Second-order statistical structure of geomagnetic field reversals

From the autocorrelation function of geomagnetic polarity intervals, it is shown that the field reversal intervals are not independent but form a process akin to the Markov process, where the random input to the model is itself a moving average process. The input to the moving average model is, however, an independent Gaussian random sequence. All the parameters in this model of the geomagnetic field reversal have been estimated. In physical terms this model implies that the mechanism of reversal possesses a memory.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Phase diagram of a hard-sphere system in a quenched random potential: A numerical study

We report numerical results for the phase diagram in the density-disorder plane of a hard-sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy, and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first-order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.

Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Random sequential multilayer deposition of different‐sized k mers on a one dimensional infinite substrate

Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.

Probing the inter-tube transport in aligned and random multiwall carbon nanotubes

The temperature and magnetic field dependence of conductivity has been used to probe the inter-tube transport in multiwall carbon nanotubes (MWNTs). The scanning electron microscopy images show highly aligned and random distribution of MWNTs. The conductivity in aligned carbon nanotube (ACNT) and random carbon nanotube (RCNT) samples at low temperature follows T-1/2 (at T < 8 K) and T-3/4 (at T > 8 K) dependence in accordance with the weak localization and electron-electron (e-e) interaction model. The values of diffusion coefficient in ACNT and RCNT are 0.25 x 10(-2) and 0.71 x 10(-2) cm(2) s(-1), respectively, indicating that larger number of inter-tube junctions in later enhances the bulk transport. The positive magnetoconductance (MC) data in both samples show that the weak localization contribution is dominant. However, the saturation of MC at higher fields and lower temperatures indicate that e-e interaction is quite significant in RCNT. The T-3/4 and T-1/2 dependence of inelastic scattering length (l(in)) in ACNT and RCNT samples show that the inelastic e-e scattering is more important in aligned tubes. (C) 2011 American Institute of Physics. doi:10.1063/1.3552911]

Pulsed laser deposition of strontium titanate thin films for dynamic random access memory applications

Polycrystalline strontium titanate (SrTiO3) films were prepared by a pulsed laser deposition technique on p-type silicon and platinum-coated silicon substrates. The films exhibited good structural and dielectric properties which were sensitive to the processing conditions. The small signal dielectric constant and dissipation factor at a frequency of 100 kHz were about 225 and 0.03 respectively. The capacitance-voltage (C-V) characteristics in metal-insulator-semiconductor structures exhibited anomalous frequency dispersion behavior and a hysteresis effect. The hysteresis in the C-V curve was found to be about 1 V and of a charge injection type. The density of interface states was about 1.79 x 10(12) cm(-2). The charge storage density was found to be 40 fC mu m(-2) at an applied electric field of 200 kV cm(-1). Studies on current-voltage characteristics indicated an ohmic nature at lower voltages and space charge conduction at higher voltages. The films also exhibited excellent time-dependent dielectric breakdown behavior.

Effect of dynamical asymmetry on the viscosity of a random copolymer melt

The variation of the viscosity as a function of the sequence distribution in an A-B random copolymer melt is determined. The parameters that characterize the random copolymer are the fraction of A monomers f, the parameter lambda which determines the correlation in the monomer identities along a chain and the Flory chi parameter chi(F) which determines the strength of the enthalpic repulsion between monomers of type A and B. For lambda>0, there is a greater probability of finding like monomers at adjacent positions along the chain, and for lambda<0 unlike monomers are more likely to be adjacent to each other. The traditional Markov model for the random copolymer melt is altered to remove ultraviolet divergences in the equations for the renormalized viscosity, and the phase diagram for the modified model has a binary fluid type transition for lambda>0 and does not exhibit a phase transition for lambda<0. A mode coupling analysis is used to determine the renormalization of the viscosity due to the dependence of the bare viscosity on the local concentration field. Due to the dissipative nature of the coupling. there are nonlinearities both in the transport equation and in the noise correlation. The concentration dependence of the transport coefficient presents additional difficulties in the formulation due to the Ito-Stratonovich dilemma, and there is some ambiguity about the choice of the concentration to be used while calculating the noise correlation. In the Appendix, it is shown using a diagrammatic perturbation analysis that the Ito prescription for the calculation of the transport coefficient, when coupled with a causal discretization scheme, provides a consistent formulation that satisfies stationarity and the fluctuation dissipation theorem. This functional integral formalism is used in the present analysis, and consistency is verified for the present problem as well. The upper critical dimension for this type of renormaliaation is 2, and so there is no divergence in the viscosity in the vicinity of a critical point. The results indicate that there is a systematic dependence of the viscosity on lambda and chi(F). The fluctuations tend to increase the viscosity for lambda<0, and decrease the viscosity for lambda>0, and an increase in chi(F) tends to decrease the viscosity. (C) 1996 American Institute of Physics.

Low electric field, easily reversible electrical set and reset processes in a Ge15Te83Si2 glass for phase change memory applications

We report here an easily reversible set-reset process in a new Ge15Te83Si2 glass that could be a promising candidate for phase change random access memory applications. The I-V characteristics of the studied sample show a comparatively low threshold electric field (E-th) of 7.3 kV/cm. Distinct differences in the type of switching behavior are achieved by means of controlling the on state current. It enables the observation of a threshold type for less than 0.7 mA beyond memory type (set) switching. The set and reset processes have been achieved with a similar magnitude of 1 mA, and with a triangular current pulse for the set process and a short duration rectangular pulse of 10 msec width for the reset operation. Further, a self-resetting effect is seen in this material upon excitation with a saw-tooth/square pulse, and their response of leading and trailing edges are discussed. About 6.5 x 10(4) set-reset cycles have been undertaken without any damage to the device. (C) 2011 American Institute of Physics. doi: 10.1063/1.3574659]

Stabilizing a pulsed field emission from an array of carbon nanotubes

In this paper, we propose a new design configuration for a carbon nanotube (CNT) array based pulsed field emission device to stabilize the field emission current. In the new design, we consider a pointed height distribution of the carbon nanotube array under a diode configuration with two side gates maintained at a negative potential to obtain a highly intense beam of electrons localized at the center of the array. The randomly oriented CNTs are assumed to be grown on a metallic substrate in the form of a thin film. A model of field emission from an array of CNTs under diode configuration was proposed and validated by experiments. Despite high output, the current in such a thin film device often decays drastically. The present paper is focused on understanding this problem. The random orientation of the CNTs and the electromechanical interaction are modeled to explain the self-assembly. The degraded state of the CNTs and the electromechanical force are employed to update the orientation of the CNTs. Pulsed field emission current at the device scale is finally obtained by using the Fowler-Nordheim equation by considering a dynamic electric field across the cathode and the anode and integration of current densities over the computational cell surfaces on the anode side. Furthermore we compare the subsequent performance of the pointed array with the conventionally used random and uniform arrays and show that the proposed design outperforms the conventional designs by several orders of magnitude. Based on the developed model, numerical simulations aimed at understanding the effects of various geometric parameters and their statistical features on the device current history are reported.

FIELD EMISSION EFFICIENCY OF A CARBON NANOTUBE ARRAY UNDER PARASITIC NONLINEARITIES

Carbon Nanotubes (CNTs) grown on substrates are potential electron sources in field emission applications. Several studies have reported the use of CNTs in field emission devices, including field emission displays, X-ray tube, electron microscopes, cathode-ray lamps, etc. Also, in recent years, conventional cold field emission cathodes have been realized in micro-fabricated arrays for medical X-ray imaging. CNTbased field emission cathode devices have potential applications in a variety of industrial and medical applications, including cancer treatment. Field emission performance of a single isolated CNT is found to be remarkable, but the situation becomes complex when an array of CNTs is used. At the same time, use of arrays of CNTs is practical and economical. Indeed, such arrays on cathode substrates can be grown easily and their collective dynamics can be utilized in a statistical sense such that the average emission intensity is high enough and the collective dynamics lead to longer emission life. The authors in their previous publications had proposed a novel approach to obtain stabilized field emission current from a stacked CNT array of pointed height distribution. A mesoscopic modeling technique was employed, which took into account electro-mechanical forces in the CNTs, as well as transport of conduction electron coupled with electron phonon induced heat generation from the CNT tips. The reported analysis of pointed arrangements of the array showed that the current density distribution was greatly localized in the middle of the array, the scatter due to electrodynamic force field was minimized, and the temperature transients were much smaller compared to those in an array with random height distribution. In the present paper we develop a method to compute the emission efficiency of the CNT array in terms of the amount of electrons hitting the anode surface using trajectory calculations. Effects of secondary electron emission and parasitic capacitive nonlinearity on the current-voltage signals are accounted. Field emission efficiency of a stacked CNT array with various pointed height distributions are compared to that of arrays with random and uniform height distributions. Effect of this parasitic nonlinearity on the emission switch-on voltage is estimated by model based simulation and Monte Carlo method.

Percolative switching in transition metal dichalcogenide field-effect transistors at room temperature

We have addressed the microscopic transport mechanism at the switching or `on-off' transition in transition metal dichalcogenide (TMDC) field-effect transistors (FETs), which has been a controversial topic in TMDC electronics, especially at room temperature. With simultaneous measurement of channel conductivity and its slow time-dependent fluctuation (or noise) in ultrathin WSe2 and MoS2 FETs on insulating SiO2 substrates where noise arises from McWhorter-type carrier number fluctuations, we establish that the switching in conventional backgated TMDC FETs is a classical percolation transition in a medium of inhomogeneous carrier density distribution. From the experimentally observed exponents in the scaling of noise magnitude with conductivity, we observe unambiguous signatures of percolation in a random resistor network, particularly, in WSe2 FETs close to switching, which crosses over to continuum percolation at a higher doping level. We demonstrate a powerful experimental probe to the microscopic nature of near-threshold electrical transport in TMDC FETs, irrespective of the material detail, device geometry, or carrier mobility, which can be extended to other classes of 2D material-based devices as well.

Evolution of multivariant microstructures with anisotropic misfit: A phase field study

We study, in two dimensions, the effect of misfit anisotropy on microstructural evolution during precipitation of an ordered beta phase from a disordered alpha matrix; these phases have, respectively, 2- and 6-fold rotation symmetries. Thus, precipitation produces three orientational variants of beta phase particles, and they have an anisotropic (and crystallographically equivalent) misfit strain with the matrix. The anisotropy in misfit is characterized using a parameter t = epsilon(yy)/epsilon(xx), where epsilon(xx) and epsilon(yy) are the principal components of the misfit strain tensor. Our phase field, simulations show that the morphology of beta phase particles is significantly influenced by 1, the level of misfit anisotropy. Particles are circular in systems with dilatational misfit (t = 1), elongated along the direction of lower principal misfit when 0 < t < 1 and elongated along the invariant direction when - 1 <= t <= 0. In the special case of a pure shear misfit strain (t = - 1), the microstructure exhibits star, wedge and checkerboard patterns; these microstructural features are in agreement with those in Ti-Al-Nb alloys.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Orientational relaxation in a random dipolar lattice: Wave-number and frequency dependence

In order to understand the role of translational modes in the orientational relaxation in dense dipolar liquids, we have carried out a computer ''experiment'' where a random dipolar lattice was generated by quenching only the translational motion of the molecules of an equilibrated dipolar liquid. The lattice so generated was orientationally disordered and positionally random. The detailed study of orientational relaxation in this random dipolar lattice revealed interesting differences from those of the corresponding dipolar liquid. In particular, we found that the relaxation of the collective orientational correlation functions at the intermediate wave numbers was markedly slower at the long times for the random lattice than that of the liquid. This verified the important role of the translational modes in this regime, as predicted recently by the molecular theories. The single-particle orientational correlation functions of the random lattice also decayed significantly slowly at long times, compared to those of the dipolar liquid.