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Ohne Zusammenfassung     

Upper and lower bounds for the shear stress in the Saint-Venant theory of flexure

Upper and lower bounds are derived for the shear stress as it is determined by Saint-Venant's theory of flexure, and used to establish the asymptotic character of the classical Strength of Materials formula in the limit of vanishing thickness.

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Résumé On dérive des limites supérieures et inférieures des contraintes tangentielles suivant la théorie de la flexion de Saint-Venant, que l'on utilise aux fins d'établir le caractère asymptotique de la formule de la Résistance des Matériaux dans le cas limite d'une épaisseur extrêmement petite.

     

Modeling of in-situ biorestoration of organic compounds in groundwater

A convergent numerical method for modeling in situ biorestoration of contaminated groundwater is outlined. This method treats systems of transport-biodegradation equations by operator splitting in time. Transport is approximated by a finite element modified method of characteristics. The biodegradation terms are split from the transport terms and treated as a system of ordinary differential equations. Numerical results for vertical cross-sectional flow are presented. The effects of variable hydraulic conductivity and variable linear adsorption are studied.     

A three-dimensional inverse problem for inhomogeneities in elastic solids

The Newtonian potential is used to solve an inverse problem in which we seek the shape of an inhomogeneity in an infinite elastic matrix under uniform applied stresses at infinity such that certain stress components are uniform on the boundary of the inhomogeneity. It is shown that ellipsoids furnish the solution of this inverse problem. Exact and general expressions for the stress and displacement are given explicitly for points in the elastic matrix outside the inhomogeneity. The solution of the corresponding plane deformation problem is found as a limiting case. Several applications are presented, and results from the literature are confirmed as special cases.     

Lifespan Theorem for simple constrained surface diffusion flows

We consider closed immersed hypersurfaces in R³ and R⁴ evolving by a special class of constrained surface diffusion flows. This class of constrained flows includes the classical surface diffusion flow. In this paper we present a Lifespan Theorem for these flows, which gives a positive lower bound on the time for which a smooth solution exists, and a small upper bound on the total curvature during this time. The hypothesis of the theorem is that the surface is not already singular in terms of concentration of curvature. This turns out to be a deep property of the initial manifold, as the lower bound on maximal time obtained depends precisely upon the concentration of curvature of the initial manifold in L² for M² immersed in R³ and additionally on the concentration in L³ for M³ immersed in R⁴. This is stronger than a previous result on a different class of constrained surface diffusion flows, as here we obtain an improved lower bound on maximal time, a better estimate during this period, and eliminate any assumption on the area of the evolving hypersurface.     

Under-three minute PCR: probing the limits of fast amplification

Nucleic acid amplification is enormously useful to the biotechnology and clinical diagnostic communities; however, to date point-of-use PCR has been hindered by thermal cycling architectures and protocols that do not allow for near-instantaneous results. In this work we demonstrate PCR amplification of synthetic SARS respiratory pathogenic targets and bacterial genomic DNA in less than three minutes in a hardware configuration utilizing convenient sample loading and disposal. Instead of sample miniaturization techniques, near-instantaneous heating and cooling of 5 μL reaction volumes is enabled by convective heat transfer of a thermal fluid through porous media combined with an integrated electrical heater. This method of rapid heat transfer has enabled 30 cycles of PCR amplification to be completed in as little as two minutes and eighteen seconds. Surprisingly, multiple enzymes have been shown to work at these breakthrough speeds on our system. A tool for measuring enzyme kinetics now exists and can allow polymerase optimization through directed evolution studies. Pairing this instrument technology with modified polymerases should result in a new paradigm for high-throughput, ultra-fast PCR and will hopefully improve our ability to quickly respond to the next viral pandemic.     

Chemical potential perturbation: a method to predict chemical potentials in periodic molecular simulations

A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of density in periodic molecular simulations. The CPP method applies a spatially varying external force field to the simulation, causing the density to depend upon position in the simulation cell. Following equilibration the homogeneous (uniform or bulk) chemical potential as a function of density can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. We compare three different methods of approximating this correction. The first method uses the van der Waals density gradient theory to approximate the inhomogeneous Helmholtz free energy density. The second method uses the local pressure tensor to approximate the homogeneous pressure. The third method uses the Triezenberg-Zwanzig definition of surface tension to approximate the inhomogeneous free energy density. If desired, the homogeneous pressure and Helmholtz free energy can also be predicted by the new method, as well as binodal and spinodal densities of a two-phase fluid region. The CPP method is tested using a Lennard-Jones (LJ) fluid at vapor, liquid, two-phase, and supercritical conditions. Satisfactory agreement is found between the CPP method and an LJ equation of state. The efficiency of the CPP method is compared to that for Widom's method under the tested conditions. In particular, the new method works well for dense fluids where Widom's method starts to fail.     

SERS spectroscopy and SERS imaging of Shewanella oneidensis using silver nanoparticles and nanowires

Facile and reproducible SERS signals from Shewanella oneidensis were obtained utilizing silver nanoparticles (AgNPs) and silver nanowires (AgNWs). Additionally, SERS images identify the distribution of SERS hot-spots. One important observation is the synergistically enhanced SERS signal when AgNPs and AgNWs are used in conjunction, due to constructively enhanced electromagnetic field.     

Photopatterning poly(p-phenylenevinylene) from xanthate precursor polymers

A simple, direct method for photopatterning poly(p-phenylenevinylene) (PPV) from a xanthate precursor polymer is presented. The effect of UV exposure on the resultant PPV is examined by UV-Vis, XPS, FTIR, and DC conductivity measurements. By optimizing the photolithographic conditions, a spatial resolution of one micron is obtained, with minimal impact to the properties of the photopatterned PPV.