scholarly journals Polymorphism in elemental silicon: Probabilistic interpretation of the realizability of metastable structures

2017 ◽  
Vol 96 (18) ◽  
Author(s):  
Eric B. Jones ◽  
Vladan Stevanović
Keyword(s):  
Probabilistic Interpretation ◽  
Elemental Silicon ◽  
Metastable Structures

Evolution of Metastable Structures in Bimetallic Catalysts from Microscopy and Machine-Learning Molecular Dynamics

2020 ◽  
Author(s):  
Jin Soo Lim ◽  
Jonathan Vandermause ◽  
Matthijs A. van Spronsen ◽  
Albert Musaelian ◽  
Christopher R. O’Connor ◽  
...  
Keyword(s):  
Machine Learning ◽  
Molecular Dynamics ◽  
Large Scale ◽  
Materials Science ◽  
Complete Characterization ◽  
Layer By Layer ◽  
Surface Restructuring ◽  
Metastable Structures ◽  
Mechanistic Investigation ◽  
Underlying Mechanisms

Restructuring of interface plays a crucial role in materials science and heterogeneous catalysis. Bimetallic systems, in particular, often adopt very different composition and morphology at surfaces compared to the bulk. For the first time, we reveal a detailed atomistic picture of the long-timescale restructuring of Pd deposited on Ag, using microscopy, spectroscopy, and novel simulation methods. Encapsulation of Pd by Ag always precedes layer-by-layer dissolution of Pd, resulting in significant Ag migration out of the surface and extensive vacancy pits. These metastable structures are of vital catalytic importance, as Ag-encapsulated Pd remains much more accessible to reactants than bulk-dissolved Pd. The underlying mechanisms are uncovered by performing fast and large-scale machine-learning molecular dynamics, followed by our newly developed method for complete characterization of atomic surface restructuring events. Our approach is broadly applicable to other multimetallic systems of interest and enables the previously impractical mechanistic investigation of restructuring dynamics.

Using Bayesian network models to incorporate uncertainty in the economic analysis of pollution abatement measures under the water framework directive

2005 ◽  
Vol 5 (6) ◽  
pp. 95-104 ◽  
Author(s):  
D.N. Barton ◽  
T. Saloranta ◽  
T.H. Bakken ◽  
A. Lyche Solheim ◽  
J. Moe ◽  
...  
Keyword(s):  
Water Quality ◽  
At Risk ◽  
Economic Valuation ◽  
Pollution Abatement ◽  
Network Models ◽  
Cost Effective ◽  
Bayesian Belief Networks ◽  
Probabilistic Interpretation ◽  
Belief Networks ◽  
Benefit Cost Analysis

The evaluation of water bodies “at risk” of not achieving the Water Framework Directive's (WFD) goal of “good status” begs the question of how big a risk is acceptable before a programme of measures should be implemented. Documentation of expert judgement and statistical uncertainty in pollution budgets and water quality modelling, combined with Monte Carlo simulation and Bayesian belief networks, make it possible to give a probabilistic interpretation of “at risk”. Combined with information on abatement costs, a cost-effective ranking of measures based on expected costs and effect can be undertaken. Combined with economic valuation of water quality, the definition of “disproportionate cost” of abatement measures compared to benefits of achieving “good status” can also be given a probabilistic interpretation. Explicit modelling of uncertainty helps visualize where research and consulting efforts are most critical for reducing uncertainty. Based on data from the Morsa catchment in South-Eastern Norway, this paper discusses the relative merits of using Bayesian belief networks when integrating biophysical modelling results in the benefit-cost analysis of derogations and cost-effectiveness ranking of abatement measures under the WFD.

Asymptotic behaviour of sample weighted circuits representing recurrent Markov chains

1990 ◽  
Vol 27 (03) ◽  
pp. 545-556 ◽  
Author(s):  
S. Kalpazidou
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Probabilistic Interpretation ◽  
Stationary Markov Chain

The asymptotic behaviour of the sequence (𝒞 n (ω), wc,n (ω)/n), is studied where 𝒞 n (ω) is the class of all cycles c occurring along the trajectory ωof a recurrent strictly stationary Markov chain (ξ n ) until time n and wc,n (ω) is the number of occurrences of the cycle c until time n. The previous sequence of sample weighted classes converges almost surely to a class of directed weighted cycles (𝒞∞, ω c ) which represents uniquely the chain (ξ n ) as a circuit chain, and ω c is given a probabilistic interpretation.

scholarly journals Diverse magnetism in stable and metastable structures of CrTe

2021 ◽  
Vol 16 (6) ◽  
Author(s):  
Na Kang ◽  
Wenhui Wan ◽  
Yanfeng Ge ◽  
Yong Liu
Keyword(s):  
Metastable Structures

Partially observable semi-Markov reward processes

1993 ◽  
Vol 30 (3) ◽  
pp. 548-560 ◽  
Author(s):  
Yasushi Masuda
Keyword(s):  
Markov Process ◽  
Counting Process ◽  
Probabilistic Interpretation ◽  
Real Domain ◽  
Semi Markov Process ◽  
Reward Process ◽  
Markov Reward ◽  
Partially Observable ◽  
Joint Behavior

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.

Diffusion Mechanisms in Sige Alloys

1999 ◽  
Vol 568 ◽  
Author(s):  
Arthur F.W. Willoughby ◽  
Janet M. Bonar ◽  
Andrew D.N. Paine
Keyword(s):  
Diffusion Processes ◽  
Dopant Diffusion ◽  
Elemental Silicon ◽  
Self Diffusion ◽  
Si Substrates ◽  
Marker Layer ◽  
Diffusion Mechanisms ◽  
Silicon And Germanium ◽  
Charged Defects

ABSTRACTInterest in diffusion processes in SiGe alloys arises from their potential in HBT's, HFET's, and optoelectronics devices, where migration over distances as small as a few nanometres can be significant. Successful modelling of these processes requires a much improved understanding of the mechanisms of self- and dopant diffusion in the alloy, although recent progress has been made. It is the purpose of this review to set this in the context of diffusion processes in elemental silicon and germanium, and to identify how this can help to elucidate behaviour in the alloy. Firstly, self diffusion processes are reviewed, from general agreement that self-diffusion in germanium is dominated by neutral and acceptor vacancies, to the position in silicon which is still uncertain. Germanium diffusion in silicon, however, appears to be via both vacancy and interstitial processes, and in the bulk alloy there is evidence for a change in dominant mechanism at around 35 percent germanium. Next, a review of dopant diffusion begins with Sb, which appears to diffuse in germanium by a mechanism similar to self-diffusion, and in silicon via monovacancies also, from marker layer evidence. In SiGe, the effects of composition and strain in epitaxial layers on Si substrates are also consistent with diffusion via vacancies, but questions still remain on the role of charged defects. The use of Sb to monitor vacancy effects such as grown-in defects by low temperature MBE, are discussed. Lastly, progress in assessing the role of vacancies and interstitials in the diffusion of boron is reviewed, which is dominated by interstitials in silicon-rich alloys, but appears to change to domination by vacancies at around 40 percent germanium, although studies in pure germanium are greatly needed.

The effect of composition and cooling rate on the structure of rapidly solidified (Fe, Ni)3Al–C alloys

1989 ◽  
Vol 4 (1) ◽  
pp. 44-49 ◽  
Author(s):  
S. A. Myers ◽  
C. C. Koch
Keyword(s):  
Cooling Rate ◽  
Base Alloy ◽  
Weight Percent ◽  
Quench Rate ◽  
Transmission Electron ◽  
Metastable Structures ◽  
Metastable Structure ◽  
The Matrix ◽  
Rapidly Solidified ◽  
Kinetics Of

There is controversy in the literature regarding the existence of the metastable γ′ phase with an ordered Ll2 structure in rapidly solidified Fe–Ni–Al–C alloys. In this study, the quench rate–metastable structure dependence was examined in the Fe–20Ni–8Al–2C (weight percent) alloy. The effect of silicon on the kinetics of phase formation was studied by adding two weight percent silicon to a base alloy of Fe–20Ni–8Al–2C. Samples were rapidly solidified in an arc hammer apparatus and examined by transmission electron microscopy. In the Fe–20Ni–8Al–2C alloy, the nonequilibrium γ′ and γ phases were found in foils 65 to 100 μm thick. At higher quench rates, i.e., thinner samples, the matrix was observed to be disordered fcc γ with K-carbide precipitates. Samples containing silicon were found to have a matrix composed of γ′ and γ structures when the foils were thicker than 40 μm. At higher quench rates, the matrix was disordered fcc γ with K-carbide precipitates. The nonequilibrium γ′ and γ structures are present in samples with or without silicon, but are observed at higher cooling rates with the addition of silicon. This sensitivity to cooling rate and composition in resulting metastable structures may explain the differences reported in the literature for these rapidly solidified materials.

scholarly journals Befriending Askey–Wilson polynomials

2014 ◽  
Vol 17 (03) ◽  
pp. 1450015 ◽  
Author(s):  
Paweł J. Szabłowski
Keyword(s):  
Characteristic Function ◽  
Hermite Polynomials ◽  
Probabilistic Interpretation ◽  
Conjugate Pair ◽  
Linear Combinations ◽  
Expansion Formula ◽  
Wilson Polynomials ◽  
The Way

We recall five families of polynomials constituting a part of the so-called Askey–Wilson scheme. We do this to expose properties of the Askey–Wilson (AW) polynomials that constitute the last, most complicated element of this scheme. In doing so we express AW density as a product of the density that makes q-Hermite polynomials orthogonal times a product of four characteristic function of q-Hermite polynomials (2.9) just pawing the way to a generalization of AW integral. Our main results concentrate mostly on the complex parameters case forming conjugate pairs. We present new fascinating symmetries between the variables and some newly defined (by the appropriate conjugate pair) parameters. In particular in (3.12) we generalize substantially famous Poisson–Mehler expansion formula (3.16) in which q-Hermite polynomials are replaced by Al-Salam–Chihara polynomials. Further we express Askey–Wilson polynomials as linear combinations of Al-Salam–Chihara (ASC) polynomials. As a by-product we get useful identities involving ASC polynomials. Finally by certain re-scaling of variables and parameters we reach AW polynomials and AW densities that have clear probabilistic interpretation.

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