Stochastic local volatility model for fx markets

Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.

New enhancement strategies for plasmon-enhanced fluorescence biosensors

This thesis investigates metallic nanostructures exhibiting surface plasmon resonance for the amplification of fluorescence signal in sandwich immunoassays. In this approach, an analyte is captured by an antibody immobilized on a plasmonic structure and detected by a subsequently bound fluorophore labeled detection antibody. The highly confined field of surface plasmons originates from collective charge oscillations which are associated with high electromagnetic field enhancements at the metal surface and allow for greatly increased fluorescence signal from the attached fluorophores. This feature allows for improving the signal-to-noise ratio in fluorescence measurements and thus advancing the sensitivity of the sensor platform. In particular, the thesis presents two plasmonic nanostructures that amplify fluorescence signal in devices that rely on epifluorescence geometry, in which the fluorophore absorbs and emits light from the same direction perpendicular to the substrate surface.rnThe first is a crossed relief gold grating that supports propagating surface plasmon polaritons (SPPs) and second, gold nanoparticles embedded in refractive index symmetric environment exhibiting collective localized surface plasmons (cLSPs). Finite-difference time-domain simulations are performed in order to design structures for the optimum amplification of established Cy5 and Alexa Fluor 647 fluorophore labels with the absorption and emission wavelengths in the red region of spectrum. The design takes into account combined effect of surface plasmon-enhanced excitation rate, directional surface plasmon-driven emission and modified quantum yield for characteristic distances in immunoassays. Homebuilt optical instruments are developed for the experimental observation of the surface plasmon mode spectrum, measurements of the angular distribution of surface plasmon-coupled fluorescence light and a setup mimicking commercial fluorescence reading systems in epifluorescence geometry.rnCrossed relief grating structures are prepared by interference lithography and multiple copies are made by UV nanoimprint lithography. The fabricated crossed diffraction gratings were utilized for sandwich immunoassay-based detection of the clinically relevant inflammation marker interleukin 6 (IL-6). The enhancement factor of the crossed grating reached EF=100 when compared to a flat gold substrate. This result is comparable to the highest reported enhancements to date, for fluorophores with relatively high intrinsic quantum yield. The measured enhancement factor excellently agrees with the predictions of the simulations and the mechanisms of the enhancement are explained in detail. Main contributions were the high electric field intensity enhancement (30-fold increase) and the directional fluorescence emission at (4-fold increase) compared to a flat gold substrate.rnCollective localized surface plasmons (cLSPs) hold potential for even stronger fluorescence enhancement of EF=1000, due to higher electric field intensity confinement. cLSPs are established by diffractive coupling of the localized surface plasmon resonance (LSPR) of metallic nanoparticles and result in a narrow resonance. Due to the narrow resonance, it is hard to overlap the cLSPs mode with the absorption and emission bands of the used fluorophore, simultaneously. Therefore, a novel two resonance structure that supports SPP and cLSP modes was proposed. It consists of a 2D array of cylindrical gold nanoparticles above a low refractive index polymer and a silver film. A structure that supports the proposed SPP and cLSP modes was prepared by employing laser interference lithography and the measured mode spectrum was compared to simulation results.rn

Optical properties of a nanomatch-like plasmonic structure

The optical properties of a match-like plasmonic nanostructure are numerically investigated using full-wave finite-difference time-domain analysis in conjunction with dispersive material models. This work is mainly motivated by the developed technique enabling reproducible fabrication of nanomatch structures as well as the growing applications that utilize the localized field enhancement in plasmonic nanostructures. Our research revealed that due to the pronounced field enhancement and larger resonance tunabilities, some nanomatch topologies show potentials for various applications in the field of, e.g., sensing as well as a novel scheme for highly reproducible tips in scanning near field optical microscopy, among others. Despite the additional degrees of freedom that are offered by the composite nature of the proposed nanomatch topology, the paper also reflects on a fundamental complication intrinsic to the material interfaces especially in the nanoscale: stoichiometric mixing. We conclude that the specificity in material modeling will become a significant issue in future research on functionalized composite nanostructures.

Extraordinary transmission through a single coaxial aperture in a thin metal film

We investigate experimentally the transmission properties of single sub-wavelength coaxial apertures in thin metal films (t = 110 nm). Enhanced transmission through a single sub-wavelength coaxial aperture illuminated with a strongly focused radially polarized light beam is reported. In our experiments we achieved up to four times enhanced transmission through a single coaxial aperture as compared to a (hollow) circular aperture with the same outer diameter.We attribute this enhancement of transmission to the excitation of a TEM-mode for illumination with radially polarized light inside the single coaxial aperture. A strong polarization contrast is observed between the transmission for radially and azimuthally polarized illumination. Furthermore, the observed transmission through a single coaxial aperture can be strongly reduced if surface plasmons are excited. The experimental results are in good agreement with finite difference time domain (FDTD) simulations.

Detecting Improvised Explosive Devices Via Forward Looking Ground Penetrating Radar

Forward-looking ground penetrating radar shows promise for detection of improvised explosive devices in active war zones. Because of certain insurmountable physical limitations, post-processing algorithm development is the most popular research topic in this field. One such investigative avenue explores the worthiness of frequency analysis during data post-processing. Using the finite difference time domain numerical method, simulations are run to test both mine and clutter frequency response. Mines are found to respond strongest at low frequencies and cause periodic changes in ground penetrating radar frequency results. These results are called into question, however, when clutter, a phenomenon generally known to be random, is also found to cause periodic frequency effects. Possible causes, including simulation inaccuracy, are considered. Although the clutter models used are found to be inadequately random, specular reflections of differing periodicity are found to return from both the mine and the ground. The presence of these specular reflections offers a potential alternative method of determining a mine’s presence.

Study of and design procedure for dual circularly polarized waveguide slot arrays

For the past sixty years, waveguide slot radiator arrays have played a critical role in microwave radar and communication systems. They feature a well-characterized antenna element capable of direct integration into a low-loss feed structure with highly developed and inexpensive manufacturing processes. Waveguide slot radiators comprise some of the highest performance—in terms of side-lobe-level, efficiency, etc. — antenna arrays ever constructed. A wealth of information is available in the open literature regarding design procedures for linearly polarized waveguide slots. By contrast, despite their presence in some of the earliest published reports, little has been presented to date on array designs for circularly polarized (CP) waveguide slots. Moreover, that which has been presented features a classic traveling wave, efficiency-reducing beam tilt. This work proposes a unique CP waveguide slot architecture which mitigates these problems and a thorough design procedure employing widely available, modern computational tools. The proposed array topology features simultaneous dual-CP operation with grating-lobe-free, broadside radiation, high aperture efficiency, and good return loss. A traditional X-Slot CP element is employed with the inclusion of a slow wave structure passive phase shifter to ensure broadside radiation without the need for performance-limiting dielectric loading. It is anticipated this technology will be advantageous for upcoming polarimetric radar and Ka-band SatCom systems. The presented design methodology represents a philosophical shift away from traditional waveguide slot radiator design practices. Rather than providing design curves and/or analytical expressions for equivalent circuit models, simple first-order design rules – generated via parametric studies — are presented with the understanding that device optimization and design will be carried out computationally. A unit-cell, S-parameter based approach provides a sufficient reduction of complexity to permit efficient, accurate device design with attention to realistic, application-specific mechanical tolerances. A transparent, start-to-finish example of the design procedure for a linear sub-array at X-Band is presented. Both unit cell and array performance is calculated via finite element method simulations. Results are confirmed via good agreement with finite difference, time domain calculations. Array performance exhibiting grating-lobe-free, broadside-scanned, dual-CP radiation with better than 20 dB return loss and over 75% aperture efficiency is presented.

Topological changes in 2D simplicial meshes for the simulation of fractures

A method for the introduction of strong discontinuities into a mesh will be developed. This method, applicable to a number of eXtended Finite Element Methods (XFEM) with intra-element strong discontinuities will be demonstrated with one specific method: the Generalized Cohesive Element (GCE) method. The algorithm utilizes a subgraph mesh representation which may insert the GCE either adaptively during the course of the analysis or a priori. Using this subgraphing algorithm, the insertion time is O(n) to the number of insertions. Numerical examples are presented demonstrating the advantages of the subgraph insertion method.

Heat transfer in microwave heating

Heat transfer is considered as one of the most critical issues for design and implement of large-scale microwave heating systems, in which improvement of the microwave absorption of materials and suppression of uneven temperature distribution are the two main objectives. The present work focuses on the analysis of heat transfer in microwave heating for achieving highly efficient microwave assisted steelmaking through the investigations on the following aspects: (1) characterization of microwave dissipation using the derived equations, (2) quantification of magnetic loss, (3) determination of microwave absorption properties of materials, (4) modeling of microwave propagation, (5) simulation of heat transfer, and (6) improvement of microwave absorption and heating uniformity. Microwave heating is attributed to the heat generation in materials, which depends on the microwave dissipation. To theoretically characterize microwave heating, simplified equations for determining the transverse electromagnetic mode (TEM) power penetration depth, microwave field attenuation length, and half-power depth of microwaves in materials having both magnetic and dielectric responses were derived. It was followed by developing a simplified equation for quantifying magnetic loss in materials under microwave irradiation to demonstrate the importance of magnetic loss in microwave heating. The permittivity and permeability measurements of various materials, namely, hematite, magnetite concentrate, wüstite, and coal were performed. Microwave loss calculations for these materials were carried out. It is suggested that magnetic loss can play a major role in the heating of magnetic dielectrics. Microwave propagation in various media was predicted using the finite-difference time-domain method. For lossy magnetic dielectrics, the dissipation of microwaves in the medium is ascribed to the decay of both electric and magnetic fields. The heat transfer process in microwave heating of magnetite, which is a typical magnetic dielectric, was simulated by using an explicit finite-difference approach. It is demonstrated that the heat generation due to microwave irradiation dominates the initial temperature rise in the heating and the heat radiation heavily affects the temperature distribution, giving rise to a hot spot in the predicted temperature profile. Microwave heating at 915 MHz exhibits better heating homogeneity than that at 2450 MHz due to larger microwave penetration depth. To minimize/avoid temperature nonuniformity during microwave heating the optimization of object dimension should be considered. The calculated reflection loss over the temperature range of heating is found to be useful for obtaining a rapid optimization of absorber dimension, which increases microwave absorption and achieves relatively uniform heating. To further improve the heating effectiveness, a function for evaluating absorber impedance matching in microwave heating was proposed. It is found that the maximum absorption is associated with perfect impedance matching, which can be achieved by either selecting a reasonable sample dimension or modifying the microwave parameters of the sample.

Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Study of particle movement in the nearshore region of Lake Superior with radioisotope tracers

Biogeochemical processes in the coastal region, including the coastal area of the Great Lakes, are of great importance due to the complex physical, chemical and biological characteristics that differ from those on either the adjoining land or open water systems. Particle-reactive radioisotopes, both naturally occurring (210Pb, 210Po and 7Be) and man-made (137Cs), have proven to be useful tracers for these processes in many systems. However, a systematic isotope study on the northwest coast of the Keweenaw Peninsula in Lake Superior has not yet been performed. In this dissertation research, field sampling, laboratory measurements and numerical modeling were conducted to understand the biogeochemistry of the radioisotope tracers and some particulate-related coastal processes. In the first part of the dissertation, radioisotope activities of 210Po and 210Pb in a variability of samples (dissolved, suspended particle, sediment trap materials, surficial sediment) were measured. A completed picture of the distribution and disequilibrium of this pair of isotopes was drawn. The application of a simple box model utilizing these field observations reveals short isotope residence times in the water column and a significant contribution of sediment resuspension (for both particles and isotopes). The results imply a highly dynamic coastal region. In the second part of this dissertation, this conclusion is examined further. Based on intensive sediment coring, the spatial distribution of isotope inventories (mainly 210Pb, 137Cs and 7Be) in the nearshore region was determined. Isotope-based focusing factors categorized most of the sampling sites as non- or temporary depositional zones. A twodimensional steady-state box-in-series model was developed and applied to individual transects with the 210Pb inventories as model input. The modeling framework included both water column and upper sediments down to the depth of unsupported 210Pb penetration. The model was used to predict isotope residence times and cross-margin fluxes of sediments and isotopes at different locations along each transect. The time scale for sediment focusing from the nearshore to offshore regions of the transect was on the order of 10 years. The possibility of sediment longshore movement was indicated by high inventory ratios of 137Cs: 210Pb. Local deposition of fine particles, including fresh organic carbon, may explain the observed distribution of benthic organisms such as Diporeia. In the last part of this dissertation, isotope tracers, 210Pb and 210Po, were coupled into a hydrodynamic model for Lake Superior. The model was modified from an existing 2-D finite difference physical-biological model which has previously been successfully applied on Lake Superior. Using the field results from part one of this dissertation as initial conditions, the model was used to predict the isotope distribution in the water column; reasonable results were achieved. The modeling experiments demonstrated the potential for using a hydrodynamic model to study radioisotope biogeochemistry in the lake, although further refinements are necessary.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

Children's and adolescent's self - assessment of metabolic control versus professional judgment: a cross-sectional retrospective and prospective cohort study

BACKGROUND Morbidity and mortality in T1DM depend on metabolic control, which is assessed by HbA1c measurements every 3-4 months. Patients' self-perception of glycemic control depends on daily blood glucose monitoring. Little is known about the congruence of patients' and professionals' perception of metabolic control in T1DM. OBJECTIVE To assess the actual patients' self-perception and objective assessment (HbA1c) of metabolic control in T1DM children and adolescents and to investigate the possible factors involved in any difference. METHODS Patients with T1DM aged 8 - 18 years were recruited in a cross-sectional, retrospective and prospective cohort study. Data collection consisted of clinical details, measured HbA1c, self-monitored blood glucose values and questionnaires assessing self and professionals' judgment of metabolic control. RESULTS 91 patients participated. Mean HbA1c was 8.03%. HbA1c was higher in patients with a diabetes duration > 2 years (p = 0.025) and in patients of lower socioeconomic level (p = 0.032). No significant correlation was found for self-perception of metabolic control in well and poorly controlled patients. We found a trend towards false-positive memory of the last HbA1c in patients with a HbA1c > 8.5% (p = 0.069) but no difference in patients' knowledge on target HbA1c between well and poorly controlled patients. CONCLUSIONS T1DM patients are aware of a target HbA1c representing good metabolic control. Ill controlled patients appear to have a poorer recollection of their HbA1c. Self-perception of actual metabolic control is similar in well and poorly controlled T1DM children and adolescents. Therefore, professionals should pay special attention that ill controlled T1DM patients perceive their HbA1c correctly.

Extension and Partitioning in an Oblique Subduction Zone, New Zealand: Constraints from Three-Dimensional Numerical Modeling

Contraction, strike slip, and extension displacements along the Hikurangi margin northeast of the North Island of New Zealand coincide with large lateral gradients in material properties. We use a finite- difference code utilizing elastic and elastic-plastic rheologies to build large- scale, three-dimensional numerical models which investigate the influence of material properties on velocity partitioning within oblique subduction zones. Rheological variation in the oblique models is constrained by seismic velocity and attenuation information available for the Hikurangi margin. We compare the effect of weakly versus strongly coupled subduction interfaces on the development of extension and the partitioning of velocity components for orthogonal and oblique convergence and include the effect of ponded sediments beneath the Raukumara Peninsula. Extension and velocity partitioning occur if the subduction interface is weak, but neither develops if the subduction interface is strong. The simple mechanical model incorporating rheological variation based on seismic observations produces kinematics that closely match those published from the Hikurangi margin. These include extension within the Taupo Volcanic Zone, uplift over ponded sediments, and dextral contraction to the south.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.