Asymptotic and numerical analysis of time-dependent wave propagation in dispersive dielectric media that exhibit fractional relaxation

This dissertation addresses electromagnetic pulse propagation through anomalously dispersive dielectric media. The Havriliak-Negami (H-N) and Cole-Cole (C-C) models capture the non-exponential nature of such dielectric relaxation phenomena, which is manifest in a variety of dispersive dielectric media. In the C-C model, the dielectric polarization is coupled to the time-dependent Maxwell\u27s equations by a fractional differential equation involving the electric field. In the H-N case, a more general pseudo-fractional differential operator describes the polarization. The development and analysis of a robust method for implementing such models is presented, with an emphasis on algorithmic efficiency. Separate numerical schemes are presented for C-C and H-N media. A straightforward numerical implementation of these models using finite-difference time-domain (FD-TD) techniques is expected to be second order accurate in both space and time. However due to the singular nature of the kernels appearing in the fractional convolution operators, the standard C-C implementation, produces first order accuracy in time. As we show, this method is equivalent to most approaches presented in the current literature, which implies that they are also first order. The desired accuracy is instead achieved by applying multistep methods to the fractional differential equation; however multistep methods are unnecessary in the H-N implementation to preserve the accuracy. Furthermore, the C-C model is a specific case of the H-N model and can therefore be constructed using the latter of these approaches. The FD-TD methods are validated by evaluating the electric field for the signaling problem, using numerical quadrature to evaluate the integral form of the solution. This is accomplished using the Green\u27s function of the dispersive medium; in addition, the behavior of pulse propagation is studied asymptotically using the Green\u27s function, which further validates the observed results of the numerical experiments

A Novel Piecewise Linear Recursive Convolution Approach for Dispersive Media Using the Finite-Difference Time-Domain Method

Peer reviewedPublisher PD

Modelado de las propiedades dieléctricas del suelo. Aplicación en el diseño de sensores para sistemas de control en agricultura de precisión

[SPA] Esta tesis doctoral se presenta bajo la modalidad de compendio de publicaciones. El agua es una sustancia clave para el desarrollo de la vida en La Tierra. Es por ello que la búsqueda de oportunidad de vida en otros planetas y satélites se basa en la presencia de agua en los mismos. La gestión ecológica del agua es necesaria para la sostenibilidad de los ecosistemas. Uno de los ecosistemas más amplios y donde el agua juega un papel más importante es el suelo, que alberga multitud de variedades de microorganismos cuya actividad, en parte resultante en la generación de nutrientes para el desarrollo de las especies vegetales, es totalmente dependiente del contenido de agua en el suelo. En zonas áridas y semiáridas, como es el caso de la cuenca Mediterránea, la escasez de agua supone un grave problema a la hora de gestionar los pocos recursos hídricos disponibles. En este caso, donde las condiciones geográficas son idóneas para el desarrollo de la agricultura, las soluciones pasan por una optimización de las técnicas de riego y un mayor control sobre los recursos hídricos. En este sentido, las técnicas de riego deficitario controlado se han mostrado exitosas en la reducción de la dotación hídrica a los cultivos en fases no críticas. Sin embargo, para realizar una aplicación prudente y eficiente de las mismas, resulta necesario monitorizar el estado hídrico de los cultivos, con el objetivo de que éstos no alcancen situaciones de estrés irreversible en términos de producción o estado vegetativo. Los indicadores que mayor información aportan sobre el estado hídrico de la planta suelen estar relacionados con variables medibles a partir de la propia planta, pero que son difícilmente automatizables debido a las operaciones de manejo asociadas. Este es el caso del potencial hídrico de tallo a mediodía medido con cámara de presión, considerado hasta la fecha como el indicador más fiable del estado hídrico de los cultivos en general. Es por ello que, para lograr una monitorización continua de esta variable, se busquen otras variables del continuo suelo-planta-atmósfera que puedan estar relacionadas y a partir de las cuales obtener una estimación indirecta. El suelo es la matriz de donde la planta adquiere la mayor parte del agua y los nutrientes que necesita para realizar la fotosíntesis. La relación entre el estado hídrico del suelo y el estado hídrico de los cultivos está más que demostrada. Sin embargo, la precisión alcanzada en los modelos de correlación entre ambos estados requiere de una mejora considerable para hacer un uso realmente fiable de los mismos, y esta mejora no solo pasa por encontrar mejores métodos de correlación, sino también por mejorar la precisión de las medidas obtenidas del suelo. Para monitorizar el estado hídrico del suelo, existen diversas metodologías que ofrecen parámetros medibles como el contenido de agua. El método de medida más extendido para monitorizar el contenido de agua en el suelo es a través del uso de sensores dieléctricos. Sin embargo, la precisión de los mismos está sujeta a diversos factores, entre ellos las características propias del suelo donde se instalan y su coste, relativamente alto para el pequeño y mediano agricultor, condicionando una implantación extensiva de la Agricultura de Precisión y limitando a veces la aplicación de algunos desarrollos únicamente a trabajos de investigación. Esta tesis, elaborada bajo la modalidad de compendio de publicaciones, aborda a través de cuatro artículos científicos la propuesta de soluciones accesibles para la medida del estado hídrico del suelo, con especial enfoque en el contenido de agua; explora las limitaciones y retos asociados con la calibración de los sensores dieléctricos de suelo; participa en la generación de nuevos conocimientos y propuestas para un mejor entendimiento del comportamiento del agua en el suelo y de su interacción con las ondas electromagnéticas; y establece nuevos enfoques y modelos que mejoran la predicción del estado hídrico de los cultivos a partir de medidas indirectas y automatizables en suelo y atmósfera. [ENG] This doctoral dissertation has been presented in the form of thesis by publication. Water is a fundamental substance for the development of life on Earth. That is why the search for life on other planets and satellites is based on the presence of water on them. Ecological water management is necessary for the sustainability of ecosystems. One of the most extensive ecosystems where water plays a major role is soil, which hosts a large variety of micro-organisms whose activity, partly resulting in the generation of nutrients for the development of plant species, is totally dependent on the water content of the soil. In arid and semi-arid regions, as it is the case in the Mediterranean basin, water scarcity is a serious problem when it comes to managing the few water resources available. In this case, where the geographical conditions are ideal for the development of agriculture, the solutions involve optimization of irrigation techniques and greater control over water resources. In this sense, regulated deficit irrigation strategies have proven to be successful in reducing the water supply to crops in non-critical periods. However, in order to apply them prudently and efficiently, it is necessary to monitor the water status of the crops, so that they do not reach irreversible stress situations in terms of yield or vegetative state. The indicators that provide the highest amount of information on the water status of the plant are usually related to variables that can be measured from the plant itself, but which are difficult to automate due to the labor and time-consuming associated operations. This is the case of the midday stem water potential measured with a pressure chamber, considered to date to be the most reliable indicator of the crop's water status in general. In order to achieve a continuous monitoring of this variable, it is necessary to look for other variables of the soil-plant-atmosphere continuum that may be related and from which to obtain an indirect estimate. Soil is the matrix from which the plant acquires most of the water and nutrients it needs for photosynthesis. The relationship between soil water status and crop water status is well established. However, the accuracy achieved in the correlation models between the two requires considerable improvement to make a truly reliable use of them, and this improvement is not only to find better correlation methods, but also to improve the accuracy of the measurements obtained from the soil. To monitor soil water status, there are several methodologies that provide measurable parameters such as water content. The most widespread measurement method for monitoring soil water content is through the use of dielectric sensors. However, the accuracy of these sensors is subject to various factors, including the characteristics of the soil where they are installed, and their relatively high cost for small and medium-sized farmers, conditioning the extensive implementation of precision agriculture and sometimes limiting the application of some developments only to research work. This thesis, elaborated under the modality of a compendium of publications, addresses through four scientific articles the proposal of affordable solutions for the measurement of soil water status, with special focus on water content; it explores the limitations and challenges associated with the calibration of soil dielectric sensors; participates in the generation of new insights and proposals for a better understanding of the behavior of water in soil and its interaction with electromagnetic waves; and establishes new approaches and models that improve the prediction of crop water status from indirect and automatable measurements in soil and atmosphere.Esta tesis doctoral se presenta bajo la modalidad de compendio de publicaciones. Está formada por un total de cuatro artículos: Article I. González-Teruel, J.D., Torres-Sánchez, R., Blaya-Ros, P.J., Toledo-Moreo, A.B., Jiménez-Buendía, M., Soto-Valles, F., 2019. Design and Calibration of a Low-Cost SDI-12 Soil Moisture Sensor. Sensors, 19, 491. DOI: 10.3390/s19030491 - Article II. González-Teruel, J.D., Jones, S.B., Soto-Valles, F., Torres-Sánchez, R., Lebron, I., Friedman, S.P., Robinson, D.A., 2020. Dielectric Spectroscopy and Application of Mixing Models Describing Dielectric Dispersion in Clay Minerals and Clayey Soils. Sensors, 20, 6678. DOI: 10.3390/s20226678 Article III. González-Teruel, J.D., Jones, S.B., Robinson, D.A., Giménez-Gallego, J., Zornoza, R., Torres-Sánchez, R., 2022. Measurement of the broadband complex permittivity of soils in the frequency domain with a low-cost Vector Network Analyzer and an Open-Ended coaxial probe. Computers and Electronics in Agriculture, 195, 106847. DOI: 10.1016/J.COMPAG.2022.106847 Article IV. González-Teruel, J.D., Ruiz-Abellon, M.C., Blanco, V., Blaya-Ros, P.J., Domingo, R., Torres-Sánchez, R., 2022. Prediction of Water Stress Episodes in Fruit Trees Based on Soil and Weather Time Series Data. Agronomy, 12, 1422. DOI: 10.3390/agronomy12061422Escuela Internacional de Doctorado de la Universidad Politécnica de CartagenaUniversidad Politécnica de CartagenaPrograma de Doctorado en Tecnologías Industriale

PROBING TEMPORAL CHANGES IN MITOCHONDRIAL MEMBRANE POTENTIAL WITH IMPEDANCE SPECTROSCOPY

The electrical properties of mitochondria provide fundamental insights into metabolic processes in health and disease. This research studies electrical impedance spectroscopy as a non-invasive, sensitive, and relatively low cost technique to monitor biological processes, such as those involving changes in mitochondrial membrane potential. Our experimental strategy first involves treating suspensions of live mitochondria with the substrate succinate to stimulate activity of succinate dehydrogenase, or more simply Complex II. This triggers electron flux through Complex II and the remaining complexes of the electron transport chain, enabling them to pump protons across the inner membrane and build up a membrane potential. Subsequent variability is introduced by adding various concentrations of the uncoupler trifluorocarbonylcyanide phenylhydrazone (FCCP) and the neurotransmitter dopamine (DA) to mitochondrial suspensions, and measuring changes in impedance. Our results show that adding succinate decreases impedance, consistent with an increase in dielectric response and membrane potential. Overall, our investigation establishes real-time impedance spectroscopy as a non-destructive, potentially powerful method for membrane potential studies of mitochondria.Physics, Department o

SOLUTION STRUCTURE, RHEOLOGY, AND NANOCOMPOSITES OF A LIQUID CRYSTALLINE POLYELECTROLYTE

High-performance polymers, most notably all-aromatic polyamides (aramids), enable the convergence of the disparate material properties, such as low density, high strength, high stiffness, and thermal stability. Sulfonated derivatives of aramids (sulfo-aramids) represent a unique class of materials that are a nexus between stiff and strong engineering materials and soft and dynamic biological matter. Specifically, sulfo-aramids are water soluble and often self-assemble into rodlike supramolecular structures in solution, similar to rodlike viruses or polypeptide helical assemblies. Such rodlike systems undergo spontaneous self-organization into a liquid crystalline (nematic) phase above a critical concentration, resulting in a high degree of local orientational order. Application of an external field, such as shear flow, can either increase or decrease the global orientational order of the nematic phase. Thus, understanding the solution structure and rheology of such phases has important implications for the fabrication of high-performance, sulfo-aramid nanocomposites. In this Dissertation, we investigate aspects of the solution structure, rheology, and nanocomposites fabricated from helical, rodlike assemblies of the sulfo-aramid, poly(2,2’- benzidine-4,4’-disulfonyl terephthalamide) (PBDT). PBDT forms a fully nematic phase at low concentrations in water, evidencing its high aspect ratio, enabling environmentally-benign fabrication of advanced nanocomposites with liquid crystalline graphene oxide or ionic liquids. Moreover, the low concentrations required for formation of a fully nematic phase enables direct interrogation of the rheological responses of the liquid crystalline rodlike assemblies. In contrast, the rheology of previously studied model LCPs are dominated by the nematic defect texture. In addition, the dynamic self-assembled nature of PBDT rodlike assemblies result in an unusual rheological behavior, known as irreversible shear-activated gelation, at high concentrations. Overall, our new insights on the solution structure and rheology of sulfo-aramids not only inform the design of advanced nanocomposites, but also provide a new platform for elucidating the flow behavior of high-aspect-ratio, charged rods.Doctor of Philosoph

Ultrafast photo-acoustic spectroscopy of super-cooled liquids

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2010.Vita. Cataloged from PDF version of thesis.Includes bibliographical references (p. 219-231).Picosecond laser ultrasonic techniques for acoustic wave generation and detection were adapted to probe longitudinal and transverse acoustic waves in liquids at gigahertz frequencies. The experimental effort was designed for the study of supercooled liquids whose slower relaxation dynamics extend to gigahertz frequencies at high temperatures and whose faster dynamics are centered uniquely in the gigahertz frequency range. The experimental approach used a unique laser pulse shaping technique and, in the case of shear acoustic waves, a crystallographically canted metal transducer layer, to generate frequency tunable compressional and shear acoustic waves. Either time-domain coherent Brillouin scattering or interferometry was used to detect the waves in or after propagation through a liquid layer. The study of liquid-state gigahertz acoustic behavior required advances in both the experimental methodology and in the theoretical modeling of the results. A particular challenge was posed by the extraordinarily strong damping of gigahertz-frequency acoustic waves in liquids at some temperature ranges. This demanded the design and construction of a liquid sample cell allowing access to a wide range of liquid thicknesses, from less than a nanometer up to several microns. This was achieved by squeezing the liquid between two specially prepared high quality optical substrates held in a non-parallel configuration by a custom-designed sample holder jig. Several metallic layer materials were used for conversion of optical pulse energy into acoustic waves that were launched into the liquid samples, and different probe geometries were developed to enable access to a wide frequency range. The developed spectroscopic strategies were then applied to the study of two liquids, glycerol and tetramethyl tetraphenyl trisiloxane (DC704). Measurements of the density responses of both liquids from 400 K to below their respective glass transition temperatures were carried out. Longitudinal acoustic waves were either monitored via time-domain Brillouin scattering in the liquid or via interferometry after transmission through variably thick liquid layers, granting access to longitudinal acoustic frequencies from 10 GHz up to about 200 GHz. The information obtained on gigahertz frequency liquid relaxation was pieced together with data from several other techniques to create broadband relaxation spectra (from millihertz up to gigahertz), allowing characterization of the complex structural relaxation dynamics over many orders of magnitude and enabling both empirical modeling and testing of the predictions of the mode-coupling theory of supercooled liquids. The requirements for gigahertz shear wave generation and detection, including the properties of the photo-acoustic transducer materials, the sample and experimental geometry, and the detection material choices, are discussed. Results on shear wave propagation in glycerol and DC704 are presented. The technique for shear wave generation and detection is not limited to the study of viscous liquids but can also be applied to liquids like water, from which initial results are presented.by Christoph Klieber.Ph.D

Modelling the linear viscoelastic rheological properties of bituminous binders

Rheology involves the study and evaluation of the flow and permanent deformation of time-and temperature-dependent materials, such as bitumen, that are stressed through the application of a force. The fundamental rheological properties of bituminous materials including bitumen are normally measured using a dynamic shear rheometer (DSR), from low to high temperatures. DSR is a powerful tool to measure elastic, viscoelastic and viscous properties of binders over a wide range of temperatures and frequencies, provided the tests are conducted in the linear viscoelastic region. Therefore, the study of bitumen rheology is crucial since its reflects the overall performance of a flexible pavement. However, it is well known that the DSR also has limitations, where the measurements are exposed to compliance (testing) errors particularly at low temperatures and/or high frequencies. In addition, conducting laboratory tests are known to be laborious, time consuming and require skilled personnel. Therefore, this research is conducted to elucidate a better understanding of the rheological properties and modelling procedures of bitumens and bituminous binders. Various materials such as unmodified bitumens, polymer-modified bitumens (PMBs) and bitumen-filler mastics, unaged and aged samples, are used in this study. An extensive literature review was undertaken to identify reliable models that can be considered as a valuable alternative tool to describe or fit the rheological properties of bitumen. These properties are commonly presented in terms of complex modulus and phase angle master curves, together with the determination of shift factor values at a particular reference temperature. In general, the complex modulus and phase angle master curves can be modelled using different techniques; nomographs, mathematical equations and mechanical models. However, the nomographs have become obsolete in recent years and tended to be replaced by the two latter models. Those models are able to satisfactorily describe the rheological properties of unmodified bitumen. However, the observations suggest a lack of agreement between measured and predicted rheological properties for binders that contain a phase transition, such as found for highly crystalline bitumen, structured bitumen with high asphaltenes content and highly modified bitumen. An attempt was made to evaluate the validity of several mathematical equations and mechanical element approach using unaged and aged unmodified bitumens and PMBs database. It is observed that the Sigmoidal, Generalised Logistic Sigmoidal, Christensen and Anderson (CA), and Christensen, Anderson and Marasteanu (CAM) Models are able to satisfactorily describe the rheological properties of unmodified bitumens. Nevertheless, they suffer from the same drawbacks where the presence of highly EVA semi-crystalline and SBS elastomeric structures render breakdowns in the complex modulus master curves. Similar discrepancies are observed when one of the mechanical models (the 2S2P1D Model) is used. To construct the master curves, different shifting methods are available. It is found that a numerical shift produced the best fit between measured and modelled data, followed by the Laboratoire Central des Ponts et Chaussées (LCPC) approach, William, Landel and Ferry (WLF), Modified Kaelble, Viscosity Temperature Susceptibility (VTS), Arrhenius and Log-Linear methods. A temperature range from 10 to 75oC is used in this study. It is worth mentioning that most of the methods are empirical and might not be applicable for all materials. Finally, the phase angle master curves must also not be neglected to yield a complete rheological properties of binders. The statistical analysis between measured and modelled data shows that the Fractional Model yielded the best correlation for a temperature range from10 to 75oC, followed by the Al-Qadi and Co-workers, CAM, CA and Kramers-Kronig relationships. An anomaly is observed between measured and descriptive data of the Kramers-Kronig relationship particularly at high frequencies and/or low temperatures. The Fractional Model is not considered suitable for practical purposes due to the high number of coefficients that need to be solved

Modelling the linear viscoelastic rheological properties of bituminous binders

Rheology involves the study and evaluation of the flow and permanent deformation of time-and temperature-dependent materials, such as bitumen, that are stressed through the application of a force. The fundamental rheological properties of bituminous materials including bitumen are normally measured using a dynamic shear rheometer (DSR), from low to high temperatures. DSR is a powerful tool to measure elastic, viscoelastic and viscous properties of binders over a wide range of temperatures and frequencies, provided the tests are conducted in the linear viscoelastic region. Therefore, the study of bitumen rheology is crucial since its reflects the overall performance of a flexible pavement. However, it is well known that the DSR also has limitations, where the measurements are exposed to compliance (testing) errors particularly at low temperatures and/or high frequencies. In addition, conducting laboratory tests are known to be laborious, time consuming and require skilled personnel. Therefore, this research is conducted to elucidate a better understanding of the rheological properties and modelling procedures of bitumens and bituminous binders. Various materials such as unmodified bitumens, polymer-modified bitumens (PMBs) and bitumen-filler mastics, unaged and aged samples, are used in this study. An extensive literature review was undertaken to identify reliable models that can be considered as a valuable alternative tool to describe or fit the rheological properties of bitumen. These properties are commonly presented in terms of complex modulus and phase angle master curves, together with the determination of shift factor values at a particular reference temperature. In general, the complex modulus and phase angle master curves can be modelled using different techniques; nomographs, mathematical equations and mechanical models. However, the nomographs have become obsolete in recent years and tended to be replaced by the two latter models. Those models are able to satisfactorily describe the rheological properties of unmodified bitumen. However, the observations suggest a lack of agreement between measured and predicted rheological properties for binders that contain a phase transition, such as found for highly crystalline bitumen, structured bitumen with high asphaltenes content and highly modified bitumen. An attempt was made to evaluate the validity of several mathematical equations and mechanical element approach using unaged and aged unmodified bitumens and PMBs database. It is observed that the Sigmoidal, Generalised Logistic Sigmoidal, Christensen and Anderson (CA), and Christensen, Anderson and Marasteanu (CAM) Models are able to satisfactorily describe the rheological properties of unmodified bitumens. Nevertheless, they suffer from the same drawbacks where the presence of highly EVA semi-crystalline and SBS elastomeric structures render breakdowns in the complex modulus master curves. Similar discrepancies are observed when one of the mechanical models (the 2S2P1D Model) is used. To construct the master curves, different shifting methods are available. It is found that a numerical shift produced the best fit between measured and modelled data, followed by the Laboratoire Central des Ponts et Chaussées (LCPC) approach, William, Landel and Ferry (WLF), Modified Kaelble, Viscosity Temperature Susceptibility (VTS), Arrhenius and Log-Linear methods. A temperature range from 10 to 75oC is used in this study. It is worth mentioning that most of the methods are empirical and might not be applicable for all materials. Finally, the phase angle master curves must also not be neglected to yield a complete rheological properties of binders. The statistical analysis between measured and modelled data shows that the Fractional Model yielded the best correlation for a temperature range from10 to 75oC, followed by the Al-Qadi and Co-workers, CAM, CA and Kramers-Kronig relationships. An anomaly is observed between measured and descriptive data of the Kramers-Kronig relationship particularly at high frequencies and/or low temperatures. The Fractional Model is not considered suitable for practical purposes due to the high number of coefficients that need to be solved