On Uniform Approximate Solutions in Bending of Symmetric Laminated Plates

A layer-wise theory with the analysis of face ply independent of lamination is used in the bending of symmetric laminates with anisotropic plies. More realistic and practical edge conditions as in Kirchhoff's theory are considered. An iterative procedure based on point-wise equilibrium equations is adapted. The necessity of a solution of an auxiliary problem in the interior plies is explained and used in the generation of proper sequence of two dimensional problems. Displacements are expanded in terms of polynomials in thickness coordinate such that continuity of transverse stresses across interfaces is assured. Solution of a fourth order system of a supplementary problem in the face ply is necessary to ensure the continuity of in-plane displacements across interfaces and to rectify inadequacies of these polynomial expansions in the interior distribution of approximate solutions. Vertical deflection does not play any role in obtaining all six stress components and two in-plane displacements. In overcoming lacuna in Kirchhoff's theory, widely used first order shear deformation theory and other sixth and higher order theories based on energy principles at laminate level in smeared laminate theories and at ply level in layer-wise theories are not useful in the generation of a proper sequence of 2-D problems converging to 3-D problems. Relevance of present analysis is demonstrated through solutions in a simple text book problem of simply supported square plate under doubly sinusoidal load.

Evolution and stability of phases in a high temperature shape memory alloy Ni49.4Ti38.6Hf12

Ni49.4Ti38.6Hf12 shape memory alloy has been characterized for structure, microstructure and transformation temperatures. The microstructure of the as-cast sample consists of B19' and R-phases, and (Ti,Hf)(2)Ni precipitate phase along the grain boundaries in the form of dendrites. The microstructure of the solution treated sample contains only B19' martensite phase, whereas a second heat treatment after solutionizing results in reappearance of the R-phase and the (Ti,Hf)(2)Ni grain boundary precipitate phase in the microstructure. A detailed microstructural examination shows the presence of precipitates having both coherent and incoherent interface with the matrix, the type of interface being dictated by the crystallographic orientation of the matrix phase. The present study shows that the (Ti,Hf)(2)Ni precipitates having coherent interface with the matrix, drive the formation of the R-phase in the microstructure. (C) 2013 Elsevier Ltd. All rights reserved.

Effect of pH on structural and magnetic properties of nanocrystalline Y3Fe5O12 by aqueous co-precipitation method

The Y3Fe5O12 (YIG) nanopowders were synthesised at different pH using co-precipitation method. The effect of pH on the phase formation of YIG is characterised using XRD, TEM, FTIR and TG/DTA. From the Scherer formula, the particle sizes of the powders were found to be 13, 19 and 28 nm for pH=10, 11 and 12 respectively. It is found that as the pH of the solution increase the particle size is also increases. It is also clear from the TG/DTA curves that as the pH is increasing the weight losses were found to be small. The nanopowders were sintered at 600, 700, 800 and 900 degrees C for 5 h using conventional sintering method. The phase formation is completed at 800 degrees C/5 h which is correlated with TG/DTA. The average grain size of the samples is found to be similar to 161 nm. The high values of M-s=23 emu g(-1) and H-c=22 Oe were recorded for the sample sintered at 900 degrees C.

How to run a campaign: Optimal control of SIS and SIR information epidemics

Information spreading in a population can be modeled as an epidemic. Campaigners (e.g., election campaign managers, companies marketing products or movies) are interested in spreading a message by a given deadline, using limited resources. In this paper, we formulate the above situation as an optimal control problem and the solution (using Pontryagin's Maximum Principle) prescribes an optimal resource allocation over the time of the campaign. We consider two different scenarios-in the first, the campaigner can adjust a direct control (over time) which allows her to recruit individuals from the population (at some cost) to act as spreaders for the Susceptible-Infected-Susceptible (SIS) epidemic model. In the second case, we allow the campaigner to adjust the effective spreading rate by incentivizing the infected in the Susceptible-Infected-Recovered (SIR) model, in addition to the direct recruitment. We consider time varying information spreading rate in our formulation to model the changing interest level of individuals in the campaign, as the deadline is reached. In both the cases, we show the existence of a solution and its uniqueness for sufficiently small campaign deadlines. For the fixed spreading rate, we show the effectiveness of the optimal control strategy against the constant control strategy, a heuristic control strategy and no control. We show the sensitivity of the optimal control to the spreading rate profile when it is time varying. (C) 2014 Elsevier Inc. All rights reserved.

Anomalous power law decay in solvation dynamics of DNA: a mode coupling theory analysis of ion contribution

Several time dependent fluorescence Stokes shift (TDFSS) experiments have reported a slow power law decay in the hydration dynamics of a DNA molecule. Such a power law has neither been observed in computer simulations nor in some other TDFSS experiments. Here we observe that a slow decay may originate from collective ion contribution because in experiments DNA is immersed in a buffer solution, and also from groove bound water and lastly from DNA dynamics itself. In this work we first express the solvation time correlation function in terms of dynamic structure factors of the solution. We use mode coupling theory to calculate analytically the time dependence of collective ionic contribution. A power law decay in seen to originate from an interplay between long-range probe-ion direct correlation function and ion-ion dynamic structure factor. Although the power law decay is reminiscent of Debye-Falkenhagen effect, yet solvation dynamics is dominated by ion atmosphere relaxation times at longer length scales (small wave number) than in electrolyte friction. We further discuss why this power law may not originate from water motions which have been computed by molecular dynamics simulations. Finally, we propose several experiments to check the prediction of the present theoretical work.

Optimal control of information epidemics modeled as Maki Thompson rumors

We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin's Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas. We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns. (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.

Polymorphic phase transition among the titania crystal structures using a solution-based approach: from precursor chemistry to nucleation process

Nanocrystalline titania are a robust candidate for various functional applications owing to its non-toxicity, cheap availability, ease of preparation and exceptional photochemical as well as thermal stability. The uniqueness in each lattice structure of titania leads to multifaceted physico-chemical and opto-electronic properties, which yield different functionalities and thus influence their performances in various green energy applications. The high temperature treatment for crystallizing titania triggers inevitable particle growth and the destruction of delicate nanostructural features. Thus, the preparation of crystalline titania with tunable phase/particle size/morphology at low to moderate temperatures using a solution-based approach has paved the way for further exciting areas of research. In this focused review, titania synthesis from hydrothermal/solvothermal method, conventional sol-gel method and sol-gel-assisted method via ultrasonication, photoillumination and ILs, thermolysis and microemulsion routes are discussed. These wet chemical methods have broader visibility, since multiple reaction parameters, such as precursor chemistry, surfactants, chelating agents, solvents, mineralizer, pH of the solution, aging time, reaction temperature/time, inorganic electrolytes, can be easily manipulated to tune the final physical structure. This review sheds light on the stabilization/phase transformation pathways of titania polymorphs like anatase, rutile, brookite and TiO2(B) under a variety of reaction conditions. The driving force for crystallization arising from complex species in solution coupled with pH of the solution and ion species facilitating the orientation of octahedral resulting in a crystalline phase are reviewed in detail. In addition to titanium halide/alkoxide, the nucleation of titania from other precursors like peroxo and layered titanates are also discussed. The nonaqueous route and ball milling-induced titania transformation is briefly outlined; moreover, the lacunae in understanding the concepts and future prospects in this exciting field are suggested.

Sensitivity of polarization fluctuations to the nature of protein-water interactions: Study of biological water in four different protein-water systems

Since the time of Kirkwood, observed deviations in magnitude of the dielectric constant of aqueous protein solution from that of neat water (similar to 80) and slower decay of polarization have been subjects of enormous interest, controversy, and debate. Most of the common proteins have large permanent dipole moments (often more than 100 D) that can influence structure and dynamics of even distant water molecules, thereby affecting collective polarization fluctuation of the solution, which in turn can significantly alter solution's dielectric constant. Therefore, distance dependence of polarization fluctuation can provide important insight into the nature of biological water. We explore these aspects by studying aqueous solutions of four different proteins of different characteristics and varying sizes, chicken villin headpiece subdomain (HP-36), immunoglobulin binding domain protein G (GB1), hen-egg white lysozyme (LYS), and Myoglobin (MYO). We simulate fairly large systems consisting of single protein molecule and 20000-30000 water molecules (varied according to the protein size), providing a concentration in the range of similar to 2-3 mM. We find that the calculated dielectric constant of the system shows a noticeable increment in all the cases compared to that of neat water. Total dipole moment auto time correlation function of water < dM(W) (0)delta M-W (t) > is found to be sensitive to the nature of the protein. Surprisingly, dipole moment of the protein and total dipole moment of the water molecules are found to be only weakly coupled. Shellwise decomposition of water molecules around protein reveals higher density of first layer compared to the succeeding ones. We also calculate heuristic effective dielectric constant of successive layers and find that the layer adjacent to protein has much lower value (similar to 50). However, progressive layers exhibit successive increment of dielectric constant, finally reaching a value close to that of bulk 4-5 layers away. We also calculate shellwise orientational correlation function and tetrahedral order parameter to understand the local dynamics and structural re-arrangement of water. Theoretical analysis providing simple method for calculation of shellwise local dielectric constant and implication of these findings are elaborately discussed in the present work. (C) 2014 AIP Publishing LLC.

BIOCARDS AND LEVEL OF ABSTRACTION

Biocards are formal descriptions of biological phenomena and their underlying functional principles. They are used in bioinspired design to document search results and to communicate the findings for use in the further design process. The present study explored the effect of abstraction level used in biocards. This was done in two workshops conducted with design students in Denmark and India. Students were given a design assignment and instructions for how to perform the BID ideation work. Half of the students were given biocards with abstract descriptions while the other half got biocards with concrete descriptions. The novelty of found solutions was evaluated by the students by rating novelty of each solution on a scale from 1 to 5. Mean values for abstract descriptions were 0,3 higher than for concrete descriptions indicating that more innovative solutions were found when students used biocards with abstract descriptions compared to concrete descriptions. The difference in mean value is significant with a confidence level better than 1%. It seems likely that more abstract descriptions in biocards helps avoiding design fixation in biomimetic design work.

Learning-Based Fast Iterative Convergence of 3-D MoM via Eigen-AGMRES Method

Three-dimensional (3-D) full-wave electromagnetic simulation using method of moments (MoM) under the framework of fast solver algorithms like fast multipole method (FMM) is often bottlenecked by the speed of convergence of the Krylov-subspace-based iterative process. This is primarily because the electric field integral equation (EFIE) matrix, even with cutting-edge preconditioning techniques, often exhibits bad spectral properties arising from frequency or geometry-based ill-conditioning, which render iterative solvers slow to converge or stagnate occasionally. In this communication, a novel technique to expedite the convergence of MoMmatrix solution at a specific frequency is proposed, by extracting and applying Eigen-vectors from a previously solved neighboring frequency in an augmented generalized minimum residual (AGMRES) iterative framework. This technique can be applied in unison with any preconditioner. Numerical results demonstrate up to 40% speed-up in convergence using the proposed Eigen-AGMRES method.

Campaigning in Heterogeneous Social Networks: Optimal Control of SI Information Epidemics

We study the optimal control problem of maximizing the spread of an information epidemic on a social network. Information propagation is modeled as a susceptible-infected (SI) process, and the campaign budget is fixed. Direct recruitment and word-of-mouth incentives are the two strategies to accelerate information spreading (controls). We allow for multiple controls depending on the degree of the nodes/individuals. The solution optimally allocates the scarce resource over the campaign duration and the degree class groups. We study the impact of the degree distribution of the network on the controls and present results for Erdos-Renyi and scale-free networks. Results show that more resource is allocated to high-degree nodes in the case of scale-free networks, but medium-degree nodes in the case of Erdos-Renyi networks. We study the effects of various model parameters on the optimal strategy and quantify the improvement offered by the optimal strategy over the static and bang-bang control strategies. The effect of the time-varying spreading rate on the controls is explored as the interest level of the population in the subject of the campaign may change over time. We show the existence of a solution to the formulated optimal control problem, which has nonlinear isoperimetric constraints, using novel techniques that is general and can be used in other similar optimal control problems. This work may be of interest to political, social awareness, or crowdfunding campaigners and product marketing managers, and with some modifications may be used for mitigating biological epidemics.