Search results for " packing"

Structure of Liquids

2014

An Introduction to the description of the static structure of simple liquids is given. The principle quantity, which describes this structure is the structure factor, which can be measured with neutron and X-ray diffraction. The structure factor is the Fourier transform of the radial pair distribution function, which describes the statistics of the atoms around a given one. Several theories are introduced for calculating this quantities. It is shown that the structure of liquid metals is dominated by their hardcore repulsion. In the low-wavenumber limit the structure factor is related to the compressibility of the liquid. In this limit deviations from the hard-core model become importent, w…

Ensemble Planning for Digital Audio Broadcasting

2003

Dichotomies properties on computational complexity of S-packing coloring problems

2015

This work establishes the complexity class of several instances of the S -packing coloring problem: for a graph G , a positive integer k and a nondecreasing list of integers S = ( s 1 , ? , s k ) , G is S -colorable if its vertices can be partitioned into sets S i , i = 1 , ? , k , where each S i is an s i -packing (a set of vertices at pairwise distance greater than s i ). In particular we prove a dichotomy between NP-complete problems and polynomial-time solvable problems for lists of at most four integers.

Electrophoresis of model colloidal spheres in low salt aqueous suspension

2004

We report on comprehensive measurements of the electrophoretic mobility μ of a highly charged spherical colloid in deionized or low salt aqueous suspensions, where fluid and crystalline order develops with increased packing fraction Φ. We propose the existence of a 'universal' shape of the μ(Φ) showing three distinct regimes: a logarithmic increase, a plateau and a logarithmic decrease. The position and the height of the plateau are found to be influenced by the particle surface properties and the electrolyte concentration. In particular, it starts once the counter-ion concentration becomes equal to the concentration of background electrolyte. This coincides only loosely with the range of Φ…

RutaRep: a computer package to design dispatching routes in the meat industry

2005

In this paper we present a computer program that has been developed to design the dispatching routes of a medium-sized meat company in Spain. We have modelled the real problem as a variant of the vehicle routing problem with Time Windows and implemented a number of heuristic algorithms based on the most advanced solution techniques for this problem. These algorithms have been embedded in a computer package that is intended to be used as a decision support system for the distribution manager. The program runs under Windows System and is straightforward to use. We also present some computational experiences based on real instances provided by the company. This experience shows important impro…

Combinatorial proofs of two theorems of Lutz and Stull

2021

Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not assumed to be Borel, or even analytic. One of the theorems states that if $K \subset \mathbb{R}^{n}$ is any set with equal Hausdorff and packing dimensions, then $$ \dim_{\mathrm{H}} π_{e}(K) = \min\{\dim_{\mathrm{H}} K,1\} $$ for almost every $e \in S^{n - 1}$. Here $π_{e}$ stands for orthogonal projection to $\mathrm{span}(e)$. The primary purpose of this paper is to present proofs for Lutz and Stull's projection theorems which do not refer to information theoretic concepts. Instead, they will rely on combinatori…

Simulation of the dynamics of hard ellipsoids

2008

We study a system of uniaxial hard ellipsoids by molecular dynamics simulations, changing both the aspect-ratio X-0 (X-0 = a/b, where a is the length of the revolution axis and b is the length of the two other axes) and the packing fraction phi. We calculate the translational and rotational mean squared displacements, the translational D-trans and the rotational D-rot diffusion coefficients and the associated isodiffusivity lines in the phi - X-0 plane. For the first time, we characterize the cage effect through the logarithmic time derivative of log and log . These quantities exhibit a minimum if the system is supercooled and we show that, consistently with our previous findings, for large…

Curve packing and modulus estimates

2018

A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c > 0$. We strengthen Marstrand's result by showing that for $p > 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} > 0$.

Enhanced sampling in simulations of dense systems

2002

In the simulations of a variety of systems we encounter the problem of large relaxation times due to the dense packing of the systems constituents. We propose an algorithm to overcome this slowing down by temporarily allowing the constituents of a 3d systems to escape into a 4th space coordinate. The idea will be exemplified for the problem of a homopolymer collapse.

Synthesis, X-ray Structure of Two Hexa-Coordinated Ni(II) Complexes with s-Triazine Hydrazine Schiff Base Ligand

2023

The hydrazine s-triazine ligand (E)-4,4’-(6-(2-(1-(pyridin-2-yl)ethylidene)hydrazinyl)-1,3,5-triazine-2,4-diyl)dimorpholine (DMPT) was used to synthesize two new Ni(II) complexes via a self-assembly technique. The two complexes were synthesized by a one-pot synthesis strategy and characterized by elemental analysis, FTIR and single-crystal X-ray diffraction analysis to be [Ni(DMPT)(H2O)3](NO3)2.3H2O (1) and [Ni(DMPT)(H2O)3](NO3)2.H2O (2). The structures of both complexes were very similar regarding the coordination sphere and counter anions, but differ only in the number of the crystal water molecules. In the case of complex 1, there are three water molecules instead of one H2O molecu…