5-летний Импакт фактор:
ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352
Том 18, 2020
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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.
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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.
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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.
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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.
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Numerical and experimental analysis of periodic patterns and sedimentation of lysozyme.
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Convectiveâ€“diffusive transport in protein crystal growth.
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Implementation of high interfacial energy anisotropy in phase field simulations.
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The kinematics of completely-faceted surfaces.
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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.
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Experimental evidence for the stability of the depletion zone around a growing protein crystal under microgravity.
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Simulation of faceted film growth in two dimensions: Microstructure, morphology, and texture.
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The geometry of Wulff crystal shapes and its relations with Riemann problems.
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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.
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Pattern formation resulting from faceted growth in zone-melted thin films.
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Non-linear behavior of lysozyme crystallization.
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Multiscale random-walk algorithm for simulating interfacial pattern formation.
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Adaptive mesh refinement computation of solidification microstructures using dynamic data structures.
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Protein crystal growth: Growth kinetics for tetragonal lysozyme crystals.
Formation of Liesegang patterns.
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A level-set method for the evolution of faceted crystals.
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Dynamic scaling in polycrystalline growth.
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Phase field simulations of faceted growth for strong anisotropy of kinetic coefficient.
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The Physics of Protein Crystallization, Solid State Physics.
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A fixed grid numerical modelling methodology for convectionâ€“diffusion mushy region phase-change problems.
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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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