Entropy Maximization and Instability of Uniformly Magnetized Plasma

A regime where a uniformly magnetized plasma could be unstable to a spatial perturbation in the magnetic field is explored. In this regime, a uniformly magnetized state does not maximize the entropy. The physical implication is discussed in the context of the current generation, the magnetic reconnection, and the dynamo effect

Testable non-linearity through entanglement measurement

A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the proposals for the gravitationally induced collapse of wave function. Here, it is shown that the consequence of the connection demonstrates a possible deviation of the theory from the standard formulation of quantum mechanics in the probability prediction of experiments. The links are identified from the fact that the analytic solution of the equation is given by Dirichlet eigenvalues which can be expressed by generalized trigonometric function. Consequently, modified formulation of Born's rule is obtained by relating the event probability of the measuement to an arbitrary exponent of the modulus of the eigenvalue solution. Such system, which is subject to the non-linear dynamic equation, illustrates the violation of the Clauser-Hore-Shimony-Holt inequality proportional to the degree of the non-linearity as it can be tested by a real experiment. Depending upon the degree, it is found that the violation can go beyond Tsirelson bound $2\sqrt{2}$ and reaches to the value of nonlocal box.Comment: 3 figure

Inrteractions [sic] between farm effluent application methods, tillage practices and soil nutrients : a thesis presented in partial fulfilment of the requirements for the degree of Master of Applied Science in Agricultural Engineering at Massey University, Palmerston North, New Zealand

Land disposal of liquid effluent has benefits for the environment and is economically viable. Firstly, it can reduce nutrient levels from wastes polluting waterways. Secondly, the land application of effluent has been the most common treatment method because it can provide some necessary nutrients for plant growth. In New Zealand, land application of farm liquid effluent is a common method for disposing agricultural wastes. However, there is little comparative information about nutrient recycling in soils treated with effluent using surface application or subsurface injection. A field trial was conducted to examine the effect of tillage on the transformation of nutrient added through dairyshed effluent. Liquid effluent was either injected at 10 cm depth or broadcast on the surface at the Massey University long-term tillage experiments which include permanent pasture, and crops sown with no-till and conventional tillage as main treatments. In the first experiment, raw dairyshed liquid effluent was applied in August 1997 at the rate of 120 m 3 ha -1 (30 kg N ha -1 equivalent). This was considered as a low rate of application. In the second experiment starting in December 1997, the application was at the rate of 600 m 3 ha -1 (150 kg N ha -1 ). At this rate, although the hydraulic loading was considered as a high rate, the nutrient loading was considered optimum. Soil samples were collected before application, after one week, one month, and two months of application, at two depths: 0-10 cm and 10-20 cm and the samples were analysed for total N, total P, NO 3 - , NH 4 + , exchangeable K, available Olsen-P. Throughout the experiments, interactions between nutrient status, methods of application and different tillage practices were analysed. In the case of injection method, soil samples were taken both in the centre of the injected row and 10cm horizontally away from the centre of row. At the low rate of application (first experiment), soil nitrogen and phosphorus status did not change significantly for up to two months after application. Soil ammonium concentration reduced immediately after one week then reduced slowly. Nitrate concentration reduced slowly during the first month and significantly reduced during the second month after application. Exchangeable K and Olsen-P were not significantly different among treatments. At the high rate of application (second experiment), levels of soil nitrogen and phosphorus reduced slightly after two months of application. Nitrate concentration in the soil increased in the first month, but steadily reduced during the second month. On the other hand, ammonium concentration reduced gradually over a period of two months. Ammonium in injected plots was higher than that in the broadcast plots. Pasture retained more ammonium concentration compared with no-till and conventional tillage plots. Moreover, nitrate content in the injection plots was similar to that in the broadcast. This may be related to low rainfall during the experiment period that may have restricted the denitrification and reduced nitrate losses through leaching. Generally, there was higher content of exchangeable K and available P in soil which resulted from effluent application. Method of effluent application had no effects on K and P concentrations. Overall, there was an increase in nutrients in soil after application of liquid effluent, especially at the topsoil. There was a greater retention of nutrients in no-till soil than the conventionally tilled soil. Subsoil injection of effluent allowed higher level of nutrient retention than the surface broadcast method. This may be due to reduced nitrogen losses caused by volatilization of ammonium

Substitutions, tiling dynamical systems and minimal self-joinings

We investigate substitution subshifts and tiling dynamical systems arising from the substitutions (1) \theta : 0 \rightarrow 001,1 \rightarrow 11001 and (2) \eta : 0 \rightarrow 001,1 \rightarrow 11100. We show that the substitution subshifts arising from \theta and \eta have minimal self-joinings and are mildly mixing. We also give a criterion for 1-dimensional tiling systems arising from \theta or \eta to have minimal self-joinings. We apply this to obtain examples of mildly mixing 1-dimensional tiling systems