Relativistic Spheres

By analyzing the Einstein's equations for the static sphere, we find that there exists a non-singular static configuration whose radius can approach its corresponding horizon size arbitrarily.Comment: 8 pages revtex, 1 ps figur

Exactly isochoric deformations of soft solids

Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus permits some volume changes, which become problematically large even at very small strains. Using a mixed coordinate transformation originally due to Gauss, we enforce the constraint of isochoric deformations exactly to develop a linear theory with perfect volume conservation that remains valid until strains become geometrically large. We demonstrate the utility of this approach by calculating the response of an infinite soft isochoric solid to a point force that leads to a nonlinear generalization of the Kelvin solution. Our approach naturally generalizes to a range of problems involving deformations of soft solids and interfaces in 2 dimensional and axisymmetric geometries, which we exemplify by determining the solution to a distributed load that mimics muscular contraction within the bulk of a soft solid

Iterative Near-Maximum-Likelihood Detection in Rank-Deficient Downlink SDMA Systems

Abstract—In this paper, a precoded and iteratively detected downlink multiuser system is proposed, which is capable of operating in rankdeficient scenarios, when the number of transmitters exceeds the number of receivers. The literature of uplink space division multiple access (SDMA) systems is rich, but at the time of writing there is a paucity of information on the employment of SDMA techniques in the downlink. Hence, we propose a novel precoded downlink SDMA (DL-SDMA) multiuser communication system, which invokes a low-complexity nearmaximum-likelihood sphere decoder and is particularly suitable for the aforementioned rank-deficient scenario. Powerful iterative decoding is carried out by exchanging extrinsic information between the precoder’s decoder and the outer channel decoder. Furthermore, we demonstrate with the aid of extrinsic information transfer charts that our proposed precoded DL-SDMA system has a better convergence behavior than its nonprecoded DL-SDMA counterpart. Quantitatively, the proposed system having a normalized system load of Ls = 1.333, i.e., 1.333 times higher effective throughput facilitated by having 1.333 times more DL-SDMA transmitters than receivers, exhibits a “turbo cliff” at an Eb/N0 of 5 dB and hence results in an infinitesimally low bit error rate (BER). By contrast, at Eb/N0 = 5 dB, the equivalent system dispensing with precoding exhibits a BER in excess of 10%. Index Terms—Iterative decoding, maximum likelihood detection, space division multiple access (SDMA) downlink, sphere decoding

Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation

The classical dynamics for a charged point particle with intrinsic spin is governed by a relativistic Hamiltonian for the orbital motion and by the Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is natural to ask whether the classical Hamiltonian (with both the orbital and spin parts) is consistent with that in the relativistic quantum theory for a spin-1/2 charged particle, which is described by the Dirac equation. In the low-energy limit, up to terms of the 7th order in $1/E_g$ ($E_g=2mc^2$ and $m$ is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation of the Dirac Hamiltonian in the presence of homogeneous and static electromagnetic fields and show that it is indeed in agreement with the classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through electromagnetic duality, this result can be generalized for a spin-1/2 dyon, which has both electric and magnetic charges and thus possesses both intrinsic electric and magnetic dipole moments. Furthermore, the relativistic quantum theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and gyroelectric ratios can be described by the Dirac-Pauli equation, which is the Dirac equation with augmentation for the anomalous electric and anomalous magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian is shown, up to the 7th order again, to be also in accord with the classical Hamiltonian.Comment: 18 page