76,264 research outputs found
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 ( and
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
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