380 research outputs found
Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem
A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second-order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter. No mesh aspect ratio assumption is made. Numerical results are presented that support our theoretical estimat
One and two dimensional tunnel junction arrays in weak Coulomb blockade regime-absolute accuracy in thermometry
We have investigated one and two dimensional (1D and 2D) arrays of tunnel
junctions in partial Coulomb blockade regime. The absolute accuracy of the
Coulomb blockade thermometer is influenced by the external impedance of the
array, which is not the same in the different topologies of 1D and 2D arrays.
We demonstrate, both by experiment and by theoretical calculations in simple
geometries, that the 1D structures are better in this respect. Yet in both 1D
and 2D, the influence of the environment can be made arbitrarily small by
making the array sufficiently large.Comment: 11 pages, 3 figure
A new iterative algorithm for solving the fictitious fluxes method problems for elliptic equations
Geometrically Induced Multiple Coulomb Blockade Gaps
We have theoretically investigated the transport properties of a ring-shaped
array of small tunnel junctions, which is weakly coupled to the drain
electrode. We have found that the long range interaction together with the
semi-isolation of the array bring about the formation of stable standing
configurations of electrons. The stable configurations break up during each
transition from odd to even number of trapped electrons, leading to multiple
Coulomb blockade gaps in the the characteristics of the system.Comment: 4 Pages (two-columns), 4 Figures, to be published in Physical Review
Letter
Asymptotic homogenisation in strength and fatigue durability analysis of composites
This is the post-print version of the Article. Copyright @ 2003 Kluwer Academic Publishers.Asymptotic homogenisation technique and two-scale convergence is used for analysis of macro-strength and fatigue durability of composites with a periodic structure under cyclic loading. The linear damage accumulation rule is employed in the phenomenological micro-durability conditions (for each component of the composite) under varying cyclic loading. Both local and non-local strength and durability conditions are analysed. The strong convergence of the strength as the structure period tends to zero is proved and its limiting value is estimated.This work was supported under the research grant GR/M24592 from the Engineering and Physical Sciences Research Council, UK
Shot Noise of Single-Electron Tunneling in 1D Arrays
We have used numerical modeling and a semi-analytical calculation method to
find the low frequency value S_{I}(0) of the spectral density of fluctuations
of current through 1D arrays of small tunnel junctions, using the ``orthodox
theory'' of single-electron tunneling. In all three array types studied, at low
temperature (kT << eV), increasing current induces a crossover from the
Schottky value S_{I}(0)=2e to the ``reduced Schottky value''
S_{I}(0)=2e/N (where N is the array length) at some crossover current I_{c}.
In uniform arrays over a ground plane, I_{c} is proportional to exp(-\lambda
N), where 1/\lambda is the single-electron soliton length. In arrays without a
ground plane, I_{c} decreases slowly with both N and \lambda. Finally, we have
calculated the statistics of I_{c} for ensembles of arrays with random
background charges. The standard deviation of I_{c} from the ensemble average
is quite large, typically between 0.5 and 0.7 of , while the
dependence of on N or \lambda is so weak that it is hidden within the
random fluctuations of the crossover current.Comment: RevTex. 21 pages of text, 10 postscript figure
Classical-to-stochastic Coulomb blockade cross-over in aluminum arsenide wires
We report low-temperature differential conductance measurements in aluminum
arsenide cleaved-edge overgrown quantum wires in the pinch-off regime. At zero
source-drain bias we observe Coulomb blockade conductance resonances that
become vanishingly small as the temperature is lowered below . We
show that this behavior can be interpreted as a classical-to-stochastic Coulomb
blockade cross-over in a series of asymmetric quantum dots, and offer a
quantitative analysis of the temperature-dependence of the resonances
lineshape. The conductance behavior at large source-drain bias is suggestive of
the charge density wave conduction expected for a chain of quantum dots.Comment: version 2: new figure 4, refined discussio
Overall Dynamic Properties of 3-D periodic elastic composites
A method for the homogenization of 3-D periodic elastic composites is
presented. It allows for the evaluation of the averaged overall frequency
dependent dynamic material constitutive tensors relating the averaged dynamic
field variable tensors of velocity, strain, stress, and linear momentum. The
formulation is based on micromechanical modeling of a representative unit cell
of a composite proposed by Nemat-Nasser & Hori (1993), Nemat-Nasser et. al.
(1982) and Mura (1987) and is the 3-D generalization of the 1-D elastodynamic
homogenization scheme presented by Nemat-Nasser & Srivastava (2011). We show
that for 3-D periodic composites the overall compliance (stiffness) tensor is
hermitian, irrespective of whether the corresponding unit cell is geometrically
or materially symmetric.Overall mass density is shown to be a tensor and, like
the overall compliance tensor, always hermitian. The average strain and linear
momentum tensors are, however, coupled and the coupling tensors are shown to be
each others' hermitian transpose. Finally we present a numerical example of a
3-D periodic composite composed of elastic cubes periodically distributed in an
elastic matrix. The presented results corroborate the predictions of the
theoretical treatment.Comment: 26 pages, 2 figures, submitted to Proceedings of the Royal Society
Crossover from time-correlated single-electron tunneling to that of Cooper pairs
We have studied charge transport in a one-dimensional chain of small
Josephson junctions using a single-electron transistor. We observe a crossover
from time-correlated tunneling of single electrons to that of Cooper pairs as a
function of both magnetic field and current. At relatively high magnetic field,
single-electron transport dominates and the tunneling frequency is given by
f=I/e, where I is the current through the chain and e is the electron's charge.
As the magnetic field is lowered, the frequency gradually shifts to f=I/2e for
I>200 fA, indicating Cooper-pair transport. For the parameters of the measured
sample, we expect the Cooper-pair transport to be incoherent.Comment: 5 pages, 4 figures; v2: minor changes, clarifications, addition
Designable electron transport features in one-dimensional arrays of metallic nanoparticles: Monte Carlo study of the relation between shape and transport
We study the current and shot noise in a linear array of metallic
nanoparticles taking explicitly into consideration their discrete electronic
spectra. Phonon assisted tunneling and dissipative effects on single
nanoparticles are incorporated as well. The capacitance matrix which determines
the classical Coulomb interaction within the capacitance model is calculated
numerically from a realistic geometry. A Monte Carlo algorithm which
self-adapts to the size of the system allows us to simulate the single-electron
transport properties within a semiclassical framework. We present several
effects that are related to the geometry and the one-electron level spacing
like e.g. a negative differential conductance (NDC) effect. Consequently these
effects are designable by the choice of the size and arrangement of the
nanoparticles.Comment: 13 pages, 12 figure
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