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On the Lawrence-Doniach and Anisotropic Ginzburg-Landau models for layered superconductors
Chapman, S. Jonathan; Du, Qiang; Gunzburger, Max D. (Siam Publications, 1995-02)
The authors consider two models, the Lawrence-Doniach and the anisotropic Ginzburg-Landau models for layered superconductors such as the recently discovered high-temperature superconductors. A mathematical description of both models is given and existence results for their solution are derived. The authors then relate the two models in the sense that they show that as the layer spacing tends to zero, the Lawrence-Doniach model reduces to the anisotropic Ginzburg-Landau model. Finally, simplified versions of the models are derived that can be used to accurately simulate high-temperature superconductors.
Issues related to least-squares finite element methods for the stokes equations
Deang, Jennifer M.; Gunzburger, Max D. (Siam Publications, 1998-10)
Least-squares finite element methods have become increasingly popular for the approximate solution of first-order systems of partial differential equations. Here, after a brief review of some existing theories, a number of issues connected with the use of such methods for the velocity-vorticity-pressure formulation of the Stokes equations in two dimensions in realistic settings are studied through a series of computational experiments. Finite element spaces that are not covered by existing theories are considered; included in these are piecewise linear approximations for the velocity. Mixed boundary conditions, which are also not covered by existing theories, are also considered, as is enhancing mass conservation. Next, problems in nonconvex polygonal regions and the resulting nonsmooth solutions are considered with a view toward seeing how accuracy can be improved. A conclusion that can be drawn from this series of computational experiments is that the use of appropriate mesh-dependent weights in the least-squares functional almost always improves the accuracy of the approximations. Concluding remarks concerning three-dimensional problems, the nonlinear Navier-Stokes equations, and the conditioning of the discrete systems are provided.
A numerical study of periodic disturbances on two-layer Couette flaw
Li, Jie; Renardy, Yuriko Y.; Renardy, Michael J. (AIP Publishing, 1998-12)
The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds numbers, and a second-order velocity interpolation. The code is validated against linear theory for the stability of two-layer Couette flow, and weakly nonlinear theory for a Hopf bifurcation. Examples of long-time wave saturation are shown. The formation of fingers for relatively small initial amplitudes as well as larger amplitudes are presented in two and three dimensions as initial-value problems. Fluids of different viscosity and density are considered, with an emphasis on the effect of the viscosity difference. Results at low Reynolds numbers show elongated fingers in two dimensions that break in three dimensions to form drops, while different topological changes take place at higher Reynolds numbers. (C) 1998 American Institute of Physics. [S1070-6631(98)00612-6].
Comment on "A numerical study of periodic disturbances on two-layer Couette flow" [Phys. Fluids 10, 3056 (1998)]
Renardy, Yuriko Y.; Li, Jie (AIP Publishing, 1999-10)
The flow of fluids with different viscosities, subjected to an interfacial perturbation, can lead to fingering and migration...
On efficient solutions to the continuous sensitivity equation using automatic differentiation
Borggaard, Jeffrey T.; Verma, Arun (Siam Publications, 2000-06)
Shape sensitivity analysis is a tool that provides quantitative information about the influence of shape parameter changes on the solution of a partial differential equation (PDE). These shape sensitivities are described by a continuous sensitivity equation (CSE). Automatic differentiation (AD) can be used to perform this sensitivity analysis without writing any additional code to solve the sensitivity equation. The approximate solution of the PDE uses a spatial discretization (mesh) that often depends on the shape parameters. Therefore, the straightforward application of AD introduces derivatives of the mesh. There are two drawbacks to this approach. First, extra computational effort (especially memory) is used in these calculations due to mesh sensitivities. Second, this mesh sensitivity information needs to be computed in order to obtain accurate results. In this work, we provide a methodology that avoids mesh sensitivities (and their drawbacks) by defining a modified PDE on a fixed domain (i.e., independent of the shape parameter) such that AD provides the desired approximation of the CSE. Using two examples, we demonstrate significant improvement in the computational effort, both in terms of floating point operations and memory requirements. We explain how these code modifications can be applied to a wide variety of practical problems with minimal changes to the original code. These changes are negligible when compared to the complexity of writing a separate solver for the sensitivity equation.
Mesh independence of Kleinman-Newton iterations for Riccati equations in Hilbert space
Burns, John A.; Sachs, Ekkehard W.; Zietsman, Lizette (Siam Publications, 2008)
In this paper we consider the convergence of the infinite dimensional version of the Kleinman-Newton algorithm for solving the algebraic Riccati operator equation associated with the linear quadratic regulator problem in a Hilbert space. We establish mesh independence for this algorithm and apply the result to systems governed by delay equations. Numerical examples are presented to illustrate the results.
Antibacterial efficacy of core-shell nanostructures encapsulating gentamicin against an in vivo intracellular Salmonella model
Ranjan, Ashish; Pothayee, Nikorn; Seleem, Mohamed N.; Tyler, Ronald D.; Brenseke, Bonnie; Sriranganathan, Nammalwar; Riffle, Judy S.; Kasimanickam, Ramanathan K. (Dove Medical Press, 2009-01-01)
Pluronic based core-shell nanostructures encapsulating gentamicin were designed in this study. Block copolymers of (PAA(+/-)Na-b-(PEO-b-PPO-b-PEO)-b-PAA(+/-)Na) were blended with PAA(-) Na(+) and complexed with the polycationic antibiotic gentamicin to form nanostructures. Synthesized nanostructures had a hydrodynamic diameter of 210 nm, zeta potentials of -0.7 (+/-0.2), and incorporated approximately 20% by weight of gentamicin. Nanostructures upon co-incubation with J774A.1 macrophage cells showed no adverse toxicity in vitro. Nanostructures administered in vivo either at multiple dosage of 5 microg g(-1) or single dosage of 15 microg g(-1) in AJ-646 mice infected with Salmonella resulted in significant reduction of viable bacteria in the liver and spleen. Histopathological evaluation for concentration-dependent toxicity at a dosage of 15 microg g(-1) revealed mineralized deposits in 50% kidney tissues of free gentamicin-treated mice which in contrast was absent in nanostructure-treated mice. Thus, encapsulation of gentamicin in nanostructures may reduce toxicity and improve in vivo bacterial clearance.
Inexact Kleinman-Newton method for Riccati equations
Feitzinger, Franziska; Hylla, Timo; Sachs, Ekkehard W. (Siam Publications, 2009-03)
In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results illustrate the efficiency of this method.
Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition
Hay, Alexander; Borggaard, Jeffrey T.; Pelletier, Dominique (Cambridge University Press, 2009-06)
The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied 'off-design'. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier-Stokes equations for large parameter changes.
Shape Sensitivity Analysis in Flow Models Using a Finite-Difference Approach
Akhtar, Imran; Borggaard, Jeffrey T.; Hay, Alexander (Hindawi Publishing Corporation, 2010)
Reduced-order models have a number of practical engineering applications for unsteady flows that require either low-dimensional approximations for analysis and control or repeated simulation over a range of parameter values. The standard method for building reduced-order models uses the proper orthogonal decomposition (POD) and Galerkin projection. However, this standard method may be inaccurate when used "off-design" (at parameter values not used to generate the POD). This phenomena is exaggerated when parameter values describe the shape of the flow domain since slight changes in shape can have a significant influence on the flow field. In this paper, we investigate the use of POD sensitivity vectors to improve the accuracy and dynamical system properties of the reduced-order models to problems with shape parameters. To carry out this study, we consider flows past an elliptic cylinder with varying thickness ratios. Shape sensitivities (derivatives of flow variables with respect to thickness ratio) computed by finite difference approximations are used to compute the POD sensitivity vectors. Numerical studies test the accuracy of the new bases to represent flow solutions over a range of parameter values.
Olefin cross-metathesis, a mild, modular approach to functionalized cellulose esters
Meng, Xiangtao; Matson, John B.; Edgar, Kevin J. (The Royal Society of Chemistry, 2014-09-02)
Olefin cross-metathesis has been demonstrated to be a modular pathway for synthesis of a series of functionalized cellulose esters. As a proof of concept, cellulose acetate was acylated with two terminally olefinic acid chlorides, pent-4-enoyl chloride and undec-10-enoyl chloride, providing olefin-terminated cellulose esters with different side-chain lengths. These ω-unsaturated cellulose esters were then reacted with a variety of cross-metathesis partners, including acrylic acid, methyl acrylate, 2-hydroxyethyl acrylate, poly(ethylene glycol) methyl ether acrylate, and allyl alcohols, using Hoveyda–Grubbs’ 2nd generation catalyst. Complete conversion to cross-metathesis products was achieved in reactions with acrylic acid or acrylates using 3–5 mol% catalyst at 40 °C within 1 h. We further demonstrate successful hydrogenation of these α,β-unsaturated esters and acids, thereby eliminating the potential for radical-induced crosslinking during storage.
Model Reduction for DAEs with an Application to Flow Control
Borggaard, Jeffrey T.; Gugercin, Serkan (Springer-Verlag Berlin, 2015-01-01)
Nucleobase-functionalized acrylic ABA triblock copolymers and supramolecular blends
Zhang, Keren; Aiba, Motohiro; Fahs, Gregory B.; Hudson, Amanda G.; Chiang, William D.; Moore, Robert Bowen; Ueda, Mitsuru; Long, Timothy E. (The Royal Society of Chemistry, 2015-01-30)
Reversible addition-fragmentation chain transfer (RAFT) polymerization afforded the unprecedented synthesis of well-defined acrylic ABA triblock copolymers with nucleobase-functionalized external blocks and a central poly(n-butyl acrylate) (PnBA) block. Size exclusion chromatography (SEC) confirmed the molecular weight and molecular weight distribution of the central block. 1H NMR spectroscopy revealed the successful chain extension of the PnBA macro-chain transfer agent (CTA) using adenine or thymine-functionalized acrylic monomers. The acrylic monomer with a flexible spacer to the pendant nucleobases promoted intermolecular recognition of nucleobases and long range segmental motion of polymer main chains. The external block glass transition temperatures (Tg's) of thymine (T) and adenine (A) functionalized blocks were 52 °C and 76 °C, respectively. Thermomechanical and morphological analysis revealed the effect of processing conditions on self-assembly and microphase-separated morphology of nucleobase-functionalized ABA copolymers. Thymine and adenine-functionalized ABA triblocks formed a thermodynamically stable, hydrogen-bonded complex upon blending. The supramolecular blend exhibited a cylindrical microphase-separated morphology with an extended plateau window compared to the individual block copolymers. The complementary hydrogen bonding between adenine and thymine formed a thermally labile, physically crosslinked, network that exhibited enhanced mechanical performance with melt processability. Thus, these ABA nucleobase-functionalized block copolymers demonstrate potential as thermoplastic elastomers for hot melt adhesives and coatings.
Imidazole-containing triblock copolymers with a synergy of ether and imidazolium sites
Jangu, Chainika; Wang, Jing-Han Helen; Wang, Dong; Fahs, Gregory B.; Heflin, James R.; Moore, Robert Bowen; Colby, Ralph H.; Long, Timothy E. (The Royal Society of Chemistry, 2015-03-06)
Reversible addition-fragmentation chain transfer (RAFT) polymerization enabled the synthesis of well-defined A-BC-A triblock copolymers containing a synergy of pendant ether and imidazolium sites. The soft central BC block comprises low Tg di(ethylene glycol) methyl ether methacrylate (DEGMEMA) and 1-(4-vinylbenzyl) methyl imidazolium units. External polystyrene blocks provide mechanical reinforcement within a nanoscale morphology. Dynamic mechanical analysis (DMA) of the A-BC-A triblock copolymers exhibited a plateau region, which suggested the formation of a microphase-separated morphology. Atomic force microscopy (AFM) and small angle X-ray scattering (SAXS) collectively probed the morphology of the A-BC-A triblock copolymers, revealing long-range order at the nanoscale dimensions. Dielectric relaxation spectroscopy (DRS) examined the ion-transport properties of ionomeric A-BC-A triblock copolymers and random copolymers with different compositions. The role of morphology was demonstrated with block copolymer nanoscale structures providing superior ionic conductivity and mechanical performance compared to random copolymers. Under a 4 V direct current (DC) applied voltage, electromechanical transducers derived from these triblock copolymer membranes with added ionic liquid showed superior actuation performance compared to a benchmark Nafion[registered sign] membrane, suggesting potential for ionic polymer device applications. This was attributed to optimum modulus, improved ionic conductivity, and microphase-separated morphology of triblock copolymers.
Imparting functional variety to cellulose ethers via olefin cross-metathesis
Dong, Yifan; Edgar, Kevin J. (The Royal Society of Chemistry, 2015-04-09)
Olefin cross-metathesis is a valuable new approach for imparting functional variety to cellulose ethers. Starting from commercially available ethyl cellulose, terminally unsaturated alkyl groups were appended as metathesis handles by reaction with allyl chloride, 5-bromo-1-pentene, 7-bromo-1-heptene and 11-bromo-1-undecene, employing sodium hydride catalyst. These olefin-terminal ethyl cellulose derivatives were then subjected to olefin cross-metathesis with a variety of electron-poor olefin substrates, including acrylic acid and acrylate esters under optimized conditions (5–10 mol% Hoveyda-Grubbs’ 2nd generation catalyst, 37 °C, 2 h). The effects of varying the length of the ω-unsaturated alkyl handle, and of the solvent systems used were evaluated. Ethyl cellulose containing a pent-4-enyl substituent performed best in cross metathesis reactions and a hept-6-enyl substituent gave similarly good results. Ethyl cellulose with allyl substituents gave low to moderate metathesis conversion (<50%), possibly due to steric effects and the proximity of the ether oxygen to the terminal olefin. Interestingly, longer tethers (undec-10-enyl) gave high conversions (up to 90%) but relatively slow reactions (ca. 12 h needed for high conversion). While limited in this study by the relatively low DS (OH) of the starting commercial ethyl cellulose materials, this methodology has strong promise for introduction of diverse functionality to cellulose ethers in chemospecific and mild fashion, enabling amorphous solid dispersion and other applications.
Peptide-based hydrogen sulphide-releasing gels
Carter, Jennifer M.; Qian, Yun; Foster, Jeffrey C.; Matson, John B. (The Royal Society of Chemistry, 2015-07-20)
An aromatic peptide amphiphile was designed for delivery of the signaling gas H2S. The peptide self-assembled in water into nanofibers that gelled upon charge screening. The non-toxic gel slowly released H2S over 15 hours, and the presence of H2S in endothelial cells was verified using a fluorescent H2S probe.
Size dependent ion-exchange of large mixed-metal complexes into Nafion® membranes
Naughton, Elise M.; Zhang, Mingqiang; Troya, Diego; Brewer, Karen J.; Moore, Robert Bowen (The Royal Society of Chemistry, 2015-08-18)
Perfluorosulfonate ionomers have been shown to demonstrate a profound affinity for large cationic complexes, and the exchange of these ions may be used to provide insight regarding Nafion® morphology by contrasting molecular size with existing morphological models. The trimetallic complex, [{(bpy)2Ru(dpp)}2RhBr2]5+, is readily absorbed by ion-exchange into Na+-form Nafion® membranes under ambient conditions. The dimensions of three different isomers of the trimetallic complex were found to be: 23.6 Å × 13.3 Å × 10.8 Å, 18.9 Å × 18.0 Å × 13.7 Å, and 23.1 Å × 12.0 Å × 11.4 Å, yielding an average molecular volume of 1.2 × 103 Å3. At equilibrium, the partition coefficient for the ion-exchange of the trimetallic complex into Nafion® from a DMF solution was found to be 5.7 × 103. Furthermore, the total cationic charge of the exchanged trimetallic complexes was found to counterbalance 86 ± 2% of the anionic SO3− sites in Nafion®. The characteristic dimensions of morphological models for the ionic domains in Nafion® were found to be comparable to the molecular dimensions of the large mixed-metal complexes. Surprisingly, SAXS analysis indicated that the complexes absorbed into the ionic domains of Nafion® without significantly changing the ionomer morphology. Given the profound affinity for absorption of these large cationic molecules, a more open-channel model for the morphology of perfluorosulfonate ionomers is more reasonable, in agreement with recent experimental findings. In contrast to smaller monometallic complexes, the time dependent uptake of the large trimetallic cations was found to be biexponential. This behavior is attributed to a fast initial ion-exchange process on the surface of the membrane, accompanied by a slower transport-limited ion-exchange for exchange sites that are buried further in the ionomer matrix.
Phosphonium-containing diblock copolymers from living anionic polymerization of 4-diphenylphosphino styrene
Schultz, Alison R.; Fahs, Gregory B.; Jangu, Chainika; Chen, Mingtao; Moore, Robert Bowen; Long, Timothy E. (The Royal Society of Chemistry, 2015-11-20)
Living anionic polymerization of 4-diphenylphosphino styrene (DPPS) achieved well-defined homopolymers, poly(DPPS-b-S) styrenic block copolymers, and poly(I-b-DPPS) diene-based diblock copolymers with predictable molecular weights and narrow polydispersities. In situ FTIR spectroscopy monitored the anionic polymerization of DPPS and tracked monomer consumption for kinetic analysis. Post-alkylation enabled controlled placement of phosphonium functionality in poly(I-b-DPPS) diblock copolymers, producing well-defined phosphonium-containing block copolymers with low degrees of compositional heterogeneity. Incorporating phosphonium charge disrupted the lamellar bulk morphology of the neutral diblock precursor and provided morphologies with interdigitated packing of alkyl chains on the phosphonium cation.
A new wavelet family based on second-order LTI-systems
Abuhamdia, Tariq; Taheri, Saied; Burns, John A. (SAGE, 2016)
In this paper, a new family of wavelets derived from the underdamped response of second-order Linear-Time-Invariant (LTI) systems is introduced. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. We show that it is possible to recover back the original signal once the Second-Order Underdamped LTI (SOULTI) wavelet is applied to decompose the signal. It is found that the SOULTI wavelet transform of a signal satisfies a linear differential equation called the reconstructing differential equation, which is closely related to the differential equation that produces the wavelet. Moreover, a time-frequency resolution is defined based on two different approaches. The new transform has useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The results obtained are presented with analytical and numerical examples. Signals with constant harmonics and signals with time-varying frequencies are analyzed, and their evolutionary spectrum is obtained. Contour mapping of the transform in the time-scale and the time-frequency domains clearly detects the change of the frequency content of the analyzed signals with respect to time. The results are compared with other wavelets results and with the short-time fourier analysis spectrograms. At the end, we propose the method of reverse wavelet transform to mitigate the edge effect.
Elucidating the Potential Biological Impact of Cellulose Nanocrystals
Camarero-Espinosa, Sandra; Endes, Carola; Mueller, Silvana; Petri-Fink, Alke; Rothen-Rutishauser, Barbara; Weder, Christoph; Clift, Martin James David; Foster, Earl Johan (MDPI, 2016-07-08)
Cellulose nanocrystals exhibit an interesting combination of mechanical properties and physical characteristics, which make them potentially useful for a wide range of consumer applications. However, as the usage of these bio-based nanofibers increases, a greater understanding of human exposure addressing their potential health issues should be gained. The aim of this perspective is to highlight how knowledge obtained from studying the biological impact of other nanomaterials can provide a basis for future research strategies to deduce the possible human health risks posed by cellulose nanocrystals.

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