Gaussian core model in two dimensions. II. Solid and fluid phase topological distribution functions

1981 ◽  
Vol 74 (7) ◽  
pp. 4020-4028 ◽  
Author(s):  
Thomas A. Weber ◽  
Frank H. Stillinger
Keyword(s):  
Fluid Phase ◽  
Two Dimensions ◽  
Distribution Functions ◽  
Core Model

scholarly journals Size-dependent thermodynamic structural selection in colloidal crystallization

2019 ◽  
Vol 5 (9) ◽  
pp. eaaw5912 ◽  
Author(s):  
Evan Pretti ◽  
Hasan Zerze ◽  
Minseok Song ◽  
Yajun Ding ◽  
Runfang Mao ◽  
...  
Keyword(s):  
Self Assembly ◽  
Colloidal Particles ◽  
Size Dependence ◽  
Fluid Phase ◽  
Two Dimensions ◽  
Size Dependent ◽  
Colloidal Crystallization ◽  
Kinetic Effects ◽  
Physical Phenomena ◽  
Surrounding Fluid

Nucleation and growth of crystalline phases play an important role in a variety of physical phenomena, ranging from freezing of liquids to assembly of colloidal particles. Understanding these processes in the context of colloidal crystallization is of great importance for predicting and controlling the structures produced. In many systems, crystallites that nucleate have structures differing from those expected from bulk equilibrium thermodynamic considerations, and this is often attributed to kinetic effects. In this work, we consider the self-assembly of a binary mixture of colloids in two dimensions, which exhibits a structural transformation from a non–close-packed to a close-packed lattice during crystal growth. We show that this transformation is thermodynamically driven, resulting from size dependence of the relative free energy between the two structures. We demonstrate that structural selection can be entirely thermodynamic, in contrast to previously considered effects involving growth kinetics or interaction with the surrounding fluid phase.

The diffusive strip method for scalar mixing in two dimensions

2010 ◽  
Vol 662 ◽  
pp. 134-172 ◽  
Author(s):  
P. MEUNIER ◽  
E. VILLERMAUX
Keyword(s):  
Diffusion Problem ◽  
Two Dimensions ◽  
Distribution Functions ◽  
Radius Of Curvature ◽  
Scalar Mixing ◽  
Mixing Properties ◽  
Convection Diffusion ◽  
Concentration Probability ◽  
Log Normal ◽  
Large Peclet Number

We introduce a new numerical method for the study of scalar mixing in two-dimensional advection fields. The position of an advected material strip is computed kinematically, and the associated convection–diffusion problem is solved using the computed local stretching rate along the strip, assuming that the diffusing strip thickness is smaller than its local radius of curvature. This widely legitimate assumption reduces the numerical problem to the computation of a single variable along the strip, thus making the method extremely fast and applicable to any large Péclet number. The method is then used to document the mixing properties of a chaotic sine flow, for which we relate the global quantities (spectra, concentration probability distribution functions (PDFs), increments) to the distributed stretching of the strip convoluted by the flow, possibly overlapping with itself. The numerical results indicate that the PDF of the strip elongation is log normal, a signature of random multiplicative processes. This property leads to exact analytical predictions for the spectrum of the field and for the PDF of the scalar concentration of a solitary strip. The present simulations offer a unique way of discovering the interaction rule for building complex mixtures which are made of a random superposition of overlapping strips leading to concentration PDFs stable by self-convolution.

Approximations to hard-core models and their application to statistical analysis

1982 ◽  
Vol 19 (A) ◽  
pp. 281-292 ◽  
Author(s):  
Mark Westcott
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Lower Bounds ◽  
Hard Core ◽  
Distribution Functions ◽  
Core Model ◽  
Upper And Lower Bounds ◽  
Nearest Neighbour ◽  
Hard Core Model

This paper derives upper and lower bounds to the distribution functions of nearest-neighbour and minimum nearest-neighbour distances between N points generated by a hard-core model on the surface of a sphere. The use of these bounds in statistical inference is discussed.

Approximations to hard-core models and their application to statistical analysis

1982 ◽  
Vol 19 (A) ◽  
pp. 281-292 ◽  
Author(s):  
Mark Westcott
Keyword(s):  
Statistical Analysis ◽  
Statistical Inference ◽  
Lower Bounds ◽  
Hard Core ◽  
Distribution Functions ◽  
Core Model ◽  
Upper And Lower Bounds ◽  
Nearest Neighbour ◽  
Hard Core Model

This paper derives upper and lower bounds to the distribution functions of nearest-neighbour and minimum nearest-neighbour distances between N points generated by a hard-core model on the surface of a sphere. The use of these bounds in statistical inference is discussed.

scholarly journals Evidence of Structural Inhomogeneities in Hard-Soft Dimeric Particles without Attractive Interactions

Materials ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 84 ◽  
Author(s):  
Gianmarco Munaò ◽  
Franz Saija
Keyword(s):  
Hard Spheres ◽  
Hard Core ◽  
Fluid Phase ◽  
Colloidal Dispersion ◽  
Systematic Investigation ◽  
Distribution Functions ◽  
Structure Factors ◽  
Soft Spheres ◽  
Wide Range ◽  
Structural Inhomogeneities

We perform Monte Carlo simulations of a simple hard-soft dimeric model constituted by two tangent spheres experiencing different interactions. Specifically, two hard spheres belonging to different dimers interact via a bare hard-core repulsion, whereas two soft spheres experience a softly repulsive Hertzian interaction. The cross correlations are soft as well. By exploring a wide range of temperatures and densities we investigate the capability of this model to document the existence of structural inhomogeneities indicating the possible onset of aggregates, even if no attraction is set. The fluid phase behavior is studied by analyzing structural and thermodynamical properties of the observed structures, in particular by computing radial distribution functions, structure factors and cluster size distributions. The numerical results are supported by integral equation theories of molecular liquids which allow for a finer and faster spanning of the temperature-density diagram. Our results may serve as a framework for a more systematic investigation of self-assembled structures of functionalized hard-soft dimers able to aggregate in a variety of structures widely oberved in colloidal dispersion.

scholarly journals Analysis of stacking disorder in ice I using pair distribution functions

2018 ◽  
Vol 51 (4) ◽  
pp. 1211-1220 ◽  
Author(s):  
Helen Y. Playford ◽  
Thomas F. Whale ◽  
Benjamin J. Murray ◽  
Matt G. Tucker ◽  
Christoph G. Salzmann
Keyword(s):  
Chemical Properties ◽  
Two Dimensions ◽  
Distribution Functions ◽  
Memory Effects ◽  
Framework Materials ◽  
Experimental Pair ◽  
Physical And Chemical ◽  
Pair Distribution Functions ◽  
Stacking Disorder ◽  
And Chemical Properties

Stacking-disordered materials display crystalline order in two dimensions but are disordered along the direction in which layered structural motifs are stacked. Countless examples of stacking disorder exist, ranging from close-packed metals, ice I and diamond to open-framework materials and small-molecule pharmaceuticals. In general, the presence of stacking disorder can have profound consequences for the physical and chemical properties of a material. Traditional analyses of powder diffraction data are often complicated by the presence of memory effects in the stacking sequences. Here it is shown that experimental pair distribution functions of stacking-disordered ice I can be used to determine local information on the fractions of cubic and hexagonal stacking. Ice is a particularly challenging material in this respect, since both the stacking disorder and the orientational disorder of the water molecules need to be described. Memory effects are found to contribute very little to the pair distribution functions, and consequently, the analysis of pair distribution functions is the method of choice for characterizing stacking-disordered samples with complicated and high-order memory effects. In the context of this work, the limitations of current structure-reconstruction approaches are also discussed.

scholarly journals A mutation in glyceraldehyde 3-phosphate dehydrogenase alters endocytosis in CHO cells.

1995 ◽  
Vol 130 (5) ◽  
pp. 1093-1104 ◽  
Author(s):  
A R Robbins ◽  
R D Ward ◽  
C Oliver
Keyword(s):  
Fluid Phase ◽  
Glycolytic Enzyme ◽  
Two Dimensions ◽  
Cdna Clones ◽  
Wild Type ◽  
Stable Transfectants ◽  
Single Nucleotide Change ◽  
Early Endosomes ◽  
Endocytic Compartments ◽  
Kinetics Of

The CHO cell mutant FD 1.3.25 exhibits both increased accumulation and altered distribution of endocytosed fluid phase tracers. Neither the rate of tracer internalization nor the kinetics of recycling from early endosomes was affected, but exocytosis from late endocytic compartments appeared to be decreased in the mutant. Endocytosed tracer moved more rapidly to the cell poles in FD1.3.25 than in wild type cells. An abundant 36-kD polypeptide was found associated with taxol-polymerized microtubules in preparations from wild type and mutant; in the former but not the latter this polypeptide could be dissociated by incubation of the microtubules in ATP or high salt. The 36-kD polypeptide co-electrophoresed in two dimensions with the monomer of the glycolytic enzyme glyceraldehyde 3-phosphate dehydrogenase (GAPDH). Analysis of cDNA clones showed that the mutant is heterozygous for this enzyme, with approximately 25% of the GAPDH RNA containing a single nucleotide change resulting in substitution of Ser for Pro234, a residue that is conserved throughout evolution. Stable transfectants of wild type cells expressing the mutant monomer at approximately 15% of the total enzyme exhibited the various changes in endocytosis observed in FD1.3.25.

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