The asymptotic behavior of densities related to the supremum of a stable process

If X is a stable process of index α∈(0, 2) whose Lévy measure has density cx−α−1 on (0, ∞), and S1=sup0x)∽Aα−1x−α as x→∞ and P(S1≤x)∽Bα−1ρ−1xαρ as x↓0. [Here ρ=P(X1>0) and A and B are known constants.] It is also known that S1 has a continuous density, m say. The main point of this note is to show that m(x)∽Ax−(α+1) as x→∞ and m(x)∽Bxαρ−1 as x↓0. Similar results are obtained for related densities.

Stress relaxation behavior of wheat dough, gluten, and gluten protein fractions

Relaxation behavior was measured for dough, gluten and gluten protein fractions obtained from the U.K. biscuitmaking flour, Riband, and the U.K. breadmaking flour, Hereward. The relaxation spectrum, in which relaxation times (tau) are related to polymer molecular size, for dough showed a broad molecular size distribution, with two relaxation processes: a major peak at short times and a second peak at times longer than 10 sec, which is thought to correspond to network structure, and which may be attributed to entanglements and physical cross-links of polymers. Relaxation spectra of glutens were similar to those for the corresponding doughs from both flours. Hereward gluten clearly showed a much more pronounced second peak in relaxation spectrum and higher relaxation modulus than Riband gluten at the same water content. In the gluten protein fractions, gliadin and acetic acid soluble glutenin only showed the first relaxation process, but gel protein clearly showed both the first and second relaxation processes. The results show that the relaxation properties of dough depend on its gluten protein and that gel protein is responsible for the network structure for dough and gluten.

Quasilimiting behavior for one-dimensional diffusions with killing

This paper extends and clarifies results of Steinsaltz and Evans [Trans. Amer. Math. Soc. 359 (2007) 1285–1234], which found conditions for convergence of a killed one-dimensional diffusion conditioned on survival, to a quasistationary distribution whose density is given by the principal eigenfunction of the generator. Under the assumption that the limit of the killing at infinity differs from the principal eigenvalue we prove that convergence to quasistationarity occurs if and only if the principal eigenfunction is integrable. When the killing at ∞ is larger than the principal eigenvalue, then the eigenfunction is always integrable. When the killing at ∞ is smaller, the eigenfunction is integrable only when the unkilled process is recurrent; otherwise, the process conditioned on survival converges to 0 density on any bounded interval.

Small time two-sided LIL behavior for Lévy processes at zero

We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.

(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.

Analysis and modeling of ants’ behavior from single to multi-body

In order to shed light on the collective behavior of social insects, we analyzed the behavior of ants from single to multi-body. In an experimental set-up, ants are placed in hemisphere without a nest and food. Trajectory of ants is recorded. From this bottom-up approach, we found that collective behavior of ants as follows: 1. Activity of single ant increases and decreases periodically. 2. Spontaneous meeting process is observed between two ants and meeting spot of two ants is localized in hemisphere. 3. Result on division of labor is obtained between two ants.

Micelle size characterization of lipopeptides produced by B. subtilis and their recovery by the two-step ultrafiltration process

The aim of this work was to investigate the lipopeptides aggregation behavior in single and mixed solutions in a wide range of concentrations, in order to optimize their separation and purification following the two-step ultrafiltration process and using large pore size membranes (up to MWCO = 300 kDa). Micelle size was determined by dynamic light scattering. In single solutions of lipopeptide both surfactin and mycosubtilin formed micelles of different size depending on their concentration, micelles of average diameter = 5–105 nm for surfactin and 8–18 nm for mycosubtilin. However when the lipopeptides were in the same solution they formed mixed micelles of different size (d = 8 nm) and probably conformation to that formed by the individual lipopeptide, this prevents their separation according to size. These lipopeptides were purified from fermentation culture by the two-step ultrafiltration process using different MWCO membranes ranging from 10 to 300 kDa. This led to their effective rejection in the first ultrafiltration step by membranes with MCWO = 10–100 kDa but poor rejection by the 300 KDa membrane. The lipopeptides were recovered at 90% purity (in relation to protein) and with 2.34 enrichment in the permeate of the second ultrafiltration step with the 100 KDa membrane upon addition of 75% ethanol.

Crooks' fluctuation theorem for a process on a two dimensional fluid field

We investigate the behavior of a two-dimensional inviscid and incompressible flow when pushed out of dynamical equilibrium. We use the two-dimensional vorticity equation with spectral truncation on a rectangular domain. For a sufficiently large number of degrees of freedom, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. We interpret this as doing work to the system. Evolving along a forward and its corresponding backward process, we find numerical evidence that the distributions of the work performed satisfy the Crooks relation. We confirm our results by proving the Crooks relation for this system rigorously.

Analysis and modeling of Diacamma workers’ behavior

It is well-known that social insects such as ants show interesting collective behaviors. How do they organize such behaviors? To expand understanding of collective behaviors of social insects, we focused on ants, Diacamma, and analyzed the behavior of a few individuals. In an experimental set-up, ants are placed in hemisphere without a nest and food and the trajectory of ants is recorded. From this bottom-up approach, we found following characteristics: 1. Activity of individuals increases and decreases periodically. 2. Spontaneous meeting process is observed between two ants and meeting spot of two ants is localized in the experimental field.

A process-based evaluation of dust-emitting winds in the CMIP5 simulation of HadGEM2-ES

Despite the importance of dust aerosol in the Earth system, state-of-the-art models show a large variety for North African dust emission. This study presents a systematic evaluation of dust emitting-winds in 30 years of the historical model simulation with the UK Met Office Earth-system model HadGEM2-ES for the Coupled Model Intercomparison Project Phase 5. Isolating the effect of winds on dust emission and using an automated detection for nocturnal low-level jets (NLLJs) allow an in-depth evaluation of the model performance for dust emission from a meteorological perspective. The findings highlight that NLLJs are a key driver for dust emission in HadGEM2-ES in terms of occurrence frequency and strength. The annually and spatially averaged occurrence frequency of NLLJs is similar in HadGEM2-ES and ERA-Interim from the European Centre for Medium-Range Weather Forecasts. Compared to ERA-Interim, a stronger pressure ridge over northern Africa in winter and the southward displaced heat low in summer result in differences in location and strength of NLLJs. Particularly the larger geostrophic winds associated with the stronger ridge have a strengthening effect on NLLJs over parts of West Africa in winter. Stronger NLLJs in summer may rather result from an artificially increased mixing coefficient under stable stratification that is weaker in HadGEM2-ES. NLLJs in the Bodélé Depression are affected by stronger synoptic-scale pressure gradients in HadGEM2-ES. Wintertime geostrophic winds can even be so strong that the associated vertical wind shear prevents the formation of NLLJs. These results call for further model improvements in the synoptic-scale dynamics and the physical parametrization of the nocturnal stable boundary layer to better represent dust-emitting processes in the atmospheric model. The new approach could be used for identifying systematic behavior in other models with respect to meteorological processes for dust emission. This would help to improve dust emission simulations and contribute to decreasing the currently large uncertainty in climate change projections with respect to dust aerosol.