On continuity of solutions for parabolic control systems and input-to-state stability

We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions. This question naturally appears when working with boundary controlled, linear partial differential equations. Here, we focus on parabolic equations which allow for operator-theoretic methods such as the holomorphic functional calculus. Moreover, we investigate stronger conditions than continuity leading to input-to-state stability with respect to Orlicz spaces. This also implies that the notions of input-to-state stability and integral-input-to-state stability coincide if additionally the uncontrolled equation is dissipative and the input space is finite-dimensional.Comment: 19 pages, final version of preprint, Prop. 6 and Thm 7 have been generalised to arbitrary Banach spaces, the assumption of boundedness of the semigroup in Thm 10 could be droppe

Input-to-state stability of unbounded bilinear control systems

We study input-to-state stability of bilinear control systems with possibly unbounded control operators. Natural sufficient conditions for integral input-to-state stability are given. The obtained results are applied to a bilinearly controlled Fokker-Planck equation.Comment: 20 pages, completely new version based on the few preliminary ideas in v1. Compared to v1, the results have been significantly generalized and extende

Characterization of Orlicz admissibility

We extend two characterizations of admissible operators with respect to L p to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly continuous semigroup and in terms of a resolvent estimate.</p

Readout of Majorana qubits

Schemes for topological quantum computation with Majorana bound states rely heavily on the ability to projectively measure products of Majorana operators. Here, we employ Markovian quantum measurement theory, including the readout device, to analyze such measurements. Specifically, we focus on the readout of Majorana qubits via continuous charge sensing of a tunnel-coupled quantum dot by a quantum point contact. We show that projective measurements of Majorana products Pi(i) (gamma) over cap (i) can be implemented by continuous charge sensing under quite general circumstances. Essential requirements are that a combined local parity (pi) over cap, involving the quantum dot charge along with the Majorana product of interest, be conserved, and that the two eigenspaces of the combined parity (pi) over cap generate distinguishable measurement signals. We find that qubit readout may have to rely on measuring noise correlations of the quantum-point-contact current. The average current encodes the qubit readout only transiently for fine-tuned parameters or in the presence of relaxation processes. We also discuss the corresponding measurement and decoherence times and consider processes, such as residual Majorana hybridizations, which are detrimental to the measurement protocol. Finally, we emphasize that the underlying mechanism-which we term symmetry-protected readout-is quite general and has further implications for both Majorana and non-Majorana systems

Irrigating Zimbabwe After Land Reform: The Potential of Farmer-Led Systems

Farmer-led irrigation is far more extensive in Zimbabwe than realised by planners and policymakers. This paper explores the pattern of farmer-led irrigation in neighbouring post-land reform smallholder resettlement sites in Zimbabwe’s Masvingo district. Across 49 farmer-led cases, 41.3 hectares of irrigated land was identified, representing two per cent of the total land area. A combination of surveys and in-depth interviews explored uses of different water extraction and distribution technologies, alongside patterns of production, marketing, processing and labour use. In-depth case studies examined the socio-technical practices involved. Based on these data, a simple typology is proposed, differentiating homestead irrigators from aspiring and commercial irrigators. The typology is linked to patterns of investment, accumulation and social differentiation across the sites. The results are contrasted with a formal irrigation scheme and a group garden in the same area. Farmer-led irrigation is more extensive but also more differentiated, suggesting a new dynamic of agrarian change. As Zimbabwe seeks to boost agricultural production following land reform, the paper argues that farmer-led irrigation offers a complementary way forward to the current emphasis on formal schemes, although challenges of water access, environmental management and equity are highlighted

A refinement of Baillon's theorem on maximal regularity

By Baillon's result, it is known that maximal regularity with respect to the space of continuous functions is rare; it implies that either the involved semigroup generator is a bounded operator or the considered space contains $c_{0}$. We show that the latter alternative can be excluded under a refined condition resembling maximal regularity with respect to $\mathrm{L}^{\infty}$.Comment: 17 page

Groundwater use for irrigation - a global inventory

Irrigation is the most important water use sector accounting for about 70% of the global freshwater withdrawals and 90% of consumptive water uses. While the extent of irrigation and related water uses are reported in statistical databases or estimated by model simulations, information on the source of irrigation water is scarce and very scattered. Here we present a new global inventory on the extent of areas irrigated with groundwater, surface water or non-conventional sources, and we determine the related consumptive water uses. The inventory provides data for 15 038 national and sub-national administrative units. Irrigated area was provided by census-based statistics from international and national organizations. A global model was then applied to simulate consumptive water uses for irrigation by water source. Globally, area equipped for irrigation is currently about 301 million ha of which 38% are equipped for irrigation with groundwater. Total consumptive groundwater use for irrigation is estimated as 545 km3 yr−1, or 43% of the total consumptive irrigation water use of 1 277 km3 yr−1. The countries with the largest extent of areas equipped for irrigation with groundwater, in absolute terms, are India (39 million ha), China (19 million ha) and the United States of America (17 million ha). Groundwater use in irrigation is increasing both in absolute terms and in percentage of total irrigation, leading in places to concentrations of users exploiting groundwater storage at rates above groundwater recharge. Despite the uncertainties associated with statistical data available to track patterns and growth of groundwater use for irrigation, the inventory presented here is a major step towards a more informed assessment of agricultural water use and its consequences for the global water cycle