Diffusional phenomena in membrane separation processes

Nowadays membrane filtration processes are used industrially as an alternative to conventional separation methods. Membrane separation methods can be divided into classes according to their separation characteristics: (i) separation by sieving action; (ii) separation due to a difference in affinity and diffusivity; (iii) separation due to a difference in charge of molecules; (iv) carrier-facilitated transport, and (v) the process of (time-) controlled released by diffusion. In all these cases diffusion processes play an important role in the transport mechanism of the solutes. Various mechanisms have been distinguished to describe the transport in membranes: transport through bulk material (dense membranes), Knudsen diffusion in narrow pores, viscous flow in wide pores or surface diffusion along pore walls. In practice, the transport can be a result of more than only one of these mechanisms. For all of these mechanisms models have been derived. The characteristics of a membrane, e.g. its crystallinity or its charge, can also have major consequences for the rate of diffusion in the membrane, and hence for the flux obtained. Apart from the diffusion transport processes in membranes mentioned above, other important diffusion processes are related to membrane processes, viz. diffusion in the boundary layer near the membrane (concentration polarization phenomena) and diffusion during membrane formation. The degree of concentration polarization is related to the magnitude of the mass transfer coefficient which, in turn, is influenced by the diffusion coefficient. The effect of concentration polarization can be rather different for the various membrane processes. The phase inversion membrane formation mechanism is determined to a large extent by the kinetic aspects during membrane formation, which are diffusion of solvent and of non-solvent and the kinetics of the phase separation itself

On the minimization of Dirichlet eigenvalues

Results are obtained for two minimization problems: $$I_k(c)=\inf \{\lambda_k(\Omega): \Omega\ \textup{open, convex in}\ \mathbb{R}^m,\ \mathcal{T}(\Omega)= c \},$$ and $$J_k(c)=\inf\{\lambda_k(\Omega): \Omega\ \textup{quasi-open in}\ \mathbb{R}^m, |\Omega|\le 1, \mathcal {P}(\Omega)\le c \},$$ where $c>0$, $\lambda_k(\Omega)$ is the $k$'th eigenvalue of the Dirichlet Laplacian acting in $L^2(\Omega)$, $|\Omega|$ denotes the Lebesgue measure of $\Omega$, $\mathcal{P}(\Omega)$ denotes the perimeter of $\Omega$, and where $\mathcal{T}$ is in a suitable class set functions. The latter include for example the perimeter of $\Omega$, and the moment of inertia of $\Omega$ with respect to its center of mass.Comment: 15 page

Do public works decrease farmers' soil degradation? Labour income and the use of fertilisers in India's semi-arid tropics

This paper investigates the possibility of using public works to stimulate farmers' fertiliser use in India's SAT. Inadequate replenishment of removed nutrients and organic matter has reduced fertility and increased erosion rates. Fertiliser use, along with other complementary measures, can help reverse this process, which ultimately leads to poverty, hunger, and further environmental degradation. In a high-risk environment like India's SAT, there may be a strong relation between off-farm income and smallholder fertiliser use. Farmers can use the main source of off-farm income, wage income, to manage risk as well as to finance inputs. Consequently, the introduction of public works programmes in areas with high dry-season unemployment may affect fertiliser use. This study confirms the relevance of risk for decisions regarding fertiliser use in two Indian villages. Nevertheless, governments cannot use employment policies to stimulate fertiliser use. Public works even decrease fertiliser use in the survey setting

Sharpness of the percolation transition in the two-dimensional contact process

For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution can only occur at $p_c$. This behavior is often called ``sharpness of the percolation transition.'' For theoretical reasons, as well as motivated by applied research, there is an increasing interest in percolation models with (weak) dependencies. For instance, biologists and agricultural researchers have used (stationary distributions of) certain two-dimensional contact-like processes to model vegetation patterns in an arid landscape (see [20]). In that context occupied clusters are interpreted as patches of vegetation. For some of these models it is reported in [20] that computer simulations indicate power-law behavior in some interval of positive length of a model parameter. This would mean that in these models the percolation transition is not sharp. This motivated us to investigate similar questions for the ordinary (``basic'') $2D$ contact process with parameter $\lambda$. We show, using techniques from Bollob\'{a}s and Riordan [8, 11], that for the upper invariant measure ${\bar{\nu}}_{\lambda}$ of this process the percolation transition is sharp. If $\lambda$ is such that (${\bar{\nu}}_{\lambda}$-a.s.) there are no infinite clusters, then for all parameter values below $\lambda$ the cluster-size distribution has exponential decay.Comment: Published in at http://dx.doi.org/10.1214/10-AAP702 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A multiple wire magnetostrictive delay line for improved signal and reduced reflections

The amplitude of the output signal per unit of cross sectional area of a magnetostrictive delay line decreases for increasing wire diameter due to the skin effect. For a fixed area a large output signal can be obtained by using a number of thin wires. An additional advantage is the reduced influence of inhomogeneities along the wires. Reflections in this multiple wire delay line can be reduced firstly by means of interference by fixing half of the number of wires to a mass and leaving the other half ends free, and/or secondly through spreading out the reflections by shifting the ends of the wires with respect to each other. A simple magneto-acoustic position measurement system using a multiple wire delay line and one single transmitting/receiving coil is demonstrated