Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

Polygonal cracks in the seasonal semi-translucent CO2 ice layer in Martian polar areas

In this paper, we use morphological and numerical methods to test the hypothesis that seasonally formed fracture patterns in the Martian polar regions result from the brittle failure of seasonal CO2 slab ice. The observations by the High Resolution Imaging Science Experiment (HiRISE) of polar regions of Mars show very narrow dark elongated linear patterns that are observed during some periods of time in spring, disappear in summer and re-appear again in the following spring. They are repeatedly formed in the same areas but they do not repeat the exact pattern from year to year. This leads to the conclusion that they are cracks formed in the seasonal ice layer. Some of models of seasonal surface processes rely on the existence of a transparent form of CO2 ice, so-called slab ice. For the creation of the observed cracks the ice is required to be a continuous media, not an agglomeration of relatively separate particles like a firn. The best explanation for our observations is a slab ice with relatively high transparency in the visible wavelength range. This transparency allows a solid state green-house effect to act underneath the ice sheet raising the pressure by sublimation from below. The trapped gas creates overpressure and the ice sheet breaks at some point creating the observed cracks. We show that the times when the cracks appear are in agreement with the model calculation, providing one more piece of evidence that CO2 slab ice covers polar areas in spring.

Design and implementation of a 3D computer game controller using inertial MEMS sensors

Though 3D computer graphics has seen tremendous advancement in the past two decades, most available mechanisms for computer interaction in 3D are high cost and targeted for industry and virtual reality applications. Recent advances in Micro-Electro-Mechanical-System (MEMS) devices have brought forth a variety of new low-cost, low-power, miniature sensors with high accuracy, which are well suited for hand-held devices. In this work a novel design for a 3D computer game controller using inertial sensors is proposed, and a prototype device based on this design is implemented. The design incorporates MEMS accelerometers and gyroscopes from Analog Devices to measure the three components of the acceleration and angular velocity. From these sensor readings, the position and orientation of the hand-held compartment can be calculated using numerical methods. The implemented prototype is utilizes a USB 2.0 compliant interface for power and communication with the host system. A Microchip dsPIC microcontroller is used in the design. This microcontroller integrates the analog to digital converters, the program memory flash, as well as the core processor, on a single integrated circuit. A PC running Microsoft Windows operating system is used as the host machine. Prototype firmware for the microcontroller is developed and tested to establish the communication between the design and the host, and perform the data acquisition and initial filtering of the sensor data. A PC front-end application with a graphical interface is developed to communicate with the device, and allow real-time visualization of the acquired data.

Analytical Parametric Model Used to Study the Influence of Electrostatic Force on Surface Coverage During Electrospinning of Polymer Fibers

Electrospinning (ES) can readily produce polymer fibers with cross-sectional dimensions ranging from tens of nanometers to tens of microns. Qualitative estimates of surface area coverage are rather intuitive. However, quantitative analytical and numerical methods for predicting surface coverage during ES have not been covered in sufficient depth to be applied in the design of novel materials, surfaces, and devices from ES fibers. This article presents a modeling approach to ES surface coverage where an analytical model is derived for use in quantitative prediction of surface coverage of ES fibers. The analytical model is used to predict the diameter of circular deposition areas of constant field strength and constant electrostatic force. Experimental results of polyvinyl alcohol fibers are reported and compared to numerical models to supplement the analytical model derived. The analytical model provides scientists and engineers a method for estimating surface area coverage. Both applied voltage and capillary-to-collection-plate separation are treated as independent variables for the analysis. The electric field produced by the ES process was modeled using COMSOL Multiphysics software to determine a correlation between the applied field strength and the size of the deposition area of the ES fibers. MATLAB scripts were utilized to combine the numerical COMSOL results with derived analytical equations. Experimental results reinforce the parametric trends produced via modeling and lend credibility to the use of modeling techniques for the qualitative prediction of surface area coverage from ES. (Copyright: 2014 American Vacuum Society.)

Simulation der peristaltischen Förderung von Stückgütern als Schüttgut

Im Beitrag wird ein neuartiges Förderprinzip zur federnden Aufnahme und zum Transport von massenhaft anfallenden Paketstrukturen vorgestellt. Das Förderprinzip beruht auf einem flächigen Tragmittel in Form eines veränderbaren, elastischen Verbundes von kleinskaligen Fördermodulen. Das konzipierte Transportprinzip mit peristaltischen Eigenschaften soll entstehende Staus der Pakete schnell auflösen und eine dedizierte Steuerung von Teilmengen zulassen, um den erforderlichen Durchsatz innerhalb eines Materialflusssystems zu erreichen. Diese Lösung ermöglicht eine sinnvolle Verknüpfung von Wirkprinzipien der Schüttgut- und Stückgutförderung zur Aufnahme und Fortbewegung von Pakete als Schüttgut. Die Grundfunktionalität des Förderkonzepts wird durch die numerische Simulation auf Basis der Diskrete Elemente Methode sowie der Mehrkörpersimulation überprüft.

Modeling of ore-forming and geoenvironmental systems: Roles of fluid flow and chemical reaction processes

Ore-forming and geoenviromental systems commonly involve coupled fluid flowand chemical reaction processes. The advanced numerical methods and computational modeling have become indispensable tools for simulating such processes in recent years. This enables many hitherto unsolvable geoscience problems to be addressed using numerical methods and computational modeling approaches. For example, computational modeling has been successfully used to solve ore-forming and mine site contamination/remediation problems, in which fluid flow and geochemical processes play important roles in the controlling dynamic mechanisms. The main purpose of this paper is to present a generalized overview of: (1) the various classes and models associated with fluid flow/chemically reacting systems in order to highlight possible opportunities and developments for the future; (2) some more general issues that need attention in the development of computational models and codes for simulating ore-forming and geoenviromental systems; (3) the related progresses achieved on the geochemical modeling over the past 50 years or so; (4) the general methodology for modeling of oreforming and geoenvironmental systems; and (5) the future development directions associated with modeling of ore-forming and geoenviromental systems.

Experimental validation of a nonlinear μ FE model based on cohesive-frictional plasticity for trabecular bone

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

Modeling asteroid collisions and impact processes

As a complement to experimental and theoretical approaches, numerical modeling has become an important component to study asteroid collisions and impact processes. In the last decade, there have been significant advances in both computational resources and numerical methods. We discuss the present state-of-the-art numerical methods and material models used in "shock physics codes" to simulate impacts and collisions and give some examples of those codes. Finally, recent modeling studies are presented, focussing on the effects of various material properties and target structures on the outcome of a collision.

Pollen records and lithology of profiles from Lobsigensee, Switzerland

Lobsigensee is a small kettle hole lake 15 km north-west of Bern on the Swiss Plateau, at an altitude of 514 m asl. Its surface is 2ha today, its maximum depth 2.7 m; it has no inlet and the overflow functions mainly during snow melting. The area was covered by Rhone ice during the Last Glaciation (map in Fig.2). Local geology, climate and vegetation are summarized in Figure 3A-C, the history of settlement in Figures 5-7. In order to reconstruct the vegetational and environmental history of the lake and its surroundings pollen analysis and other bio- and isotope stratigraphies were applied to twelve profiles cored across the basin with modified Livingstone corers (Fig.3 D). (1) The standard diagram: The central core LQ-90 is described as the standard pollen diagram (Chapter 3) with 10 local pollen assemblage zones of the Late-Glacial (local PAZ Ll to Ll0, from about 16'000(7) to 10'000 years BP) and 20 PAZ of the Holocene (local PAZ L11 to L30), see Figs. 8-10 and 20-24. Local PAZ L 1 to L3 are in the Late-Glacial clay and record the vegetational development after the ice retreat: L1 shows very low pollen concentration and high Pinus percentages due to long-distance transport and reworking; the latter mechanism is corroborated by the findings of thermophilous and pre-Quaternary taxa. Local PAZ L2 has a high di versi ty of non-arboreal pollen (NAP) and reflects the Late-Glacial steppe rich in heliophilous species. Local PAZ L3 is similar but additionally rich in Betula nana and Sal1x, thus reflecting a "shrub tundra". The PAZ L1 to L3 belong to the Oldest Dryas biozone. Local PAZ L4 to L 10 are found in the gyttja of the profundal or in the lake marl of the littoral and record the Late-Glacial forests. L4 is the shrub phase of reforestation with very high Junlperus and rapidly increasing Betula percentages. L5 is the PAZ with a first, L7 with a second dominance of tree-birches, separated by L6 showing a depression in the Betula curve. L4 to L7 can be assigned to the Balling biozone. Possible correlation of the Betula depression to the Older Dryas biozone is discussed. In local PAZ L8 Plnus immigrates and expands. L9 shows a facies difference in that Plnus dominates over Betula in littoral but not in profundal spectra. L8 and L9 belong to the Allerod biozone. In its youngest part the volcanic ash from Laach/Eifel is regularly found (11,000 BP). The local PAZ Ll0 corresponds to the Younger Dryas blozone. The merely slight increase of the NAP indicates that the pine forests of the lowland were not strongly affected by a cooler climate. In order to evaluate the significance of the littoral accumulation of coniferous pollen the littoral profile LQ-150 is compared to the profundal. Radiocarbon stratigraphies derived from different materials are presented in Figures 13 and 14 and in Tables 2 and 3. The hard-water errors in the gyttja samples and the carbonate samples are similar. The samples of terrestrial plant macrofossils are not affected by hard-water errors. Two plateaux of constant age appear in the age-depth relationship; their consequence for biostratigraphy as well as pollen concentration and influx diagrams are discussed. Radiocarbon ages of the Late-Glacial pollen zones are shown in Table 10. The Holocene vegetational history is recorded in the local PAZ L 11 to L30. After a Preboreal (PAZ L11) dominated by pine and birch the expansions of Corylus, Ulmus and Quercus are very rapid. Among these taxa Corylus dominates dur ing the Boreal (PAZ L 12 and L 1 3), whereas the components of the mixed oak forest dominate in the Older Atlantic (PAZ L14 to L16). In the Younger Atlantic (PAZ L 17 to L 19) Fagus and Alnus play an increasing, the mixed oak forest a decreasing role. During the period of local PAZ L19 Neolithic settlers lived on the shore of Lobsigensee. During the Subboreal (PAZ L20 and L21) and the Older Subatlantic (L22 to L25) strong fluctuations of Fagus and often antagonistic peaks of NAP, Alnus, Betula and Corylus can be interpreted as signs of human impact on vegetation. L23 is characterized not only by high values of NAP (especially apophytes and anthropochorous species) but also by the appearance of Juglans, Castanea and Secale which point to the Roman colonization of the area. For a certain period during the Younger Subatlantic (PAZ L26 to L30) the lake was used for retting hemp (Cannabis). Later the dominance of Quercus pollen indicates the importance of wood pastures. The youngest sediments reflect the wide-spread agricultural grass lands and the plantation of Pinus and Picea. Radiocarbon dates for the Holocene are given in Figure 23 and Table 4, the extrapolated ages of the Holocene pollen zones in Table 15. (2) The cross sections: Figures 25 and 26 give a summary of the litho- and palynostratigraphy of the two cross sections. Based on 11 Late-Glacial and 9 Holocene pollen diagrams (in addition to the standard ones), the consistency of the criteria for the definition of the pollen zones is examined in Tables 7 and 8 for the Late-Glacial and in Tables 11 to 14 for the Holocene. Sediment thicknesses across the basin for each pollen zone are presented in these tables as well as in Figures 43 to 45 for the Late-Glacial and in Figures 59 to 65 for the Holocene. Sediment focusing can explain differences between the gyttja cores of the profundal. Focusing is more than compensated for through "stretching" by carbonate precipitation on the littoral terrace. Pollen influx to the cross section are discussed (Chapters 4.1.5. and 4.2.3.). (3) The regional pollen zones: Based on some selected sites between Lake Geneva and Lake Constance regional pollen zones are proposed (Table 16, 17 and 19). (4) Paleoecology: Climatic change in the Late-Glacial can be inferred from Coleoptera, Trichoptera, Chironomidae and d18O of carbonates: a distinct warming is recorded around 12' 600 BP and around 10' 000 BP. The Younger Dryas biozone (10'700-10'000 BP) was the only cooling found in the Late-Glacial. The Betula depression often correlated wi th the Older Dryas biozone was possibl not colder but dryer than the previous period. During the Holocene the lowland site is not very sensitive to the minor climatic changes. Table 22 summarizes climatic and trophic changes before 8'000 BP as deduced from various biostratigraphies studied by a number of authors. Ostracods, Chironomids and fossil pigments indicate that anoxic conditions prevailed during the BoIling (possibly meromixis). Changes in the lake level are illustrated in Figure 74. A first lake-level lowering occurred in the early Holocene (10'000 to 9'000 BP), a second during the Atlantic (about 6'800 to 5'200 BP). The first "shrinking" of the lake volume resulted in a eutrophication recorded by laminations in the profundal and by pigments of Cyanophyceae. The second fall in water level corresponds to an increase of Nymphaeaceae. Human impact can be inferred in three ways: eutrophication of the lake (since the Neolithic), changes of terrestrial vegetation by deforestations (cyclicity of Fagus, see Figures 78 to 80), and enhanced erosion (increasing sedimentation rates by inwashed clay, particularly since the Roman Colonization, see Figures 49 and 81). Summary: This paper was planned as the final report on Lobsigensee. However, a number of issues are not answered but can only be asked more precisely, for example: (1) For the two periods with the highest rates of change, Le. the Bolling and the Preboreal biozones, pollen influx may reflect vegetation dynamics. Detailed investigations of these periods in annually laminated sediments are planned. (2) Biostratigraphies other than palynostratigraphy are needed to estimate the degree of linkage or independence in the development of terrestrial and lacustrine ecosystems. Often our sampling intervals were not identical, thus influencing our temporal resolution. (3) 6180- and 14C-stratigraPhies with high resolution will elucidate the leads and lags of these dynamic periods. Plateaux of constant age in the age-depth relationship have a strong bearing on both biological and geophysical understanding of Late-Glacial and early Holocene developments. (4) Numerical methods applied to the pollen diagrams of the cross section will help to quantify the significance of similari ties and dissimilarities across a single basin (with Prof. Birks). (5) Numerical methods applied to different sites on the Swiss Plateau and on the transect across the Alps will be helpful in evaluating the influence of different environmental factors (with Prof. Birks). (6) A new map 1: 1000 with 50cm-contour lines prov ided by Prof. Zurbuchen will be combined with a grid of cores sampling the transition from lake marl to peat enabling us to calculate paleo-volumes of the lake. This is interesting for the two "shrinking periods" (in Fig. 74A numbers 2-6 and 7-10), both accompanied by eutrophication. The pal eo-volume during the Neoli thic set tlement of the Cortaillod culture linked wi th an est l.mate of trophic change derived from diatoms (Prof. Smol in prep.) could possibly give an indication of the size of the human population of this period. (7) For the period with the antagonism between Fagus peaks and ABC-peaks close collaboration between palynologists, geochemists and archeologists should enable us to determine the influence of prehistoric and historic people on vegetation (collaboration with Prof. Stockli and Prof. Herzig). (8) The core LL-75 taken with a "cold letter box" will be analysed for major and trace elements by Dr. Sturm for 210pb and 137Cs by Prof.von Gunten and for pollen. We will see if our local PAZ L30 really corresponds to the surface sediment and if the small seepage lake reflects modern pollution.

WCSPH viscosity diffusion processes in vortex flows

The aim of this paper is to clarify the role played by the most commonly used viscous terms in simulating viscous laminar flows using the weakly compressible approach in the context of smooth particle hydrodynamics (WCSPH). To achieve this, Takeda et al. (Prog. Theor. Phys. 1994; 92(5):939–960), Morris et al. (J. Comput. Phys. 1997; 136:214–226) and Monaghan–Cleary–Gingold's (Appl. Math. Model. 1998; 22(12):981–993; Monthly Notices of the Royal Astronomical Society 2005; 365:199–213) viscous terms will be analysed, discussing their origins, structures and conservation properties. Their performance will be monitored with canonical flows of which related viscosity phenomena are well understood, and in which boundary effects are not relevant. Following the validation process of three previously published examples, two vortex flows of engineering importance have been studied. First, an isolated Lamb–Oseen vortex evolution where viscous effects are dominant and second, a pair of co-rotating vortices in which viscous effects are combined with transport phenomena. The corresponding SPH solutions have been compared to finite-element numerical solutions. The SPH viscosity model's behaviour in modelling the viscosity related effects for these canonical flows is adequate

Cargas explosivas sobre pilares y forjados modelados con elementos tipo viga y lámina

Los fenómenos de impacto y explosión sobre estructuras de hormigón tienen efectos en muchos casos catastróficos a pesar de su reducida probabilidad. Las estructuras de hormigón no suelen estar diseñadas para resistir este tipo de solicitaciones dinámicas. El análisis numérico mediante elementos finitos con integración explícita permite una aproximación suficiente a los efectos de la onda explosiva sobre pilares y forjados de estructuras reticuladas de hormigón. Los materiales recientemente implementados en LS-Dyna para hormigón como el CSCM [1], para elementos de continuo 3D, y la formulación que proporciona la debida compatibilidad con los elementos viga de acero dispuestos de forma segregada, permite estudiar de forma realista modelos detallados de pilares y forjados. Pero las limitaciones computacionales hacen inviable emplear estos métodos en estructuras completas. Como alternativa es posible usar modelos de elementos estructurales de vigas y láminas para el análisis de estas estructuras. Sin embargo es necesario un adecuado ajuste de parámetros y propiedades en estos modelos. Este trabajo muestra un método con en el que obtener modelos de elementos estructurales, elementos viga y lámina, usando modelos de material [2] adecuados para ellos, junto a un procedimiento para incluir la armadura de forma adecuada. Utilizando este método es posible representar con suficiente aproximación el comportamiento de modelos detallados realistas de forjados y pilares de estructuras reticuladas de hormigón frente a acciones explosivas, posibilitando el análisis de una estructura completa frente a explosión.

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics.

A novel time integration scheme is presented for the numerical solution of the dynamics of discrete systems consisting of point masses and thermo-visco-elastic springs. Even considering fully coupled constitutive laws for the elements, the obtained solutions strictly preserve the two laws of thermo dynamics and the symmetries of the continuum evolution equations. Moreover, the unconditional control over the energy and the entropy growth have the effect of stabilizing the numerical solution, allowing the use of larger time steps than those suitable for comparable implicit algorithms. Proofs for these claims are provided in the article as well as numerical examples that illustrate the performance of the method.

Safety assessment of underground vehicles passing over highly resilient straight tracks in the presence of a broken rail

In this paper, vehicle-track interaction for a new slab track design, conceived to reduce noise and vibration levels has been analyzed, assessing the derailment risk for trains running on curved track when encountering a broken rail. Two different types of rail fastening systems with different elasticities have been analysed and compared. Numerical methods were used in order to simulate the dynamic behaviour of the train-track interaction. Multibody system (MBS) modelling techniques were combined with techniques based on the finite element method (FEM). MBS modelling was used for modelling the vehicle and FEM for simulating the elastic track. The simulation model was validated by comparing simulated results to experimental data obtained in field testing. During the simulations various safety indices, characteristic of derailment risk, were analysed. The simulations realised at the maximum running velocity of 110 km/h showed a similar behaviour for several track types. When reducing the running speed, the safety indices worsened for both cases. Although the worst behaviour was observed for the track with a greater elasticity, in none of the simulations did a derailment occur when running over the broken rail.

Análisis de los parámetros que definen un modelo de daño aplicado al deterioro de la capacidad resistente de paredes arteriales

El comportamiento mecánico de las paredes arteriales constituye un ingrediente fundamental para entender enfermedades cardiovasculares como las disecciones aórticas o la fisuración de placas de ateroma. El fenómeno mecánico que subyace en estas enfermedades es el fallo constitutivo del material, que puede deberse a la degradación de las propiedades mecánicas del tejido, a la aplicación de una carga excesiva o la concentración de tensiones que tiene lugar en traumatizaciones de la íntima. Un modelo que busque reproducir este comportamiento biomecánico debe incorporar además la información histológica de las paredes arteriales, formadas en una primera aproximación por una matriz acuosa incompresible y dos familias de fibras dispuestas helicoidalmente. De entre los modelos mecánicos existentes cabe destacar los modelos de daño, que con un conjunto pequeño de parámetros son capaces de reproducir la degradación de la capacidad resistente tanto en la matriz como en las fibras. Esta simplicidad convierte a esta clase de modelos en una herramienta muy útil para estudiar este fenómeno. En este trabajo se presenta un estudio para un modelo de daño de los parámetros que lo definen, asociados a la imposición de la incompresibilidad de la matriz acuosa y a las evoluciones del daño en dicha matriz y en las dos familias de fibras. Se incluye una revisión de las técnicas existentes para imponer la incompresibilidad, un resumen bibliográfico de la caracterización experimental de los parámetros materiales y un análisis de su influencia en el comportamiento estructural de la aorta, analizada mediante ensayos de tracción

Dynamic Effects On Culverts for High Speed Trains

Culverts are very common in recent railway lines. Wild life corridors and drainage conducts often fall in this category of partially buried structures. Their dynamic behavior has received far less attention than other structures such as bridges but its large number makes that study an interesting challenge from the point of view of safety and savings. In this paper a complete study of a culvert, including on-site measurements as well as numerical modelling, will be presented. The structure belongs to the high speed railway line linking Segovia and Valladolid, in Spain. The line was opened to traffic in 2004. Its dimensions (3x3m) are the most frequent along the line. Other factors such as reduced overburden (0.6m) and an almost right angle with the track axis make it an interesting example to extract generalized conclusions. On site measurements have been performed in the structure recording the dynamic response at selected points of the structure during the passage of high speed trains at speeds ranging between 200 and 300km/h. The measurements by themselves provide a good insight into the main features of the dynamic behaviour of the structure. A 3D finite element model of the structure, representing its key features was also studied as it allows further understanding of the dynamic response to the train loads . In the paper the discrepancies between predicted and measured vibration levels will be analyzed and some advices on numerical modelling will be proposed