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

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

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

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

Towards single-electron metrology

We review the status of the understanding of single-electron transport (SET) devices with respect to their applicability in metrology. Their envisioned role as the basis of a high-precision electrical standard is outlined and is discussed in the context of other standards. The operation principles of single electron transistors, turnstiles and pumps are explained and the fundamental limits of these devices are discussed in detail. We describe the various physical mechanisms that influence the device uncertainty and review the analytical and numerical methods needed to calculate the intrinsic uncertainty and to optimise the fabrication and operation parameters. Recent experimental results are evaluated and compared with theoretical predictions. Although there are discrepancies between theory and experiments, the intrinsic uncertainty is already small enough to start preparing for the first SET-based metrological applications.Comment: 39 pages, 14 figures. Review paper to be published in International Journal of Modern Physics

On the effective shear speed in 2D phononic crystals

The quasistatic limit of the antiplane shear-wave speed ('effective speed') $c$ in 2D periodic lattices is studied. Two new closed-form estimates of $c$ are derived by employing two different analytical approaches. The first proceeds from a standard background of the plane wave expansion (PWE). The second is a new approach, which resides in $\mathbf{x}$-space and centers on the monodromy matrix (MM) introduced in the 2D case as the multiplicative integral, taken in one coordinate, of a matrix with components being the operators with respect to the other coordinate. On the numerical side, an efficient PWE-based scheme for computing $c$ is proposed and implemented. The analytical and numerical findings are applied to several examples of 2D square lattices with two and three high-contrast components, for which the new PWE and MM estimates are compared with the numerical data and with some known approximations. It is demonstrated that the PWE estimate is most efficient in the case of densely packed stiff inclusions, especially when they form a symmetric lattice, while in general it is the MM estimate that provides the best overall fitting accuracy.Comment: 13 pages, 9 figure

Internal control in the system of innovation management in the modern business environment

Introduction: At present, modern companies need to combine tasks of control and innovation development for successful functioning. Internal control should promote innovation activities and stimulate it. One of tasks of the internal control system at a company is timely identification and sustained support of innovation development. Methods: The authors use scientific methods of research, such as analysis and synthesis, deduction and induction, the laws of dialectics. As special methods, the authors used methods of innovation theory and management theory. The study is based on the works of such scientists as J. A. Schumpeter, N. D. Kondratyev, D. C. North, M. E. Porter, and K. S. Mullakhmetov. Results: The authors consider requirements to modern innovation development of the company; substantiate role of control as the main function of management; reveal features of internal control in the system of innovation management; formulate recommendations to improvement of internal control for active change of key indicators of economic activity of the company and suggest to use flexible (adaptive) control for increase in competitiveness of the company in the conditions of innovation development. Discussion: Innovation activity involves changing the key indicators that can lead to loss of the current position in the market. Risk of loss of competitiveness poses more threat for the company, than risk of loss of current profits. The control system must consider benefits and risks of innovation activities of the company. It is necessary to control key indicators of the company and to strive for their growth. Closing statement: Flexible control in innovation management system of the company will allow reducing risks of strategic changes when preserving the current market positions, Serials Publications Pvt. Ltd

A Numerical Study of Transport and Shot Noise at 2D Hopping

We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with the completely random distribution of localized sites in both space and energy, within a broad range of the applied electric field $E$ and temperature $T$, both within and beyond the variable-range hopping region. The calculated properties include not only dc current and statistics of localized site occupation and hop lengths, but also the current fluctuation spectrum. Within the calculation accuracy, the model does not exhibit $1/f$ noise, so that the low-frequency noise at low temperatures may be characterized by the Fano factor $F$. For sufficiently large samples, $F$ scales with conductor length $L$ as $(L_c/L)^{\alpha}$, where $\alpha=0.76\pm 0.08 < 1$, and parameter $L_c$ is interpreted as the average percolation cluster length. At relatively low $E$, the electric field dependence of parameter $L_c$ is compatible with the law $L_c\propto E^{-0.911}$ which follows from directed percolation theory arguments.Comment: 17 pages, 8 figures; Fixed minor typos and updated reference

High-frequency homogenization for periodic media

This article is available open access through the publisher’s website at the link below. Copyright @ 2010 The Royal Society.An asymptotic procedure based upon a two-scale approach is developed for wave propagation in a doubly periodic inhomogeneous medium with a characteristic length scale of microstructure far less than that of the macrostructure. In periodic media, there are frequencies for which standing waves, periodic with the period or double period of the cell, on the microscale emerge. These frequencies do not belong to the low-frequency range of validity covered by the classical homogenization theory, which motivates our use of the term ‘high-frequency homogenization’ when perturbing about these standing waves. The resulting long-wave equations are deduced only explicitly dependent upon the macroscale, with the microscale represented by integral quantities. These equations accurately reproduce the behaviour of the Bloch mode spectrum near the edges of the Brillouin zone, hence yielding an explicit way for homogenizing periodic media in the vicinity of ‘cell resonances’. The similarity of such model equations to high-frequency long wavelength asymptotics, for homogeneous acoustic and elastic waveguides, valid in the vicinities of thickness resonances is emphasized. Several illustrative examples are considered and show the efficacy of the developed techniques.NSERC (Canada) and the EPSRC