This chapter provides a brief review of some algorithms used to construct model granular media (p... more This chapter provides a brief review of some algorithms used to construct model granular media (packings of spheres), together with a comparison of results obtained on tessellations of those packings. The computational algorithms involve several techniques, including: a Random Sequential Adsorption approach (RSA), an Event-Driven model (ED), a Molecular Dynamics code (MD), a Smoothed Particle Hydrodynamics approach (SPH) and the classical static algorithm for dense packings of spheres. These techniques model static or dynamic interactions between the particles and give different geometries even for the same mean solid fraction. These numerical methods can apply to two or three-dimensional packings.
Orientation of water molecules in the vicinity of the globular protein SNase is studied. It is sh... more Orientation of water molecules in the vicinity of the globular protein SNase is studied. It is shown that two types of characteristic orientations can be distinguished among molecules in direct contact with the protein. Approximately 44% of these molecules are oriented by their OH vector towards the nearest protein atom forming a donor hydrogen bond; 20% of them are directed by their oxygen towards the nearest atom while their protons are directed mainly away from the protein. By forming a network of hydrogen bonds with other water molecules, these molecules initiate orientation correlations in the protein environment within a region of 0.45 nm. More distant water molecules are arranged randomly with respect to the protein. The orientation is described by the angle between vector N directed from the water molecule to the nearest protein atom and characteristic vectors of the water molecule (directions OH, OL, and dipole moment D). A more detailed information about orientations is retrieved from a two-dimensional distribution diagram P(cos(θ), φ) representing direction N in a spherical coordinate system associated with the water molecule. The diagram provides an unambiguous description for the orientation of water molecules and allows a quantitative calculation of the fraction of molecules with a specified orientation.
ABSTRACT One-dimensional and two-dimensional distributions of the characteristics introduced prev... more ABSTRACT One-dimensional and two-dimensional distributions of the characteristics introduced previously for the forms of Delaunay simplices - tetrahedricity and octahedricity - have been investigated in computer models of a crystal, a liquid and an amorphous solid. It has been established that in the absence of thermal perturbations (in the proper structure of the liquid and in an amorphous substance) there exists a distinguishable class of simplices with five almost equal edges and the sixth being longer. This class of simplices named isopentacmons, in turn includes the types of good tetrahedra and good quartoctahedra (a quarter of octahedron). In disordered systems the fraction of tetrahedra relative to quartoctahedra exceeds substantially that in the FCC crystal.
Delaunay simplexes are very helpful instrument for analysis of computer models of atomic, molecul... more Delaunay simplexes are very helpful instrument for analysis of computer models of atomic, molecular and granular systems. This paper illustrates their application to the current physical problems. The first one is the structure of non-crystalline packing of spheres. Recently it got the advance thanks to application of the Delaunay simplexes with quantitative measures of simplex shape. The second important problem is recognition and analysis of intermolecular voids. Delaunay simplex represents “the simplicial cavities”, and any complex void is a cluster of such cavities..
C использованием полноатомного молекулярно-динамического моделирования исследовали подвижность мо... more C использованием полноатомного молекулярно-динамического моделирования исследовали подвижность молекул в гидратной оболочке глобулярного белка SNase в водном растворе с косольвентами (мочевина и триметиламиноксид). Для молекул, изначально расположенных в последовательных слоях вокруг белка, рассчитывали средние смещения за один и тот же короткий промежуток времени. Это позволило характеризовать диффузионную подвижность молекул в зависимости от расстояния до белка. Показано, что молекулы растворителя имеют пониженную подвижность вблизи белка, а при удалении от него подвижность молекул увеличивается неравномерно, коррелируя с положением максимумов функции распределения соответствующих молекул вокруг белка. За пределами второго максимума этих функций подвижность достигает своих объемных значений как для воды, так и для косольвентов.
ABSTRACT An analysis of the relative distribution of Delaunay simplexes is formulated as a proble... more ABSTRACT An analysis of the relative distribution of Delaunay simplexes is formulated as a problem of analyzing their characteristics at the nodes of a Voronoi grid. We found a typical cluster in the simplexes of the tetrahedral and octahedral form (the basic structural elements of simple liquids) and we determined their processing thresholds.
This chapter provides a brief review of some algorithms used to construct model granular media (p... more This chapter provides a brief review of some algorithms used to construct model granular media (packings of spheres), together with a comparison of results obtained on tessellations of those packings. The computational algorithms involve several techniques, including: a Random Sequential Adsorption approach (RSA), an Event-Driven model (ED), a Molecular Dynamics code (MD), a Smoothed Particle Hydrodynamics approach (SPH) and the classical static algorithm for dense packings of spheres. These techniques model static or dynamic interactions between the particles and give different geometries even for the same mean solid fraction. These numerical methods can apply to two or three-dimensional packings.
Orientation of water molecules in the vicinity of the globular protein SNase is studied. It is sh... more Orientation of water molecules in the vicinity of the globular protein SNase is studied. It is shown that two types of characteristic orientations can be distinguished among molecules in direct contact with the protein. Approximately 44% of these molecules are oriented by their OH vector towards the nearest protein atom forming a donor hydrogen bond; 20% of them are directed by their oxygen towards the nearest atom while their protons are directed mainly away from the protein. By forming a network of hydrogen bonds with other water molecules, these molecules initiate orientation correlations in the protein environment within a region of 0.45 nm. More distant water molecules are arranged randomly with respect to the protein. The orientation is described by the angle between vector N directed from the water molecule to the nearest protein atom and characteristic vectors of the water molecule (directions OH, OL, and dipole moment D). A more detailed information about orientations is retrieved from a two-dimensional distribution diagram P(cos(θ), φ) representing direction N in a spherical coordinate system associated with the water molecule. The diagram provides an unambiguous description for the orientation of water molecules and allows a quantitative calculation of the fraction of molecules with a specified orientation.
ABSTRACT One-dimensional and two-dimensional distributions of the characteristics introduced prev... more ABSTRACT One-dimensional and two-dimensional distributions of the characteristics introduced previously for the forms of Delaunay simplices - tetrahedricity and octahedricity - have been investigated in computer models of a crystal, a liquid and an amorphous solid. It has been established that in the absence of thermal perturbations (in the proper structure of the liquid and in an amorphous substance) there exists a distinguishable class of simplices with five almost equal edges and the sixth being longer. This class of simplices named isopentacmons, in turn includes the types of good tetrahedra and good quartoctahedra (a quarter of octahedron). In disordered systems the fraction of tetrahedra relative to quartoctahedra exceeds substantially that in the FCC crystal.
Delaunay simplexes are very helpful instrument for analysis of computer models of atomic, molecul... more Delaunay simplexes are very helpful instrument for analysis of computer models of atomic, molecular and granular systems. This paper illustrates their application to the current physical problems. The first one is the structure of non-crystalline packing of spheres. Recently it got the advance thanks to application of the Delaunay simplexes with quantitative measures of simplex shape. The second important problem is recognition and analysis of intermolecular voids. Delaunay simplex represents “the simplicial cavities”, and any complex void is a cluster of such cavities..
C использованием полноатомного молекулярно-динамического моделирования исследовали подвижность мо... more C использованием полноатомного молекулярно-динамического моделирования исследовали подвижность молекул в гидратной оболочке глобулярного белка SNase в водном растворе с косольвентами (мочевина и триметиламиноксид). Для молекул, изначально расположенных в последовательных слоях вокруг белка, рассчитывали средние смещения за один и тот же короткий промежуток времени. Это позволило характеризовать диффузионную подвижность молекул в зависимости от расстояния до белка. Показано, что молекулы растворителя имеют пониженную подвижность вблизи белка, а при удалении от него подвижность молекул увеличивается неравномерно, коррелируя с положением максимумов функции распределения соответствующих молекул вокруг белка. За пределами второго максимума этих функций подвижность достигает своих объемных значений как для воды, так и для косольвентов.
ABSTRACT An analysis of the relative distribution of Delaunay simplexes is formulated as a proble... more ABSTRACT An analysis of the relative distribution of Delaunay simplexes is formulated as a problem of analyzing their characteristics at the nodes of a Voronoi grid. We found a typical cluster in the simplexes of the tetrahedral and octahedral form (the basic structural elements of simple liquids) and we determined their processing thresholds.
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