Mesh shape and anisotropic elements : theory and practice

The relationship between the shape of finite elements in unstructured meshes and the error that results in the numerical solution is of increasing importance as finite elements are used to solve problems with highly anisotropic and, often, very complex solutions. This issue is explored in terms of a priori and a posteriori error estimates, and through consideration of the practical issues associated with assessing element shape quality and implementing an adaptive finite element solver

Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains

Exact analytic calculations in spin-1/2 XY chains, show the presence of long-time tails in the asymptotic dynamics of spatially inhomogeneous excitations. The decay of inhomogeneities, for $t\to \infty$, is given in the form of a power law $$(t/\tau_{Q}) ^{-\nu_{Q}}$$ where the relaxation time $\tau_{Q}$ and the exponent $\nu_{Q}$ depend on the wave vector $Q$, characterizing the spatial modulation of the initial excitation. We consider several variants of the XY model (dimerized, with staggered magnetic field, with bond alternation, and with isotropic and uniform interactions), that are grouped into two families, whether the energy spectrum has a gap or not. Once the initial condition is given, the non-equilibrium problem for the magnetization is solved in closed form, without any other assumption. The long-time behavior for $t\to \infty$ can be obtained systematically in a form of an asymptotic series through the stationary phase method. We found that gapped models show critical behavior with respect to $Q$, in the sense that there exist critical values $Q_{c}$, where the relaxation time $\tau_{Q}$ diverges and the exponent $\nu_{Q}$ changes discontinuously. At those points, a slowing down of the relaxation process is induced, similarly to phenomena occurring near phase transitions. Long-lived excitations are identified as incommensurate spin density waves that emerge in systems undergoing the Peierls transition. In contrast, gapless models do not present the above anomalies as a function of the wave vector $Q$.Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical Review

Measurement of e⁺e⁻-->e⁺e⁻ and e⁺e⁻-->gammagamma at energies up to 36.7 GeV

e+e- +- +- ... + e e und e e + yy wurden bel Energlen zwischen 33.0 und 36.7 GeV gemessen. Die Ergebnisse stimmen mit den Vorhersagen der Quantenelektrodynamik überein. Ein Vergleich mit dem Standardmodell der elektroschwachen Wechselwirkung liefert sin 20w= 0.25 ± 0.13

Action potentials in abscisic acid-deficient tomato mutant generated spontaneously and evoked by electrical stimulation

Action potentials generated spontaneously (SAPs) and evoked by electrical stimulation (APs) in tomato plants (Solanum lycopersicum L.) cv. Micro-Tom ABA-deficient mutants (sitiens—MTsit) and its wild type (MTwt) were characterized by continuous monitoring of electrical activity for 66 h and by application of an electrical stimulation supplied extracellularly. MTsit generated SAPs which spread along the stem, including petioles and roots with an amplitude of 44.6 ± 4.4 mV, half-time (t½) of 33.1 ± 2.9 s and velocity of 5.4 ± 1.0 cm min−1. Amplitude and velocity were 43 and 108 % higher in MTsit than in MTwt, respectively. The largest number of SAPs was registered in the early morning in both genotypes. MTsit was less responsive to electrical stimuli. The excitation threshold and the refractory period were greater in MTsit than in MTwt. After current application, APs were generated in the MTwt with 21.2 ± 2.4 mV amplitude and propagated with 5.6 ± 0.5 cm min−1 velocity. Lower intensity stimuli did not trigger APs in these plants. In MTsit APs were measured with amplitude of 26.8 ± 4.8 mV and propagated with velocity of 8.5 ± 0.1 cm min−1

Nanopore-based kinetics analysis of individual antibody-channel and antibody-antigen interactions

<p>Abstract</p> <p>Background</p> <p>The UNO/RIC Nanopore Detector provides a new way to study the binding and conformational changes of individual antibodies. Many critical questions regarding antibody function are still unresolved, questions that can be approached in a new way with the nanopore detector.</p> <p>Results</p> <p>We present evidence that different forms of channel blockade can be associated with the same antibody, we associate these different blockades with different orientations of "capture" of an antibody in the detector's nanometer-scale channel. We directly detect the presence of antibodies via reductions in channel current. Changes to blockade patterns upon addition of antigen suggest indirect detection of antibody/antigen binding. Similarly, DNA-hairpin anchored antibodies have been studied, where the DNA linkage is to the carboxy-terminus at the base of the antibody's Fc region, with significantly fewer types of (lengthy) capture blockades than was observed for free (un-bound) IgG antibody. The introduction of chaotropic agents and its effects on protein-protein interactions have also been observed.</p> <p>Conclusion</p> <p>Nanopore-based approaches may eventually provide a direct analysis of the complex conformational "negotiations" that occur upon binding between proteins.</p

A novel, fast, HMM-with-Duration implementation – for application with a new, pattern recognition informed, nanopore detector

<p>Abstract</p> <p>Background</p> <p>Hidden Markov Models (HMMs) provide an excellent means for structure identification and feature extraction on stochastic sequential data. An HMM-with-Duration (HMMwD) is an HMM that can also exactly model the hidden-label length (recurrence) distributions – while the regular HMM will impose a best-fit geometric distribution in its modeling/representation.</p> <p>Results</p> <p>A Novel, Fast, HMM-with-Duration (HMMwD) Implementation is presented, and experimental results are shown that demonstrate its performance on two-state synthetic data designed to model Nanopore Detector Data. The HMMwD experimental results are compared to (i) the ideal model and to (ii) the conventional HMM. Its accuracy is clearly an improvement over the standard HMM, and matches that of the ideal solution in many cases where the standard HMM does not. Computationally, the new HMMwD has all the speed advantages of the conventional (simpler) HMM implementation. In preliminary work shown here, HMM feature extraction is then used to establish the first pattern recognition-informed (PRI) sampling control of a Nanopore Detector Device (on a "live" data-stream).</p> <p>Conclusion</p> <p>The improved accuracy of the new HMMwD implementation, at the same order of computational cost as the standard HMM, is an important augmentation for applications in gene structure identification and channel current analysis, especially PRI sampling control, for example, where speed is essential. The PRI experiment was designed to inherit the high accuracy of the well characterized and distinctive blockades of the DNA hairpin molecules used as controls (or blockade "test-probes"). For this test set, the accuracy inherited is 99.9%.</p