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STABILITY AND REPRODUCIBILITY OF THE DIMERIC MOTIF IN THE CRYSTALS OF THIOETHERS OF 3-BROMO-5-HYDROXY-1- (4-METHYLBENZYL)-1,5-DIHYDRO-2
H -PYRROL-2-ONESAbstractWe confirm our previously formulated rule about the possibility of a spontaneous resolution of enantiomers of a series of...
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The role of randomly packed particles on macroscopic elastic bonded grain properties
Bonded discrete element method (DEM) models utilize networks of bonds between discrete particles to simulate continuum behaviors of real materials,...
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The Isostatic Conjecture
We show that a jammed packing of disks with generic radii, in a generic container, is such that the minimal number of contacts occurs and there is...
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Tammes Problem and Contact Number for Spheres in Spaces of Constant Curvature
In this paper, we consider the problem on the contact number of a sphere in a three-dimensional hyperbolic space and a three-dimensional spherical...
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Structure of Liquid Jets and Wetting Front in the Refrigerant Mixture Falling Films at Various Contact Angles
AbstractThe paper presents 3D numerical modeling of spreading dynamics of R21 (mol. fraction: 0.9) and R114 refrigerant mixture film. We considered...
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A new class of discrete conformal structures on surfaces with boundary
We introduce a new class of discrete conformal structures on surfaces with boundary, which have nice interpretations in 3-dimensional hyperbolic...
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A Bird’s-Eye View of Amorphous Solids
In this chapter, we set the groundwork for the mathematical description of disordered or amorphous solids by introducing the fundamental concepts of...
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Combinatorics Encoding Geometry: The Legacy of Bill Thurston in the Story of One Theorem
This chapter presents a whirlwind tour of some results surrounding the Koebe–Andre’ev–Thurston Theorem, Bill Thurston’s seminal circle packing...
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Introduction
A planar graph is a graph that can be drawn in the plane, with vertices represented by points and edges represented by non-crossing curves. There are...
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Related Topics
In this chapter we briefly review some aspects of the literature on circle packing that unfortunately we do not have space to get into in depth in...
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Weak Interaction Based Interpretation of Crystal Packing Characteristics of Aromatic Rings Accumulating Molecules: Hirshfeld Surface Analyses Reinforced X-ray Crystal Study on 1,8-Dibenzoyl-7-Ethoxynaphthalen-2-ol and Its 2-Ethoxylated Homologue
The molecular environments in the crystal of two dibenzoylnaphthalene derivatives, having similar molecular formulas with a difference of only one...
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Investigating the source of hysteresis in the soil–water characteristic curve using the multiphase lattice Boltzmann method
The soil–water characteristic curve (SWCC) is the most fundamental relationship in unsaturated soil mechanics, relating the amount of water in the...
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Elasticity
In Chap. 1 , we have considered how atoms/molecules/grains interact and self-organize into forming solid...
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Deformation characteristics of inherently anisotropic granular media under repeated traffic loading: a DEM study
The cardioid-shaped loading path induced by moving traffic has been reproduced in the virtual element test of granular media using the discrete...
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Packing Soft Convex Polygons in an Optimized Convex Container
Packing soft convex polygonal objects in an optimized convex container is considered. The shape of the soft object can be changed in certain limits,...
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Preparation, crystallographic feature, synthon investigation and Hirshfeld surface analysis of both 3D supramolecular anhydrous organic salts constructed by triphenylmethylamine, 3-nitrophthalic acid and 5-nitroisophthalic acid
The complex role of the non-covalent contacts in a wide kind of areas ranging from chemistry, biology, catalysis, material science, to medicinal...
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Circle Packings
We will now turn to the discrete setting and discuss the theory of circle packings.
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Recurrence, Transience, Liouville and Speed
In this chapter, we study the behavior of the simple random walk (SRW) on infinite Boltzmann planar maps of the plane under...
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Optimization Design of the Multi-Layer Cross-Sectional Layout of An Umbilical Based on the GA-GLM
Marine umbilical is one of the key equipment for subsea oil and gas exploitation, which is usually integrated by a great number of different...
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DEM study on the effect of particle shape on the shear behaviour of granular materials
This study investigates the effects of particle convexity, sphericity and aspect ratio (AR) on the behaviour of sheared granular materials using...
