Search results for "PACKING"
showing 10 items of 150 documents
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…
Trunk Packing Revisited
2007
For trunk packing problems only few approximation schemes are known, mostly designed for the European standard DIN 70020 [6] with equally sized boxes [8, 9, 11, 12]. In this paper two discretized approaches for the US standard SAE J1100 [10] are presented, which make use of different box sizes. An exact branch-and-bound algorithm for weighted independent sets on graphs is given, using the special structure of the SAE standard. Another branch-and-bound packing algorithm using linear programs is presented. With these algorithms axis-oriented packings of different box sizes in an arbitrary trunk geometry can be computed efficiently.
Progress in the benchmark exercise for analyzing the lithiate breeder pebble bed thermo-mechanical behaviour
2006
The Helium Cooled Pebble Bed (HCPB) Blanket is one of the reference concepts for the European Breeding Blanket Programme for DEMO. In the reference blanket module, alternate layers of lithiated ceramics and beryllium pebbles act, respectively, as tritium breeder and neutron multiplier. The thermo-mechanical behaviour of both the pebble beds and their performances in reactor relevant conditions are also dependent on the pebble size and cell geometries (bed thickness, pebble packing factor, bed thermal conductivity). Therefore, in the EU Fusion Technology Programme, several out-of-pile experimental test campaigns have been performed to determine these behaviours. Theoretical calculations have…
Modelling mass transfer properties in a biotrickling filter for the removal of isopropanol
2014
Abstract A study was carried out to model mass transfer properties in biotrickling filters, treating isopropanol as the target pollutant. This study was extended to the mass transfer of oxygen related to the fact that the treatment of hydrophilic compounds by biotrickling filtration is often limited by oxygen. A simple method for each compound was developed based on their physical properties. The influence of temperature on Henry’s law constant of isopropanol was determined. An increase of 1.8 per 10 °C for the dimensionless Henry’s law constant was obtained. The determination of the overall mass transfer coefficients of isopropanol (KGa) was carried out, obtaining values between 500 and 18…
Molecular dynamics investigation of the premelting effects of Lennard-Jones (111) surfaces
1987
Molecular dynamics simulations have been performed to study the premelting effects of noble-gas surfaces (argon) close to but below the bulk melting temperature. In particular, the increase of disorder as a function of temperature at (111) surface has been considered. The truncated Lennard-Jones (6-12) potential is used to describe the interactions between particles. Surface premelting has been analyzed by means of total energies, trajectory plots, mean sequare displacement functions, diffusion coefficients, vacancy concentrations and two-dimensional order parameters. The (111) surface starts to disorder by vacancy formation, which leads to the premelting of the surface layer far below the …
Formation of Laves phases in buoyancy matched hard sphere suspensions.
2018
Colloidal Laves phases (LPs) are promising precursors for photonic materials. Laves phases have not yet been observed to form in experiments on colloidal suspensions of hard spheres (HS), even though they have been reported in computer simulations. LP formation so far has been achieved only for binary mixtures of colloidal charged spheres or ligand-stabilized nano-particles after drying. Using static light scattering, we monitored LP formation and annealing in a binary mixture of buoyant hard sphere approximants (size ratio Γ = 0.77, number or molar fraction of small spheres xS = 0.76) for volume fractions in the fluid-crystal coexistence regions. All samples spontaneously formed MgZn2 type…