Superfast non-linear diffusion: capillary transport in particulate porous media

The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by SFDE that robustly convey a time power law of spreading as seen in our experiments.

Investigation of the impact of feeding Lactobacillus plantarum CRL 1815 encapsulated in microbially derived polymers on the rat faecal microbiota

AIMS: The aim of this study was to evaluate the impact of the administration of microencapsulated Lactobacillus plantarum CRL 1815 with two combinations of microbially derived polysaccharides, xanthan : gellan gum (1%:0·75%) and jamilan : gellan gum (1%:1%), on the rat faecal microbiota. METHODS AND RESULTS: A 10-day feeding study was performed for each polymer combination in groups of 16 rats fed either with placebo capsules, free or encapsulated Lact. plantarum or water. The composition of the faecal microbiota was analysed by fluorescence in situ hybridization and temporal temperature gradient gel electrophoresis. Degradation of placebo capsules was detected, with increased levels of polysaccharide-degrading bacteria. Xanthan : gellan gum capsules were shown to reduce the Bifidobacterium population and increase the Clostridium histolyticum group levels, but not jamilan : gellan gum capsules. Only after administration of jamilan : gellan gum-probiotic capsules was detected a significant increase in Lactobacillus-Enterococcus group levels compared to controls (capsules and probiotic) as well as two bands were identified as Lact. plantarum in two profiles of ileum samples. CONCLUSIONS: Exopolysaccharides constitute an interesting approach for colon-targeted delivery of probiotics, where jamilan : gellan gum capsules present better biocompatibility and promising results as a probiotic carrier. SIGNIFICANCE AND IMPACT OF STUDY: This study introduces and highlights the importance of biological compatibility in the encapsulating material election, as they can modulate the gut microbiota by themselves, and the use of bacterial exopolysaccharides as a powerful source of new targeted-delivery coating material.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

Radar bright band correction using the linear depolarisation ratio

The enhanced radar return associated with melting snow, ‘the bright band’, can lead to large overestimates of rain rates. Most correction schemes rely on fitting the radar observations to a vertical profile of reflectivity (VPR) which includes the bright band enhancement. Observations show that the VPR is very variable in space and time; large enhancements occur for melting snow, but none for the melting graupel in embedded convection. Applying a bright band VPR correction to a region of embedded convection will lead to a severe underestimate of rainfall. We revive an earlier suggestion that high values of the linear depolarisation ratio (LDR) are an excellent means of detecting when bright band contamination is occurring and that the value of LDR may be used to correct the value of Z in the bright band.

On the approximation of local and linear radiative damping in the middle atmosphere

The validity of approximating radiative heating rates in the middle atmosphere by a local linear relaxation to a reference temperature state (i.e., ‘‘Newtonian cooling’’) is investigated. Using radiative heating rate and temperature output from a chemistry–climate model with realistic spatiotemporal variability and realistic chemical and radiative parameterizations, it is found that a linear regressionmodel can capture more than 80% of the variance in longwave heating rates throughout most of the stratosphere and mesosphere, provided that the damping rate is allowed to vary with height, latitude, and season. The linear model describes departures from the climatological mean, not from radiative equilibrium. Photochemical damping rates in the upper stratosphere are similarly diagnosed. Threeimportant exceptions, however, are found.The approximation of linearity breaks down near the edges of the polar vortices in both hemispheres. This nonlinearity can be well captured by including a quadratic term. The use of a scale-independentdamping rate is not well justified in the lower tropical stratosphere because of the presence of a broad spectrum of vertical scales. The local assumption fails entirely during the breakup of the Antarctic vortex, where large fluctuations in temperature near the top of the vortex influence longwave heating rates within the quiescent region below. These results are relevant for mechanistic modeling studies of the middle atmosphere, particularly those investigating the final Antarctic warming.

Design of delay-tolerant linear dispersion codes

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. This will damage some of the key properties of the space-time codes and can lead to substantial performance degradation. In this paper, we study the design of linear dispersion codes (LDCs) for such asynchronous cooperative communication networks. Firstly, the concept of conventional LDCs is extended to the delay-tolerant version and new design criteria are discussed. Then we propose a new design method to yield delay-tolerant LDCs that reach the optimal Jensen's upper bound on ergodic capacity as well as minimum average pairwise error probability. The proposed design employs stochastic gradient algorithm to approach a local optimum. Moreover, it is improved by using simulated annealing type optimization to increase the likelihood of the global optimum. The proposed method allows for flexible number of nodes, receive antennas, modulated symbols and flexible length of codewords. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Analysis of the variability of auditory brainstem response components through linear regression

(ABR) is of fundamental importance to the investiga- tion of the auditory system behavior, though its in- terpretation has a subjective nature because of the manual process employed in its study and the clinical experience required for its analysis. When analyzing the ABR, clinicians are often interested in the identi- fication of ABR signal components referred to as Jewett waves. In particular, the detection and study of the time when these waves occur (i.e., the wave la- tency) is a practical tool for the diagnosis of disorders affecting the auditory system. In this context, the aim of this research is to compare ABR manual/visual analysis provided by different examiners. Methods: The ABR data were collected from 10 normal-hearing subjects (5 men and 5 women, from 20 to 52 years). A total of 160 data samples were analyzed and a pair- wise comparison between four distinct examiners was executed. We carried out a statistical study aiming to identify significant differences between assessments provided by the examiners. For this, we used Linear Regression in conjunction with Bootstrap, as a me- thod for evaluating the relation between the responses given by the examiners. Results: The analysis sug- gests agreement among examiners however reveals differences between assessments of the variability of the waves. We quantified the magnitude of the ob- tained wave latency differences and 18% of the inves- tigated waves presented substantial differences (large and moderate) and of these 3.79% were considered not acceptable for the clinical practice. Conclusions: Our results characterize the variability of the manual analysis of ABR data and the necessity of establishing unified standards and protocols for the analysis of these data. These results may also contribute to the validation and development of automatic systems that are employed in the early diagnosis of hearing loss.

Chapter 17: X-Ray rheology of liquid crystal polymers

X-ray Rheology is an experimental technique which uses time-ressolved x-ray scattering as probe of the molecular level structural reorganisation which accompanies flow. It provides quantitative information on the direction alignment and on the level of global orientation. This information is very helpful in interpreting the classic rheological data on liquid crystal polymers. In this research we use data obtained from a cellulose derivate which exhibits a thermotropic liquid crystal phase. We show how increased shear rates lead to a rapid rise in the global orientation and we related this to therories of flow in liquid crystal polymers from the literature. We show that the relaxation time is independent of the prior shear rate.

Healable supramolecular polymers

This mini-review details the recent development of self-healing and mendable polymeric materials which take advantage of the reversible characteristics of non-covalent interactions during their physical recovery process. Supramolecular polymer systems which undergo spontaneous (autonomous) healing, as well as those which require external stimuli to initiate the healing process (healable/mendable), are introduced and discussed. Supramolecular polymers offer key advantages over alternative approaches, as these materials can typically withstand multiple healing cycles without substantial loss of performance, as a consequence of the highly directional and fully reversible non-covalent interactions present within the polymer matrix.

Retrieval characteristics of non-linear sea surface temperature from the Advanced Very High Resolution Radiometer

Criteria are proposed for evaluating sea surface temperature (SST) retrieved from satellite infra-red imagery: bias should be small on regional scales; sensitivity to atmospheric humidity should be small; and sensitivity of retrieved SST to surface temperature should be close to 1 K K−1. Their application is illustrated for non-linear sea surface temperature (NLSST) estimates. 233929 observations from the Advanced Very High Resolution Radiometer (AVHRR) on Metop-A are matched with in situ data and numerical weather prediction (NWP) fields. NLSST coefficients derived from these matches have regional biases from −0.5 to +0.3 K. Using radiative transfer modelling we find that a 10% increase in humidity alone can change the retrieved NLSST by between −0.5 K and +0.1 K. A 1 K increase in SST changes NLSST by <0.5 K in extreme cases. The validity of estimates of sensitivity by radiative transfer modelling is confirmed empirically.

Expression of epitope-tagged LMW glutenin subunits in the starchy endosperm of transgenic wheat and their incorporation into glutenin polymers

The low-molecular-weight (LMW) glutenin subunits are components of the highly cross-linked glutenin polymers that confer viscoelastic properties to gluten and dough. They have both quantitative and qualitative effects on dough quality that may relate to differences in their ability to form the inter-chain disulphide bonds that stabilise the polymers. In order to determine the relationship between dough quality and the amounts and properties of the LMW subunits, we have transformed the pasta wheat cultivars Svevo and Ofanto with three genes encoding proteins, which differ in their numbers or positions of cysteine residues. The transgenes were delivered under control of the high-molecular-weight (HMW) subunit 1Dx5 gene promoter and terminator regions, and the encoded proteins were C-terminally tagged by the introduction of the c-myc epitope. Stable transformants were obtained with both cultivars, and the use of a specific antibody to the c-myc epitope tag allowed the transgene products to be readily detected in the complex mixture of LMW subunits. A range of transgene expression levels was observed. The addition of the epitope tag did not compromise the correct folding of the trangenic subunits and their incorporation into the glutenin polymers. Our results demonstrate that the ability to specifically epitope-tag LMW glutenin transgenes can greatly assist in the elucidation of their individual contributions to the functionality of the complex gluten system.