Similitude applied to centrifugal scaling of unsaturated flow

Centrifuge experiments modeling single-phase flow in prototype porous media typically use the same porous medium and permeant. Then, well-known scaling laws are used to transfer the results to the prototype. More general scaling laws that relax these restrictions are presented. For permeants that are immiscible with an accompanying gas phase, model-prototype (i.e., centrifuge model experiment-target system) scaling is demonstrated. Scaling is shown to be feasible for Miller-similar (or geometrically similar) media. Scalings are presented for a more, general class, Lisle-similar media, based on the equivalence mapping of Richards' equation onto itself. Whereas model-prototype scaling of Miller-similar media can be realized easily for arbitrary boundary conditions, Lisle-similarity in a finite length medium generally, but not always, involves a mapping to a moving boundary problem. An exception occurs for redistribution in Lisle-similar porous media, which is shown to map to spatially fixed boundary conditions. Complete model-prototype scalings for this example are derived.

Integrable Kondo impurity in one-dimensional q-deformed t-J models

Integrable Kondo impurities in two cases of one-dimensional q-deformed t-J models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

Model for gas-liquid flow through wet porous medium

A method involving bubbling of air through a fibrous filter immersed in water has recently been investigated (Agranovski et al. [1]). Experimental results showed that the removal efficiency for ultra-fine aerosols by such filters was greatly increased compared to dry filters. Nuclear Magnetic Resonance (NMR) imaging was used to examine the wet filter and to determine the nature of the gas flow inside the filter (Agranovski et al. [2]). It was found that tortuous preferential pathways (or flow tubes) develop within the filter through which the air flows and the distribution of air and water inside the porous medium has been investigated. The aim of this paper is to investigate the geometry of the pathways and to make estimates of the flow velocities and particle removal efficiency in such pathways. A mathematical model of the flow of air along the preferred pathways has been developed and verified experimentally. Even for the highest realistic gas velocity the flow field was essentially laminar (Re approximate to 250). We solved Laplace's equation for stream function to map trajectories of particles and gas molecules to investigate the possibility of their removal from the carrier.

Dynamics of trapped Bose-Einstein condensates: Beyond the mean-field

Since dilute Bose gas condensates were first experimentally produced, the Gross-Pitaevskii equation has been successfully used as a descriptive tool. As a mean-field equation, it cannot by definition predict anything about the many-body quantum statistics of condensate. We show here that there are a class of dynamical systems where it cannot even make successful predictions about the mean-field behavior, starting with the process of evaporative cooling by which condensates are formed. Among others are parametric processes, such as photoassociation and dissociation of atomic and molecular condensates.

General properties of cosmological models with an isotropic singularity

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a gamma-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

Estimation of crystalline phase present in the glucose crystal-solution mixture by water activity measurement

The amount of crystalline fraction present in monohydrate glucose crystal-solution mixture up to 110% crystal in relation to solution (crystal:solution=110:100) was determined by water activity measurement. It was found that the water activity had a strong linear correlation (R-2=0.994) with the amount of glucose present above saturation. Difference in the water activities of the crystal-solution mixture (a(w1)) and the supersaturated solution (a(w2)) by re-dissolving the crystalline fraction allowed calculation of the amount of crystalline phase present (DeltaG) in the mixture by an equation DeltaG=846.97(a(w1)-a(w2)). Other methods such as Raoult's, Norrish and Money-Born equations were also tested for the prediction of water activity of supersaturated glucose solution. (C) 2003 Swiss Society of Food Science and Technology. Published by Elsevier Science Ltd. All rights reserved.

Predicting sheetwash and rill erosion over the Australian continent

Soil erosion is a major environmental issue in Australia. It reduces land productivity and has off-site effects of decreased water quality. Broad-scale spatially distributed soil erosion estimation is essential for prioritising erosion control programs and as a component of broader assessments of natural resource condition. This paper describes spatial modelling methods and results that predict sheetwash and rill erosion over the Australian continent using the revised universal soil loss equation (RUSLE) and spatial data layers for each of the contributing environmental factors. The RUSLE has been used before in this way but here we advance the quality of estimation. We use time series of remote sensing imagery and daily rainfall to incorporate the effects of seasonally varying cover and rainfall intensity, and use new digital maps of soil and terrain properties. The results are compared with a compilation of Australian erosion plot data, revealing an acceptable consistency between predictions and observations. The modelling results show that: (1) the northern part of Australia has greater erosion potential than the south; (2) erosion potential differs significantly between summer and winter; (3) the average erosion rate is 4.1 t/ha. year over the continent and about 2.9 x 10(9) tonnes of soil is moved annually which represents 3.9% of global soil erosion from 5% of world land area; and (4) the erosion rate has increased from 4 to 33 times on average for agricultural lands compared with most natural vegetated lands.

A comparison of the self-association behavior of the plant cyclotides kalata B1 and kalata B2 via analytical ultracentrifugation

The recently discovered cyclotides kalata B1 and kalata B2 are miniproteins containing a head-to-tail cyclized backbone and a cystine knot motif, in which disulfide bonds and the connecting backbone segments form a ring that is penetrated by the third disulfide bond. This arrangement renders the cyclotides extremely stable against thermal and enzymatic decay, making them a possible template onto which functionalities can be grafted.We have compared the hydrodynamic properties of two prototypic cyclotides, kalata B1 and kalata B2, using analytical ultracentrifugation techniques. Direct evidence for oligomerization of kalata B2 was shown by sedimentation velocity experiments in which a method for determining size distribution of polydisperse molecules in solution was employed. The shape of the oligomers appears to be spherical. Both sedimentation velocity and equilibrium experiments indicate that in phosphate buffer kalata B1 exists mainly as a monomer, even at millimolar concentrations. In contrast, at 1.6 mM, kalata B2 exists as an equilibrium mixture of monomer (30%), tetramer (42%), octamer (25%), and possibly a small proportion of higher oligomers. The results from the sedimentation equilibrium experiments show that this self-association is concentration dependent and reversible. We link our findings to the three-dimensional structures of both cyclotides, and propose two putative interaction interfaces on opposite sides of the kalata B2 molecule, one involving a hydrophobic interaction with the Phe(6), and the second involving a charge-charge interaction with the Asp(25) residue. An understanding of the factors affecting solution aggregation is of vital importance for future pharmaceutical application of these molecules.

Ladder operators for integrable one-dimensional lattice models

A generalised ladder operator is used to construct the conserved operators for any one-dimensional lattice model derived from the Yang-Baxter equation. As an example, the low order conserved operators for the XYh model are calculated explicitly.

Asymptotically almost periodic solutions for abstract neutral integro-differential equations

We study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations which arise in the study of heat conduction in fading memory material is considered. (C) 2011 Elsevier Inc. All rights reserved.

Investigation of the electrical and electrochemical properties of nanocomposites from V2O5, polypyrrole, and polyaniline

In this work, an investigation of the electrical and electrochemical properties responsible for the energy storage capability of nanocomposites has been carried out. We demonstrate that, in the case of the V2O5 xerogel and the nanocomposites polypyrrole (Ppy)/V2O5 and polyaniline (PANI)/V2O5, the quadratic logistic equation (QLE) can be used to fit the inverse of the resistance values as a function of the injected charge in non-steady-state conditions. This contributes to a phenomenological understanding of the lithium ion and electron transport. The departure of the experimental curve from the fitting observed for the V2O5 xerogel can be attributed to the trapping sites formed during the lithium electroinsertion, which was observed by electrochemical impedance spectroscopy. The amount of trapping sites was obtained on the basis of the QLE. Similar values used to fit the inverse of the resistance were also used to fit the absorbance changes, which is also associated with the small polaron hopping from the V(IV) to the V(V) sites. On the other hand, there was good agreement between the experimental and the theoretical data when the profile of the inverse of the resistance as a function of the amount of inserted lithium ions of the nanocomposites Ppy/V2O5 and PANI/ V2O5 was concerned. We suggest that the presence of the conducting polymers is responsible for the different electrical profile of the V2O5 xerogel compared with those of the nanocomposites. In the latter case, interactions between the lithium ions and oxygen atoms from V2O5 are shielded, thus decreasing the trapping effect of lithium ions in the V2O5 sites. The different values of the lithium ion diffusion coefficient into these intercalation materials are in agreement with this hypothesis.

Self-assembled films from WO(3): Electrochromism and lithium ion diffusion

WO(3)/chitosan and WO(3)/chitosan/poly(ethylene oxide) (PEO) films were prepared by the layer-by-layer method. The presence of chitosan enabled PEO to be carried into the self-assembled structure, contributing to an increase in the Li(+) diffusion rate. On the basis of the galvanostatic intermittent titration technique (GITT) and the quadratic logistic equation (QLE), a spectroelectrochemical method was used for determination of the ""optical"" diffusion coefficient (D(op)), enabling analysis of the Li(+) diffusion rate and, consequently, the coloration front rate in these host matrices. The D(op) values within the WO(3)/chitosan/PEO film were significantly higher than those within the WO(3)/chitosan film, mainly for higher values of injected charge. The presence of PEO also ensured larger accessibility to the electroactive sites, in accordance with the method employed here. Hence, this spectroelectrochemical method allowed us to separate the contribution of the diffusion process from the number of accessible electroactive sites in the materials, thereby aiding a better understanding of the useful electrochemical and electrochromic properties of these films for use in electrochromic devices. (C) 2010 Elsevier B.V. All rights reserved.

Global solutions for abstract neutral differential equations

We study the existence of global solutions for a class of abstract neutral differential equation defined on the whole real axis. Some concrete applications related to ordinary and partial differential equations are considered. (C) 2009 Elsevier Ltd. All rights reserved.