Urysohn Forest for Aleatoric Uncertainty Quantification

This paper focuses on building models of stochastic systems with aleatoric uncertainty. The main novelty is an algorithm of boosted ensemble training of multiple models for obtaining a probability distribution of an individual output as a function of the system input. The second novel contribution is a new regression model to be used in the ensemble. The model is a multi-layered tree of hierarchically-connected discrete Urysohn operators (or generalised additive models, which are mathematically equivalent to the discrete Urysohn operators in this case). Since multiple models (trees) are trained in the ensemble, the authors refer them as an Urysohn forest. The source code is freely available online

Localisation of stress-affected chemical reactions in solids described by coupled mechanics-diffusion-reaction models

Chemical reactions in solids can induce chemical expansion of the solid that causes the emergence of the mechanical stresses, which, in turn, can affect the rate of the reaction. A typical example of this is the reaction of Si lithiation, where the stresses can inhibit the reaction up to the reaction locking. The reactions in solids can take place within some volume (bulk reactions) or localise at a chemical reaction front (localised reactions). These cases are typically described by different thermo-chemo-mechanical theories that contain the source/sink terms either in the bulk or at the propagating infinitely-thin interface, respectively. However, there are reactions that can reveal both regimes; hence, there is a need to link the theories describing the bulk and the localised (sharp-interface) reactions. The present paper bridges this gap and shows that when a certain structure of the Helmholtz free energy density is adopted (based on the ideas from the phase-field methods), it is possible to obtain (in the limit) the same driving force for the chemical reaction (hence, the same reaction kinetics) as derived within the theory of the sharp-interface chemical reactions based on the chemical affinity tensor

A two-scale framework for coupled mechanics-diffusion-reaction processes

There is a wide range of industrially-relevant problems where mechanical stresses directly affect kinetics of chemical reactions. For example, this includes formation of oxide layers on parts of micro-electro-mechanical systems (MEMS) and lithiation of Si in Li-ion batteries. Detailed understanding of these processes requires thermodynamically-consistent theories describing the coupled thermo-chemo-mechanical behaviour of those systems. Furthermore, as the majority of materials used in those systems have complex microstructures, multiscale modelling techniques are required for efficient simulation of their behaviour. Hence, the purpose of the present paper is two-fold: (1) to derive a thermodynamically-consistent thermo-chemo-mechanical theory; and (2) to propose a two-scale modelling approach based on the concept of computational homogenisation for the considered theory. The theory and the two-scale computational approach are implemented and tested using a number of computational examples, including the case of the reaction locking due to mechanical stresses

Stability of chemical reaction fronts in solids:Analytical and numerical approaches

Localized chemical reactions in deformable solids are considered. A chemical transformation is accompanied by the transformation strain and emerging mechanical stresses, which affect the kinetics of the chemical reaction front to the reaction arrest. A chemo-mechanical coupling via the chemical affinity tensor is used, in which the stresses affect the reaction rate. The emphasis is made on the stability of the propagating reaction front in the vicinity of the blocked state. There are two major novel contributions. First, it is shown that for a planar reaction front, the diffusion of the gaseous-type reactant does not influence the stability of the reaction front – the stability is governed only by the mechanical properties of solid reactants and stresses induced by the transformation strain and the external loading, which corresponds to the mathematically analogous phase transition problem. Second, the comparison of two computational approaches to model the reaction front propagation is performed – the standard finite-element method with a remeshing technique to resolve the moving interface is compared to the cut-finite-element-based approach, which allows the interface to cut through the elements and to move independently of the finite-element mesh. For stability problems considered in the present paper, the previously-developed implementation of the cut-element approach has been extended with the additional post-processing procedure that obtains more accurate stresses and strains, relying on the fact that the structured grid is used in the implementation. The approaches are compared using a range of chemo-mechanical problems with stable and unstable reaction fronts.</p

Enhanced effects on extracting \gamma from untagged B^0 and B_s decays

The weak phase \gamma can be determined using untagged B^0\to DK_S or B_s\to D\phi, D\eta^{(')} decays. In the past, the small lifetime difference y\equiv \Delta\Gamma/(2\Gamma) has been neglected in B^0, while the CP violating parameter \epsilon\equiv 1-|q/p|^2 has been neglected in both B^0-\bar B^0 and B_s-\bar B_s mixing. We estimate the effect of neglecting y and \epsilon. We find that in D decays to flavor states this introduces a systematic error, which is enhanced by a large ratio of Cabibbo-allowed to doubly Cabibbo-suppressed D decay amplitudes.Comment: one reference added, to be submitted for publication in Physics Letters

CP violation in B meson decays

Recent CP asymmetry measurements in tree-dominated processes, $B^0\to \pi^+\pi^-, \rho^+\rho^-, \rho^{\pm}\pi^{\mp}, B^+\to DK^+$, and in penguin-dominated decays, $B \to \pi^0 K_S, \eta' K_S, \phi K_S$, are interpreted in the framework of the Kobayashi-Maskawa (KM) mechanism of CP violation. The KM phase emerges as the dominant source of CP violation in tree-dominated decays, which are beginning to constrain the unitarity triangle beyond other constraints. Improving precision of CP asymmetry measurements in penguin-dominated decays may indicate the need for new physics.Comment: Talk presented at the Sixth International Conference on Hyperons, Charm and Beauty Hadrons, IIT, Chicago, June 27--July 3 200

Examination of Flavor Symmetry in B,Bs→KπB, B_s \to K \pi Decays

We study a relation between the weak phase $\gamma$ and the rates and CP asymmetries of several $K \pi$ decays of $B^+$, $B^0$, and $B_s$, emphasizing the impact of the latter measurements. Current data indicate large SU(3) breaking in the strong phases or failure of factorization (including its application to penguin amplitudes) in $K \pi$ modes of $B^0$ and $B_s$. SU(3) and factorization only remain approximately valid if the branching ratio for $B_s \to K^- \pi^+$ exceeds its current value of $(5.27 \pm 1.17) \times 10^{-6}$ by at least 42%, or if a parameter $\xi$ describing ratios of form factors and decay constants is shifted from its nominal value by more than twice its estimated error.Comment: 10 pages, 4 figures. Misprints in some exponents corrected; one experimental value and some discussion update