Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions

We derive the energy levels associated with the even-parity wave functions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of solution of the harmonic oscillator problem.Comment: 9 pages, 3 figure

Delayed mortality effects cut the malaria transmission potential of insecticide resistant mosquitoes

Malaria transmission has been substantially reduced across Africa through the distribution of long-lasting insecticidal nets (LLINs). However, the emergence of insecticide resistance within mosquito vectors risks jeopardizing the future efficacy of this control strategy. The severity of this threat is uncertain because the consequences of resistance for mosquito fitness are poorly understood: while resistant mosquitoes are no longer immediately killed upon contact with LLINs, their transmission potential may be curtailed because of longer-term fitness costs that persist beyond the first 24 h after exposure. Here, we used a Bayesian state-space model to quantify the immediate (within 24 h of exposure) and delayed (>24 h after exposure) impact of insecticides on daily survival and malaria transmission potential of moderately and highly resistant laboratory populations of the major African malaria vector Anopheles gambiae. Contact with LLINs reduced the immediate survival of moderately and highly resistant An. gambiae strains by 60–100% and 3–61%, respectively, and delayed mortality impacts occurring beyond the first 24 h after exposure further reduced their overall life spans by nearly one-half. In total, insecticide exposure was predicted to reduce the lifetime malaria transmission potential of insecticide-resistant vectors by two-thirds, with delayed effects accounting for at least one-half of this reduction. The existence of substantial, previously unreported, delayed mortality effects within highly resistant malaria vectors following exposure to insecticides does not diminish the threat of growing resistance, but posits an explanation for the apparent paradox of continued LLIN effectiveness in the presence of high insecticide resistance

Analytical study of tunneling times in flat histogram Monte Carlo

We present a model for the dynamics in energy space of multicanonical simulation methods that lends itself to a rather complete analytic characterization. The dynamics is completely determined by the density of states. In the \pm J 2D spin glass the transitions between the ground state level and the first excited one control the long time dynamics. We are able to calculate the distribution of tunneling times and relate it to the equilibration time of a starting probability distribution. In this model, and possibly in any model in which entering and exiting regions with low density of states are the slowest processes in the simulations, tunneling time can be much larger (by a factor of O(N)) than the equilibration time of the probability distribution. We find that these features also hold for the energy projection of single spin flip dynamics.Comment: 7 pages, 4 figures, published in Europhysics Letters (2005

Agricultural land systems : modelling past, present and future regional dynamics

This thesis arises from the understanding of how the integration of concepts, tools, techniques, and methods from geographic information science (GIS) can provide a formalised knowledge base for agricultural land systems in response to future agricultural and food system challenges. To that end, this thesis focuses on understanding the potential application of GIS-based approaches and available spatial data sources for modelling regional agricultural land-use and production dynamics in Portugal. The specific objectives of this thesis are addressed in seven chapters in Parts II through V, each corresponding to one scientific article that was either published or is being considered for publication in peer-reviewed international scientific journals. In Part II, Chapter 2 summarises the body of knowledge and provides the context for the contribution of this thesis within the scientific domain of agricultural land systems. In Part III, Chapters 3 and 4 explore remotely sensed and Volunteered Geographic Information (VGI) data, multitemporal and multisensory approaches, and a variety of statistical methods for mapping, quantifying, and assessing regional agricultural land dynamics in the Beja district. In Part IV, Chapters 5–7 explore the CA-Markov model, Markov chain model, machine learning, and model-agnostic approach, as well as a set of spatial metrics and statistical methods for modelling the factors and spatiotemporal changes of agricultural land use in the Beja district. In Part V, Chapter 8 explores an area-weighting GIS-based technique, a spatiotemporal data cube, and statistical methods to model the spatial distribution across time for regional agricultural production in Portugal. The case studies in the thesis contribute practical and theoretical knowledge by demonstrating the strengths and limitations of several GIS-based approaches. Together, the case studies demonstrate the underlying principles that underpin each approach in a way that allows us to infer their potentiality and appropriateness for modelling regional agricultural land-use and production dynamics, stimulating further research along this line. Generally, this thesis partly reflects the state-of-art of land-use modelling and contribute significantly to the introduction of advances in agricultural system modelling research and land-system science