Nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices

We prove the moments of the directed polymer partition function GZ, using an exact position space renormalization group scheme on a hierarchical lattice. After sufficient iteration the characteristic functionf(n)=lnGZⁿ of the probability (Z) converges to a stable limitf ^*(n). For smalln the limiting behavior is independent of the initial distribution, while for largen,f ^*(n) is completely determined by it and is thus nonuniversal. There is a smooth crossover between the two regimes for small effective dimensions, and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution. For large effective dimensions there is a sharp transition between the two regimes, and analytical continuation from integer moments ton0 is not possible. Replica arguments can account for most features of the observed results.     

Borel summability of the perturbation series in a hierarchical λ(▽φ)4 model

We prove Borel summability of the perturbation series for the dielectric constant and the free energy density for the hierarchical ()⁴ lattice model. Our methods are based on nonperturbative renormalization group analysis of the model.On leave from the Department of Mathematical Methods of Physics, Warsaw University, Poland.Supported in part by the Center for Interdisciplinary Research, Bielefeld University, Germany.     

Multivariate comparison of concentration profiles in materials analysis

Hierarchical cluster analysis (HCA) and principal components analysis (PCA) were applied to find groups between similar depth-profiles in thin-layers investigated by Rutherford backscattering spectrometry (RBS).HCA yields in one run an objective hierarchy of similarity for several profiles. Among the similarity coefficients examined the linear measure, the Euclidean distance and the exponential measure respond with different sensitivity to overall shifts in direction of the concentration axis, whereas the correlation measure relates to parallelism of the profiles.For agglomerative HCA with Euclidean distance, a lowest significant linkage level has been defined by use of Fisher'sF-test. For divisive HCA based also on Euclidean distance, the maximum of a separating function marks the most separating cluster step. The outcomes of both proposals agree for the data set investigated.PCA is useful for verifying the results of HCA and yields additional information about the data structure. In the actual example quite different positions of features (concentrations at definite depths) in the space of the two first principal components hint at peculiarities during the metallurgical coating process.     

Copper‐Bismuth Bimetallic Microspheres for Selective Electrocatalytic Reduction of CO2 to Formate

Electrocatalytic carbon dioxide reduction holds great promise for reducing the atmospheric CO₂ level and alleviating the energy crisis. High‐performance electrocatalysts are often required in order to lower the high overpotential and expedite the sluggish reaction kinetics of CO₂ electroreduction. Copper is a promising candidate metal. However, it usually suffers from the issues of poor stability and low product selectivity. In this work, bimetallic Cu‐Bi is obtained by reducing the microspherical copper bismuthate (CuBi₂O₄) for selectively catalyzing the CO₂ reduction to formate (HCOO^–). The bimetallic Cu‐Bi electrocatalyst exhibits high activity and selectivity with the Faradic efficiency over 90% in a wide potential window. A maximum Faradaic efficiency of ~95% is obtained at –0.93 V versus reversible hydrogen electrode. Furthermore, the catalyst shows high stability over 6 h with Faradaic efficiency of ~95%. This study provides an important clue in designing new functional materials for CO₂ electroreduction with high activity and selectivity.     

A study for quality evaluation of Taxilli Herba from different hosts based on fingerprint-activity relationship modeling and multivariate statistical analysis

In this study, a fingerprint-activity relationship modeling between chemical fingerprints and antirheumatic activity was established, and multivariate statistical analysis was used to evaluate the quality of Taxilli Herba (TH) from different hosts. Characteristic fingerprints of 20 batches of TH samples were generated by high-performance liquid chromatography coupled with triple quadrupole-time of flight tandem mass spectrometry (HPLC-Triple TOF-MS/MS), and the similarity analysis was calculated based on thirteen common characteristic peaks by hierarchical clustering analysis (HCA). Subsequently, nine efficacy markers were discovered by combining fingerprints and antirheumatic activity through grey correlation analysis (GCA) and bivariate correlation analysis (BCA). Meanwhile, the content of 5 constituents in 9 markers was determined by high-performance liquid chromatography coupled with triple quadrupole-linear ion trap tandem mass spectrometry (HPLC-QTRAP-MS/MS). The comprehensive quality of TH was assessed using multivariate statistical analysis, including principal components analysis (PCA) and technique for order preference by similarity to ideal solution (TOPSIS). The results showed that a high dose of TH extract could markedly ameliorate arthritis damage compared to other doses, with flavonoids playing an important role in the antirheumatic activity. The comprehensive quality of samples from Morus alba L. (SS) was superior to those from Liquidambar formosana Hance (FXS). The present study will demonstrate the markers associated with efficacy, and provide an applicable strategy for more comprehensive quality control and evaluation of TH.     

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.