection, a principle governing growth orientation in vapor-deposited layers.
Vekilov, P. G. and Chernov, A. A.,
The Physics of Protein Crystallization, Solid State Physics.
Voller, V. R. and Prakash, C.,
A fixed grid numerical modelling methodology for convectionâ€“diffusion mushy region phase-change problems.
Watson, S. and Norris, S.,
Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation.
Watson, S., Otto, F., Rubinstein, B., and Davis, S.,
Coarsening dynamics of the convective Cahnâ€“Hilliard equation.
Wettlaufer, J. S., Jackson, M., and Elbaum, M.,
A geometric model for anisotropic crystal growth.
Wild, C., Herres, N., and Koidl, P.,
Texture formation in polycrystalline diamond films.
Frage der geshwindigkeit des wachstums und der anflosung der kristallflachen.
Yokoyama, E. and Sekerka, R. F.,
A numerical study of the combined effect of anisotropic surface tension and interface kinetics on pattern formation during the growth of two-dimensional crystals.
Zhang, J. and Adams, J.,
FACET: A novel model of simulation and visualization of polycrystalline thin film growth.
Zhang, J. and Adams, J.,
Modeling and visualization of polycrystalline thin film growth.
Zhao, H.-K., Merriman, B., Osher, S., and Wang, L.,
Capturing the behavior of bubbles and drops using the variational level set approach.
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