Some adsorption-nucleation-based models for electrochemical phase formation

A new class of models which are based on adsorption, nucleation growth and their coupling is discussed. In particular, the potentiostatic response of a model that involves nucleative phase growth via direct incorporation and adsorptive discharge of metal ions on the free area is analysed for both instantaneous and progressive nucleation. This model is able to predict certain experimental features in the potentiostatic transient, like the initial fall, shoulder or maximum (as well as minimum) which have not been predicted by models analysed hitherto.Limiting behaviour for short and long times as well as a description of the above-mentioned features in terms of model parameters are given.A special case of the above model, viz. a reversible adsorption–nucleation model, wherein the adsorption is very fast, is shown to give rise to transients which can be distinguished from the pure nucleation-growth transients only by its parametric dependence, but not by the form.

Minimal Triangulations of Manifolds

Finding vertex-minimal triangulations of closed manifolds is a very difficult problem. Except for spheres and two series of manifolds, vertex-minimal triangulations are known for only few manifolds of dimension more than 2 (see the table given at the end of Section 5). In this article, we present a brief survey on the works done in last 30 years on the following:(i) Finding the minimal number of vertices required to triangulate a given pl manifold. (ii) Given positive integers n and d, construction of n-vertex triangulations of different d-dimensional pl manifolds. (iii) Classifications of all the triangulations of a given pl manifold with same number of vertices.In Section 1, we have given all the definitions which are required for the remaining part of this article. A reader can start from Section 2 and come back to Section 1 as and when required. In Section 2, we have presented a very brief history of triangulations of manifolds. In Section 3,we have presented examples of several vertex-minimal triangulations. In Section 4, we have presented some interesting results on triangulations of manifolds. In particular, we have stated the Lower Bound Theorem and the Upper Bound Theorem. In Section 5, we have stated several results on minimal triangulations without proofs. Proofs are available in the references mentioned there. We have also presented some open problems/conjectures in Sections 3 and 5.

Minimal unsatisfiable sets: Classification and bounds

Proving the unsatisfiability of propositional Boolean formulas has applications in a wide range of fields. Minimal Unsatisfiable Sets (MUS) are signatures of the property of unsatisfiability in formulas and our understanding of these signatures can be very helpful in answering various algorithmic and structural questions relating to unsatisfiability. In this paper, we explore some combinatorial properties of MUS and use them to devise a classification scheme for MUS. We also derive bounds on the sizes of MUS in Horn, 2-SAT and 3-SAT formulas.

Solar dynamo models with realistic internal rotation

Solar dynamo models based on differential rotation inferred from helioseismology tend to produce rather strong magnetic activity at high solar latitudes, in contrast to the observed fact that sunspots appear at low latitudes. We show that a meridional circulation penetrating below the tachocline can solve this problem.

Minimal triangulation, complementarity and projective planes

Brehm and Kuhnel proved that if M-d is a combinatorial d-manifold with 3d/2 + 3 vertices and \ M-d \ is not homeomorphic to Sd then the combinatorial Morse number of M-d is three and hence d is an element of {0, 2, 4, 8, 16} and \ M-d \ is a manifold like a projective plane in the sense of Eells and Kuiper. We discuss the existence and uniqueness of such combinatorial manifolds. We also present the following result: ''Let M-n(d) be a combinatorial d-manifold with n vertices. M-n(d) satisfies complementarity if and only if d is an element of {0, 2, 4, 8, 16} with n = 3d/2 + 3 and \ M-n(d) \ is a manifold like a projective plane''.

Real-time monitoring of critical nodes with minimal number of Phasor Measurement Units

This paper presents a method for placement of Phasor Measurement Units, ensuring the monitoring of vulnerable buses which are obtained based on transient stability analysis of the overall system. Real-time monitoring of phase angles across different nodes, which indicates the proximity to instability, the very purpose will be well defined if the PMUs are placed at buses which are more vulnerable. The issue is to identify the key buses where the PMUs should be placed when the transient stability prediction is taken into account considering various disturbances. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set with key buses identified from transient stability analysis. Results on IEEE-14 bus system are presented to illustrate the proposed approach.

Time and Frequency Domain Finite Element Models for Axial Wave Analysis in Hyperelastic Rods

The propagation of axial waves in hyperelastic rods is studied using both time and frequency domain finite element models. The nonlinearity is introduced using the Murnaghan strain energy function and the equations governing the dynamics of the rod are derived assuming linear kinematics. In the time domain, the standard Galerkin finite element method, spectral element method, and Taylor-Galerkin finite element method are considered. A frequency domain formulation based on the Fourier spectral method is also developed. It is found that the time domain spectral element method provides the most efficient numerical tool for the problem considered.

Thermodynamic Models for the Size-dependent Melting of Nanoparticles: Different Hypotheses

A careful comparison of the experimental results reported in the literature reveals different variations of the melting temperature even for the same materials. Though there are different theoretical models, thermodynamic model has been extensively used to understand different variations of size-dependent melting of nanoparticles. There are different hypotheses such as homogeneous melting (HMH), liquid nucleation and growth (LNG) and liquid skin melting (LSM) to resolve different variations of melting temperature as reported in the literature. HMH and LNG account for the linear variation where as LSM is applied to understand the nonlinear behaviour in the plot of melting temperature against reciprocal of particle size. However, a bird's eye view reveals that either HMH or LSM has been extensively used by experimentalists. It has also been observed that not a single hypothesis can explain the size-dependent melting in the complete range. Therefore we describe an approach which can predict the plausible hypothesis for a given data set of the size-dependent melting temperature. A variety of data have been analyzed to ascertain the hypothesis and to test the approach.

Semi empirical models for selectivity of supercritical carbon dioxide for solid mixtures

Selectivity of the particular solvent to separate a mixture is essential for the optimal design of a separation process. Supercritical carbon dioxide (SCCO2) is widely used as a solvent in the extraction, purification and separation of specialty chemicals. The effect of the temperature and pressure on selectivity is complicated and varies from system to system. The effect of temperature and pressure on selectivity of SCCO2 for different solid mixtures available in literature was analyzed. In this work, we have developed two model equations to correlate the selectivity in terms of temperature and pressure. The model equations have correlated the selectivity of SCCO2 satisfactorily for 18 solid mixtures with an average absolute relative deviation (AARD) of around 5%. (C) 2012 Elsevier B.V. All rights reserved.

Quenching of Meridional Circulation in Flux Transport Dynamo Models

Guided by the recent observational result that the meridional circulation of the Sun becomes weaker at the time of the sunspot maximum, we have included a parametric quenching of the meridional circulation in solar dynamo models such that the meridional circulation becomes weaker when the magnetic field at the base of the convection zone is stronger. We find that a flux transport solar dynamo tends to become unstable on including this quenching of meridional circulation if the diffusivity in the convection zone is less than about 2x10(11) cm(2) s(-1). The quenching of alpha, however, has a stabilizing effect and it is possible to stabilize a dynamo with low diffusivity with sufficiently strong alpha-quenching. For dynamo models with high diffusivity, the quenching of meridional circulation does not produce a large effect and the dynamo remains stable. We present a solar-like solution from a dynamo model with diffusivity 2.8x10(12) cm(2) s(-1) in which the quenching of meridional circulation makes the meridional circulation vary periodically with solar cycle as observed and does not have any other significant effect on the dynamo.

Pricing Defaultable Bonds in a Markov Modulated Market

We address the problem of pricing defaultable bonds in a Markov modulated market. Using Merton's structural approach we show that various types of defaultable bonds are combination of European type contingent claims. Thus pricing a defaultable bond is tantamount to pricing a contingent claim in a Markov modulated market. Since the market is incomplete, we use the method of quadratic hedging and minimal martingale measure to derive locally risk minimizing derivative prices, hedging strategies and the corresponding residual risks. The price of defaultable bonds are obtained as solutions to a system of PDEs with weak coupling subject to appropriate terminal and boundary conditions. We solve the system of PDEs numerically and carry out a numerical investigation for the defaultable bond prices. We compare their credit spreads with some of the existing models. We observe higher spreads in the Markov modulated market. We show how business cycles can be easily incorporated in the proposed framework. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low risk-free interest rate, high payout rate and high volatility.

Bose-Hubbard models in confining potentials: Inhomogeneous mean-field theory

We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.

Analysis of Conformational Variation in Macromolecular Structural Models

Experimental conditions or the presence of interacting components can lead to variations in the structural models of macromolecules. However, the role of these factors in conformational selection is often omitted by in silico methods to extract dynamic information from protein structural models. Structures of small peptides, considered building blocks for larger macromolecular structural models, can substantially differ in the context of a larger protein. This limitation is more evident in the case of modeling large multi-subunit macromolecular complexes using structures of the individual protein components. Here we report an analysis of variations in structural models of proteins with high sequence similarity. These models were analyzed for sequence features of the protein, the role of scaffolding segments including interacting proteins or affinity tags and the chemical components in the experimental conditions. Conformational features in these structural models could be rationalized by conformational selection events, perhaps induced by experimental conditions. This analysis was performed on a non-redundant dataset of protein structures from different SCOP classes. The sequence-conformation correlations that we note here suggest additional features that could be incorporated by in silico methods to extract dynamic information from protein structural models.

Inclusion of body doping in compact models for fully-depleted common double gate MOSFET adapted to gate-oxide thickness asymmetry

Since it is difficult to find the analytical solution of the governing Poisson equation for double gate MOSFETs with the body doping term included, the majority of the compact models are developed for undoped-body devices for which the analytical solution is available. Proposed is a simple technique to included a body doping term in such surface potential based common double gate MOSFET models also by taking into account any differences between the gate oxide thickness. The proposed technique is validated against TCAD simulation and found to be accurate as long as the channel is fully depleted.

How good are the simulations of tropical SST-rainfall relationship by IPCC AR4 atmospheric and coupled models?

The failure of atmospheric general circulation models (AGCMs) forced by prescribed SST to simulate and predict the interannual variability of Indian/Asian monsoon has been widely attributed to their inability to reproduce the actual sea surface temperature (SST)-rainfall relationship in the warm Indo-Pacific oceans. This assessment is based on a comparison of the observed and simulated correlation between the rainfall and local SST. However, the observed SSTconvection/rainfall relationship is nonlinear and for this a linear measure such as the correlation is not an appropriate measure. We show that the SST-rainfall relationship simulated by atmospheric and coupled general circulation models in IPCC AR4 is nonlinear, as observed, and realistic over the tropical West Pacific (WPO) and the Indian Ocean (IO). The SST-rainfall pattern simulated by the coupled versions of these models is rather similar to that from the corresponding atmospheric one, except for a shift of the entire pattern to colder/warmer SSTs when there is a cold/warm bias in the coupled version.