Flux Transport Dynamos: From Kinematics to Dynamics

Over the past several decades, Flux-Transport Dynamo (FTD) models have emerged as a popular paradigm for explaining the cyclic nature of solar magnetic activity. Their defining characteristic is the key role played by the mean meridional circulation in transporting magnetic flux and thereby regulating the cycle period. Most FTD models also incorporate the so-called Babcock-Leighton (BL) mechanism in which the mean poloidal field is produced by the emergence and subsequent dispersal of bipolar active regions. This feature is well grounded in solar observations and provides a means for assimilating observed surface flows and fields into the models in order to forecast future solar activity, to identify model biases, and to clarify the underlying physical processes. Furthermore, interpreting historical sunspot records within the context of FTD models can potentially provide insight into why cycle features such as amplitude and duration vary and what causes extreme events such as Grand Minima. Though they are generally robust in a modeling sense and make good contact with observed cycle features, FTD models rely on input physics that is only partially constrained by observation and that neglects the subtleties of convective transport, convective field generation, and nonlinear feedbacks. Here we review the formulation and application of FTD models and assess our current understanding of the input physics based largely on complementary 3D MHD simulations of solar convection, dynamo action, and flux emergence.

Agglomeration front dynamics: Drying in sessile nano-particle laden droplets

The drying of sessile, nano-silica laden water droplet is studied under ambient conditions, in the absence of any convection. The drying process can be divided into two distinct regimes. During regime 1, the outer edge of the droplet remains pinned and particles agglomerate at the droplet periphery similar to the traditional coffee ring. However in regime 2, with further evaporation, both the liquid contact line and the agglomeration front starts moving radially inwards from the initial contact edge. The contact between the liquid and the agglomerate is maintained throughout regime 2 and the vaporisation driven liquid edge recession essentially drives the inward growth of the particle deposition. Fast kinetics of particle aggregation results in rapid growth of this agglomeration front as seen from the experiments. A theoretical formulation involving a simplistic model of the agglomeration front growth based on particle mass balance has been proposed. (C) 2014 Elsevier Ltd. All rights reserved,

A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems

A finite difference method for a time-dependent singularly perturbed convection-diffusion-reaction problem involving two small parameters in one space dimension is considered. We use the classical implicit Euler method for time discretization and upwind scheme on the Shishkin-Bakhvalov mesh for spatial discretization. The method is analysed for convergence and is shown to be uniform with respect to both the perturbation parameters. The use of the Shishkin-Bakhvalov mesh gives first-order convergence unlike the Shishkin mesh where convergence is deteriorated due to the presence of a logarithmic factor. Numerical results are presented to validate the theoretical estimates obtained.

Influence of plate length and plate cooling rate on solidification and microstructure of A356 alloy produced by oblique plate

A356 alloy melt solidifies partially when it flows down on an oblique plate cooled from bottom by counter flowing water. Columnar dendrites are continuously formed on the plate wall. Because of the forced convection, these dendrites are sheared off into equiaxed/fragmented grains and then washed away continuously by producing semisolid slurry at plate exit. Plate cooling rate provides required extent/amount of solidification whereas plate length enables necessary shear for producing semisolid slurry of desired quality. Slurry obtained is solidified in metal mould to produce semisolid-cast billets of desired microstructure. Furthermore, semisolid-cast billets are also heat-treated to improve surface quality. Microstructures of both semisolid-cast and heat-treated billets are compared. The effects of plate length and plate cooling rate on solidification and microstructure of billets produced by using oblique plate are illustrated. Three different plate lengths (200 mm, 250 mm, 300 mm) associated with three different heat transfer coefficients (1000, 2000 and 2500 W/(m(2).K)) are involved. Plate length of 250 mm with heat transfer coefficient of 2000 W/(m(2).K) gives fine and globular microstructures and is the optimum as there is absolutely no possibility of sticking of slurry to plate wall.

Improved design methodology for the development of electrically actuated MEMS structures

A comprehensive design flow is proposed for the design of Micro Electro Mechanical Systems that are fabricated using SOIMUMPs process. Many of the designers typically do not model the temperature dependency of electrical conductivity, thermal conductivity and convection coefficient, as it is very cumbersome to create/incorporate the same in the existing FEM simulators. Capturing these dependencies is very critical particularly for structures that are electrically actuated. Lookup tables that capture the temperature dependency of electrical conductivity, thermal conductivity and convection coefficient are created. These look up tables are taken as inputs for a commercially available FEM simulator to model the semiconductor behavior. It is demonstrated that when temperature dependency for all the above mentioned parameters is not captured, then the error in estimation of the maximum temperature (for a given structure) could be as high as 30%. Error in the estimated resistance value under the same conditions is as high as 40%. When temperature dependency of the above mentioned parameters is considered then error w.r.t the measured values is less than 5%. It is evident that error in temperature estimates leads to erroneous results from mechanical simulations as well.

Gamma oscillations in the midbrain spatial attention network: linking circuits to function

Gamma-band (25-140 Hz) oscillations are ubiquitous in mammalian forebrain structures involved in sensory processing, attention, learning and memory. The optic tectum (01) is the central structure in a midbrain network that participates critically in controlling spatial attention. In this review, we summarize recent advances in characterizing a neural circuit in this midbrain network that generates large amplitude, space-specific, gamma oscillations in the avian OT, both in vivo and in vitro. We describe key physiological and pharmacological mechanisms that produce and regulate the structure of these oscillations. The extensive similarities between midbrain gamma oscillations in birds and those in the neocortex and hippocampus of mammals, offer important insights into the functional significance of a midbrain gamma oscillatory code.

THREE-LAYER FLUID FLOW OVER A SMALL OBSTRUCTION ON THE BOTTOM OF A CHANNEL

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms.

Decreasing intensity of monsoon low-frequency intraseasonal variability over India

Understanding the changing nature of the intraseasonal oscillatory (ISO) modes of Indian summer monsoon manifested by active and break phase, and their association with extreme rainfall events are necessary for probabilistic estimation of flood-related risks in a warming climate. Here, using ground-based observed rainfall, we define an index to measure the strength of monsoon ISOs and show that the relative strength of the northward-propagating low-frequency ISO (20-60 days) modes have had a significant decreasing trend during the past six decades, possibly attributed to the weakening of large-scale circulation in the region during monsoon season. This reduction is compensated by a gain in synoptic-scale (3-9 days) variability. The decrease in low-frequency ISO variability is associated with a significant decreasing trend in the percentage of extreme events during the active phase of the monsoon. However, this decrease is balanced by significant increasing trends in the percentage of extreme events in the break and transition phases. We also find a significant rise in the occurrence of extremes during early and late monsoon months, mainly over eastern coastal regions. Our study highlights the redistribution of rainfall intensity among periodic (low-frequency) and non-periodic (extreme) modes in a changing climate scenario.

Interaction of a vortex ring with a single bubble: bubble and vorticity dynamics

The interaction of a single bubble with a single vortex ring in water has been studied experimentally. Measurements of both the bubble dynamics and vorticity dynamics have been done to help understand the two-way coupled problem. The circulation strength of the vortex ring (Gamma) has been systematically varied, while keeping the bubble diameter (D-b) constant, with the bubble volume to vortex core volume ratio (V-R) also kept fixed at about 0.1. The other important parameter in the problem is a Weber number based on the vortex ring strength. (We = 0.87 rho(Gamma/2 pi a)(2)/(sigma/D-b); a = vortex core radius, sigma = surface tension), which is varied over a large range, We = 3-406. The interaction between the bubble and ring for each of the We cases broadly falls into four stages. Stage I is before capture of the bubble by the ring where the bubble is drawn into the low-pressure vortex core, while in stage II the bubble is stretched in the azimuthal direction within the ring and gradually broken up into a number of smaller bubbles. Following this, in stage III the bubble break-up is complete and the resulting smaller bubbles slowly move around the core, and finally in stage IV the bubbles escape. Apart from the effect of the ring on the bubble, the bubble is also shown to significantly affect the vortex ring, especially at low We (We similar to 3). In these low-We cases, the convection speed drops significantly compared to the base case without a bubble, while the core appears to fragment with a resultant large decrease in enstrophy by about 50 %. In the higher-We cases (We > 100), there are some differences in convection speed and enstrophy, but the effects are relatively small. The most dramatic effects of the bubble on the ring are found for thicker core rings at low We (We similar to 3) with the vortex ring almost stopping after interacting with the bubble, and the core fragmenting into two parts. The present idealized experiments exhibit many phenomena also seen in bubbly turbulent flows such as reduction in enstrophy, suppression of structures, enhancement of energy at small scales and reduction in energy at large scales. These similarities suggest that results from the present experiments can be helpful in better understanding interactions of bubbles with eddies in turbulent flows.

Event-triggered sampling using signal extrema for instantaneous amplitude and instantaneous frequency estimation

Event-triggered sampling (ETS) is a new approach towards efficient signal analysis. The goal of ETS need not be only signal reconstruction, but also direct estimation of desired information in the signal by skillful design of event. We show a promise of ETS approach towards better analysis of oscillatory non-stationary signals modeled by a time-varying sinusoid, when compared to existing uniform Nyquist-rate sampling based signal processing. We examine samples drawn using ETS, with events as zero-crossing (ZC), level-crossing (LC), and extrema, for additive in-band noise and jitter in detection instant. We find that extrema samples are robust, and also facilitate instantaneous amplitude (IA), and instantaneous frequency (IF) estimation in a time-varying sinusoid. The estimation is proposed solely using extrema samples, and a local polynomial regression based least-squares fitting approach. The proposed approach shows improvement, for noisy signals, over widely used analytic signal, energy separation, and ZC based approaches (which are based on uniform Nyquist-rate sampling based data-acquisition and processing). Further, extrema based ETS in general gives a sub-sampled representation (relative to Nyquistrate) of a time-varying sinusoid. For the same data-set size captured with extrema based ETS, and uniform sampling, the former gives much better IA and IF estimation. (C) 2015 Elsevier B.V. All rights reserved.

Surface motions and intraplate continental deformation in Alaska driven by mantle flow

The degree to which the lithosphere and mantle are coupled and contribute to surface deformation beneath continental regions remains a fundamental question in the field of geodynamics. Here we use a new approach with a surface deformation field constrained by GPS, geologic, and seismicity data, together with a lithospheric geodynamic model, to solve for tractions inferred to be generated by mantle convection that (1) drive extension within interior Alaska generating southward directed surface motions toward the southern convergent plate boundary, (2) result in accommodation of the relative motions between the Pacific and North America in a comparatively small zone near the plate boundary, and (3) generate the observed convergence within the North American plate interior in the Mackenzie mountains in northwestern Canada. The evidence for deeper mantle influence on surface deformation beneath a continental region suggests that this mechanism may be an important contributing driver to continental plate assemblage and breakup.

Magnetometry using Ramsey interferometry in a Yb atomic beam

We use the Ramsey separated oscillatory fields technique in a 400 degrees C thermal beam of ytterbium (Yb) atoms to measure the Larmor precession frequency (and hence the magnetic field) with high precision. For the experiment, we use the strongly allowed S-1(0) P-1(1) transition at 399 nm, and choose the odd isotope Yb-171 with nuclear spin I = 1/2, so that the ground state has only two magnetic sublevels m(F) = +/- 1/2. With a magnetic field of 22.2 G and a separation of about 400 mm between the oscillatory fields, the central Ramsey fringe is at 16.64 kHz and has a width of 350 Hz. The technique can be readily adapted to a cold atomic beam, which is expected to give more than an order-of-magnitude improvement in precision. The signal-to-noise ratio is comparable to other techniques of magnetometry; therefore it should be useful for all kinds of precision measurements such as searching for a permanent electric dipole moment in atoms.

Simulations of impinging droplets with surfactant-dependent dynamic contact angle

An arbitrary Lagrangian-Eulerian (ALE) finite element scheme for computations of soluble surfactant droplet impingement on a horizontal surface is presented. The numerical scheme solves the time-dependent Navier-Stokes equations for the fluid flow, scalar convection-diffusion equation for the surfactant transport in the bulk phase, and simultaneously, surface evolution equations for the surfactants on the free surface and on the liquid-solid interface. The effects of surfactants on the flow dynamics are included into the model through the surface tension and surfactant-dependent dynamic contact angle. In particular, the dynamic contact angle (theta(d)) of the droplet is defined as a function of the surfactant concentration at the contact line and the equilibrium contact angle (theta(0)(e)) of the clean surface using the nonlinear equation of state for surface tension. Further, the surface forces are included into the model as surface divergence of the surface stress tensor that allows to incorporate the Marangoni effects without calculating the surface gradient of the surfactant concentration on the free surface. In addition to a mesh convergence study and validation of the numerical results with experiments, the effects of adsorption and desorption surfactant coefficients on the flow dynamics in wetting, partially wetting and non-wetting droplets are studied in detail. It is observed that the effects of surfactants are more in wetting droplets than in the non-wetting droplets. Further, the presence of surfactants at the contact line reduces the equilibrium contact angle further when theta(0)(e) is less than 90 degrees, and increases it further when theta(0)(e) is greater than 90 degrees. Nevertheless, the presence of surfactants has no effect on the contact angle when theta(0)(e) = 90 degrees. The numerical study clearly demonstrates that the surfactant-dependent contact angle has to be considered, in addition to the Marangoni effect, in order to study the flow dynamics and the equilibrium states of surfactant droplet impingement accurately. The proposed numerical scheme guarantees the conservation of fluid mass and of the surfactant mass accurately. (C) 2015 Elsevier Inc. All rights reserved.

Role of upward leaders in modifying the induced currents in solitary down-conductors during a nearby lightning strike to ground

Electromagnetic field produced by a lightning strike to ground causes significant induction to tall objects in the vicinity. The frequency of occurrence of such nearby ground strikes can be higher than the number of direct strikes. Therefore, a complete knowledge on these induced currents is of practical relevance. However, limited efforts towards the characterisation of such induced currents in tall down-conductors could be seen in the literature. Due to the intensification of the background field caused by the descending stepped leader, tall towers/down-conductors can launch upward leaders of significant length. The nonlinearity in the conductance of upward leader and the surrounding corona sheath can alter the characteristics of the induced currents. Preliminary aspects of this phenomenon have been studied by the author previously and the present work aims to perform a detailed investigation on the role of upward leaders in modifying the characteristics of the induced currents. A consistent model for the upward leader, which covers all the essential electrical aspects of the phenomena, is employed. A first order arc model for representing the conductance of upward leader and a field dependant quadratic conductivity model for the corona sheath is employed. The initial gradient in the upward leader and the field produced by the return stroke forms the excitation. The dynamic electromagnetic response is determined by solving the wave equation using thin-wire time-domain formulation. Simulations are carried out initially to ascertain the role of individual parameters, including the length of the upward leader. Based on the simulation results, it is shown that the upward leader enhances the induced current, and when significant in length, can alter the waveshape of induced current from bipolar oscillatory to unipolar. The duration of the induced current is governed by the length of upward leader, which in turn is dependant on the return stroke current and the effective length of the down-conductor. If the current during the upward leader developmental phase is considered along with that after the stroke termination to ground, it would present a bipolar current pulse. (C) 2015 Elsevier Ltd. All rights reserved.

PERIODIC CONTROLS IN AN OSCILLATING DOMAIN: CONTROLS VIA UNFOLDING AND HOMOGENIZATION

An optimal control problem in a two-dimensional domain with a rapidly oscillating boundary is considered. The main features of this article are on two points, namely, we consider periodic controls in the thin periodic slabs of period epsilon > 0, a small parameter, and height O(1) in the oscillatory part, and the controls are characterized using unfolding operators. We then do a homogenization analysis of the optimal control problems as epsilon -> 0 with L-2 as well as Dirichlet (gradient-type) cost functionals.