(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

New mathematical modeling approach for predicting microbial inactivation by high hydrostatic pressure

A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.

CASCADE: An Agent Based Framework For Modeling The Dynamics Of Smart Electricity Systems

The Complex Adaptive Systems, Cognitive Agents and Distributed Energy (CASCADE) project is developing a framework based on Agent Based Modelling (ABM). The CASCADE Framework can be used both to gain policy and industry relevant insights into the smart grid concept itself and as a platform to design and test distributed ICT solutions for smart grid based business entities. ABM is used to capture the behaviors of diff erent social, economic and technical actors, which may be defi ned at various levels of abstraction. It is applied to understanding their interactions and can be adapted to include learning processes and emergent patterns. CASCADE models ‘prosumer’ agents (i.e., producers and/or consumers of energy) and ‘aggregator’ agents (e.g., traders of energy in both wholesale and retail markets) at various scales, from large generators and Energy Service Companies down to individual people and devices. The CASCADE Framework is formed of three main subdivisions that link models of electricity supply and demand, the electricity market and power fl ow. It can also model the variability of renewable energy generation caused by the weather, which is an important issue for grid balancing and the profi tability of energy suppliers. The development of CASCADE has already yielded some interesting early fi ndings, demonstrating that it is possible for a mediating agent (aggregator) to achieve stable demandfl attening across groups of domestic households fi tted with smart energy control and communication devices, where direct wholesale price signals had previously been found to produce characteristic complex system instability. In another example, it has demonstrated how large changes in supply mix can be caused even by small changes in demand profi le. Ongoing and planned refi nements to the Framework will support investigation of demand response at various scales, the integration of the power sector with transport and heat sectors, novel technology adoption and diffusion work, evolution of new smart grid business models, and complex power grid engineering and market interactions.

Structure of the planetary boundary layer over southeast England: modeling and measurements

The Weather Research and Forecasting model was applied to analyze variations in the planetary boundary layer (PBL) structure over Southeast England including central and suburban London. The parameterizations and predictive skills of two nonlocal mixing PBL schemes, YSU and ACM2, and two local mixing PBL schemes, MYJ and MYNN2, were evaluated over a variety of stability conditions, with model predictions at a 3 km grid spacing. The PBL height predictions, which are critical for scaling turbulence and diffusion in meteorological and air quality models, show significant intra-scheme variance (> 20%), and the reasons are presented. ACM2 diagnoses the PBL height thermodynamically using the bulk Richardson number method, which leads to a good agreement with the lidar data for both unstable and stable conditions. The modeled vertical profiles in the PBL, such as wind speed, turbulent kinetic energy (TKE), and heat flux, exhibit large spreads across the PBL schemes. The TKE predicted by MYJ were found to be too small and show much less diurnal variation as compared with observations over London. MYNN2 produces better TKE predictions at low levels than MYJ, but its turbulent length scale increases with height in the upper part of the strongly convective PBL, where it should decrease. The local PBL schemes considerably underestimate the entrainment heat fluxes for convective cases. The nonlocal PBL schemes exhibit stronger mixing in the mean wind fields under convective conditions than the local PBL schemes and agree better with large-eddy simulation (LES) studies.