Field gradient CPMG applied on postmortem muscles

As a new approach, Carr-Purcell-Meiboom-Gill (CPMG) experiments were performed in vitro on porcine muscles (n = 10) during the period from 15 min to 85 min postmortem and again at 24 h postmortem in the absence (G = 0) and the presence of an external field gradient (G = 0.5*10(-3) T/m), which was applied throughout the CPMG sequence. The experiments were performed on low-field nuclear magnetic resonance (NMR) equipment (0.47 T). Due to the inclusion of different pre-slaughter treatments (adrenaline treatment and pre-slaughter exercise/electrical stunning), the muscles could be divided into (I) a group (n = 5) characterized by a reduced decrease in pH postmortem and a high water-holding capacity and (II) a group (n = 5) characterized by an increased rate of pH decrease postmortem and a low water-holding capacity. Distributed analysis of the CPMG data revealed two major relaxation populations with relaxation times about 30-40 and 200-500 ms, respectively, and comparison of data obtained with G = 0 and G = 0.5*10(-3) T/m revealed effects of the external gradient on the relaxation time of both the two relaxation populations, which implies that both diffusion and relaxation contributes to the relaxation of the two populations. At 24 h postmortem the effect of the external field gradient on the relaxation time was significantly affected by muscle group (I vs. II), which reveals local differences in water diffusion in the two meat qualities. Finally, the discriminatory power with regard to muscle group (I vs. II) was investigated for data acquired with G = 0 and G = F = 0.5*10(-3) T/m, and both the two types of data were found highly suitable for separation of muscles according to meat quality.     

On a micro-sphere based remodelling formulation for orthotropic soft biological tissue

An essential property of biological tissues in vivo is the ability to adapt according to respective loading conditions--for example by changing its mass, shape, or internal structure, the latter for instance being associated with fibre reorientation and often denoted as remodelling. In this contribution, a three-dimensional micro-sphere-based constitutive model for anisotropic soft biological tissue is presented, which includes these fibre-reorientation-related remodelling effects. As a key aspect, time-dependent remodelling effects are incorporated by introducing evolution equations for the referential orientations of the integration directions, as present in the computational micro-sphere approach. Based on this, a remodelling formulation for the orthotropic case with two mean fibre orientations will be presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Semidefinite and linear programming integrality gaps for scheduling identical machines

Sherali and Adams (SIAM J Discrete Math 3:411–430, 1990) and Lovász and Schrijver (SIAM J Optim 1:166–190, 1991) developed systematic procedures to construct the hierarchies of relaxations known as lift-and-project methods. They have been proven to be a strong tool for developing approximation algorithms, matching the best relaxations known for problems like Max-Cut and Sparsest-Cut. In this work we provide lower bounds for these hierarchies when applied over the configuration LP for the problem of scheduling identical machines to minimize the makespan. First we show that the configuration LP has an integrality gap of at least 1024/1023 by providing a family of instances with 15 different job sizes. Then we show that for any integer n there is an instance with n jobs in this family such that after \(\varOmega (n)\) rounds of the Sherali–Adams (\(\text {SA}\)) or the Lovász–Schrijver (\(\text {LS}_+\)) hierarchy the integrality gap remains at least 1024/1023.     

Parameter Identification for Inelastic Constitutive Models

The identification of material parameters of constitutive models is based on identification experiments. Since even specimens from the same lot show high deviations in the experimental data, the identification of the material parameters leads to different results for one and the same material. The number of identification experiments is usually not large enough for a statistical analysis of the deviations in the identified parameters. In order to overcome this problem we present a method of stochastic simulation which is based on time series analysis for generating artificial data with the same stochastic behaviour as the experimental data. The stochastic simulations allow an investigation of the confidence in the fits of the material parameters. We validate the stochastic simulations by comparing the results of the parameter identification from experimental data with the results from artificial data. The presented simulation method applied here turns out to be a suitable tool for generating artificial data for various kinds of analysis purposes. However, it is very important to take into account that the machines which perform the experiments do not maintain constant strain rates in the loading history of the tension and cyclic experiments.     

Time-resolved vibrational spectroscopy

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Time-resolved vibrational spectroscopy     

Improved measurement of the hydrogen 1S-2S transition frequency

We have measured the 1S-2S transition frequency in atomic hydrogen via two-photon spectroscopy on a 5.8 K atomic beam. We obtain f(1S-2S) = 2,466,061,413,187,035 (10) Hz for the hyperfine centroid, in agreement with, but 3.3 times better than the previous result [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)]. The improvement to a fractional frequency uncertainty of 4.2 × 10(-15) arises mainly from an improved stability of the spectroscopy laser, and a better determination of the main systematic uncertainties, namely, the second order Doppler and ac and dc Stark shifts. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.