Wrinkled and slack membranes: nonlinear 3D elasticity solutions via smooth DMS-FEM and experiment

The smooth DMS-FEM, recently proposed by the authors, is extended and applied to the geometrically nonlinear and ill-posed problem of a deformed and wrinkled/slack membrane. A key feature of this work is that three-dimensional nonlinear elasticity equations corresponding to linear momentum balance, without any dimensional reduction and the associated approximations, directly serve as the membrane governing equations. Domain discretization is performed with triangular prism elements and the higher order (C1 or more) interelement continuity of the shape functions ensures that the errors arising from possible jumps in the first derivatives of the conventional C0 shape functions do not propagate because the ill-conditioned tangent stiffness matrices are iteratively inverted. The present scheme employs no regularization and exhibits little sensitivity to h-refinement. Although the numerically computed deformed membrane profiles do show some sensitivity to initial imperfections (nonplanarity) in the membrane profile needed to initiate transverse deformations, the overall patterns of the wrinkles and the deformed shapes appear to be less so. Finally, the deformed profiles, computed through the DMS FEM-based weak formulation, are compared with those obtained through an experiment on an ultrathin Kapton membrane, wherein wrinkles form because of the applied boundary displacement conditions. Comparisons with a reported experiment on a rectangular membrane are also provided. These exercises lend credence to the feasibility of the DMS FEM-based numerical route to computing post-wrinkled membrane shapes. Copyright (c) 2012 John Wiley & Sons, Ltd.

Selective colorimetric detection of nanomolar Cr (VI) in aqueous solutions using unmodified silver nanoparticles

In this study we present a colorimetric detection method for Cr (VI) in aqueous solution based on as synthesized silver nanoparticles (Ag NPs) without surface functionalization. The method principle involves reduction of Cr (VI) to Cr (III) by excess reductant present in as synthesized Ag NP dispersion, and subsequent aggregation of Ag NPs by Cr (III) leading to red-shift of the surface plasmon resonance (SPR) peak. The UV-vis absorption spectra. Zeta potentials, dynamic light scattering measurements, and scanning electron microscopy (SEM) confirmed the aggregation of the Ag NPs. Under the optimized conditions, a good linear relationship (correlation coefficient r=0.981) was obtained between the ratio of the absorbance at 550 nm to that at 390 nm (A(550/390)) and the concentration of Cr (VI) over the range of 10(-3)-10(-9) M 50 mg/L to 50 ng/L]. The reported probe has a limit of detection down to 1 nM, which, to the best of our knowledge, is the lowest ever reported for the colorimetric detection of Cr (VI). Furthermore, a remarkable feature of this method is that it involves a simple technique exhibiting high selectivity to Cr (VI) over other tested heavy metal ions. (C) 2012 Elsevier BM. All rights reserved.

Electrocatalytic oxidation of 1,2-propanediol on electrodeposited Pd-poly(3,4-ethylenedioxythiophene) nanodendrite films in alkaline medium

Electrochemical deposition of Pd on conducting polymer poly(3,4-ethylenedioxythiophene) (PEDOT) coated carbon paper electrode results in the formation of a stable dendritic film of Pd. In the absence of the PEDOT under-layer, Pd deposition is smooth and non-dendritic. Both Pd-PEDOT/C and Pd/C electrodes are studied for electrooxidation of 1,2-propanediol (PD) in an alkaline electrolyte. Owing to enhanced surface area and surface defects on dendritic Pd, the Pd-PEDOT/C electrode exhibits greater catalytic activity than the Pd/C electrode. Cyclic voltammetry studies suggest that peak current density increases with an increase in concentrations of PD and NaOH in the electrolyte. Repetitive cyclic voltammetry and amperometry studies indicate that Pd-PEDOT/C electrode possesses a high electrochemical stability with greater catalytic activity than Pd/C electrode toward electrooxidation of PD. (C) 2012 Elsevier Ltd. All rights reserved.

Excellent performance of Pt-free cathode in alkaline direct methanol fuel cell at room temperature

We report the room temperature cell performance of alkaline direct methanol fuel cells (ADMFCs) with nitrogen-doped carbon nanotubes (NCNTs) as cathode materials. NCNTs show excellent oxygen reduction reaction activity and methanol tolerance in alkaline medium. The open-circuit-voltage (OCV) as well as the power density of ADMFCs first increases and then saturates with NCNT loading. Similarly, the OCV initially increases and reaches saturation with the increase in the concentration of methanol feed stock. Overall, NCNTs exhibit excellent catalytic activity and stability with respect to Pt based cathodes.

Effect of Metal Ions (Ag, Co, Ni, and Pd) on the Visible Light Degradation of Rhodamine B by Carbon-Covered Alumina-Supported TiO2 in Aqueous Solutions

Metal-ion (Ag, Co, Ni, and Pd) doped TiO2 nanocatalysts were successfully embedded on carbon-covered alumina supports. The CCA-embedded catalysts were crystalline and had a high surface area compared to the free metal-ion doped titania nanocatalysts while they still retained the anatase phase of the core TiO2. These catalysts were photocatalytically active under solar light irradiation. Rhodamine B was used as a model pollutant and the reactivity followed a pseudo-first-order reaction kinetics. The reaction rate of the CCA-supported catalysts was Pd > Ag > Co > Ni. Among the ratios of the CCA:catalyst used, it was found that the 1:1 ratio had the fastest reaction rate, followed by the 1:2 ratio, while the 2:1 ratio exhibited the lowest reaction rate. The CCA/metal-ion doped titania were found to have photocatalytic activities comparable with those of CCA-supported titania.

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N vertical bar N = 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal W-3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N - 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N >= 4, the sl(N|N - 1) theory admits smooth supersymmetric conical defects.

Organophotocatalysis in nanostructured soft gel materials as tunable reaction vessels: comparison with homogeneous and micellar solutions

Riboflavin tetraacetate-catalyzed aerobic photooxidation of 1-(4-methoxyphenyl)ethanol was investigated as a model reaction under blue visible light in different soft gel materials, aiming to establish their potential as reaction vessels for photochemical transformations. Three strategies involving different degrees of organization of the catalyst within the gel network were explored, and the results compared to those obtained in homogeneous and micellar solutions. In general, physical entrapment of both the catalyst and the substrate under optimized concentrations into several hydrogel matrices (including low-molecular-weight and biopolymer-based gels) allowed the photooxidation with conversions between 55 and 100% within 120 min (TOF similar to 0.045-0.08 min(-1); k(obs) similar to 0.011-0.028 min(-1)), albeit with first-order rates ca. 1-3-fold lower than in solution under comparable non-stirred conditions. Remarkably, the organogel made of a cyclohexane-based bisamide gelator in CH3CN not only prevented the photodegradation of the catalyst but also afforded full conversion in less than 60 min (TOF similar to 0.167 min(-1); k(obs) similar to 0.073 min(-1)) without the need of additional proton transfer mediators (e. g., thiourea) as it occurs in CH3CN solutions. In general, the gelators could be recycled without detriment to their gelation ability and reaction rates. Moreover, kinetics could be fine-tuned according to the characteristics of the gel media. For instance, entangled fibrillar networks with relatively high mechanical strength were usually associated with lower reaction rates, whereas wrinkled laminated morphologies seemed to favor the reaction. In addition, the kinetics results showed in most cases a good correlation with the aeration efficiency of the gel media.

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part I: zero and extrapolated boundary conditions

The mathematical model for diffuse fluorescence spectroscopy/imaging is represented by coupled partial differential equations (PDEs), which describe the excitation and emission light propagation in soft biological tissues. The generic closed-form solutions for these coupled PDEs are derived in this work for the case of regular geometries using the Green's function approach using both zero and extrapolated boundary conditions. The specific solutions along with the typical data types, such as integrated intensity and the mean time of flight, for various regular geometries were also derived for both time-and frequency-domain cases. (C) 2013 Optical Society of America

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part II: comparison and validation

The analytical solutions for the coupled diffusion equations that are encountered in diffuse fluorescence spectroscopy/ imaging for regular geometries were compared with the well-established numerical models, which are based on the finite element method. Comparison among the analytical solutions obtained using zero boundary conditions and extrapolated boundary conditions (EBCs) was also performed. The results reveal that the analytical solutions are in close agreement with the numerical solutions, and solutions obtained using EBCs are more accurate in obtaining the mean time of flight data compared to their counterpart. The analytical solutions were also shown to be capable of providing bulk optical properties through a numerical experiment using a realistic breast model. (C) 2013 Optical Society of America

Generating string solutions in BTZ

Integrability of classical strings in the BTZ black hole enables the construction and study of classical string propagation in this background. We first apply the dressing method to obtain classical string solutions in the BTZ black hole. We dress time like geodesics in the BTZ black hole and obtain open string solutions which are pinned on the boundary at a single point and whose end points move on time like geodesics. These strings upon regularising their charge and spins have a dispersion relation similar to that of giant magnons. We then dress space like geodesics which start and end on the boundary of the BTZ black hole and obtain minimal surfaces which can penetrate the horizon of the black hole while being pinned at the boundary. Finally we embed the giant gluon solutions in the BTZ background in two different ways. They can be embedded as a spiral which contracts and expands touching the horizon or a spike which originates from the boundary and touches the horizon.

Multiple parents crossover operators: A new approach removes the overlapping solutions for sequencing problems

Maintaining population diversity throughout generations of Genetic Algorithms (GAs) is key to avoid premature convergence. Redundant solutions is one cause for the decreasing population diversity. To prevent the negative effect of redundant solutions, we propose a framework that is based on the multi-parents crossover (MPX) operator embedded in GAs. Because MPX generates diversified chromosomes with good solution quality, when a pair of redundant solutions is found, we would generate a new offspring by using the MPX to replace the redundant chromosome. Three schemes of MPX will be examined and will be compared against some algorithms in literature when we solve the permutation flowshop scheduling problems, which is a strong NP-Hard sequencing problem. The results indicate that our approach significantly improves the solution quality. This study is useful for researchers who are trying to avoid premature convergence of evolutionary algorithms by solving the sequencing problems.

Electrocatalytic oxidation of C-3-aliphatic alcohols on electrodeposited Pd-PEDOT nanodendrites in Alkaline medium

Nanodendritic Pd is electrodeposited on poly(3,4-ethylenedioxythiophene) (PEDOT) coated carbon paper electrode. Electrodeposited Pd is non-dendritic in the absence of PEDOT. The electrooxidation of C-3-aliphatic alcohols, namely, propanol (PA), 1,2- propanediol (1, 2-PD), 1, 3-propanediol (1, 3-PD), and glycerol (GL) is studied in 1.0 M NaOH. The catalytic activity of nanodendritic Pd is greater than that of non-dendritic Pd for oxidation of the four alcohols molecules. Among those molecules the oxidation rate increases as: PA< 1, 2-PD < 1, 3-PD < GL. The cyclic voltammetric oxidation current peak appearing in the reverse direction of the sweep is greatly influenced by the nature of alcohol. The reduction of oxide film on Pd surface is attributed to affect the magnitude of backward peak current density. The amperometry and repeated cyclic voltammetry data suggest a high stability of nanodendritic Pd in alkaline medium. Glycerol is expected to be an appropriate alcohol for application as a fuel in alkaline fuel cells at nanodendritic electrodeposited Pd.

Interfacial growth as a model of tube-width heterogeneities in concentrated solutions of stiff polymers

Recent experimental measurements of the distribution P(w) of transverse chain fluctuations w in concentrated solutions of F-actin filaments B. Wang, J Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010); J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgessner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)] are shown to be well-fit to an expression derived from a model of the conformations of a single harmonically confined weakly bendable rod. The calculation of P(w) is carried out essentially exactly within a path integral approach that was originally applied to the study of one-dimensional randomly growing interfaces. Our results are generally as successful in reproducing experimental trends as earlier approximate results obtained from more elaborate many-chain treatments of the confining tube potential.

Closed-form solutions for non-uniform Euler-Bernoulli free-free beams

In this paper, the free vibration of a non-uniform free-free Euler-Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free-free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free-free beam numerical codes. (C) 2013 Elsevier Ltd. All rights reserved.

Interfacial growth as a model of tube-width heterogeneities in concentrated solutions of stiff polymers

Recent experimental measurements of the distribution P(w) of transverse chain fluctuations w in concentrated solutions of F-actin filaments B. Wang, J Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010); J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgessner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)] are shown to be well-fit to an expression derived from a model of the conformations of a single harmonically confined weakly bendable rod. The calculation of P(w) is carried out essentially exactly within a path integral approach that was originally applied to the study of one-dimensional randomly growing interfaces. Our results are generally as successful in reproducing experimental trends as earlier approximate results obtained from more elaborate many-chain treatments of the confining tube potential. (C) 2013 AIP Publishing LLC.