First passages in bounded domains: When is the mean first passage time meaningful?

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(ω) distribution of the random variable ω=τ1/(τ1+τ2), which is a measure for how similar the first passage times τ1 and τ2 are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(ω) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(ω), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.

Entire functions uniformly bounded on balls of a Banach space

Let X be an in�finite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B1 � X and unbounded on another given ball B2 � X have been obtained. In this paper we consider the problem of �finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection. RESUMEN. Sea X un espacio de Banach complejo de dimensión infinita. En este trabajo, los autores estudian el problema de encontrar una función entera en X que esté uniformemente acotada en una colección de de bolas en X y que no esté acotada en las bolas de otra colección.

Unconformity-bounded stratigraphic units (UBSUs) in an italian alluvial-plain area: recognizing and dating

We studied the coastal zone of the Tavoliere di Puglia plain, (Puglia region, southern Italy) with the aim to recognize the main unconformities, and therefore, the unconformity-bounded stratigraphic units (UBSUs; Salvador 1987, 1994) forming its Quaternary sedimentary fill. Recognizing unconformities is particularly problematic in an alluvial plain, due to the difficulties in distinguishing the unconformities that bound the UBSUs. So far, the recognition of UBSUs in buried successions has been made mostly by using seismic profiles. Instead, in our case, the unavailability of the latter has prompted us to address the problem by developing a methodological protocol consisting of the following steps: I) geological survey in the field; II) draft of a preliminary geological setting based on the field-survey results; III) dating of 102 samples coming from a large number of boreholes and some outcropping sections by means of the amino acid racemization (AAR) method applied to ostracod shells and 14C dating, filtering of the ages and the selection of valid ages; IV) correction of the preliminary geological setting in the light of the numerical ages; definition of the final geological setting with UBSUs; identification of a ‘‘hypothetical’’ or ‘‘attributed time range’’ (HTR or ATR) for each UBSU, the former very wide and subject to a subsequent modification, the latter definitive; V) cross-checking between the numerical ages and/or other characteristics of the sedimentary bodies and/or the sea-level curves (with their effects on the sedimentary processes) in order to restrict also the hypothetical time ranges in the attributed time ranges. The successful application of AAR geochronology to ostracod shells relies on the fact that the ability of ostracods to colonize almost all environments constitutes a tool for correlation, and also allow the inclusion in the same unit of coeval sediments that differ lithologically and paleoenvironmentally. The treatment of the numerical ages obtained using the AAR method required special attention. The first filtering step was made by the laboratory (rejection criteria a and b). Then, the second filtering step was made by testing in the field the remaining ages. Among these, in fact, we never compared an age with a single preceding and/or following age; instead, we identified homogeneous groups of numerical ages consistent with their reciprocal stratigraphic position. This operation led to the rejection of further numerical ages that deviate erratically from a larger, homogeneous age population which fits well with its stratigraphic position (rejection criterion c). After all of the filtering steps, the valid ages that remained were used for the subdivision of the sedimentary sequences into UBSUs together with the lithological and paleoenvironmental criteria. The numerical ages allowed us, in the first instance, to recognize all of the age gaps between two consecutive samples. Next, we identified the level, in the sedimentary thickness that is between these two samples, that may represent the most suitable UBSU boundary based on its lithology and/or the paleoenvironment. The recognized units are: I) Coppa Nevigata sands (NEA), HTR: MIS 20–14, ATR: MIS 17–16; II) Argille subappennine (ASP), HTR: MIS 15–11, ATR: MIS 15–13; III) Coppa Nevigata synthem (NVI), HTR: MIS 13–8, ATR: MIS 12–11; IV) Sabbie di Torre Quarto (STQ), HTR: MIS 13–9.1, ATR: MIS 11; V) Amendola subsynthem (MLM1), HTR: MIS 12–10, ATR: MIS 11; VI) Undifferentiated continental unit (UCI), HTR: MIS 11–6.2, ATR: MIS 9.3–7.1; VII) Foggia synthem (TGF), ATR: MIS 6; VIII) Masseria Finamondo synthem (TPF), ATR: Upper Pleistocene; IX) Carapelle and Cervaro streams synthem (RPL), subdivided into: IXa) Incoronata subsynthem (RPL1), HTR: MIS 6–3; ATR: MIS 5–3; IXb) Marane La Pidocchiosa–Castello subsynthem (RPL3), ATR: Holocene; X) Masseria Inacquata synthem (NAQ), ATR: Holocene. The possibility of recognizing and dating Quaternary units in an alluvial plain to the scale of a marine isotope stage constitutes a clear step forward compared with similar studies regarding other alluvial-plain areas, where Quaternary units were dated almost exclusively using their stratigraphic position. As a result, they were generically associated with a geological sub-epoch. Instead, our method allowed a higher detail in the timing of the sedimentary processes: for example, MIS 11 and MIS 5.5 deposits have been recognized and characterized for the first time in the study area, highlighting their importance as phases of sedimentation.

Bounded non-deterministic planning for multimedia adaptation

This paper proposes a novel combination of artificial intelligence planning and other techniques for improving decision-making in the context of multi-step multimedia content adaptation. In particular, it describes a method that allows decision-making (selecting the adaptation to perform) in situations where third-party pluggable multimedia conversion modules are involved and the multimedia adaptation planner does not know their exact adaptation capabilities. In this approach, the multimedia adaptation planner module is only responsible for a part of the required decisions; the pluggable modules make additional decisions based on different criteria. We demonstrate that partial decision-making is not only attainable, but also introduces advantages with respect to a system in which these conversion modules are not capable of providing additional decisions. This means that transferring decisions from the multi-step multimedia adaptation planner to the pluggable conversion modules increases the flexibility of the adaptation. Moreover, by allowing conversion modules to be only partially described, the range of problems that these modules can address increases, while significantly decreasing both the description length of the adaptation capabilities and the planning decision time. Finally, we specify the conditions under which knowing the partial adaptation capabilities of a set of conversion modules will be enough to compute a proper adaptation plan.

Communication-efficient and crash-quiescent Omega with unknown membership

The failure detector class Omega (Ω) provides an eventual leader election functionality, i.e., eventually all correct processes permanently trust the same correct process. An algorithm is communication-efficient if the number of links that carry messages forever is bounded by n, being n the number of processes in the system. It has been defined that an algorithm is crash-quiescent if it eventually stops sending messages to crashed processes. In this regard, it has been recently shown the impossibility of implementing Ω crash quiescently without a majority of correct processes. We say that the membership is unknown if each process pi only knows its own identity and the number of processes in the system (that is, i and n), but pi does not know the identity of the rest of processes of the system. There is a type of link (denoted by ADD link) in which a bounded (but unknown) number of consecutive messages can be delayed or lost. In this work we present the first implementation (to our knowledge) of Ω in partially synchronous systems with ADD links and with unknown membership. Furthermore, it is the first implementation of Ω that combines two very interesting properties: communication-efficiency and crash-quiescence when the majority of processes are correct. Finally, we also obtain with the same algorithm a failure detector () such that every correct process eventually and permanently outputs the set of all correct processes.

Bubble growth by injection of gas into viscous liquids in cylindrical and conical tubes.

The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wall.

Laminar flow of a gas in a tube with large temperature differences.

The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wall

Performance of Scheduling Policies in Adversarial Networks with Non-synchronized Clocks

In this paper we generalize the Continuous Adversarial Queuing Theory (CAQT) model (Blesa et al. in MFCS, Lecture Notes in Computer Science, vol. 3618, pp. 144–155, 2005) by considering the possibility that the router clocks in the network are not synchronized. We name the new model Non Synchronized CAQT (NSCAQT). Clearly, this new extension to the model only affects those scheduling policies that use some form of timing. In a first approach we consider the case in which although not synchronized, all clocks run at the same speed, maintaining constant differences. In this case we show that all universally stable policies in CAQT that use the injection time and the remaining path to schedule packets remain universally stable. These policies include, for instance, Shortest in System (SIS) and Longest in System (LIS). Then, we study the case in which clock differences can vary over time, but the maximum difference is bounded. In this model we show the universal stability of two families of policies related to SIS and LIS respectively (the priority of a packet in these policies depends on the arrival time and a function of the path traversed). The bounds we obtain in this case depend on the maximum difference between clocks. This is a necessary requirement, since we also show that LIS is not universally stable in systems without bounded clock difference. We then present a new policy that we call Longest in Queues (LIQ), which gives priority to the packet that has been waiting the longest in edge queues. This policy is universally stable and, if clocks maintain constant differences, the bounds we prove do not depend on them. To finish, we provide with simulation results that compare the behavior of some of these policies in a network with stochastic injection of packets.

Performance of Scheduling Policies in Adversarial Networks with Non-synchronized Clocks

In this paper we generalize the Continuous Adversarial Queuing Theory (CAQT) model (Blesa et al. in MFCS, Lecture Notes in Computer Science, vol. 3618, pp. 144–155, 2005) by considering the possibility that the router clocks in the network are not synchronized. We name the new model Non Synchronized CAQT (NSCAQT). Clearly, this new extension to the model only affects those scheduling policies that use some form of timing. In a first approach we consider the case in which although not synchronized, all clocks run at the same speed, maintaining constant differences. In this case we show that all universally stable policies in CAQT that use the injection time and the remaining path to schedule packets remain universally stable. These policies include, for instance, Shortest in System (SIS) and Longest in System (LIS). Then, we study the case in which clock differences can vary over time, but the maximum difference is bounded. In this model we show the universal stability of two families of policies related to SIS and LIS respectively (the priority of a packet in these policies depends on the arrival time and a function of the path traversed). The bounds we obtain in this case depend on the maximum difference between clocks. This is a necessary requirement, since we also show that LIS is not universally stable in systems without bounded clock difference. We then present a new policy that we call Longest in Queues (LIQ), which gives priority to the packet that has been waiting the longest in edge queues. This policy is universally stable and, if clocks maintain constant differences, the bounds we prove do not depend on them. To finish, we provide with simulation results that compare the behavior of some of these policies in a network with stochastic injection of packets.

Estrategias innovadoras para la gestión del riesgo de sequía en sistemas ganaderos extensivos

La vulnerabilidad de los sistemas ganaderos de pastoreo pone en evidencia la necesidad de herramientas para evaluar y mitigar los efectos de la sequía. El avance en la teledetección ha despertado el interés por explotar potenciales aplicaciones, y está dando lugar a un intenso desarrollo de innovaciones en distintos campos. Una de estas áreas es la gestión del riesgo climático, en donde la utilización de índices de vegetación permite la evaluación de la sequía. En esta investigación, se analiza el impacto de la sequía y se evalúa el potencial de nuevas tecnologías como la teledetección para la gestión del riesgo de sequía en sistemas de ganadería extensiva. Para ello, se desarrollan tres aplicaciones: (i) evaluar el impacto económico de la sequía en una explotación ganadera extensiva de la dehesa de Andalucía, (ii) elaborar mapas de vulnerabilidad a la sequía en pastos de Chile y (iii) diseñar y evaluar el potencial de un seguro indexado para sequía en pastos en la región de Coquimbo en Chile. En la primera aplicación, se diseña un modelo dinámico y estocástico que integra aspectos climáticos, ecológicos, agronómicos y socioeconómicos para evaluar el riesgo de sequía. El modelo simula una explotación ganadera tipo de la dehesa de Andalucía para el período 1999-2010. El método de Análisis Histórico y la simulación de MonteCarlo se utilizan para identificar los principales factores de riesgo de la explotación, entre los que destacan, los periodos de inicios del verano e inicios de invierno. Los resultados muestran la existencia de un desfase temporal entre el riesgo climático y riesgo económico, teniendo este último un periodo de duración más extenso en el tiempo. También, revelan que la intensidad, frecuencia y duración son tres atributos cruciales que determinan el impacto económico de la sequía. La estrategia de reducción de la carga ganadera permite aminorar el riesgo, pero conlleva una disminución en el margen bruto de la explotación. La segunda aplicación está dedicada a la elaboración de mapas de vulnerabilidad a la sequia en pastos de Chile. Para ello, se propone y desarrolla un índice de riesgo económico (IRESP) sencillo de interpretar y replicable, que integra factores de riesgo y estrategias de adaptación para obtener una medida del Valor en Riesgo, es decir, la máxima pérdida esperada en un año con un nivel de significación del 5%.La representación espacial del IRESP pone en evidencia patrones espaciales y diferencias significativas en la vulnerabilidad a la sequía a lo largo de Chile. Además, refleja que la vulnerabilidad no siempre esta correlacionada con el riesgo climático y demuestra la importancia de considerar las estrategias de adaptación. Las medidas de autocorrelación espacial revelan que el riesgo sistémico es considerablemente mayor en el sur que en el resto de zonas. Los resultados demuestran que el IRESP transmite información pertinente y, que los mapas de vulnerabilidad pueden ser una herramienta útil en el diseño de políticas y toma de decisiones para la gestión del riesgo de sequía. La tercera aplicación evalúa el potencial de un seguro indexado para sequía en pastos en la región de Coquimbo en Chile. Para lo cual, se desarrolla un modelo estocástico para estimar la prima actuarialmente justa del seguro y se proponen y evalúan pautas alternativas para mejorar el diseño del contrato. Se aborda el riesgo base, el principal problema de los seguros indexados identificado en la literatura y, que está referido a la correlación imperfecta del índice con las pérdidas de la explotación. Para ello, se sigue un enfoque bayesiano que permite evaluar el impacto en el riesgo base de las pautas de diseño propuestas: i) una zonificación por clúster que considera aspectos espacio-temporales, ii) un período de garantía acotado a los ciclos fenológicos del pasto y iii) umbral de garantía. Los resultados muestran que tanto la zonificación como el periodo de garantía reducen el riesgo base considerablemente. Sin embargo, el umbral de garantía tiene un efecto ambiguo sobre el riesgo base. Por otra parte, la zonificación por clúster contribuye a aminorar el riesgo sistémico que enfrentan las aseguradoras. Estos resultados han puesto de manifiesto que un buen diseño de contrato puede tener un doble dividendo, por un lado aumentar su utilidad y, por otro, reducir el coste del seguro. Un diseño de contrato eficiente junto con los avances en la teledetección y un adecuado marco institucional son los pilares básicos para el buen funcionamiento de un programa de seguro. Las nuevas tecnologías ofrecen un importante potencial para la innovación en la gestión del riesgo climático. Los avances en este campo pueden proporcionar importantes beneficios sociales en los países en desarrollo y regiones vulnerables, donde las herramientas para gestionar eficazmente los riesgos sistémicos como la sequía pueden ser de gran ayuda para el desarrollo. The vulnerability of grazing livestock systems highlights the need for tools to assess and mitigate the adverse impact of drought. The recent and rapid progress in remote sensing has awakened an interest for tapping into potential applications, triggering intensive efforts to develop innovations in a number of spheres. One of these areas is climate risk management, where the use of vegetation indices facilitates assessment of drought. This research analyzes drought impacts and evaluates the potential of new technologies such as remote sensing to manage drought risk in extensive livestock systems. Three essays in drought risk management are developed to: (i) assess the economic impact of drought on a livestock farm in the Andalusian Dehesa, (ii) build drought vulnerability maps in Chilean grazing lands, and (iii) design and evaluate the potential of an index insurance policy to address the risk of drought in grazing lands in Coquimbo, Chile. In the first essay, a dynamic and stochastic farm model is designed combining climate, agronomic, socio-economic and ecological aspects to assess drought risk. The model is developed to simulate a representative livestock farm in the Dehesa of Andalusia for the time period 1999-2010. Burn analysis and MonteCarlo simulation methods are used to identify the significance of various risk sources at the farm. Most notably, early summer and early winter are identified as periods of peak risk. Moreover, there is a significant time lag between climate and economic risk and this later last longer than the former. It is shown that intensity, frequency and duration of the drought are three crucial attributes that shape the economic impact of drought. Sensitivity analysis is conducted to assess the sustainability of farm management strategies and demonstrates that lowering the stocking rate reduces farmer exposure to drought risk but entails a reduction in the expected gross margin. The second essay, mapping drought vulnerability in Chilean grazing lands, proposes and builds an index of economic risk (IRESP) that is replicable and simple to interpret. This methodology integrates risk factors and adaptation strategies to deliver information on Value at Risk, maximum expected losses at 5% significance level. Mapping IRESP provides evidence about spatial patterns and significant differences in drought vulnerability across Chilean grazing lands. Spatial autocorrelation measures reveal that systemic risk is considerably larger in the South as compared to Northern or Central Regions. Furthermore, it is shown that vulnerability is not necessarily correlated with climate risk and that adaptation strategies do matter. These results show that IRESP conveys relevant information and that vulnerability maps may be useful tools to assess policy design and decision-making in drought risk management. The third essay develops a stochastic model to estimate the actuarially fair premium and evaluates the potential of an indexed insurance policy to manage drought risk in Coquimbo, a relevant livestock farming region of Chile. Basis risk refers to the imperfect correlation of the index and farmer loses and is identified in the literature as a main limitation of index insurance. A Bayesian approach is proposed to assess the impact on basis risk of alternative guidelines in contract design: i) A cluster zoning that considers space-time aspects, ii) A guarantee period bounded to fit phenological cycles, and iii) the triggering index threshold. Results show that both the proposed zoning and guarantee period considerably reduces basis risk. However, the triggering index threshold has an ambiguous effect on basis risk. On the other hand, cluster zoning contributes to ameliorate systemic risk faced by the insurer. These results highlighted that adequate contract design is important and may result in double dividend. On the one hand, increasing farmers’ utility and, secondly, reducing the cost of insurance. An efficient contract design coupled with advances in remote sensing and an appropriate institutional framework are the basis for an efficient operation of an insurance program. The new technologies offer significant potential for innovation in climate risk managements. Progress in this field is capturing increasing attention and may provide important social gains in developing countries and vulnerable regions where the tools to efficiently manage systemic risks, such as drought, may be a means to foster development.

Mejoras tecnológicas en el reciclado de residuos de construcción y demolición (RCD)

La tesis doctoral “Mejoras Tecnológicas en el Reciclado de Residuos de Construcción y Demolición (RCD)” investiga la utilización de los separadores hidráulicos para mejorar la calidad de los áridos reciclados, y se demuestra que es un equipo más eficiente que las técnicas actuales basadas en la simple separación por densidad. En la tesisn se ha realizado inicialmente una revisión de la situación del sector, para a continuación centrarse en los sistemas de separación utilizados en las plantas de valorización españolas. Una vez analizados éstos y en particular los de tipo hidráulico, de los que se resume un estudio comparativo, se ha procedido a ensayar a escala de Laboratorio el comportamiento de un separador hidráulico de aceleración diferencial con diversos materiales procedentes de tres plantas de reciclaje. Adicionalmente fueron probadas otras técnicas, como es la separación magnética para mejorar la calidad de los productos reciclados. En vista de los buenos resultados de la investigación, se procede a escalar los ensayos con equipo piloto y distintas composiciones de naturaleza cerámica y hormigón. El equipo utilizado fue un jig de 3´x 1´ en el que se ensayaron las tres muestras con resultados diferentes. La limpieza de los materiales impropios y el yeso fue positiva en las tres muestras, y únicamente la separación entre sí de los componentes pétreos, resultó dependiente de su proporción en la mezcla, obteniéndose los mejores resultados en las muestras con menor cantidad de materiales cerámicos. Finalmente, se procede a analizar en un laboratorio reconocido las propiedades de los áridos reciclados obtenidos en la separación hidráulica por jig, y constatar las mejoras conseguidas para su utilización como materiales de construcción en usos ligados y no ligados. Todo lo anterior permite afirmar que los equipos de separación hidráulica con aceleración diferencial (jig) presentan una innovación tecnológica en el reciclado de los residuos de construcción y demolición (RCD). ABSTRACT The doctoral thesis “Technological Improvements in Recycling of Construction and Demolition Waste (C&DW)” researches the hydraulic separators utilization in order to improve the recycled aggregates quality, demonstrating that the equipment is more efficient than the current techniques based on the simple density separation. This doctoral thesis has been initially done reviewing the situation of the sector and focusing afterwards on the separation systems used at the Spanish recovery facilities. Once analyzed these and, particularly, the hydraulic type ones, from which a comparative study has been summarized, the behavior of a differential acceleration hydraulic separator with various materials coming from three recycling plants has been tested at laboratory scale. Additionally other techniques have been tested, such as the magnetic separation to improve the quality of recycled products. In view of the good investigation results, the testing process scaled up by using pilot equipment and different ceramics and concrete compositions. The equipment utilized was a jig 3” x 1”, in which the three samples were tested with different results. The unsuitable materials and gypsum cleanliness was positive on the three samples and only the separation among the stony components turned out to be dependent of its proportion in the mixing, obtaining the best results in the samples with less quantity of ceramic materials. Finally, the properties of the recycled aggregates obtained by jig hydraulic separation are analyzed at a recognized laboratory and the improvements gained for their utilization as construction materials, in bounded and unbounded uses, are stated. The facts cited are a basis for affirming that the hydraulic separator equipments with differential acceleration (jig) offer a technological innovation in the Recycling of Construction and Demolition Waste (C&DW).

Dimensional synthesis of a spherical parallel manipulator based on the evaluation of global performance indexes

In this work, the dimensional synthesis of a spherical Parallel Manipulator (PM) with a -1S kinematic chain is presented. The goal of the synthesis is to find a set of parameters that defines the PM with the best performance in terms of workspace capabilities, dexterity and isotropy. The PM is parametrized in terms of a reference element, and a non-directed search of these parameters is carried out. First, the inverse kinematics and instantaneous kinematics of the mechanism are presented. The latter is found using the screw theory formulation. An algorithm that explores a bounded set of parameters and determines the corresponding value of global indexes is presented. The concepts of a novel global performance index and a compound index are introduced. Simulation results are shown and discussed. The best PMs found in terms of each performance index evaluated are locally analyzed in terms of its workspace and local dexterity. The relationship between the performance of the PM and its parameters is discussed, and a prototype with the best performance in terms of the compound index is presented and analyzed.

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

Theory of a probe in a strong magnetic field

An asymptotic analysis of the Langmuir-probe problem in a quiescent, fully ionized plasma in a strong magnetic field is performed, for electron cyclotron radius and Debye length much smaller than probe radius, and this not larger than either ion cyclotron radius or mean free path. It is found that the electric potential, which is not confined to a sheath, controls the diffusion far from the probe; inside the magnetic tube bounded by the probe cross section the potential overshoots to a large value before decaying to its value in the body of the plasma. The electron current is independent of the shape of the body along the field and increases with ion temperature; due to the overshoot in the potential, (1) the current at negative voltages does not vary exponentially, (2) its magnitude is strongly reduced by the field, and (3) the usual sharp knee at space potential, disappears. In the regions of the C-V diagram studied the ion current is negligible or unaffected by the field. Some numerical results are presented.The theory, which fails beyond certain positive voltage, fields useful results for weak fields, too.

Influence of Atmospheric Conditions on mmWave CATR Facilities: Formulation and Compensation Scheme

The performance of a CATR relies on the planarity of the synthesized test wave, which is generated within a bounded volume for which specifications are drawn. Millimetre-wave facilities deal with the classical limitations of this frequency band, among which two become critical in our analysis: time-extensive acquisition campaigns and impact of environmental variables. Both features become more evident when increasing the frequency of operation. The variation in atmospheric variables, such as humidity, temperature and pressure has an influence over the performance of all the elements of the facility. The instrumentation behavior is influenced both by the warming up process, and the ambience conditions that surround the equipment. On the changes of the atmosphere itself, they affect the electromagnetic wave propagation, given the physical link between the conditions of the atmosphere and its electric properties as an electromagnetic waves propagation medium