720 research outputs found
Extensions of Effective Medium Theory of Transport in Disordered Systems
Effective medium theory of transport in disordered systems, whose basis is
the replacement of spatial disorder by temporal memory, is extended in several
practical directions. Restricting attention to a 1-dimensional system with bond
disorder for specificity, a transformation procedure is developed to deduce,
from given distribution functions characterizing the system disorder, explicit
expressions for the memory functions. It is shown how to use the memory
functions in the Lapace domain forms in which they first appear, and in the
time domain forms which are obtained via numerical inversion algorithms, to
address time evolution of the system beyond the asymptotic domain of large
times normally treated. An analytic but approximate procedure is provided to
obtain the memories, in addition to the inversion algorithm. Good agreement of
effective medium theory predictions with numerically computed exact results is
found for all time ranges for the distributions used except near the
percolation limit as expected. The use of ensemble averages is studied for
normal as well as correlation observables. The effect of size on effective
mediumtheory is explored and it is shown that, even in the asymptotic limit,
finite size corrections develop to the well known harmonic mean prescription
for finding the effective rate. A percolation threshold is shown to arise even
in 1-d for finite (but not infinite) systems at a concentration of broken bonds
related to the system size. Spatially long range transfer rates are shown to
emerge naturally as a consequence of the replacement of spatial disorder by
temporal memories, in spite of the fact that the original rates possess nearest
neighbor character. Pausing time distributions in continuous time random walks
corresponding to the effective medium memories are calculated.Comment: 15 pages, 11 figure
Lagrange formulation of the symmetric teleparallel gravity
We develop a symmetric teleparallel gravity model in a space-time with only
the non-metricity is nonzero, in terms of a Lagrangian quadratic in the
non-metricity tensor. We present a detailed discussion of the variations that
may be used for any gravitational formulation. We seek Schwarzschild-type
solutions because of its observational significance and obtain a class of
solutions that includes Schwarzschild-type, Schwarzschild-de Sitter-type and
Reissner-Nordstr\"{o}m-type solutions for certain values of the parameters. We
also discuss the physical relevance of these solutions.Comment: Corrected typos, Accepted for publication in IJMP-
Symmetric Teleparallel Gravity: Some exact solutions and spinor couplings
In this paper we elaborate on the symmetric teleparallel gravity (STPG)
written in a non-Riemannian spacetime with nonzero nonmetricity, but zero
torsion and zero curvature. Firstly we give a prescription for obtaining the
nonmetricity from the metric in a peculiar gauge. Then we state that under a
novel prescription of parallel transportation of a tangent vector in this
non-Riemannian geometry the autoparallel curves coincides with those of the
Riemannian spacetimes. Subsequently we represent the symmetric teleparallel
theory of gravity by the most general quadratic and parity conserving
lagrangian with lagrange multipliers for vanishing torsion and curvature. We
show that our lagrangian is equivalent to the Einstein-Hilbert lagrangian for
certain values of coupling coefficients. Thus we arrive at calculating the
field equations via independent variations. Then we obtain in turn conformal,
spherically symmetric static, cosmological and pp-wave solutions exactly.
Finally we discuss a minimal coupling of a spin-1/2 field to STPG.Comment: Accepted for publication in the International Journal of Modern
Physics
Effects of disorder in location and size of fence barriers on molecular motion in cell membranes
The effect of disorder in the energetic heights and in the physical locations
of fence barriers encountered by transmembrane molecules such as proteins and
lipids in their motion in cell membranes is studied theoretically. The
investigation takes as its starting point a recent analysis of a periodic
system with constant distances between barriers and constant values of barrier
heights, and employs effective medium theory to treat the disorder. The
calculations make possible, in principle, the extraction of confinement
parameters such as mean compartment sizes and mean intercompartmental
transition rates from experimentally reported published observations. The
analysis should be helpful both as an unusual application of effective medium
theory and as an investigation of observed molecular movements in cell
membranes.Comment: 9 pages, 5 figure
Fault Models for Quantum Mechanical Switching Networks
The difference between faults and errors is that, unlike faults, errors can
be corrected using control codes. In classical test and verification one
develops a test set separating a correct circuit from a circuit containing any
considered fault. Classical faults are modelled at the logical level by fault
models that act on classical states. The stuck fault model, thought of as a
lead connected to a power rail or to a ground, is most typically considered. A
classical test set complete for the stuck fault model propagates both binary
basis states, 0 and 1, through all nodes in a network and is known to detect
many physical faults. A classical test set complete for the stuck fault model
allows all circuit nodes to be completely tested and verifies the function of
many gates. It is natural to ask if one may adapt any of the known classical
methods to test quantum circuits. Of course, classical fault models do not
capture all the logical failures found in quantum circuits. The first obstacle
faced when using methods from classical test is developing a set of realistic
quantum-logical fault models. Developing fault models to abstract the test
problem away from the device level motivated our study. Several results are
established. First, we describe typical modes of failure present in the
physical design of quantum circuits. From this we develop fault models for
quantum binary circuits that enable testing at the logical level. The
application of these fault models is shown by adapting the classical test set
generation technique known as constructing a fault table to generate quantum
test sets. A test set developed using this method is shown to detect each of
the considered faults.Comment: (almost) Forgotten rewrite from 200
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