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.

An extended finite element model coupled with level set method for stable pitting corrosion

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution), which requires only three inputs, namely the solid metal concentration, saturation concentration of the dissolved metal ions and diffusion coefficient. A combined eXtended Finite Element Model (XFEM) and level set method is developed in this paper. The extended finite element model handles the jump discontinuity in the metal concentrations at the interface, by using discontinuous-derivative enrichment formulation for concentration discontinuity at the interface. This eliminates the requirement of using front conforming mesh and re-meshing after each time step as in conventional finite element method. A numerical technique known as level set method tracks the position of the moving interface and updates it over time. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed method is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions.

An extended finite-element model coupled with level set method for analysis of growth of corrosion pits in metallic structures

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution). The interface experiences a jump discontinuity in metal concentration. The extended finite-element model (XFEM) handles this jump discontinuity by using discontinuous-derivative enrichment formulation, eliminating the requirement of using front conforming mesh and re-meshing after each time step as in the conventional finite-element method. However, prior interface location is required so as to solve the governing equations for concentration field for which a numerical technique, the level set method, is used for tracking the interface explicitly and updating it over time. The level set method is chosen as it is independent of shape and location of the interface. Thus, a combined XFEM and level set method is developed in this paper. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed model is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions. An empirical model for pitting potential is also derived based on the finite-element results. Studies show that pitting profile depends on factors such as ion concentration, solution pH and temperature to a large extent. Studying the individual and combined effects of these factors on pitting potential is worth knowing, as pitting potential directly influences corrosion rate.

A spectral multiscale method for wave propagation analysis: Atomistic-continuum coupled simulation

In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in system description across the interface between two scales, can be satisfactorily overcome by the proposed method. We propose an efficient spectral domain decomposition of the total fine scale displacement along with a potent macroscale equation in the Laplace domain to eliminate the spurious interfacial reflection. We use Laplace transform based spectral finite element method to model the macroscale, which provides the optimum approximations for required dynamic responses of the outer atoms of the simulated microscale region very accurately. This new method shows excellent agreement between the proposed multiscale model and the full molecular dynamics (MD) results. Numerical experiments of wave propagation in a 1D harmonic lattice, a 1D lattice with Lennard-Jones potential, a 2D square Bravais lattice, and a 2D triangular lattice with microcrack demonstrate the accuracy and the robustness of the method. In addition, under certain conditions, this method can simulate complex dynamics of crystalline solids involving different spatial and/or temporal scales with sufficient accuracy and efficiency. (C) 2014 Elsevier B.V. All rights reserved.

Long range emission enhancement and anisotropy in coupled quantum dots induced by aligned gold nanoantenna

Quantum dot arrays have been projected as the material of choice for next generation displays and photodetectors. Extensive ongoing research aims at improving optical and electrical efficiencies of such devices. We report experimental results on non-local long range emission intensity enhancement and anisotropy in quantum dot assemblies induced by isolated and partially aligned gold nanoantennas. Spatially resolved photoluminescence clearly demonstrate that the effect is maximum, when the longitudinal surface plasmon resonance of the nanoantenna is resonant with the emission maxima of the quantum dots. We estimated the decay length of this enhancement to be similar to 2.6 mu m, which is considerably larger than the range of near field interaction of metal nanoantenna. Numerical simulations qualitatively capture the near field behavior of the nanorods but fail to match the experimentally observed non-local effects. We have suggested how strong interactions of quantum dots in the close packed assemblies, mediated by the nanoantennas, could lead to such observed behavior. (C) 2014 AIP Publishing LLC.

Development and Evaluation of Statistical Downscaling Models for Monthly Precipitation

Several statistical downscaling models have been developed in the past couple of decades to assess the hydrologic impacts of climate change by projecting the station-scale hydrological variables from large-scale atmospheric variables simulated by general circulation models (GCMs). This paper presents and compares different statistical downscaling models that use multiple linear regression (MLR), positive coefficient regression (PCR), stepwise regression (SR), and support vector machine (SVM) techniques for estimating monthly rainfall amounts in the state of Florida. Mean sea level pressure, air temperature, geopotential height, specific humidity, U wind, and V wind are used as the explanatory variables/predictors in the downscaling models. Data for these variables are obtained from the National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) reanalysis dataset and the Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled Global Climate Model, version 3 (CGCM3) GCM simulations. The principal component analysis (PCA) and fuzzy c-means clustering method (FCM) are used as part of downscaling model to reduce the dimensionality of the dataset and identify the clusters in the data, respectively. Evaluation of the performances of the models using different error and statistical measures indicates that the SVM-based model performed better than all the other models in reproducing most monthly rainfall statistics at 18 sites. Output from the third-generation CGCM3 GCM for the A1B scenario was used for future projections. For the projection period 2001-10, MLR was used to relate variables at the GCM and NCEP grid scales. Use of MLR in linking the predictor variables at the GCM and NCEP grid scales yielded better reproduction of monthly rainfall statistics at most of the stations (12 out of 18) compared to those by spatial interpolation technique used in earlier studies.

Assignment of the C-13 NMR spectrum by correlation to dipolar coupled proton-pairs and estimation of order parameters of a thiophene based liquid crystal

Materials with widely varying molecular topologies and exhibiting liquid crystalline properties have attracted considerable attention in recent years. C-13 NMR spectroscopy is a convenient method for studying such novel systems. In this approach the assignment of the spectrum is the first step which is a non-trivial problem. Towards this end, we propose here a method that enables the carbon skeleton of the different sub-units of the molecule to be traced unambiguously. The proposed method uses a heteronuclear correlation experiment to detect pairs of nearby carbons with attached protons in the liquid crystalline core through correlation of the carbon chemical shifts to the double-quantum coherences of protons generated through the dipolar coupling between them. Supplemented by experiments that identify non-protonated carbons, the method leads to a complete assignment of the spectrum. We initially apply this method for assigning the C-13 spectrum of the liquid crystal 4-n-pentyl-4'-cyanobiphenyl oriented in the magnetic field. We then utilize the method to assign the aromatic carbon signals of a thiophene based liquid crystal thereby enabling the local order-parameters of the molecule to be estimated and the mutual orientation of the different sub-units to be obtained.

A strongly coupled anisotropic fluid from dilaton driven holography

We consider a system consisting of 5 dimensional gravity with a negative cosmological constant coupled to a massless scalar, the dilaton. We construct a black brane solution which arises when the dilaton satisfies linearly varying boundary conditions in the asymptotically AdS(5) region. The geometry of this black brane breaks rotational symmetry while preserving translational invariance and corresponds to an anisotropic phase of the system. Close to extremality, where the anisotropy is big compared to the temperature, some components of the viscosity tensor become parametrically small compared to the entropy density. We study the quasi normal modes in considerable detail and find no instability close to extremality. We also obtain the equations for fluid mechanics for an anisotropic driven system in general, working upto first order in the derivative expansion for the stress tensor, and identify additional transport coefficients which appear in the constitutive relation. For the fluid of interest we find that the parametrically small viscosity can result in a very small force of friction, when the fluid is enclosed between appropriately oriented parallel plates moving with a relative velocity.

Performance evaluation of AR4 Climate Models in simulating daily precipitation over the Indian region using skill scores

The ability of Coupled General Circulation Models (CGCMs) participating in the Intergovernmental Panel for Climate Change's fourth assessment report (IPCC AR4) for the 20th century climate (20C3M scenario) to simulate the daily precipitation over the Indian region is explored. The skill is evaluated on a 2.5A degrees x 2.5A degrees grid square compared with the Indian Meteorological Department's (IMD) gridded dataset, and every GCM is ranked for each of these grids based on its skill score. Skill scores (SSs) are estimated from the probability density functions (PDFs) obtained from observed IMD datasets and GCM simulations. The methodology takes into account (high) extreme precipitation events simulated by GCMs. The results are analyzed and presented for three categories and six zones. The three categories are the monsoon season (JJASO - June to October), non-monsoon season (JFMAMND - January to May, November, December) and for the entire year (''Annual''). The six precipitation zones are peninsular, west central, northwest, northeast, central northeast India, and the hilly region. Sensitivity analysis was performed for three spatial scales, 2.5A degrees grid square, zones, and all of India, in the three categories. The models were ranked based on the SS. The category JFMAMND had a higher SS than the JJASO category. The northwest zone had higher SSs, whereas the peninsular and hilly regions had lower SS. No single GCM can be identified as the best for all categories and zones. Some models consistently outperformed the model ensemble, and one model had particularly poor performance. Results show that most models underestimated the daily precipitation rates in the 0-1 mm/day range and overestimated it in the 1-15 mm/day range.

Hybrid Elements for Modelling Squeeze Film Effects Coupled with Structural Interactions in Vibratory MEMS Devices

We present a hybrid finite element based methodology to solve the coupled fluid structure problem of squeeze film effects in vibratory MEMS devices, such as gyroscopes, RF switches, and 2D resonators. The aforementioned devices often have a thin plate like structure vibrating normally to a fixed substrate, and are generally not perfectly vacuum packed. This results in a thin air film being trapped between the vibrating plate and the fixed substrate which behaves like a squeeze film offering both stiffness and damping. For accurate modelling of such devices the squeeze film effects must be incorporated. Extensive literature is available on squeeze film modelling, however only a few studies address the coupled fluid elasticity problem. The majority of the studies that account for the plate elasticity coupled with the fluid equation, either use approximate mode shapes for the plate or use iterative solution strategies. In an earlier work we presented a single step coupled methodology using only one type of displacement based element to solve the coupled problem. The displacement based finite element models suffer from locking issues when it comes to modelling very thin structures with the lateral dimensions much larger than the plate thickness as is typical in MEMS devices with squeeze film effects. In this work we present another coupled formulation where we have used hybrid elements to model the structural domain. The numerical results show a huge improvement in convergence and accuracy with coarse hybrid mesh as compared to displacement based formulations. We further compare our numerical results with experimental data from literature and find them to be in good accordance.

Inductively coupled reactive ion etching studies on sputtered yttria stabilized zirconia thin films in SF6, Cl-2, and BCl3 chemistries

Downscaling of yttria stabilized zirconia (YSZ) based electrochemical devices and gate oxide layers requires successful pattern transfer on YSZ thin films. Among a number of techniques available to transfer patterns to a material, reactive ion etching has the capability to offer high resolution, easily controllable, tunable anisotropic/isotropic pattern transfer for batch processing. This work reports inductively coupled reactive ion etching studies on sputtered YSZ thin films in fluorine and chlorine based plasmas and their etch chemistry analyses using x-ray photoelectron spectroscopy. Etching in SF6 plasma gives an etch rate of 7 nm/min chiefly through physical etching process. For same process parameters, in Cl-2 and BCl3 plasmas, YSZ etch rate is 17 nm/min and 45 nm/min, respectively. Increased etch rate in BCl3 plasma is attributed to its oxygen scavenging property synergetic with other chemical and physical etch pathways. BCl3 etched YSZ films show residue-free and smooth surface. The surface atomic concentration ratio of Zr/Y in BCl3 etched films is closer to as-annealed YSZ thin films. On the other hand, Cl-2 etched films show surface yttrium enrichment. Selectivity ratio of YSZ over silicon (Si), silicon dioxide (SiO2) and silicon nitride (Si3N4) are 1:2.7, 1:1, and 1:0.75, respectively, in BCl3 plasma. YSZ etch rate increases to 53 nm/min when nonoxygen supplying carrier wafer like Si3N4 is used. (C) 2015 American Vacuum Society.

Giant actuation in bulk carbon nanotubes under coupled electric and magnetic fields

We report an enhanced actuation in bulk carbon nanotubes (CNTs) under coupled electric and magnetic fields, which is much higher than that evaluated in the presence of individual fields. Coupled electric and magnetic fields induce a directional actuation demonstrating a transformation from polarity independent to dependent actuation behavior of CNTs. Both qualitative and quantitative analyses are performed to understand this transformation in the bulk CNTs. Moreover, actuations along radial and axial directions of CNTs have also demonstrated a similar directional behavior.

Kinetics of CO oxidation on palladium using microkinetics coupled with reaction route analysis

A plausible microkinetic model has been proposed for the CO oxidation reaction catalysed by palladium (Pd) with the kinetic parameters obtained from the literature. A robust rate expression using the reaction route analysis has been developed for the presented microkinetic scheme and the obtained rate expressions have been validated against the experimental data presented in the literature. A wide range of experimental conditions ranging from single Pd crystals under ultra-high vacuum conditions and impregnated Pd used for fixed bed experiments under atmospheric pressure has been used to validate the reaction mechanism. (C) 2015 Elsevier Ltd. All rights reserved.

Biodiesel Exhaust Treatment with Dielectric Barrier Discharges Coupled with Industrial Waste Byproducts

Biodiesel run engines are gaining popularity since the last few years as a viable alternative to conventional petro-diesel based engines. In biodiesel exhaust the content of volatile organic compounds, oil mist, and mass of particulate matter is considerably lower. However, the concentration of oxides of nitrogen (NOx) is relatively higher. In this paper the biodiesel exhaust from a stationary engine is treated under controlled laboratory conditions for removal of NOx using dielectric barrier discharge plasma in cascade with adsorbents prepared from abundantly available industrial waste byproducts like red mud and copper slag. Results were compared with gamma-alumina, a commercial adsorbent. Two different dielectric barrier discharge (DBD) reactors were tested for their effectiveness under Repetitive pulses /AC energization. NOx removal as high as 80% was achieved with pulse energized reactors when cascaded with red mud as adsorbent.

Coupled Mechanisms of Precipitation and Atomization in Burning Nanofluid Fuel Droplets

Understanding the combustion characteristics of fuel droplets laden with energetic nanoparticles (NP) is pivotal for lowering ignition delay, reducing pollutant emissions and increasing the combustion efficiency in next generation combustors. In this study, first we elucidate the feedback coupling between two key interacting mechanisms, namely, secondary atomization and particle agglomeration; that govern the effective mass fraction of NPs within the droplet. Second, we show how the initial NP concentration modulates their relative dominance leading to a masterslave configuration. Secondary atomization of novel nanofuels is a crucial process since it enables an effective transport of dispersed NPs to the flame (a pre-requisite condition for NPs to burn). Contrarily, NP agglomeration at the droplet surface leads to shell formation thereby retaining NPs inside the droplet. In particular, we show that at dense concentrations shell formation (master process) dominates over secondary atomization (slave) while at dilute particle loading it is the high frequency bubble ejections (master) that disrupt shell formation (slave) through its rupture and continuous outflux of NPs. This results in distinct combustion residues at dilute and dense concentrations, thereby providing a method of manufacturing flame synthesized microstructures with distinct morphologies.