Properties Of Sphere Packings Research Articles

Thermal and hydraulic properties of sphere packings using a novel lattice Boltzmann model

A novel LB model is introduced to deal with the thermal and hydraulic properties in porous media. The pressure and density are separated in the proposed incompressible LB model and solid volume fraction is embedded in the formulations. Moreover, a modified thermal LB model is proposed that is shown to be more accurate than the Gue’s type of models. This model treats the energy equation with the second order of accuracy without any additional terms. The model is employed in a packing of monodisperse spherical particles within a rectangular channel. The results of new model have been improved as compared to the analytical solution.

Some properties of three-periodic sphere packings

Some properties of sphere packings are reviewed. Candidates for the least-dense packings of one kind of sphere for different coordination numbers are identified and described. Some topological properties of sphere packing nets are also described.

An Extension of Craig's Family of Lattices

AbstractLet p be a prime, and let ζp be a primitive p-th root of unity. The lattices in Craig's family are (p –1)-dimensional and are geometrical representations of the integral ℤ[ζp]-ideals 〈1–ζp〉i , where i is a positive integer. This lattice construction technique is a powerful one. Indeed, in dimensions p – 1 where 149 ≤ p ≤ 3001, Craig's lattices are the densest packings known. Motivated by this, we construct (p – 1)(q – 1)-dimensional lattices from the integral ℤ[ζpq]-ideals 〈1 – ζp〉i〈1 – ζq〉j, where p and q are distinct primes and i and j are positive integers. In terms of sphere-packing density, the new lattices and those in Craig's family have the same asymptotic behavior. In conclusion, Craig's family is greatly extended while preserving its sphere-packing properties.

Lattice-Based Linear Precoding for MIMO Channels With Transmitter CSI

Herein, the design of linear dispersion codes for multiple-input multiple-output communication systems is investigated. The receiver as well as the transmitter are assumed to have perfect knowledge of the channel, and the receiver is assumed to employ maximum likelihood detection. We propose to use linear precoding and lattice invariant operations to transform the channel matrix into a lattice generator matrix with large minimum distance separation. With appropriate approximations, it is shown that this corresponds to selecting lattices with good sphere-packing properties. Lattice invariant transformations are then used to minimize the power consumption. An algorithm for this power minimization is presented along with a lower bound on the optimization. Numerical results indicate significant gains by using the proposed method compared to channel diagonalization with adaptive bit loading.

Hexagonal Multiple Phase-and-Amplitude-Shift-Keyed Signal Sets

Selection of a particular signal set array for a bandwidthConstrained multiple phase-and-amplitude-shift-keyed (MPASK) communication system for a linear additive Gaussian noise channel requires consideration of factors such as average and/or peak power versus symbol error probability, signal amplitude dynamic range, simplicity of generation and detection, and number of bit errors per symbol error (Gray code properties). A simple technique is presented for generating and optimally detecting the honeycomb (hexagonal.) signal set, i.e., the signal set that has the tightest sphere-packing properties. The symbol and bit error probability performance of this set is compared to other two-dimensional signal sets that have been investigated in the literature, and is shown to be slightly superior from an average power standpoint. The paper concludes with a comparison of all of these signal sets from the standpoint of the factors listed above.