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

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 $I-V$ 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

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

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 $250 {\rm mK}$. 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

Collective Transport in Arrays of Quantum Dots

(WORDS: QUANTUM DOTS, COLLECTIVE TRANSPORT, PHYSICAL EXAMPLE OF KPZ) Collective charge transport is studied in one- and two-dimensional arrays of small normal-metal dots separated by tunnel barriers. At temperatures well below the charging energy of a dot, disorder leads to a threshold for conduction which grows linearly with the size of the array. For short-ranged interactions, one of the correlation length exponents near threshold is found from a novel argument based on interface growth. The dynamical exponent for the current above threshold is also predicted analytically, and the requirements for its experimental observation are described.Comment: 12 pages, 3 postscript files included, REVTEX v2, (also available by anonymous FTP from external.nj.nec.com, in directory /pub/alan/dotarrays [as separate files]) [replacement: FIX OF WRONG VERSION, BAD SHAR] March 17, 1993, NEC

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