Interval Methods for Model Qualification: Methodology and Advanced Application

An actual model in simulation (e.g. in chemistry) or control (e.g. in robotics) is often too complex to use, and sometimes impossible to obtain. To handle a system in practice, a simplification of the real model is often necessary. This simplification goes through some hypotheses made on the system or the modeling approach. These hypotheses are rarely verified whereas they could lead to an inadmissible model, over approximated for its use. In this paper, we propose a method that qualifies the simplification validity for all models that can be expressed by real-valued variables involved in closed-form relations and depending on parameters. We based our approach on a verification of a quality threshold on the hypothesis relevance. This method, based on interval analysis, checks the acceptance of the hypothesis in a full range of the whole model space, and gives bounds on the quality threshold and on the model parameters. Our approach is experimentally validated on a robotic application.     

Sensitivity indices for multivariate outputs

We define and study a generalization of Sobol sensitivity indices for the case of a vector output.     

Optimal Cross Hedging of Insurance Derivatives

Abstract

We consider insurance derivatives depending on an external physical risk process, for example, a temperature in a low dimensional climate model. We assume that this process is correlated with a tradable financial asset. We derive optimal strategies for exponential utility from terminal wealth, determine the indifference prices of the derivatives, and interpret them in terms of diversification pressure. Moreover, we check the optimal investment strategies for standard admissibility criteria. Finally, we compare the static risk connected with an insurance derivative to the reduced risk due to a dynamic investment into the correlated asset. We show that dynamic hedging reduces the risk aversion in terms of entropic risk measures by a factor related to the correlation.     

Patterns in parabolic problems with nonlinear boundary conditions

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem.     

Weak and strong coupling theories for polarizable colloids and nanoparticles

A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nanoparticles. In the case of monovalent ions, we derive a weak-coupling theory that explicitly accounts for the ion-image interaction, leading to a modified Poisson-Boltzmann equation. For suspensions with multivalent counterions, a strong-coupling theory is used to calculate the density profile near the colloidal surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distribution in the far field. All the results are compared with the Monte?Carlo simulations, showing an excellent agreement between the theory and the simulations.     

Contact dynamics in a gently vibrated granular pile

We use multispeckle diffusive wave spectroscopy to probe the micron-scale dynamics of a water-saturated granular pile submitted to discrete gentle taps. The typical time scale between plastic events is found to increase dramatically with the number of applied taps. Furthermore, this microscopic dynamics weakly depends on the solid fraction of the sample. This process is largely analogous to the aging phenomenon observed in thermal glassy systems. We propose a heuristic model where this slowing-down mechanism is associated with a slow evolution of the distribution of the contact forces between particles. This model accounts for the main features of the observed dynamics.     

Simultaneous achievement of polarization attraction and Raman amplification in isotropic optical fibers

We present a theoretical analysis and experimental demonstration of the combined effects of polarization attraction and Raman amplification in isotropic optical fibers. The polarization attraction process is based on four-wave mixing interaction of counterpropagating pump and signal waves. We show that this technique can be used for the design of a highly efficient nonlinear system that permits the simultaneous processing of repolarization and amplification of light waves in dielectric media.     

Finite size effects on structure and magnetism in mass-selected CoPt nanoparticles

In this paper, the one-way absorption property in one-dimensional dielectric/metal photonic crystal structure with a dielectric defect layer is studied. The effects of incident angle and state of polarization on one-way absorption behaviour of the anti-resonant (AR) mode are investigated. The normally incident wave from left to right propagation is totally allowed to penetrate to the structure but right to left propagation totally reflected at the same wavelength. It is found that, with increasing of the incident angle, the AR mode shifts to the lower wavelengths and its intensity decreases. Simultaneously, another AR mode with reversed one-way property appears at higher wavelength. The one-way behaviour on absorption is observed at the both states of polarizations but is localized on different wavelengths. Those effects, are suggesting that the proposed structure can be used as a direction sense polarization splitter or reflector/antireflector device.     

Mass Spectrometry of Some Benzylidene Imidazolidinediones and Thiazolidinediones. II- chlorobenzyl imidazolidinedione and Fluoro or Chlorobenzyl Thiazolidinedione Compounds

In the present investigation, a study of the electron impact mass spectrometry data is reported for seven compounds of a series of some 3-(4-chlorobenzyl)-5-benzylidene-imidazolidine-2, 4-diones and 3-(4-fluoro or chlorobenzyl)-5-benzylidene-thiazolidine-2, 4-diones previously synthesized.