This thesis is divided into two topics: the development of a procedure for wind serviceability design of steel buildings and the development of a simple linear response history analysis for building codes. In the United States the building codes are generally silent on the issue of serviceability. This has led to a wide variation in design practices related to service level wind loads. Chapter 2 of this thesis contains a literature review which discusses pertinent aspects of wind drift serviceability, including selecting the mean recurrence interval (MRI), mathematical modeling of the structure, and establishment of rational deformation limits. Chapter 3 contains a journal article submitted to Engineering Journal which describes the recommended procedure for damage based wind serviceability design of steel structures. The procedure uses a broad range of MRIs, bases damage measurement on shear strains, includes all sources of deformation in the model, and bases deformation limits on fragility curves. Chapter 4 of this thesis contains a literature review which examines issues related to performing linear response history analysis. Chapter 5 contains a conference paper submitted to the Tenth U.S. National Conference on Earthquake Engineering which serves as a position paper promoting the inclusion of a linear response history analysis procedure in future editions of the NEHRP Recommended Seismic Provisions and ASCE 7. The procedure address the following issues: selection and scaling of ground motions, the use of spectral matched ground motions, design for dependent actions, and the scaling of responses with the response modification coefficient (R) and the deflection amplification factor (Cd). / Master of Science

This thesis reviews the parameters required to perform linear response history analysis according to Chapter 16 of the American Standard ASCE 7-10. A careful analysis is presented about the selection of ground motions using real records and using artificial records generated such that their response spectrum matches with a defined target spectrum; three different techniques are studied for the generation of these artificial records. Also, this document revises the scaling of ground motion techniques in the American Standard ASCE-7 as well as in other seismic codes. It presents a detailed analysis of the variables influencing the scaling of ground motions, and it suggests a new scaling technique for linear response history analysis. The assumptions made establishing the flexibility of the diaphragms are also analyzed as well as dynamic methods to include accidental torsion when doing a linear response history analysis. Other modeling issues such as the orientation of the ground motion axis, scaling of element forces and displacements, orthogonal loading, solution techniques, P-Delta effects, modeling of the basement, and calculation of drifts are also studied in the context of linear response history analysis. The thesis concludes with suggested code language for linear response history analysis intended to be considered in future editions of the American Standard ASCE 7. / Master of Science

<p> Block copolymers are a class of soft materials which can self-assemble into a variety of ordered structures. One method to induce new structures is the application of an external field such as an electric field. Previously, studies of the field-induced phase transitions are based on the assumption that the structural change follows certain symmetry pattern or simply using real-space numerical methods. The goal of the current project is to develop a simple analytic method to predict the structural change. Our approach is based on a linear response theory, in which the external field is taken as a perturbation and the lowest-order contribution to the solution is computed. We applied our method to the Landau-Brazovskii theory which is valid close to the order-disorder transition point of diblock copolymers. The result shows that there will be an additional term to the order parameter as a response to the external field. The structural change can be predicted by a new Fourier expansion of the order parameter. As an example, we examined the structural change of a body-centered cubic phase under an applied electric field.</p> / Thesis / Master of Science (MSc)

This study estimated soybean yield responses to K fertilizer using trials data from 18 sites in Mississippi from 2011-2016. Eight response functions were fitted, including linear, linear plateau, quadratic, quadratic-plateau, square root quadratic, spherical plateau, exponential, and exponential-plateau functions. The ratio of high responsive, low responsive, and no responsive sites to K rates is 3:3:12 respectively. The response functions led to different predicted optimal K rates, and the best response function for each site was determined by the Vuong closeness test and economic loss analysis. The predicted economically optimal K rates are 157, 73, and 0 lb/acre for high, low, and no response sites respectively, and the average optimal K rate is 55 lb/acre. Compared to the currently used regional uniform K fertilizer rate of 80 lb/acre, the response-based K rates are expected to generate soybean production gain of about $14 per acre for Mississippi soybean producers.

In dieser Arbeit werden Algorithmen für die Berechnung elektronischer Korrelations- und Anregungsenergien mittels der Coupled-Cluster Methode auf adaptiven Gittern entwickelt und implementiert. Die jeweiligen Funktionen und Operatoren werden adaptiv durch Multiskalenanalyse dargestellt, was eine Basissatz unabängige Beschreibung mit kontrollierter numerischer Genauigkeit ermöglicht. Gleichungen für die Coupled-Cluster Methode werden in einem verallgemeinerten Rahmen, unabhängig von virtuellen Orbitalen und globalen Basissätzen, neu formuliert. Hierzu werden die amplitudengewichteten Anregungen in virtuelle Orbitale ersetzt durch Anregungen in n-Elektronenfunktionen, welche durch Gleichungen im n-Elektronen Ortsraum bestimmt sind. Die erhaltenen Gleichungen können, analog zur Basissatz abh¨angigen Form, mit leicht angepasster Interpretation diagrammatisch dargestellt werden. Aufgrund des singulären Coulomb Potentials werden die Arbeitsgleichungen mit einem explizit korrelierten Ansatz regularisiert. Coupled-Cluster singles mit genäherten doubles (CC2) und ähnliche Modelle werden, für geschlossenschalige Systeme und in regularisierter Form, in die MADNESS Bibliothek (eine allgemeine Bibliothek zur Darstellung von Funktionen und Operatoren mittels Multiskalenanalyse) implementiert. Mit der vorgestellten Methode können elektronische CC2 Paarkorrelationsenergien und Anregungsenergien mit bestimmter numerischer Genauigkeit unabhängig von globalen Basissätzen berechnet werden, was anhand von kleinen Molekülen verifiziert wird / In this work algorithms for the computation of electronic correlation and excitation energies with the Coupled-Cluster method on adaptive grids are developed and implemented. The corresponding functions and operators are adaptively represented with multiresolution analysis allowing a basis-set independent description with controlled numerical accuracy. Equations for the coupled-cluster model are reformulated in a generalized framework independent of virtual orbitals and global basis-sets. For this, the amplitude weighted excitations into virtuals are replaced by excitations into n-electron functions which are determined by projected equations in the n-electron position space. The resulting equations can be represented diagrammatically analogous to basis-set dependent approaches with slightly adjusted rules of interpretation. Due to the singular Coulomb potential, the working equations are regularized with an explicitly correlated ansatz. Coupled-cluster singles with approximate doubles (CC2) and similar models are implemented for closed-shell systems and in regularized form into the MADNESS library (a general library for the representation of functions and operators with multiresolution analysis). With the presented approach electronic CC2 pair-correlation energies and excitation energies can be computed with definite numerical accuracy and without dependence on global basis sets, which is verified on small molecules.

In der vorliegenden Arbeit wird eine einheitliche und allumfassende Theorie der Nicht-linearen Polarisationsspektroskopie in der Frequenzdomäne (NLPF) aufgestellt. Dies Methode basiert auf der in einer isotropen Farbstofflösung durch ein polarisiertes, monochromatisches Laserfeldes (pump) erzeugten Anisotropie, die mittels eines weiteren monochromatischen Laserfeldes (probe), mit einer um 45° gegenüber dem Pumpfeld gedrehten Polarisationsrichtung geprobt wird. Ausgehend von den grundlegenden Gleichungen für den nichtlinearen Respons molekularer Systeme auf elektromagnetische Felder wird das zweidimensional NLPF-spektrum hergeleitet, und zwar sowohl in der niedrigsten Ordnung Störungstheorie als auch unter Verwendung eines selbstkonsistenten Ansatzes für beliebige Pumpfeldstärken. In der niedrigsten Ordnung Störungstheorie können drei in ihrer Frequenzabhängigkeit sich unterscheidende Arten von Ausdrücke explizit angegeben werden. Diese sind drei Areten von Peaks im NLPF-spektrum zuzuordnen: Den T2-peaks, dem T1-peaks und den Zweiphotonen-peaks. Letztere sind unter Normalbedingungen im allgemeinen nicht beobachtbar und wurden daher nicht weiter behandelt. Die in dieser Arbeit erstmals gelungene, allgemeine und einheitliche theoretische Beschreibung der T1- und T2-peaks in NLPF-spektren von Mehrniveausystemen stellt einen Durchbruch hin zu einer allumfassenden Subbandenanalyse mittels NLPF dar. Durch Einbeziehung der teilweise bereits bekannten Auswirkungen homogener und inhomogener Linienverbreiterung und spektraler Diffusion auf NLPF-spektren, sowie deren Verallgemeinerung im Ramen der Theorie nichtmarkowscher Dissipationsprozesse, konnte eine Methodik entwickelt werden, die es erlaubt, NLPF-spektren molekularer und supramolekularer Systeme in Bezug auf das ihnen zugrundeliegende Termschema mit Übergangsfrequenzen und -dipolen, die homogenen und inhomogenen Linienbreiten, sowie dem zugeordneten Energierelaxations- und -transferpfad mitsamt zugehörigen Raten zu analysieren. Die in dieser Arbeit vorgestellte und über frühere rudimentäre Ansätze weit hinausgehende Theorie der NLPF bei starken Pumpfeldern, die auf einem selbstkonsistenten Ansatz für den Fourier-transformierten statistischen Operator beruhen, eröffnet ein komplett neues Feld von Anwendungen der NLPF. Für Zweiniveausysteme konnten die selbstkonsistenten Gleichung vollständig analytisch gelöst werden. Dabei konnten die Querverbindungen zur nichtlinearen Absorption und zum optischen Starkeffekt aufgezeigt werden. Aus der resultierenden Sättigungskurve für das NLPF-signal kann die Sättigungsintensität mit hoher Genauigkeit bestimmt werden. Diese kann unter Heranziehen der aus Analyse des T1-peaks bei niedrigen Intensitäten gewonnen Energierelaxationsrate und der analog aus T2-peakanalyse erhaltenen homogenen Linienbreite zur Bestimmung der Dipolstärke des Übergangs ohne Bestimmung der Farbstoffkonzentration verwendet werden. Dies erweist sich insbesondere bei der Analyse molekularer Aggregation als vorteilhaft. Durch Abbildung auf das gelöste Zweiniveauproblem konnte die Methodik auch auf spezielle Mehrniveausysteme übertragen werden. Eine analytische Lösung für allgemeine Mehrniveausysteme scheiterte jedoch an der komplizierten Orientierungsmittelung über die isotrope Verteilung der Übergangsdipole. Beide oben beschriebenen Methoden, Subbandanalyse bei niedrigen und Bestimmung der Übergangsdipolstärke bei hohen Pumpintensitäten, wurden in der vorliegenden Arbeit zur Untersuchung der Natur der angeregten Zustände in photosynthetischen Antennen von Purpurbakterien und höheren Pflanzen eingesetzt. Für die periphere lichtsammelnde Antenne LH2 des Purpurbakteriums Rhodobacter sphaeroides ergab die T2-peakanalyse der B850-absorptionsbande überraschenderweise zwei Subbanden, die im Absorptionsspektrum selbst bei tiefsten Temperaturen nicht aufzufinden gewesen wären. Eine Erklärung für die in Bezug auf die Oszilatorstärke asymmetrische Aufspaltung der B850-bande konnte allerdings nicht gefunden werden. Für den LH2 des sehr ähnliche Purpurbakterium Rhodospirillium molischianum konnte keine Aufspaltung der B850-bande festgestellt werden. Vielmehr liegt eine überwiegend homogen verbreiterte Bande mit einer homogener Linienbreite (FWHM) von 474±10 cm-1 und einem oberen limit für die inhomogene Linienbreite von 120 cm-1 vor. Daher wurde Rhodospirillium molischianum ausgewählt, um Delokalisation der Anregung im B850-aggregat mittels pumpintensitätsabhängiger NLPF zu untersuchen. Die Frage nach der Delokalisationslänge im B850-aggregat gab und gibt teilweise immer noch Anlass zu hitzigen Debatten. Das Ergebnis einer Ausdehnung der Anregung über 3-4 Bakteriochlorophylle des B850-aggregats der vorliegenden Arbeit unterstützt die aus Exciton-Exciton gewonnen Resultate. Weder eine vollständig lokalisierte noch vollständig delokalisierte Beschreibung war mit dem hier präsentierten Ergebnis in Übereinstimmung zu bringen. Auch im Hauptlichtsammelkomplex höherer Pflanzen LHC II konnte mittels pumpintensitätsabhängiger NLPF-spektren Delokalisation der Anregung über mindestens ein Chlì¥Á / In the work be presented a standard theory of non-linear polarization spectroscopy in the frequency domain (NLPF) will be established. The NLPF technique based on anisotropy induced in a dye-solution, which is isotropic elsewhere, by a polarized monochromatic pump laser field. This is probed by a second laser field, which polarization direction is turned of 45 degree in respect to that of the pump. From the fundamental equations describing the non-linear response of molecular systems on electromagnetic fields, the two-dimensional NLPF spectrum is deduced for arbitrary pump-intensities. At low pump-intensities a subband analysis by NLPF has been established. This allows one to study the term scheme and energy relaxation path of molecular and supra-molecular systems by their NLPF-spectra. This includes the determination of transition-frequencies and -dipole orientations, homogeneous and inhomogeneous linewidths, as well as energy relaxation rates. Furthermore, using a self-connsistent approach, the pump-fieled dependence of the NLPF-spectrum has been deduced for the two-level system in general and also for specific multi-level systems. This method allows one to determine the oscillator strength without knowledge of the concentration, what is quite useful for studying molecular aggregates. Applications are presented to the peripheral light harvesting antenna LH2 of purple bacteria and the light harvesting complexes LHC II and CP 29 of higher plants.

Ceramic-matrix composites of alumina and silicon carbide whiskers have recently found novel commercial application as electromagnetic absorbers. However, a detailed understanding of how materials issues influence the composite electrical response, which underpins this application, has been absent until now. In this project, such composites were electrically measured over a wide range of conditions and modeled in terms of various aspects of the microstructure in order to understand how they work. For this purpose, three types of composites were made by different methods from the same set of ceramic powder blends loaded with different volume fractions of whiskers. In doing so, the interfaces between whiskers, the preferred orientations of whiskers, and the structure of electrically-connected whisker clusters were varied; the whisker aspect-ratio distributions were the same for all methods. At the electrode interfaces, Schottky barriers at the junctions of the electrically-percolating wide-bandgap semiconductor whiskers on the surface were responsible for a significant portion of the total measured impedance. The associated electrical response was studied on the microscopic and macroscopic level, and the gap between these different scales was bridged. Also, a modeling approach was developed for the non-linear behavior of the composite which results from these barriers. In regards to the whiskers within the composite bulk, the effects of various factors on the wide-band frequency dependence of the dielectric response and dc conductivity were explained and contextualized for the electromagnetic absorber application. Such factors include whisker preferred orientation, electrical percolation and cluster structure, the interfaces between electrically-connected SiC whiskers, and porosity. A quantitative correlation between the anisotropy of the microstructure and that of the conductivity was found, and was understood in terms of the interfacial SiC-Al2O3-SiC conduction mechanism. This behavior was shown to differ from the behavior commonly observed for other disordered mixtures of relatively conductive particles dispersed inside insulating polymer hosts. A description of this new mechanism was developed based on an observed correlation between the temperature dependencies of the static and radio-frequency electrical responses. Also, the aforementioned non-linear response model was expanded upon to describe conduction through and across electrically-percolated clusters. The model demonstrates how loading and interface behavior influence the topology and the strength of the non-linear response of the clusters.

Si le noyau atomique peut sembler aujourd'hui un système bien connu, sa description microscopique théorique comporte toujours des lacunes : décrire la structure nucléaire des noyaux tout le long de la charte des noyaux de manière satisfaisante par une seule interaction s'avère encore compliqué aujourd'hui.Les interactions les plus performantes et les plus utilisées pour atteindre ce but sont les interactions effectives. On peut généralement classer celles-ci en deux catégories: celles de portée finie et celles de portée nulle. L'interaction de Skyrme, dont il est principalement question dans ce manuscrit, appartient à la deuxième catégorie. Apparue dans les années 50 comme un développement en gradients à l'ordre 2, sa simplicité en a longtemps fait une interaction de choix. Une collaboration internationale, UNEDF, a toutefois montré que l'interaction en l'état était trop limitée pour reproduire correctement les données expérimentales actuelles et qu'il était nécessaire d'y trouver des extensions. Ce manuscrit propose une telle extension, décrivant le processus aboutissant à l'utilisation d'un développement en gradients jusqu'à l'ordre 6.Après avoir présenté les principales forces effectives utilisées dans le cadre de la structure nucléaire, nous montrerons le comportement de cette nouvelle interaction dans le modèle idéal de la matière infinie et son application dans la description des étoiles à neutrons. Nous verrons ainsi que les performances de notre interaction se sont avérées prometteuses. La comparaison des mêmes propriétés pour des potentiels de portée finie a validé ce constat. Notre extension à l'interaction de Skyrme offre à minima des performances comparables dans ce modèle.En conséquence, nous détaillerons également dans la suite du manuscrit la manière dont nous avons poursuivi le développement de notre nouvelle interaction en l'adaptant pour la description de noyaux sphériques. La dernière partie présente le processus d'ajustement de notre interaction, visant à une description des noyaux le long de la charte nucléaire. Une paramétrisation issue d'un tel ajustement sera enfin proposée / The nucleus may seem well known, but its microscopic description still isn't perfect. Describing accurately the nuclei along the nuclear chart remain complicated.Nowadays, the effective interactions are the best choice to achieve such a goal, and can be sorted in two categories: finite-range and zero-range. Skyrme interaction, the main subject of this report, belongs to the latter. Used since the 50s because of its simplicity, it is an expansion of gradients up to the 2th order. However, an international collaboration, UNEDF, showed recently that this interaction was too limited to describe all the nuclear constraints given by experimental datas. The conclusion was the necessity of Skyrme interaction extensions.This thesis is describing the process from the design of the interaction to its use in nuclei and in fitting procedures.First, we review the requirements and the construction of a general nuclear interactions, and the main interactions used in nuclear structure, both finite and zero range.We then show the behaviour of these interactions in a perfect model: the infinite nuclear matter. This is considered a preliminary test for every interaction aiming to describe nuclei, and the performances of our interactions are discussed, along the performances of the other models.The last part of the thesis is the adaptation of our extension for calculations of nuclei. Furthermore, the fitting procedure of our extended Skyrme interaction on both infinite nuclear matter and nuclei quantities is detailed. A resulting parametrisation is presented at the end of the thesis, aiming to describe more accurately the nuclear chart and the additional physic provided by the new terms

Conventional therapeutic techniques treat the patient by delivering a biotherapeutic to the entire body rather than the target tissue. In the case of chemotherapy, the biotherapeutic is a drug that kills healthy and diseased cells indiscriminately which can lead to undesirable side effects. With targeted delivery, biotherapeutics can be delivered directly to the diseased tissue significantly reducing exposure to otherwise healthy tissue. Typical composite delivery devices are minimally composed of a stimuli responsive polymer, such as poly(N-isopropylacrylamide), allowing for triggered release when heated beyond approximately 32 °C, and magnetic nanoparticles which enable targeting as well as provide a mechanism for stimulus upon alternating magnetic field heating. Although more traditional methods, such as emulsion polymerization, have been used to realize these composite devices, the synthesis is problematic. Poisonous surfactants that are necessary to prevent agglomeration must be removed from the finished polymer, increasing the time and cost of the process. This study seeks to further explore non-toxic, biocompatible, non-residual, photochemical methods of creating stimuli responsive nanogels to advance the targeted biotherapeutic delivery field. Ultraviolet photopolymerization promises to be more efficient, while ensuring safety by using only biocompatible substances. The reactants selected for nanogel fabrication were N-isopropylacrylamide as monomer, methylene bisacrylamide as cross-linker, and Irgacure 2959 as ultraviolet photo-initiator. The superparamagnetic nanoparticles for encapsulation were approximately 10 nm in diameter and composed of magnetite to enable remote delivery and enhanced triggered release properties. Early investigations into the interactions of the polymer and nanoparticles employ a pioneering experimental setup, which allows for coincident turbidimetry and alternating magnetic field heating of an aqueous solution containing both materials. Herein, a low-cost, scalable, and rapid, custom ultraviolet photo-reactor with in-situ, spectroscopic monitoring system is used to observe the synthesis as the sample undergoes photopolymerization. This method also allows in-situ encapsulation of the magnetic nanoparticles simplifying the process. Size characterization of the resulting nanogels was performed by Transmission Electron Microscopy revealing size-tunable nanogel spheres between 50 and 800 nm by varying the ratio and concentration of the reactants. Nano-Tracking Analysis indicates that the nanogels exhibit minimal agglomeration as well as provides a temperature-dependent particle size distribution. Optical characterization utilized Fourier Transform Infrared and Ultraviolet Spectroscopy to confirm successful polymerization. When samples of the nanogels encapsulating magnetic nanoparticles were subjected to an alternating magnetic field a temperature increase was observed indicating that triggered release is possible. Furthermore, a model, based on linear response theory that innovatively utilizes size distribution data, is presented to explain alternating magnetic field heating results. The results presented here will advance targeted biotherapeutic delivery and have a wide range of applications in medical sciences like oncology, gene delivery, cardiology and endocrinology.

Die vorliegende Arbeit befasst sich mit der Anwendung des kürzlich entwickelten 'Functional Approach' zur Elektrodynamik in Medien auf das Modell des freien homogenen Elektronengases. Basierend auf einer ausschließlich mikroskopischen Feldtheorie wird gezeigt, dass mittels universell gültiger Relationen zwischen Antwortfunktionen sowohl alle relevanten optischen als auch magnetischen (linearen) Materialeigenschaften allein aus der Strom-Strom-Korrelation gewonnen werden können. Dabei ist es essentiell, alle Berechnungen auf dem vollen Stromdichteoperator aufzubauen, also auf der Summe aus diamagnetischem, orbitalem und spinoriellem Anteil. Weiterhin wird anhand der magnetischen Suszeptibilität demonstriert, dass im Allgemeinen die Unterscheidung zwischen eigenen und direkten Antwortfunktionen nicht zu vernachlässigen ist. Schließlich wird mit dem „Lindhard-Integral-Theorem“ bewiesen, dass nicht nur der longitudinale, sondern auch der transversale Anteil des vollen frequenz- und wellenvektorabhängigen fundamentalen Antworttensors des freien Elektronengases komplett durch das charakteristische Lindhard-Integral bestimmt ist.:Introduction I Microscopic electrodynamics in media 1 Classical electrodynamics 1.1 Covariant formulation 1.2 Temporal gauge 1.3 Free Green function 1.4 Total functional derivatives 2 Electrodynamics in media 2.1 Field identifications 2.2 Fundamental response tensor 2.3 Universal response relations 2.4 Direct and proper response 2.5 Isotropic and combined limits 2.6 Full Green function 2.7 Wave equations in media and dispersion relations II Application to the free electron gas 3 Fundamental response tensor 3.1 Electromagnetic current density 3.2 Kubo-Greenwood formulae 3.3 Diamagnetic, orbital and spinorial contribution 3.4 Spin susceptibility vs. spinorial current response 4 London model and diamagnetic response 4.1 Interpretation as response function 4.2 Application of universal response relations 4.3 Spin correction 5 Full current response 5.1 Dimensionless formulae 5.2 Lindhard integral theorem 5.3 Laurent expansions 5.4 Optical properties 5.5 Magnetic properties Conclusion Appendix A - Notation Appendix B - Formulary B.1 Basic analysis and vector calculus B.2 Special relativity theory B.3 Fourier transformation B.4 Functional derivatives B.5 Projectors and Helmholtz' theorem B.6 Complex analysis Appendix C - Yang-Mills gauge theory C.1 Field strength tensor C.2 Minimal coupling principle C.3 Gauge invariant quantities and equations Appendix D - Periodic solids D.1 Partitioning of reciprocal space D.2 Homogeneous limit Appendix E - Electromagnetic spectrum Bibliography Acknowledgements Errata / This thesis is concerned with the application of the recently developed 'Functional Approach' to electrodynamics of media to the model of the free homogeneous electron gas. Based on an exclusively microscopic field theory it is shown that with the help of universally valid relations between response functions, all relevant optical and magnetic (linear) materials properties can be extracted from the mere current-current response. For this purpose, it is essential to base all calculations on the full current density operator, i.e. the sum of diamagnetic, orbital and spinorial contributions. Furthermore, we use the example of the magnetic susceptibility to demonstrate that the distinction between proper and direct response functions is in general crucial. Lastly, with the “Lindhard integral theorem” we prove that not only the longitudinal but also the transverse part of the full frequency- and wavevector-dependent fundamental response tensor of the free electron gas is completely determined by the characteristic Lindhard integral.:Introduction I Microscopic electrodynamics in media 1 Classical electrodynamics 1.1 Covariant formulation 1.2 Temporal gauge 1.3 Free Green function 1.4 Total functional derivatives 2 Electrodynamics in media 2.1 Field identifications 2.2 Fundamental response tensor 2.3 Universal response relations 2.4 Direct and proper response 2.5 Isotropic and combined limits 2.6 Full Green function 2.7 Wave equations in media and dispersion relations II Application to the free electron gas 3 Fundamental response tensor 3.1 Electromagnetic current density 3.2 Kubo-Greenwood formulae 3.3 Diamagnetic, orbital and spinorial contribution 3.4 Spin susceptibility vs. spinorial current response 4 London model and diamagnetic response 4.1 Interpretation as response function 4.2 Application of universal response relations 4.3 Spin correction 5 Full current response 5.1 Dimensionless formulae 5.2 Lindhard integral theorem 5.3 Laurent expansions 5.4 Optical properties 5.5 Magnetic properties Conclusion Appendix A - Notation Appendix B - Formulary B.1 Basic analysis and vector calculus B.2 Special relativity theory B.3 Fourier transformation B.4 Functional derivatives B.5 Projectors and Helmholtz' theorem B.6 Complex analysis Appendix C - Yang-Mills gauge theory C.1 Field strength tensor C.2 Minimal coupling principle C.3 Gauge invariant quantities and equations Appendix D - Periodic solids D.1 Partitioning of reciprocal space D.2 Homogeneous limit Appendix E - Electromagnetic spectrum Bibliography Acknowledgements Errata