Long-range order in a hard disk model in statistical mechanics
نویسنده
چکیده
We model two-dimensional crystals by a configuration space in which every admissible configuration is a hard disk configuration and a perturbed version of some triangular lattice with side length one. In this model we show that, under the uniform distribution, expected configurations in a given box are arbitrarily close to some triangular lattice whenever the particle density is chosen sufficiently high. This choice can be made independent of the box size.
منابع مشابه
Geometrical frustration in two dimensions: idealizations and realizations of a hard-disk fluid in negative curvature.
We examine a simple hard-disk fluid with no long-range interactions on the two-dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable, one-parameter model of disordered monodisperse hard disks. We extend free-area theory and the virial expans...
متن کاملInitial Results of Testing Some Statistical Properties of Hard Disks Workload in Personal Computers in Terms of Non-Extensive Entropy and Long-Range Dependencies
The aim of this paper is to present some preliminary results and non-extensive statistical properties of selected operating system counters related to hard drive behaviour. A number of experiments have been carried out in order to generate the workload and analyse the behaviour of computers during man–machine interaction. All analysed computers were personal ones, worked under Windows operating...
متن کاملA Numerical Investigation of TBM Disc Cutter Life Prediction in Hard Rocks
There is a direct relationship between the efficiency of mechanized excavation in hard rocks and that of disc cutters. Disc cutter wear is an important effective factor involved in the functionality of tunnel boring machines. Replacement of disc cutters is a time-consuming and costly activity that can significantly reduce the TBM utilization and advance rate, and has a major effect on the total...
متن کاملارائه یک مدل ریاضی جدید برای نفوذ پرتابه تکهای در هدف سرامیکی نیمه بینهایت
In this paper by analyzing the penetration mechanics of the segmented rods into semi-infinite ceramic targets, a mathematical model is provided to predict segmented rod projectiles penetration into semi-infinite ceramic targets. In analysis three factors of segments length, segments distance and number of segments are considered. Results suggest that the most important factor in penetration dep...
متن کاملMolecular dynamics simulation of a binary mixture lubricant for use in hard disk interfaces
In Hard Disk Drives (HDD), it is necessary to decrease the Flying Height (FH) between the head and the disk (currently, FH is around 3-5 nm) so as to increase recording densities. Retaining the solid lubricant has become a difficult proposition owing to intermittent contact between the surfaces. ZTMD and Z are used as solid lubricant to lubricate these interfaces. In this paper, the behavior of...
متن کامل