The high energy semiclassical asymptotics of loci of roots of fundamental solutions for polynomial potentials

In the case of polynomial potentials all solutions to 1-D Schroedinger equation are entire functions totally determined by loci of their roots and their behaviour at infinity. In this paper a description of the first of the two properties is given for fundamental solutions for the high complex energy limit when the energy is quantized or not. In particular due to the fact that the limit considered is semiclassical it is shown that loci of roots of fundamental solutions are collected of selected Stokes lines (called exceptional) specific for the solution considered and are distributed along these lines in a specific way. A stable asymptotic limit of loci of zeros of fundamental solutions on their exceptional Stokes lines has island forms and there are infintely many of such roots islands on exceptional Stokes lines escaping to infinity and a finite number of them on exceptional Stokes lines which connect pairs of turning points. The results obtained for asymptotic roots distributions of fundamental solutions in the semiclassical high (complex) energy limit are of a general nature for polynomial potentials.Comment: 41 pages, 14 figure

Fractal properties of quantum spacetime

We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to quantum gravity. In particular we analyze the cases of a quantum sphere and of \k-Minkowski, the latter being relevant in the context of quantum gravity.Comment: 4 pages, 2 figures; some minor corrections; reference adde

Labor markets and labor allocative efficiency among farm households in western Kenya

This paper evaluates how efficiently farm households allocate labor between farm and offfarm activities. It estimates farm and off-farm labor supply functions to determine the factors that influence labor allocation. Both the shadow wage and the off-farm wage rate are included as regressors in the supply functions. The study reveals that, on average, farm households are inefficient, but when linked to labor markets their productivity and internal efficiency increase. The decision to sell labor is influenced by location, and off-farm employment is difficult to find, particularly for the better educated. Interventions should aim to increase opportunities for off-farm employment for persons with skills or with higher than the basic level of education, and to reduce the cost of participating in labor markets, for example by improving rural infrastructure. Addressing failures in rural financial markets would save poor households from having to sell their labor for less than they get from their farm

Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics

Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed for the corresponding Borel functions. Its main property is to order the singularity structure of the Borel plane in a hierarchical way by an increasing complexity of this structure starting from the analytic one. This allows us to study the Borel plane singularity structure in a systematic way. Examples of such structures are considered for linear, harmonic and anharmonic potentials. Together with the best approximation provided by the semiclassical series the exponentially small contribution completing the approximation are considered. A natural method of constructing such an exponential asymptotics relied on the Borel plane singularity structures provided by the topological expansion is developed. The method is used to form the semiclassical series including exponential contributions for the energy levels of the anharmonic oscillator.Comment: 46 pages, 22 EPS figure

Failure of classical elasticity in auxetic foams

A recent derivation [P.H. Mott and C.M. Roland, Phys. Rev. B 80, 132104 (2009).] of the bounds on Poisson's ratio, v, for linearly elastic materials showed that the conventional lower limit, -1, is wrong, and that v cannot be less than 0.2 for classical elasticity to be valid. This is a significant result, since it is precisely for materials having small values of v that direct measurements are not feasible, so that v must be calculated from other elastic constants. Herein we measure directly Poisson's ratio for four materials, two for which the more restrictive bounds on v apply, and two having values below this limit of 0.2. We find that while the measured v for the former are equivalent to values calculated from the shear and tensile moduli, for two auxetic materials (v < 0), the equations of classical elasticity give inaccurate values of v. This is experimental corroboration that the correct lower limit on Poisson's ratio is 0.2 in order for classical elasticity to apply.Comment: 9 pages, 2 figure

Managing soil fertility diversity to enhance resource use efficiencies in smallholder farming systems: a case from Murewa District, Zimbabwe

Smallholder farms in sub-Saharan African exhibit substantial heterogeneity in soil fertility, and nutrient resource allocation strategies that address this variability are required to increase nutrient use efficiencies. We applied the Field-scale resource Interactions, use Efficiencies and Long-term soil fertility Development (FIELD) model to explore consequences of various manure and fertilizer application strategies on crop productivity and soil organic carbon (SOC) dynamics on farms varying in resource endowment in a case study village in Murewa District, Zimbabwe. FIELD simulated a rapid decline in SOC and maize yields when native woodlands were cleared for maize cultivation without fertilizer inputs coupled with removal of crop residues. Applications of 10 t manure ha-1 year-1 for 10 years were required to restore maize productivity to the yields attainable under native woodland. Long-term application of manure at 5 and 3 t ha-1 resulted in SOC contents comparable to zones of high and medium soil fertility observed on farms of wealthy cattle owners. Targeting manure application to restore SOC to 50–60% of contents under native woodlands was sufficient to increase productivity to 90% of attainable yields. Short-term increases in crop productivity achieved by reallocating manure to less fertile fields were short-lived on sandy soils. Preventing degradation of the soils under intensive cultivation is difficult, particularly in low input farming systems, and attention should be paid to judicious use of the limited nutrient resources to maintain a degree of soil fertility that supports good crop response to fertilizer applicatio