Lagrangian approximations and weak solutions of the Navier-Stokes equations

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.

Field measurements of the CO2 evolution rate under different crops during an irrigation cycle in a mountain oasis of Oman

For millennia oasis agriculture has been the backbone of rural livelihood in the desertic Sultanate of Oman. However, little is known about the functioning of these oasis systems, in particular with respect to the C turnover. The objective was to determine the effects of crop, i.e. alfalfa, wheat and bare fallow on the CO2 evolution rate during an irrigation cycle in relation to changes in soil water content and soil temperature. The gravimetric soil water content decreased from initially 24% to approximately 16% within 7 days after irrigation. The mean CO2 evolution rates increased significantly in the order fallow (27.4 mg C m^−2 h^−1) < wheat (45.5 mg C m^−2 h^−1) < alfalfa (97.5 mg C m^−2 h^−1). It can be calculated from these data that the CO2 evolution rate of the alfalfa root system was nearly four times higher than the corresponding rate in the wheat root system. The decline in CO2 evolution rate, especially during the first 4 days after irrigation, was significantly related to the decline in the gravimetric water content, with r = 0.70. CO2 evolution rate and soil temperature at 5 cm depth were negatively correlated (r = -0.56,n = 261) due to increasing soil temperature with decreasing gravimetric water content.

Plant genetic diversity, irrigation and nutrient cycling in traditional mountain oases of northern Oman

Little is known about plant biodiversity, irrigation management and nutrient fluxes as criteria to assess the sustainability of traditional irrigation agriculture in eastern Arabia. Therefore interdisciplinary studies were conducted over 4 yrs on flood-irrigated fields dominated by wheat (Triticum spp.), alfalfa (Medicago sativa L.) and date palm (Phoenix dactylifera L.) in two mountain oases of northern Oman. In both oases wheat landraces consisted of varietal mixtures comprising T. aestivum and T. durum of which at least two botanical varieties were new to science. During irrigation cycles of 6-9 days on an alfalfa-planted soil, volumetric water contents ranged from 30-13%. For cropland, partial oasis balances (comprising inputs of manure, mineral fertilizers, N2-fixation and irrigation water, and outputs of harvested products) were similar for both oases, with per hectare annual surpluses of 131 kg N, 37 kg P and 84 kg K at Balad Seet and of 136 kg N, 16 kg P and 66 kg K at Maqta. Respective palm grove surpluses, in contrast were with 303 kg N, 38 kg P, and 173 kg K ha^-1 yr^-1 much higher at Balad Seet than with 84 kg N, 14 kg P and 91 kg K ha^-1 yr^-1 at Maqta. The results show that the sustainability of these irrigated landuse systems depends on a high quality of the irrigation water with low Na but high CaCO3, intensive recycling of manure and an elaborate terrace structure with a well tailored water management system that allows adequate drainage.

Redox reactions of group 5 elements, including element 105, in aqueous solutions

Standard redox potentials E^0(M^z+x/M^z+) in acidic solutions for group 5 elements including element 105 (Ha) and the actinide, Pa, have been estimated on the basis of the ionization potentials calculated via the multiconfiguration Dirac-Fock method. Stability of the pentavalent state was shown to increase along the group from V to Ha, while that of the tetra- and trivalent states decreases in this direction. Our estimates have shown no extra stability of the trivalent state of hahnium. Element 105 should form mixed-valence complexes by analogy with Nb due to the similar values of their potentials E^0(M^3+/M^2+). The stability of the maximumoxidation state of the elements decreases in the direction 103 > 104 > 105.

The electronic structure of anionic halide complexes of element 105 in aqueous solutions and their extraction by aliphatic amines

To study the complex formation of group 5 elements (Nb, Ta, Ha, and pseudoanalog Pa) in aqueous HCI solutions of medium and high concentrations the electronic structures of anionic complexes of these elements [MCl_6]^-, [MOCl_4]^-, [M(OH)-2 Cl_4]^-, and [MOCl_5]^2- have been calculated using the relativistic Dirac-Slater Discrete-Variational Method. The charge density distribution analysis has shown that tantalum occupies a specific position in the group and has the highest tendency to form the pure halide complex, [TaCl_6-. This fact along with a high covalency of this complex explains its good extractability into aliphatic amines. Niobium has equal trends to form pure halide [NbCl_6]^- and oxyhalide [NbOCl_5]^2- species at medium and high acid concentrations. Protactinium has a slight preference for the [PaOCl_5]^2- form or for the pure halide complexes with coordination number higher than 6 under these conditions. Element 105 at high HCl concentrations will have a preference to form oxyhalide anionic complex [HaOCl_5]^2- rather than [HaCl_6]^-. For the same sort of anionic oxychloride complexes an estimate has been done of their partition between the organic and aqueous phases in the extraction by aliphatic amines, which shows the following succession of the partition coefficients: P_Nb < P_Ha < P_Pa.

Approximate solutions and error estimates for a Stokes boundary value problem

The aim of this paper is the numerical treatment of a boundary value problem for the system of Stokes' equations. For this we extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the system of Stokes' equations in two dimensions. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.

On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Nutrient cycling and nutrient use efficiency in urban and peri-urban agriculture of Kabul, Afghanistan

Like elsewhere also in Kabul, Afghanistan urban and peri-urban agriculture (UPA) has often been accused of being resource inefficient and unsustainable causing negatives externalities to community health and to the surroundings. These arise from the inappropriate management and use of agricultural inputs, including often pesticides and inter-city wastes containing heavy metal residues and pathogens. To address these concerns, parallel studies with the aims of quantification of carbon (C), nitrogen (N), phosphorus (P) and potassium (K) horizontal and vertical fluxes; the assessment of heavy metal and pathogen contaminations of UPA produce, and an economic analysis of cereal, vegetable and grape production systems conducted for two years in UPA of Kabul from April 2008 to October 2009. The results of the studies from these three UPA diverse production systems can be abridged as follows: Biennial net balances in vegetable production systems were positive for N (80 kg ha-1 ), P (75 kg ha-1) and C (3,927 kg ha-1), negative for K (-205 kg ha-1), whereas in cereal production systems biennial horizontal balances were positive for P (20 kg ha-1 ) and C (4,900 kg ha-1) negative for N (-155 kg ha-1) and K (-355 kg ha-1) and in vineyards corresponding values were highly positive for N (295 kg ha-1), P (235 kg ha-1), C (3,362 kg ha-1) and slightly positive for K (5 kg ha-1). Regardless of N and C gaseous emissions, yearly leaching losses of N and P in selected vegetable gardens varied from 70 - 205 kg N ha-1 and 5 - 10 kg P ha-1. Manure and irrigation water contributed on average 12 - 79% to total Inputs of N, P, K and C, 10 - 53% to total inputs of C in the gardens and fields. The elevated levels of heavy metal and pathogen loads on fresh UPA vegetables reflected contamination from increasing traffic in the city, deposits of the past decades of war, lacking collection and treatment of raw inter-city wastes which call for solutions to protect consumer and producer health and increase reliability of UPA productions. A cost-revenue analysis of all inputs and outputs of cereal, vegetable and grapes production systems over two years showed substantial differences in net UPA household income. To confirm these results, more detailed studies are needed, but tailoring and managing the optimal application of inputs to crop needs will significantly enhance farmer’s better revenues as will as environmental and produce quality.

Clay pot irrigation for tomato (Lycopersicon esculentum Mill) production in the north east semiarid region of Ethiopia

Water shortage is one of the major constraints for production of horticultural crops in arid and semiarid regions. A field experiment was conducted to determine irrigation water and fertilizer use efficiency, growth and yield of tomato under clay pot irrigation at the experimental site of Sekota Dryland Agricultural Research Center, Lalibela, Ethiopia in 2009/10. The experiment comprised of five treatments including furrow irrigated control and clay pot irrigation with different plant population and fertilization methods, which were arranged in Randomized Complete Block Design with three replications. The highest total and marketable fruit yields were obtained from clay pot irrigation combined with application of nitrogen fertilizer with irrigation water irrespective of difference in plant population. The clay pot irrigation had seasonal water use of up to 143.71 mm, which resulted in significantly higher water use efficiency (33.62 kg m^-3) as compared to the furrow irrigation, which had a seasonal water use of 485.50 mm, and a water use efficiency of 6.67 kg m^-3. Application of nitrogen fertilizer with irrigation water in clay pots improved fertilizer use efficiency of tomato by up to 52% than band application with furrow or clay pot irrigation. Thus, clay pot irrigation with 33,333 plants ha^-1 and nitrogen fertilizer application with irrigation water in clay pots was the best method for increasing the yield of tomato while economizing the use of water and nitrogen fertilizer in a semiarid environment.

Evaluating partial root-zone irrigation and mulching in okra (Abelmoschus esculentus L.) under a sub-humid tropical climate

The field experiments were conducted to compare the alternate partial root-zone irrigation (APRI) with and without black plastic mulch (BPM) with full root-zone irrigation (FRI) in furrow-irrigated okra (Abelmoschus esculentus L. Moench) at Bhubaneswar, India. APRI means that one of the two neighbouring furrows was alternately irrigated during consecutive watering. FRI was the conventional method where every furrow was irrigated during each watering. The used irrigation levels were 25% available soil moisture depletion (ASMD), 50% ASMD, and 75% ASMD. The plant growth and yield parameters were observed to be significantly (p < 0.05) higher with frequent irrigation (at 25% ASMD) under all irrigation strategies. However, APRI + BPM produced the maximum plant growth and yield using 22% and 56% less water over APRI without BPM and FRI, respectively. The highest pod yield (10025 kg ha^-1) was produced under APRI at 25% ASMD + BPM, which was statistically at par with the pod yield under APRI at 50% ASMD + BPM. Irrigation water use efficiency (IWUE), which indicates the pod yield per unit quantity of irrigation water, was estimated to be highest (12.3 kg m^-3) under APRI at 50% ASMD + BPM, followed by APRI at 25% ASMD + BPM. Moreover, the treatment APRI at 50% ASMD + BPM was found economically superior to other treatments, generating more net return (US $ 952 ha^-1) with higher benefit–cost ratio (1.70).

Comparison of different methods in estimating potential evapotranspiration at Muda Irrigation Scheme of Malaysia

Evapotranspiration (ET) is a complex process in the hydrological cycle that influences the quantity of runoff and thus the irrigation water requirements. Numerous methods have been developed to estimate potential evapotranspiration (PET). Unfortunately, most of the reliable PET methods are parameter rich models and therefore, not feasible for application in data scarce regions. On the other hand, accuracy and reliability of simple PET models vary widely according to regional climate conditions. The objective of the present study was to evaluate the performance of three temperature-based and three radiation-based simple ET methods in estimating historical ET and projecting future ET at Muda Irrigation Scheme at Kedah, Malaysia. The performance was measured by comparing those methods with the parameter intensive Penman-Monteith Method. It was found that radiation based methods gave better performance compared to temperature-based methods in estimation of ET in the study area. Future ET simulated from projected climate data obtained through statistical downscaling technique also showed that radiation-based methods can project closer ET values to that projected by Penman-Monteith Method. It is expected that the study will guide in selecting suitable methods for estimating and projecting ET in accordance to availability of meteorological data.

Bud development, flowering and fruit set of Moringa oleifera Lam. (Horseradish Tree) as affected by various irrigation levels

Moringa oleifera is becoming increasingly popular as an industrial crop due to its multitude of useful attributes as water purifier, nutritional supplement and biofuel feedstock. Given its tolerance to sub-optimal growing conditions, most of the current and anticipated cultivation areas are in medium to low rainfall areas. This study aimed to assess the effect of various irrigation levels on floral initiation, flowering and fruit set. Three treatments namely, a 900 mm (900IT), 600 mm (600IT) and 300 mm (300IT) per annum irrigation treatment were administered through drip irrigation, simulating three total annual rainfall amounts. Individual inflorescences from each treatment were tagged during floral initiation and monitored throughout until fruit set. Flower bud initiation was highest at the 300IT and lowest at the 900IT for two consecutive growing seasons. Fruit set on the other hand, decreased with the decrease in irrigation treatment. Floral abortion, reduced pollen viability as well as moisture stress in the style were contributing factors to the reduction in fruiting/yield observed at the 300IT. Moderate water stress prior to floral initiation could stimulate flower initiation, however, this should be followed by sufficient irrigation to ensure good pollination, fruit set and yield.

More than irrigation - The Balinese Subak system as a unique form of cooperative water resource management in Indonesia

For over 1,000 years, the Balinese have developed a unique system of democratic and sustainable water irrigation. It has shaped the cultural landscapes of Bali and enables local communities to manage the ecology of terraced rice fields at the scale of whole watersheds. The Subak system has made the Balinese the most productive rice growers in Indonesia and ensures a high level of food sovereignty for a dense population on the volcanic island. The Subak system provides a vibrant example of a diverse, ecologically sustainable, economically productive and democratic water management system that is also characterized by its nonreliance on fossil fuel derivatives or heavy machinery. In 2012, UNESCO has recognized five rice terraces and their water temples as World Heritage site and supports its conservation and protection. However, the fragile Subak system is threatened for its complexity and interconnectedness by new agricultural practices and increasing tourism on the island.

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.