Valve leaflet‐inspired elastomeric scaffolds with tunable and anisotropic mechanical properties

Fibrous scaffolds, which can mimic the elastic and anisotropic mechanical properties of native tissues, hold great promise in recapitulating the native tissue microenvironment. We previously fabricated electrospun fibrous scaffolds made of hybrid synthetic elastomers (poly(1,3‐diamino‐2‐hydroxypropane‐co‐glycerol sebacate)‐co‐poly (ethylene glycol) (APS‐co‐PEG) and polycaprolactone (PCL)) to obtain uniaxial mechanical properties similar to those of human aortic valve leaflets. However, conventional electrospinning process often yields scaffolds with random alignment, which fails to recreate the anisotropic nature of most of the soft tissues such as native heart valves. Inspired by the structure of native valve leaflet, we designed a novel valve leaflet‐inspired ring‐shaped collector to modulate the electrospun fiber alignment and studied the effect of polymer formulation (PEG amount [mole %] in APS‐co‐PEG; ratio between APS‐co‐PEG and PCL; and total polymer concentration) in tuning the biaxial mechanical properties of the fibrous scaffolds. The fibrous scaffolds collected on the ring‐shaped collector displayed anisotropic biaxial mechanical properties, suggesting that their biaxial mechanical properties are closely associated with the fiber alignment in the scaffold. Additionally, the scaffold stiffness was easily tuned by changing the composition and concentration of the polymer blend. Human valvular interstitial cells (hVICs) cultured on these anisotropic scaffolds displayed aligned morphology as instructed by the fiber alignment. Overall, we generated a library of biologically relevant fibrous scaffolds with tunable mechanical properties, which will guide the cellular alignment.     

Solution of non-linear Klein–Gordon equation with a quadratic non-linear term by Adomian decomposition method

Non-linear PDEs are systematically solved by the decomposition method of Adomian for general boundary conditions described by boundary operator equations. In the present case the solution of the non-linear Klein–Gordon equation has been considered as an illustration of the decomposition method of Adomian.     

A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem

We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the well-known SDP relaxation of maxcut is formulated as a semi-infinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting; this constitutes the pricing (column generation) phase of the algorithm. Cutting planes based on the polyhedral theory of the maxcut problem are then added to the primal problem in order to improve the SDP relaxation; this is the cutting phase of the algorithm. We provide computational results, and compare these results with a standard SDP cutting plane scheme. Research supported in part by NSF grant numbers CCR–9901822 and DMS–0317323. Work done as part of the first authors Ph.D. dissertation at RPI.     

A dispersed fluorescence and ab initio investigation of the X2B1 and A2A1 electronic states of the PH2 molecule

In this work, the X2B1 and A2A1 electronic states of the phosphino (PH2) free radical have been studied by dispersed fluorescence and ab initio methods. PH2 molecules were produced in a molecular free-jet apparatus by laser vaporizing a silicon rod in the presence of phosphine (PH3) gas diluted in helium. The laser-induced fluorescence, from the excited A2A1 electronic state down to the ground electronic state, was dispersed and analyzed. Ten (upsilon1upsilon2upsilon3) vibrationally excited levels of the ground electronic state, with upsilon1 < or = 2, upsilon2 < or = 6, and upsilon3 = 0, have been observed. Ab initio potential-energy surfaces for the X2B1 and A2A1 electronic states have been calculated at 210 points. These two states correlate with a 2Pi(u) state at linearity and they interact by the Renner-Teller coupling and spin-orbit coupling. Using the ab initio potential-energy surfaces with our RENNER computer program system, the vibronic structure and relative intensities of the A2A1 --> X2B1 emission band system have been calculated in order to corroborate the experimental assignments.     

Magnetic anomalies in single crystalline ErPd2Si2

Considering certain interesting features in the previously reported ¹⁶⁶Er Mössbauer effect, and neutron diffraction data on the polycrystalline form of ErPd₂Si₂ crystallizing in the ThCr₂Si₂-type tetragonal structure, we have carried out magnetic measurements (1.8–300 K) on the single crystalline form of this compound. We observe significant anisotropy in the absolute values of magnetization (indicating that the easy axis is c-axis) as well as in features due to magnetic ordering in the plot of magnetic susceptibility χ versus temperature T at low temperatures. The χ(T) data reveal that there is a pseudo-low-dimensional magnetic order setting in at 4.8 K, with a three-dimensional antiferromagnetic order setting in at a lower temperature (3.8 K). A new finding in the χ(T) data is that, for H∥〈1 1 0〉 but not for H∥〈0 0 1〉, there is a broad shoulder in the range 8–20 K, indicative of the existence of magnetic correlations above 5 K as well, which could be related to the previously reported slow-relaxation-dominated Mössbauer spectra. Interestingly, the temperature coefficient of electrical resistivity is found to be isotropic; no feature due to magnetic ordering could be detected in the electrical resistivity data at low temperatures, which is attributed to magnetic Brillioun-zone boundary gap effects. The results reveal the complex nature of magnetism of this compound.     

A parallel interior point decomposition algorithm for block angular semidefinite programs

We present a two phase interior point decomposition framework for solving semidefinite (SDP) relaxations of sparse maxcut, stable set, and box constrained quadratic programs. In phase 1, we suitably modify the matrix completion scheme of Fukuda et al. (SIAM J. Optim. 11:647–674, 2000) to preprocess an existing SDP into an equivalent SDP in the block-angular form. In phase 2, we solve the resulting block-angular SDP using a regularized interior point decomposition algorithm, in an iterative fashion between a master problem (a quadratic program); and decomposed and distributed subproblems (smaller SDPs) in a parallel and distributed high performance computing environment. We compare our MPI (Message Passing Interface) implementation of the decomposition algorithm on the distributed Henry2 cluster with the OpenMP version of CSDP (Borchers and Young in Comput. Optim. Appl. 37:355–369, 2007) on the IBM Power5 shared memory system at NC State University. Our computational results indicate that the decomposition algorithm (a) solves large SDPs to 2–3 digits of accuracy where CSDP runs out of memory; (b) returns competitive solution times with the OpenMP version of CSDP, and (c) attains a good parallel scalability. Comparing our results with Fujisawa et al. (Optim. Methods Softw. 21:17–39, 2006), we also show that a suitable modification of the matrix completion scheme can be used in the solution of larger SDPs than was previously possible.     

Enhanced electrical resistivity before Néel order in the metals RCuAs2 (R=Sm,Gd, Tb,and Dy)

We report an unusual temperature (T) dependent electrical resistivity (rho) behavior in a class of ternary intermetallic compounds of the type RCuAs2 (R=rare earths). For some rare earths (Sm, Gd, Tb, and Dy) with negligible 4f hybridization, there is a pronounced minimum in rho(T) far above respective Néel temperatures (T(N)). However, for the rare earths which are more prone to exhibit such a rho(T) minimum due to 4f-covalent mixing and the Kondo effect, this minimum is depressed. These findings, difficult to explain within the hitherto-known concepts, present an interesting scenario in magnetism.     

Enhancement of proton mobility and mitigation of methanol crossover in sPEEK fuel cells by an organically modified titania nanofiller

An organically functionalized titania, TiO₂-RSO₃H, was evaluated as filler in sulfonated polyetheretherketone (sPEEK)-based composite membranes for application in high temperature direct methanol fuel cells. The presence of propylsulfonic acid groups covalently bound onto the TiO₂ surface and the nanometric nature of the additive were analyzed by Raman spectroscopy and transmission electron microscopy, respectively. The properties of the sPEEK/TiO₂-RSO₃H composite membranes were compared with those of the pure sPEEK membranes and those of the sPEEK/TiO₂ composite membranes containing pristine titania nanoparticles at same filler content. Water and methanol transport properties were investigated by NMR methods, including relaxation times and self-diffusion coefficients as function of temperature (up to 130 °C), and pressure (from 0 up to 2 kbar). The incorporation of the nanoadditivies in the sPEEK polymer demonstrates considerable effects on the morphology and stiffness of the membranes, as well as on the transport properties and barrier effect to the methanol crossover. In particular, the functionalization by propylsulfonic acid groups promotes a higher reticulation between the polymeric chains, increasing the tortuosity of the methanol diffusional paths, so reducing the molecular diffusion, while the proton mobility increases being favored by the Grotthus-type mechanism. Conductivity measurements point out that the filler surface functionalization avoids the reduction of the overall proton conduction of the electrolyte due to the embedding of the low-conducting TiO₂. Finally, remarkable improvements were found when using the sPEEK/TiO₂-RSO₃H composite membrane as electrolyte in a DMFC, in terms of reduced methanol crossover and higher current and power density delivered.     

The application of vinylogous iminium salt derivatives to an efficient synthesis of the pyrrole containing alkaloids Rigidin and Rigidin E

Studies directed on the synthesis of the pyrrole containing marine natural products Rigidin and Rigidin E via vinylogous iminium salts are described. The successful strategy relies on the formation of a 2,4-disubstituted pyrrole from a vinamidinium salt followed by acylation at the 5-position of pyrrole. Halogenation and aminocarbonylation at the 3-position of pyrrole followed by hydrolysis of the ester group at C-2 and subsequent Curtius rearrangement generates the pyrrolopyrimidine skeleton. A final deprotection step completes the synthesis of Rigidin and Rigidin E.