Uncertainty quantification in a chemical system using error estimate-based mesh adaption

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.     

On Suboptimal LCS-alignments for Independent Bernoulli Sequences with Asymmetric Distributions

Let X = X ₁ ... X _n and Y = Y ₁ ... Y _n be two binary sequences with length n. A common subsequence of X and Y is any subsequence of X that at the same time is a subsequence of Y; The common subsequence with maximal length is called the longest common subsequence (LCS) of X and Y. LCS is a common tool for measuring the closeness of X and Y. In this note, we consider the case when X and Y are both i.i.d. Bernoulli sequences with the parameters ϵ and 1 − ϵ, respectively. Hence, typically the sequences consist of large and short blocks of different colors. This gives an idea to the so-called block-by-block alignment, where the short blocks in one sequence are matched to the long blocks of the same color in another sequence. Such and alignment is not necessarily a LCS, but it is computationally easy to obtain and, therefore, of practical interest. We investigate the asymptotical properties of several block-by-block type of alignments. The paper ends with the simulation study, where the of block-by-block type of alignments are compared with the LCS.     

Non-linear dielectric spectra of ferroelectric liquid crystals

Abstract

The non-linear dielectric relaxation spectroscopy has been recently developed and applied to soft materials such as polymers. We have applied this new method to the S*_C phases of some ferroelectric liquid crystals. Under a weak AC electric field, the original and third order harmonic frequency components of electric displacement are proportional to the first and third powers of the applied electric field, respectively. The linear spectrum obtained from the original frequency component shows the relaxation of Debye type and the third order non-linear spectrum shows the relaxation with an extended form of Debye type to the non-linear case. The third order non-linear dielectric increment is found to be negative, which implies that the dielectric non-linearity of the liquid crystal in the S*_C phase is due to the saturation of molecular dipole moments induced by the applied electric field. The temperature dependence of the linear and third order non-linear spectra in the S*_C phase are also studied. Both spectra do not change their forms much through the whole temperature range of the S*_C phase. In the vicinity of the S_A–S*_C transition temperature, the critical behaviour is more remarkable in the third order spectrum than in the linear one.     

Radiation-induced degradation of aqueous 2–chlorophenol assisted by zeolites

Journal of Radioanalytical and Nuclear Chemistry - This study aims to demonstrate that zeolite has the potential to increase the efficiency of radiolysis treatment of aqueous organic pollutants by...     

On the structure of the Bochner–Martinelli residue currents

The paper presents a survey of the main results of I.M. Vinogradov.