Effect of hydrogel particle additives on water-accessible pore structure of sandy soils: A custom pressure plate apparatus and capillary bundle model

To probe the effects of hydrogel particle additives on the water-accessible pore structure of sandy soils, we introduce a custom pressure plate method in which the volume of water expelled from a wet granular packing is measured as a function of applied pressure. Using a capillary bundle model, we show that the differential change in retained water per pressure increment is directly related to the cumulative cross-sectional area distribution $f(r)$ of the water-accessible pores with radii less than $r$. This is validated by measurements of water expelled from a model sandy soil composed of 2 mm diameter glass beads. In particular, the expelled water is found to depend dramatically on sample height and that analysis using the capillary bundle model gives the same pore size distribution for all samples. The distribution is found to be approximately log-normal, and the total cross-sectional area fraction of the accessible pore space is found to be $f_0=0.34$. We then report on how the pore distribution and total water-accessible area fraction are affected by superabsorbent hydrogel particle additives, uniformly mixed into a fixed-height sample at varying concentrations. Under both fixed volume and free swelling conditions, the total area fraction of water-accessible pore space in a packing decreases exponentially as the gel concentration increases. The size distribution of the pores is significantly modified by the swollen hydrogel particles, such that large pores are clogged while small pores are formed

The Ultraviolet flash accompanying GRBs from neutron-rich internal shocks

In the neutron-rich internal shocks model for Gamma-ray Burts (GRBs), the Lorentz factors (LFs) of ions shells are variable, so are the LFs of accompanying neutron shells. For slow neutron shells with a typical LF tens, the typical beta-decay radius reads R_{\beta,s} several 10^{14} cm, which is much larger than the typical internal shocks radius 10^{13} cm, so their impact on the internal shocks may be unimportant. However, as GRBs last long enough (T_{90}>20(1+z) s), one earlier but slower ejected neutron shell will be swept successively by later ejected ion shells in the range 10^{13}-10^{15} cm, where slow neutrons have decayed significantly. We show in this work that ion shells interacting with the beta-decay products of slow neutron shells can power a ultraviolet (UV) flash bright to 12th magnitude during the prompt gamma-ray emission phase or slightly delayed, which can be detected by the upcoming Satellite SWIFT in the near future.Comment: 6 pages (2 eps figures), accepted for publication in ApJ

Stability Analysis of Turing Patterns Generated by the Schnakenberg Model

We consider the following Schnakenberg model on the interval (−1, 1): ut = D1u − u + vu2 in (−1, 1), vt = D2v + B − vu2 in (−1, 1), u (−1) = u (1) = v (−1) = v (1) = 0, where D1 > 0, D2 > 0, B>0. We rigorously show that the stability of symmetric N−peaked steady-states can be reduced to computing two matrices in terms of the diffusion coefficients D1,D2 and the number N of peaks. These matrices and their spectra are calculated explicitly and sharp conditions for linear stability are derived. The results are verified by some numerical simulations

Rain water transport and storage in a model sandy soil with hydrogel particle additives

We study rain water infiltration and drainage in a dry model sandy soil with superabsorbent hydrogel particle additives by measuring the mass of retained water for non-ponding rainfall using a self-built 3D laboratory set-up. In the pure model sandy soil, the retained water curve measurements indicate that instead of a stable horizontal wetting front that grows downward uniformly, a narrow fingered flow forms under the top layer of water-saturated soil. This rain water channelization phenomenon not only further reduces the available rain water in the plant root zone, but also affects the efficiency of soil additives, such as superabsorbent hydrogel particles. Our studies show that the shape of the retained water curve for a soil packing with hydrogel particle additives strongly depends on the location and the concentration of the hydrogel particles in the model sandy soil. By carefully choosing the particle size and distribution methods, we may use the swollen hydrogel particles to modify the soil pore structure, to clog or extend the water channels in sandy soils, or to build water reservoirs in the plant root zone

Stability of cluster solutions in a cooperative consumer chain model

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag Berlin Heidelberg 2012.We study a cooperative consumer chain model which consists of one producer and two consumers. It is an extension of the Schnakenberg model suggested in Gierer and Meinhardt [Kybernetik (Berlin), 12:30-39, 1972] and Schnakenberg (J Theor Biol, 81:389-400, 1979) for which there is only one producer and one consumer. In this consumer chain model there is a middle component which plays a hybrid role: it acts both as consumer and as producer. It is assumed that the producer diffuses much faster than the first consumer and the first consumer much faster than the second consumer. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. In the small diffusion limit we construct cluster solutions in an interval which have the following properties: The spatial profile of the third component is a spike. The profile for the middle component is that of two partial spikes connected by a thin transition layer. The first component in leading order is given by a Green's function. In this profile multiple scales are involved: The spikes for the middle component are on the small scale, the spike for the third on the very small scale, the width of the transition layer for the middle component is between the small and the very small scale. The first component acts on the large scale. To the best of our knowledge, this type of spiky pattern has never before been studied rigorously. It is shown that, if the feedrates are small enough, there exist two such patterns which differ by their amplitudes.We also study the stability properties of these cluster solutions. We use a rigorous analysis to investigate the linearized operator around cluster solutions which is based on nonlocal eigenvalue problems and rigorous asymptotic analysis. The following result is established: If the time-relaxation constants are small enough, one cluster solution is stable and the other one is unstable. The instability arises through large eigenvalues of order O(1). Further, there are small eigenvalues of order o(1) which do not cause any instabilities. Our approach requires some new ideas: (i) The analysis of the large eigenvalues of order O(1) leads to a novel system of nonlocal eigenvalue problems with inhomogeneous Robin boundary conditions whose stability properties have been investigated rigorously. (ii) The analysis of the small eigenvalues of order o(1) needs a careful study of the interaction of two small length scales and is based on a suitable inner/outer expansion with rigorous error analysis. It is found that the order of these small eigenvalues is given by the smallest diffusion constant ε22.RGC of Hong Kon

Super-reflection and Cloaking Based on Zero Index Metamaterial

A zero index metamaterial (ZIM) can be utilized to block wave (super-reflection) or conceal objects completely (cloaking). The "super-reflection" device is realized by a ZIM with a perfect electric (magnetic) conductor inclusion of arbitrary shape and size for a transverse electric (magnetic) incident wave. In contrast, a ZIM with a perfect magnetic (electric) conductor inclusion for a transverse electric (magnetic) incident wave can be used to conceal objects of arbitrary shape. The underlying physics here is determined by the intrinsic properties of the ZIM

Effects of topological edge states on the thermoelectric properties of Bi nanoribbons

Using first-principles calculations combined with Boltzmann transport theory, we investigate the effects of topological edge states on the thermoelectric properties of Bi nanoribbons. It is found that there is a competition between the edge and bulk contributions to the Seebeck coefficients. However, the electronic transport of the system is dominated by the edge states because of its much larger electrical conductivity. As a consequence, a room temperature value exceeding 3.0 could be achieved for both p- and n-type systems when the relaxation time ratio between the edge and the bulk states is tuned to be 1000. Our theoretical study suggests that the utilization of topological edge states might be a promising approach to cross the threshold of the industrial application of thermoelectricity