On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.     

Automated,high performance,flow-through chemiluminescence microarray for the multiplexed detection of phycotoxins

A novel multiplexed immunoassay for the analysis of phycotoxins in shellfish samples has been developed. Therefore, a regenerable chemiluminescence (CL) microarray was established which is able to analyze automatically three different phycotoxins (domoic acid (DA), okadaic acid (OA) and saxitoxin (STX)) in parallel on the analysis platform MCR3. As a test format an indirect competitive immunoassay format was applied. These phycotoxins were directly immobilized on an epoxy-activated PEG chip surface. The parallel analysis was enabled by the simultaneous addition of all analytes and specific antibodies on one microarray chip. After the competitive reaction, the CL signal was recorded by a CCD camera. Due to the ability to regenerate the toxin microarray, internal calibrations of phycotoxins in parallel were performed using the same microarray chip, which was suitable for 25 consecutive measurements. For the three target phycotoxins multi-analyte calibration curves were generated. In extracted shellfish matrix, the determined LODs for DA, OA and STX with values of 0.5 ± 0.3 μg L⁻¹, 1.0 ± 0.6 μg L⁻¹, and 0.4 ± 0.2 μg L⁻¹ were slightly lower than in PBS buffer. For determination of toxin recoveries, the observed signal loss in the regeneration was corrected. After applying mathematical corrections spiked shellfish samples were quantified with recoveries for DA, OA, and STX of 86.2%, 102.5%, and 61.6%, respectively, in 20 min. This is the first demonstration of an antibody based phycotoxin microarray.     

Chemiluminescence microarrays in analytical chemistry: a critical review

Multi-analyte immunoassays on microarrays and on multiplex DNA microarrays have been described for quantitative analysis of small organic molecules (e.g., antibiotics, drugs of abuse, small molecule toxins), proteins (e.g., antibodies or protein toxins), and microorganisms, viruses, and eukaryotic cells. In analytical chemistry, multi-analyte detection by use of analytical microarrays has become an innovative research topic because of the possibility of generating several sets of quantitative data for different analyte classes in a short time. Chemiluminescence (CL) microarrays are powerful tools for rapid multiplex analysis of complex matrices. A wide range of applications for CL microarrays is described in the literature dealing with analytical microarrays. The motivation for this review is to summarize the current state of CL-based analytical microarrays. Combining analysis of different compound classes on CL microarrays reduces analysis time, cost of reagents, and use of laboratory space. Applications are discussed, with examples from food safety, water safety, environmental monitoring, diagnostics, forensics, toxicology, and biosecurity. The potential and limitations of research on multiplex analysis by use of CL microarrays are discussed in this review. Figure

Achievements in the development of CL microarray analysis platforms     

Local vs. global redundancy – trade-offs between resilience against cascading failures and frequency stability

When designing or extending electricity grids, both frequency stability and resilience against cascading failures have to be considered amongst other aspects of energy security and economics such as construction costs due to total line length. Here, we compare an improved simulation model for cascading failures with state-of-the-art simulation models for short-term grid dynamics. Random ensembles of realistic power grid topologies are generated using a recent model that allows for a tuning of global vs local redundancy. The former can be measured by the algebraic connectivity of the network, whereas the latter can be measured by the networks transitivity. We show that, while frequency stability of an electricity grid benefits from a global form of redundancy, resilience against cascading failures rather requires a more local form of redundancy and further analyse the corresponding trade-off.     

The impact of model detail on power grid resilience measures

Extreme events are a challenge to natural as well as man-made systems. For critical infrastructure like power grids, we need to understand their resilience against large disturbances. Recently, new measures of the resilience of dynamical systems have been developed in the complex system literature. Basin stability and survivability respectively assess the asymptotic and transient behavior of a system when subjected to arbitrary, localized but large perturbations in frequency and phase. To employ these methods that assess power grid resilience, we need to choose a certain model detail of the power grid. For the grid topology we considered the Scandinavian grid and an ensemble of power grids generated with a random growth model. So far the most popular model that has been studied is the classical swing equation model for the frequency response of generators and motors. In this paper we study a more sophisticated model of synchronous machines that also takes voltage dynamics into account, and compare it to the previously studied model. This model has been found to give an accurate picture of the long term evolution of synchronous machines in the engineering literature for post fault studies. We find evidence that some stable fix points of the swing equation become unstable when we add voltage dynamics. If this occurs the asymptotic behavior of the system can be dramatically altered, and basin stability estimates obtained with the swing equation can be dramatically wrong. We also find that the survivability does not change significantly when taking the voltage dynamics into account. Further, the limit cycle type asymptotic behaviour is strongly correlated with transient voltages that violate typical operational voltage bounds. Thus, transient voltage bounds are dominated by transient frequency bounds and play no large role for realistic parameters.     

Rigidity percolation in particle-laden foams

We study the viscoelastic behavior of aqueous foam mixed with solid noncolloidal particles. We show that adding a tiny amount of grains can enhance the elastic and loss shear moduli by more than 1 order of magnitude. The scaling of these moduli with solid volume fraction is in qualitative agreement with that predicted by an effective-medium rigidity percolation model. We present a simple model, based on capillary attraction, to explain the particle-size dependence of the threshold.     

Existence of solutions for semilinear elliptic boundary value problems on arbitrary open sets

We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set Ω. We make no assumptions about the open set Ω and very mild regularity assumptions on the semilinearity f, plus a coerciveness assumption which depends on the optimal Poincaré–Steklov constant λ₁. The proof is based on Schaefer’s fixed point theorem applied to a sequence of truncated problems. We state a simple uniqueness result. We also generalize the results to Robin boundary conditions [17].