Boundary perturbations and the Helmholtz equation in three dimensions

We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.

Evaluating FuncSION: A software for automated synthesis of design solutions for stimulating ideation during mechanical conceptual design

The goal of the work reported in this paper is to use automated, combinatorial synthesis to generate alternative solutions to be used as stimuli by designers for ideation. FuncSION, a computational synthesis tool that can automatically synthesize solution concepts for mechanical devices by combining building blocks from a library, is used for this purpose. The objectives of FuncSION are to help generate a variety of functional requirements for a given problem and a variety of concepts to fulfill these functions. A distinctive feature of FuncSION is its focus on automated generation of spatial configurations, an aspect rarely addressed by other computational synthesis programs. This paper provides an overview of FuncSION in terms of representation of design problems, representation of building blocks, and rules with which building blocks are combined to generate concepts at three levels of abstraction: topological, spatial, and physical. The paper then provides a detailed account of evaluating FuncSION for its effectiveness in providing stimuli for enhanced ideation.

Comprehending the Formation of Eutectics and Cocrystals in Terms of Design and Their Structural Interrelationships

The phenomenon of cocrystallization, which encompasses the art of making multicomponent organic solids such as cocrystals, solid solutions, eutectics, etc. for novel applications, has been less studied in terms of reliably and specifically obtaining a desired cocrystallization product and the issues that govern their formation. Further, the design, structural, and functional aspects of organic eutectics have been relatively unexplored as compared to solid solutions and cocrystals well-established by crystal engineering principles. Recently, eutectics were proposed to be designable materials on par with cocrystals, and herein we have devised a systematic approach, based on the same crystal engineering principles, to specifically and desirably make both eutectics and cocrystals for a given system. The propensity for strong homomolecular synthons over weak heteromolecular synthons and vice versa during supramolecular growth was successfully utilized to selectively obtain eutectics and cocrystals, respectively, in two model systems and in two drug systems. A molecular level understanding of the formation of eutectics and cocrystals and their structural interrelationships which is significant from both fundamental and application viewpoints is discussed. On the other hand, the obscurity in establishing a low melting combination as a eutectic or a cocrystal is resolved through phase diagrams.

A framework for post-silicon realization of arbitrary instruction extensions on reconfigurable data-paths

In this paper we present a framework for realizing arbitrary instruction set extensions (IE) that are identified post-silicon. The proposed framework has two components viz., an IE synthesis methodology and the architecture of a reconfigurable data-path for realization of the such IEs. The IE synthesis methodology ensures maximal utilization of resources on the reconfigurable data-path. In this context we present the techniques used to realize IEs for applications that demand high throughput or those that must process data streams. The reconfigurable hardware called HyperCell comprises a reconfigurable execution fabric. The fabric is a collection of interconnected compute units. A typical use case of HyperCell is where it acts as a co-processor with a host and accelerates execution of IEs that are defined post-silicon. We demonstrate the effectiveness of our approach by evaluating the performance of some well-known integer kernels that are realized as IEs on HyperCell. Our methodology for realizing IEs through HyperCells permits overlapping of potentially all memory transactions with computations. We show significant improvement in performance for streaming applications over general purpose processor based solutions, by fully pipelining the data-path. (C) 2014 Elsevier B.V. All rights reserved.

A shortest path tree based algorithm for relay placement in a wireless sensor network and its performance analysis

In this paper, we study a problem of designing a multi-hop wireless network for interconnecting sensors (hereafter called source nodes) to a Base Station (BS), by deploying a minimum number of relay nodes at a subset of given potential locations, while meeting a quality of service (QoS) objective specified as a hop count bound for paths from the sources to the BS. The hop count bound suffices to ensure a certain probability of the data being delivered to the BS within a given maximum delay under a light traffic model. We observe that the problem is NP-Hard. For this problem, we propose a polynomial time approximation algorithm based on iteratively constructing shortest path trees and heuristically pruning away the relay nodes used until the hop count bound is violated. Results show that the algorithm performs efficiently in various randomly generated network scenarios; in over 90% of the tested scenarios, it gave solutions that were either optimal or were worse than optimal by just one relay. We then use random graph techniques to obtain, under a certain stochastic setting, an upper bound on the average case approximation ratio of a class of algorithms (including the proposed algorithm) for this problem as a function of the number of source nodes, and the hop count bound. To the best of our knowledge, the average case analysis is the first of its kind in the relay placement literature. Since the design is based on a light traffic model, we also provide simulation results (using models for the IEEE 802.15.4 physical layer and medium access control) to assess the traffic levels up to which the QoS objectives continue to be met. (C) 2014 Elsevier B.V. All rights reserved.

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|(n-1)e(beta vertical bar x vertical bar 2)/2, beta >= 0, x is an element of R-n. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.

Mixed finite elements for electromagnetic analysis

The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized formulation); (ii) A formulation based on a vector and a scalar potential. Both these strategies have some shortcomings. The penalty method does not completely get rid of the spurious modes, and both methods are incapable of predicting singular eigenvalues in non-convex domains. Some non-zero spurious eigenvalues are also predicted by these methods on non-convex domains. In this work, we develop mixed finite element formulations which predict the eigenfrequencies (including their multiplicities) accurately, even for nonconvex domains. The main feature of the proposed mixed finite element formulation is that no ad-hoc terms are added to the formulation as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables. We show that the formulation works even for inhomogeneous domains where `double noding' is used to enforce the appropriate continuity requirements at an interface. For two-dimensional problems, the shape of the domain can be arbitrary, while for the three-dimensional ones, with our current formulation, only regular domains (which can be nonconvex) can be modeled. Since eigenfrequencies are modeled accurately, these elements also yield accurate results for driven problems. (C) 2014 Elsevier Ltd. All rights reserved.

Modal tailoring and closed-form solutions for rotating non-uniform Euler-Bernoulli beams

In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse problem approach. We assume a polynomial mode shape function for a particular mode, which satisfies all the four boundary conditions of a rotating beam, along with the internal nodes. Using this assumed mode shape function, we determine the linear mass and fifth order stiffness variations of the beam which are typical of helicopter blades. Thus, it is found that an infinite number of such beams exist whose fourth order governing differential equation possess a closed form solution for certain polynomial variations of the mass and stiffness, for both cantilever and pinned-free boundary conditions corresponding to hingeless and articulated rotors, respectively. A detailed study is conducted for the first, second and third modes of a rotating cantilever beam and the first and second elastic modes of a rotating pinned-free beam, and on how to pre-select the internal nodes such that the closed-form solutions exist for these cases. The derived results can be used as benchmark solutions for the validation of rotating beam numerical methods and may also guide nodal tailoring. (C) 2014 Elsevier Ltd. All rights reserved.

Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

Recent NMR Methodological Developments for Chiral Analysis in Isotropic Solutions

Chiral auxiliaries are used for NMR spectroscopic study of enantiomers. Often the presence of impurities, severe overlap of peaks, excessive line broadening and complex multiplicity pattern restricts the chiral analysis using 1D H-1 NMR spectrum. There are few approaches to resolve the overlapped peaks. One approach is to use suitable chiral auxiliary, which induces large chemical shift difference between the discriminated peaks (Delta delta(R,S)) and minimize the overlap. Another direction of approach is to design appropriate NMR experiments to circumvent some of these problems, viz, enhancing spectral resolution, unravelling the superimposed spectra of enantiomers, and reduction of spectral complexity. Large number of NMR techniques, such as two dimensional selective F-1 decoupling, RES-TOCSY, multiple quantum detection, frequency selective homodecoupling, band selective homodecoupling, broadband homodecoupling, etc. have been reported for such a purpose. Many of these techniques have aided in chiral analysis for molecules of diverse functionality in the presence of chiral auxiliaries. The present review summarizes the recently reported NMR experimental methodologies, with a special emphasis on the work carried out in authors' laboratory.

Synergistic Effect of Mo plus Cu Codoping on the Photocatalytic Behavior of Metastable TiO2 Solid Solutions

Codoping with Cu and Mo is shown to have a synergistic effect on the photocatalytic activity of TiO2. The enhancement in activity is observed only if the synthesis route results in TiO2 in which (Cu, Mo) codopants are forced into the TiO2 lattice. Using X-ray photoelectron spectroscopy, Cu and Mo are shown to be present in the +2 and +6 oxidation states, respectively. A systematic study of the ternary system shows that TiO2 containing 6 mol % CuO and 1.5 mol % MoO3 is the most active ternary composition. Ab initio calculations show that codoping of TiO2 using (Mo, Cu) introduces levels above the valence band, and below the conduction band, resulting in a significant reduction in the band gap (similar to 0.8 eV). However, codoping also introduces deep defect states, which can have a deleterious impact on photoactivity. This helps rationalize the narrow compositional window over which the enhancement in photocatalytic activity is observed.

Energy-efficient, delay-constrained, QoS-aware broadcast for cooperative wireless sensor networks

The problem of delay-constrained, energy-efficient broadcast in cooperative wireless networks is NP-complete. While centralised setting allows some heuristic solutions, designing heuristics in distributed implementation poses significant challenges. This is more so in wireless sensor networks (WSNs) where nodes are deployed randomly and topology changes dynamically due to node failure/join and environment conditions. This paper demonstrates that careful design of network infrastructure can achieve guaranteed delay bounds and energy-efficiency, and even meet quality of service requirements during broadcast. The paper makes three prime contributions. First, we present an optimal lower bound on energy consumption for broadcast that is tighter than what has been previously proposed. Next, iSteiner, a lightweight, distributed and deterministic algorithm for creation of network infrastructure is discussed. iPercolate is the algorithm that exploits this structure to cooperatively broadcast information with guaranteed delivery and delay bounds, while allowing real-time traffic to pass undisturbed.

Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies. (c) 2015 AIP Publishing LLC.

A New Successive Displacement Type Load Flow Algorithm and its Application to Radial Systems

A new successive displacement type load flow method is developed in this paper. This algorithm differs from the conventional Y-Bus based Gauss Seidel load flow in that the voltages at each bus is updated in every iteration based on the exact solution of the power balance equation at that node instead of an approximate solution used by the Gauss Seidel method. It turns out that this modified implementation translates into only a marginal improvement in convergence behaviour for obtaining load flow solutions of interconnected systems. However it is demonstrated that the new approach can be adapted with some additional refinements in order to develop an effective load flow solution technique for radial systems. Numerical results considering a number of systems-both interconnected and radial, are provided to validate the proposed approach.