Chua [IEEE Trans. Circuit Theory 1, 507 (1971).] argued that, in addition to the standard resistors, capacitors, and inductors, there must be a fourth fundamental element in electrical circuits, which he called a memory resistor or memristor. Strukov et al. [Nature (London) 453, 80 (2008)] showed how memristive behavior arises in some thin semiconducting films. Unlike other passive elements, however, a memristor with large sizes cannot be fabricated, because scale up of a memristor to dimensions of the order of microns causes loss of the memristive effect by decreasing the width of the doped region relative to the overall size of the memristor. A microscale memristor is, however, essential to most of the potential applications. One way of fabricating such a microscale memristor without losing the memristive effect is to make a network of very small interconnected memristors. We report the results of numerical simulations of electrical currents in such networks of interconnected memristors, as well as memristors and Ohmic conductors. The memristor networks exhibit a rich variety of interesting properties, including weakly and strongly memristive regimes, a possible first-order transition at the connectivity threshold, generation of second harmonics in the strongly memristive regime, and the universal dependence of the network's strength on the frequency. Moreover, we show that the polarity of the memristors can play an important role in the overall properties of the memristor network, in particular its speed of switching, which may have a potentially important application to faster computers. None of these properties are exhibited by linear resistor networks, or even by nonlinear resistor networks without a memory effect.

Abstract. We report the results of three dimensional molecular dynamic simulations on the angle of repose of a sandpile formed by pouring mono-sized cohesionless spherical grains into a granular Hele-Shaw cell. In particular, we are interested to investigate the effects of those variables which may impact significantly on pattern formation of granular mixtures in Hele-Shaw cells. The results indicate that the frictional forces influence remarkably the formation of pile on the grain level. Furthermore, We see that increasing grain insertion rate decreases slightly the angle of repose. We also find that in accordance with experimental results, the cell thickness is another significant factor and the angle of repose decays exponentially by increasing the cell thickness. It is shown that this effect can be interpreted as a cross-over from two to three dimensions. In fact, using grains with different sizes shows that the behavior of the angle of repose when both size and cell thickness are varied is controlled by a scaled function of the ratio of these two variables. † corresponding author

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We present a new mode of transport of spherical particles in a horizontally vibrated channel with sawtooth-shaped side walls. The underlying driving mechanism is based on an interplay of directional energy injection transformed by the sidewall collisions and density-dependent interparticle collisions. Experiments and matching numerics show that the average particle velocity reaches a maximum at 60% of the maximal filling density. Introducing a spatial phase shift between the channel boundaries increases the transport velocity by an order of magnitude.

We present an accurate and efficient algorithm to calculate the electrostatic interaction of charged point particles with partially periodic boundary conditions that are confined along the nonperiodic direction by two metallic parallel plates. The method preserves the original boundary conditions and hence, it does not introduce any kind of artifacts. In addition, it enjoys the quasilinear complexity of O (N ln(N )), where N being the number of particles in the simulation box. In fact, based on the superposition principle in electrostatics, the problem is split into two electrostatic problems where each one can be calculated by the appropriate Poisson solver. In this paper we apply the method to sodium chloride ultrathin films and investigate its dielectric response with respect to external bias voltage. We show how accurately in this method one can obtain the total charge induced on metallic boundaries to an arbitrary precision.