Stochastic Behaviour of European Stock Indices

in Flavell, Richard (Ed.) Modelling Reality and Personal Modelling (1993)

Stochastic Dimension Reduction Techniques for Uncertainty Quantification of Multiphysics Systems

Conference (2012, April 02)

Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be ... [more ▼]

Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be captured throughout the whole system, the so-called curse of dimensionality. We present techniques for mitigating the curse of dimensionality in network-coupled multiphysics systems by using the structure of the network to transform uncertainty representations as they pass between components. Examples from the simulation of nuclear power plants will be discussed. [less ▲]

Stochastic excitation of non-radial modes. I. High-angular-degree p modes

in Astronomy and Astrophysics (2008), 478

Context: Turbulent motions in stellar convection zones generate acoustic energy, part of which is then supplied to normal modes of the star. Their amplitudes result from a balance between the efficiencies ... [more ▼]

Context: Turbulent motions in stellar convection zones generate acoustic energy, part of which is then supplied to normal modes of the star. Their amplitudes result from a balance between the efficiencies of excitation and damping processes in the convection zones. Aims: We develop a formalism that provides the excitation rates of non-radial global modes excited by turbulent convection. As a first application, we estimated the impact of non-radial effects on excitation rates and amplitudes of the high-angular-degree modes that are observed on the Sun. Methods: A model of stochastic excitation by turbulent convection was developed to compute the excitation rates and then successfully applied to solar radial modes. We generalise this approach to the case of non-radial global modes. This enables us to estimate the energy supplied to high-(l) acoustic modes. Qualitative arguments, as well as numerical calculations, are used to illustrate the results. Results: We find that non-radial effects for p modes are non-negligible: - For high-n modes (i.e. typically n > 3) and for high values of l, the power supplied to the oscillations depends on the mode inertia. - For low-n modes, independent of the value of l, the excitation is dominated by the non-radial components of the Reynolds stress term. Conclusions: Our numerical investigation of high-l p modes shows that the validity of the present formalism is limited to l < 500 due to the spatial separation of scale assumption. Thus, a model for very high-l p-mode excitation rates calls for further theoretical developments; however, the formalism is valid for solar g modes, which will be investigated in a paper in preparation. [less ▲]

Stochastic Fertility, Moral Hazard, and the Design of Pay-As-You-Go Pension Plans

in CESifo Economic Studies (2011), 57(2), 332348

This article models a two-period overlapping generations economy in the steady state where the realization of the quantity/quality number of children depends on an initial investment in children and on a ... [more ▼]

This article models a two-period overlapping generations economy in the steady state where the realization of the quantity/quality number of children depends on an initial investment in children and on a random shock. It shows that the implementation of the first-best allocation, in which the effort level is publicly observable, requires a subsidy on the investment in children. There should also be full insurance with respect to second-period consumption and pensions must be invariant to the number of children. On the other hand, when investment is unobservable and one cannot subsidize it, the full insurance property goes away. In this case, pensions must be linked positively to the number of children. [less ▲]

Stochastic generation of meteorological variables and effects on global models of water and carbon cycles in vegetation and soils

in Journal of Hydrology (1998), 213(1-4), 318-334

Global models of water and carbon cycles in continental vegetation and soils are usually forced with monthly mean climatic data-sets and thus neglect day to day variations of the weather. This treatment ... [more ▼]

Global models of water and carbon cycles in continental vegetation and soils are usually forced with monthly mean climatic data-sets and thus neglect day to day variations of the weather. This treatment may be justified for empirical models based on parametrizations validated at a monthly timescale. Mechanistic models handling hydrological and biological processes at much shorter timescales might, however, be largely affected by such an approximation, since the various processes described are highly nonlinear. A random generator of daily precipitations and temperatures applicable at the global scale has thus been developed from worldwide meteorological data covering 6 years of observations. The probability of a wet day is correlated to the weather encountered the previous day. The amount of precipitation, the daily mean temperature and the diurnal. range of temperature are described from the statistical point of view by the cumulative distribution functions (CDF) of three random variables. The CDF's a relative to temperatures are different for rainy and dry days. This stochastically generated weather field is used as input to IBM (Improved Bucket Model) and CARAIB (CARbon Assimilation In the Biosphere), two global models of respectively soil hydrology and vegetation productivity. Large differences in both the geographical distribution and the global value of soil water, vegetation productivity and carbon stocks are obtained between the model runs using monthly uniform weather on one side and randomly generated weather on the other. The main contribution to this difference at the global scale arises from the precipitation generation occurring as a result of high degree of nonlinearity of the interception scheme used in IBM. (C) 1998 Elsevier Science B.V. All rights reserved. [less ▲]

Stochastic gravito-inertial modes discovered by CoRoT in the hot Be star HD 51452

in Astronomy and Astrophysics (2012), 546

Context. Be stars are rapidly rotating stars with a circumstellar decretion disk. They usually undergo pressure and/or gravity pulsation modes excited by the κ-mechanism, i.e. an effect of the opacity of ... [more ▼]

Context. Be stars are rapidly rotating stars with a circumstellar decretion disk. They usually undergo pressure and/or gravity pulsation modes excited by the κ-mechanism, i.e. an effect of the opacity of iron-peak elements in the envelope of the star. In the Milky Way, p-modes are observed in stars that are hotter than or equal to the B3 spectral type, while g-modes are observed at the B2 spectral type and cooler. <BR /> Aims: We observed a B0IVe star, HD 51452, with the high-precision, high-cadence photometric CoRoT satellite and high-resolution, ground-based HARPS and SOPHIE spectrographs to study its pulsations in great detail. We also used the lower resolution spectra available in the BeSS database. <BR /> Methods: We analyzed the CoRoT and spectroscopic data with several methods: Clean-NG, FreqFind, and a sliding window method. We also analyzed spectral quantities, such as the violet over red (V/R) emission variations, to obtain information about the variation in the circumstellar environment. We calculated a stellar structure model with the ESTER code to test the various interpretation of the results. <BR /> Results: We detect 189 frequencies of variations in the CoRoT light curve in the range between 0 and 4.5 c d[SUP]-1[/SUP]. The main frequencies are also recovered in the spectroscopic data. In particular we find that HD 51452 undergoes gravito-inertial modes that are not in the domain of those excited by the κ-mechanism. We propose that these are stochastic modes excited in the convective zones and that at least some of them are a multiplet of r-modes (i.e. subinertial modes mainly driven by the Coriolis acceleration). Stochastically excited gravito-inertial modes had never been observed in any star, and theory predicted that their very low amplitudes would be undetectable even with CoRoT. We suggest that the amplitudes are enhanced in HD 51452 because of the very rapid stellar rotation. In addition, we find that the amplitude variations of these modes are related to the occurrence of minor outbursts. <BR /> Conclusions: Thanks to CoRoT data, we have detected a new kind of pulsations in HD 51452, which are stochastically excited gravito-inertial modes, probably due to its very rapid rotation. These modes are probably also present in other rapidly rotating hot Be stars. The CoRoT space mission, launched on December 27, 2006, has been developed and is operated by CNES, with the contribution of Austria, Belgium, Brazil, ESA (RSSD, and Science Programs), Germany, and Spain. This work uses observations partly made with the HARPS instrument at the 3.6-m ESO telescope (La Silla, Chile) in the framework of the LP182.D-0356, as well as data obtained with Sophie at OHP and from the BeSS database.Table 3 is available in electronic form at <A href="http://www.aanda.org">http://www.aanda.org</A> [less ▲]

Stochastic modeling in mechanics: course material

Learning material (2013)

Stochastic modelling of micro-organisms displacements in a stirred-tank bioreactor

Poster (2010)

Stochastic models to study the impact of mixing on a fed-batch culture of Saccharomyces cerevisiae.

in Biotechnology Progress (2006), 22(1), 259-69

The mechanisms of interaction between microorganisms and their environment in a stirred bioreactor can be modeled by a stochastic approach. The procedure comprises two submodels: a classical stochastic ... [more ▼]

The mechanisms of interaction between microorganisms and their environment in a stirred bioreactor can be modeled by a stochastic approach. The procedure comprises two submodels: a classical stochastic model for the microbial cell circulation and a Markov chain model for the concentration gradient calculus. The advantage lies in the fact that the core of each submodel, i.e., the transition matrix (which contains the probabilities to shift from a perfectly mixed compartment to another in the bioreactor representation), is identical for the two cases. That means that both the particle circulation and fluid mixing process can be analyzed by use of the same modeling basis. This assumption has been validated by performing inert tracer (NaCl) and stained yeast cells dispersion experiments that have shown good agreement with simulation results. The stochastic model has been used to define a characteristic concentration profile experienced by the microorganisms during a fermentation test performed in a scale-down reactor. The concentration profiles obtained in this way can explain the scale-down effect in the case of a Saccharomyces cerevisiae fed-batch process. The simulation results are analyzed in order to give some explanations about the effect of the substrate fluctuation dynamics on S. cerevisiae. [less ▲]

Stochastic Uncertainty Quantification of Eddy Currents in the Human Body by Polynomial Chaos Decomposition

Scientific conference (2011, July 07)