A Gaussian quadrature analysis of linear sweep voltammetry

The application of Gaussian Quadrature (GQ) procedures to the evaluation of i—E curves in linear sweep voltammetry is advocated. It is shown that a high degree of precision is achieved with these methods and the values obtained through GQ are in good agreement with (and even better than) the values reported in literature by Nicholson-Shain, for example. Another welcome feature with GQ is its ability to be interpreted as an elegant, efficient analytic approximation scheme too. A comparison of the values obtained by this approach and by a recent scheme based on series approximation proposed by Oldham is made and excellent agreement is shown to exist.

A semi-analytical particle filter for identification of nonlinear oscillators

Particle filters find important applications in the problems of state and parameter estimations of dynamical systems of engineering interest. Since a typical filtering algorithm involves Monte Carlo simulations of the process equations, sample variance of the estimator is inversely proportional to the number of particles. The sample variance may be reduced if one uses a Rao-Blackwell marginalization of states and performs analytical computations as much as possible. In this work, we propose a semi-analytical particle filter, requiring no Rao-Blackwell marginalization, for state and parameter estimations of nonlinear dynamical systems with additively Gaussian process/observation noises. Through local linearizations of the nonlinear drift fields in the process/observation equations via explicit Ito-Taylor expansions, the given nonlinear system is transformed into an ensemble of locally linearized systems. Using the most recent observation, conditionally Gaussian posterior density functions of the linearized systems are analytically obtained through the Kalman filter. This information is further exploited within the particle filter algorithm for obtaining samples from the optimal posterior density of the states. The potential of the method in state/parameter estimations is demonstrated through numerical illustrations for a few nonlinear oscillators. The proposed filter is found to yield estimates with reduced sample variance and improved accuracy vis-a-vis results from a form of sequential importance sampling filter.

Grids with multiple batch systems for performance enhancement of multi-component and parameter sweep parallel applications

In this work, we evaluate the benefits of using Grids with multiple batch systems to improve the performance of multi-component and parameter sweep parallel applications by reduction in queue waiting times. Using different job traces of different loads, job distributions and queue waiting times corresponding to three different queuing policies(FCFS, conservative and EASY backfilling), we conducted a large number of experiments using simulators of two important classes of applications. The first simulator models Community Climate System Model (CCSM), a prominent multi-component application and the second simulator models parameter sweep applications. We compare the performance of the applications when executed on multiple batch systems and on a single batch system for different system and application configurations. We show that there are a large number of configurations for which application execution using multiple batch systems can give improved performance over execution on a single system.

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

Quadrature generation techniques for frequency multiplication based oscillators

Frequency multiplication (FM) can be used to design low power frequency synthesizers. This is achieved by running the VCO at a much reduced frequency, while employing a power efficient frequency multiplier, and also thereby eliminating the first few dividers. Quadrature signals can be generated by frequency- multiplying low frequency I/Q signals, however this also multiplies the quadrature error of these signals. Another way is generating additional edges from the low-frequency oscillator (LFO) and develop a quadrature FM. This makes the I-Q precision heavily dependent on process mismatches in the ring oscillator. In this paper we examine the use of fewer edges from LFO and a single stage polyphase filter to generate approximate quadrature signals, which is then followed by an injection-locked quadrature VCO to generate high- precision I/Q signals. Simulation comparisons with the existing approach shows that the proposed method offers very good phase accuracy of 0.5deg with only a modest increase in power dissipation for 2.4 GHz IEEE 802.15.4 standard using UMC 0.13 mum RFCMOS technology.

Synchronization of globally coupled two-state stochastic oscillators with a state-dependent refractory period

We present a model of identical coupled two-state stochastic units, each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition.

A Nearly Exact Reformulation of the Girsanov Linearization for Stochastically Driven Nonlinear Oscillators

The Girsanov linearization method (GLM), proposed earlier in Saha, N., and Roy, D., 2007, ``The Girsanov Linearisation Method for Stochastically Driven Nonlinear Oscillators,'' J. Appl. Mech., 74, pp. 885-897, is reformulated to arrive at a nearly exact, semianalytical, weak and explicit scheme for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the reformulated linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories while weakly applying the Girsanov correction (the Radon-Nikodym derivative) for the linearization errors. The semianalyticity is due to an explicit linearization of the nonlinear drift terms and it plays a crucial role in keeping the Radon-Nikodym derivative ``nearly bounded'' above by the inverse of the linearization time step (which means that only a subset of linearized trajectories with low, yet finite, probability exceeds this bound). Drift linearization is conveniently accomplished via the first few (lower order) terms in the associated stochastic (Ito) Taylor expansion to exclude (multiple) stochastic integrals from the numerical treatment. Similarly, the Radon-Nikodym derivative, which is a strictly positive, exponential (super-) martingale, is converted to a canonical form and evaluated over each time step without directly computing the stochastic integrals appearing in its argument. Through their numeric implementations for a few low-dimensional nonlinear oscillators, the proposed variants of the scheme, presently referred to as the Girsanov corrected linearization method (GCLM), are shown to exhibit remarkably higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own.

Globally coupled stochastic two-state oscillators: Fluctuations due to finite numbers

Infinite arrays of coupled two-state stochastic oscillators exhibit well-defined steady states. We study the fluctuations that occur when the number N of oscillators in the array is finite. We choose a particular form of global coupling that in the infinite array leads to a pitchfork bifurcation from a monostable to a bistable steady state, the latter with two equally probable stationary states. The control parameter for this bifurcation is the coupling strength. In finite arrays these states become metastable: The fluctuations lead to distributions around the most probable states, with one maximum in the monostable regime and two maxima in the bistable regime. In the latter regime, the fluctuations lead to transitions between the two peak regions of the distribution. Also, we find that the fluctuations break the symmetry in the bimodal regime, that is, one metastable state becomes more probable than the other, increasingly so with increasing array size. To arrive at these results, we start from microscopic dynamical evolution equations from which we derive a Langevin equation that exhibits an interesting multiplicative noise structure. We also present a master equation description of the dynamics. Both of these equations lead to the same Fokker-Planck equation, the master equation via a 1/N expansion and the Langevin equation via standard methods of Ito calculus for multiplicative noise. From the Fokker-Planck equation we obtain an effective potential that reflects the transition from the monomodal to the bimodal distribution as a function of a control parameter. We present a variety of numerical and analytic results that illustrate the strong effects of the fluctuations. We also show that the limits N -> infinity and t -> infinity(t is the time) do not commute. In fact, the two orders of implementation lead to drastically different results.

Complex patterns arise through spontaneous symmetry breaking in dense homogeneous networks of neural oscillators

There has been much interest in understanding collective dynamics in networks of brain regions due to their role in behavior and cognitive function. Here we show that a simple, homogeneous system of densely connected oscillators, representing the aggregate activity of local brain regions, can exhibit a rich variety of dynamical patterns emerging via spontaneous breaking of permutation or translational symmetries. Upon removing just a few connections, we observe a striking departure from the mean-field limit in terms of the collective dynamics, which implies that the sparsity of these networks may have very important consequences. Our results suggest that the origins of some of the complicated activity patterns seen in the brain may be understood even with simple connection topologies.

Unsteady Compressible Boundary-Layer Flow On The Stagnation Line Of An Infinite Swept Cylinder

Numerical solutions of flow and heat transfer process on the unsteady flow of a compressible viscous fluid with variable gas properties in the vicinity of the stagnation line of an infinite swept cylinder are presented. Results are given for the case where the unsteady temperature field is produced by (i) a sudden change in the wall temperature (enthalpy) as the impulsive motion is started and (ii) a sudden change in the free-stream velocity. Solutions for the simultaneous development of the thermal and momentum boundary layers are obtained by using quasilinearization technique with an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady-state distribution. Results are presented for the skin friction and heat transfer coefficients as well as for the velocity and enthalpy profiles. The effects of wail enthalpy parameter, sweep parameter, fluid properties and transpiration cooling on the heat transfer and skin friction are considered.

Higher-Order Nonlinearity In Accretion Disks: Quasi-Periodic Oscillations Of Black Hole And Neutron Star Sources And Their Spin

We propose a unified model to explain Quasi-Periodic Oscillation (QPO), particularly of high frequency, observed from black hole and neutron star systems globally. We consider accreting systems to be damped harmonic oscillators exhibiting epicyclic oscillations with higher-order nonlinear resonance to explain QPO. The resonance is expected to be driven by the disturbance from the compact object at its spin frequency. The model explains various properties parallelly for both types of the compact object. It describes QPOs successfully for ten different compact sources. Based on this, we predict the spin frequency of the neutron star Sco X-1 and specific angular momentum of black holes GRO J1655–40, XTE J1550–564, H1743–322, and GRS 1915+105.

Extended Kalman filters using explicit and derivative-free local linearizations

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.

Structure and Rheology of Cationic Molecular Hydrogels of Quinuclidine Grafted Bile Salts. Influence of the Ionic Strength and Counter-Ion type

Quinuclidine grafted cationic bile salts are forming salted hydrogels. An extensive investigation of the effect of the electrolyte and counterions on the gelation has been envisaged. The special interest of the quinuclidine grafted bile salt is due to its broader experimental range of gelation to study the effect of electrolyte. Rheological features of the hydrogels are typical of enthalpic networks exhibiting a scaling law of the elastic shear modulus with the concentration (scaling exponent 2.2) modeling cellular solids in which the bending modulus is the dominant parameter. The addition of monovalent salt (NaCl) favors the formation of gels in a first range (0.00117 g cm-3 (0.02 M) < TNaCl < 0.04675 g cm-3 (0.8 M)). At larger salt concentrations, the gels become more heterogeneous with nodal zones in the micron scale. Small-angle neutron scattering experiments have been used to characterize the rigid fibers ( ≈ 68 Å) and the nodal zones. Stress sweep and creeprecovery measurements are used to relate the lack of linear viscoelastic domain to a mechanism of disentanglement of the fibers from their associations into fagots. The electrostatic interactions can be screened by addition of salt to induce a progressive evolution toward flocculation. SEM, UV absorbance, and SAXS study of the Bragg peak at large Q-values complete the investigation.

Electrochemical phase formation (ECPF): Nucleation growth vis-a-vis adsorption models

The nucleataon growth model of electrochemical phase formation is analysed for the hnear potential sweep input Apart from deducing diagnostic criteria and method~ of estimating model parameters, the predictions of the nucleation growth model are compared and contrasted with those of a sample adsorption model A dastlnCtlOn is made possible between adsorption and phase transition, which seems useful for understanding the nature of ECPF phenomena, especially underpotentlal deposition (UPD).

Viscoelastic Properties of Nanocrystalline Films of Semiconducting Chalcogenides at Liquid/Liquid Interface

The interfacial shear rheological properties of a continuous single-crystalline film of CuS and a 3D particulate gel of CdS nanoparticles (3−5 nm in diameter) formed at toluene−water interfaces have been studied. The ultrathin films (50 nm in thickness) are formed in situ in the shear cell through a reaction at the toluene−water interface between a metal−organic compound in the organic layer and an appropriate reagent for sulfidation in the aqueous layer. Linear viscoelastic spectra of the nanofilms reveal solid-like rheological behavior with the storage modulus higher than the loss modulus over the range of angular frequencies probed. Large strain amplitude sweep measurements on the CdS nanofilms formed at different reactant concentrations suggest that they form a weakly flocculated gel. Under steady shear, the films exhibit a yield stress, followed by a steady shear thinning at high shear rates. The viscoelastic and flow behavior of these films that are in common with those of many 3D “soft” materials like gels, foams, and concentrated colloidal suspensions can be described by the “soft” glassy rheology model.