Dynamical Heterogeneity and Nonlinear Susceptibility in Short-Ranged Attractive Supercooled Liquids

Recent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here, we study in detail the behavior of non-linear, higher-order correlation functions that measure the growth of length scales associated with dynamical heterogeneity in both types of systems. We find that this measure is qualitatively different in the repulsive and attractive cases with regards to the wave vector dependence as well as the time dependence of the standard non-linear four-point dynamical susceptibility. We discuss the implications of these results for the general understanding of dynamical heterogeneity in glass-forming liquids.

Sustainable Catalysis : Rational Pd Loading on MIL-101Cr-NH2 for More Efficient and Recyclable Suzuki-Miyaura Reactions

Palladium nanoparticles have been immobilized into an amino-functionalized metal-organic framework (MOF), MIL-101Cr-NH2, to form Pd@MIL-101Cr-NH2. Four materials with different loadings of palladium have been prepared (denoted as 4-, 8-, 12-, and 16wt%Pd@MIL-101Cr-NH2). The effects of catalyst loading and the size and distribution of the Pd nanoparticles on the catalytic performance have been studied. The catalysts were characterized by using scanning electron microscopy (SEM), transmission electron microscopy (TEM), Fourier-transform infrared (FTIR) spectroscopy, powder X-ray diffraction (PXRD), N-2-sorption isotherms, elemental analysis, and thermogravimetric analysis (TGA). To better characterize the palladium nanoparticles and their distribution in MIL-101Cr-NH2, electron tomography was employed to reconstruct the 3D volume of 8wt%Pd@MIL-101Cr-NH2 particles. The pair distribution functions (PDFs) of the samples were extracted from total scattering experiments using high-energy X-rays (60keV). The catalytic activity of the four MOF materials with different loadings of palladium nanoparticles was studied in the Suzuki-Miyaura cross-coupling reaction. The best catalytic performance was obtained with the MOF that contained 8wt% palladium nanoparticles. The metallic palladium nanoparticles were homogeneously distributed, with an average size of 2.6nm. Excellent yields were obtained for a wide scope of substrates under remarkably mild conditions (water, aerobic conditions, room temperature, catalyst loading as low as 0.15mol%). The material can be recycled at least 10times without alteration of its catalytic properties.

Fluctuations in and out of equilibrium: Thermalization, quantum measurements and Coulomb disorder

This purely theoretical thesis covers aspects of two contemporary research fields: the non-equilibrium dynamics in quantum systems and the electronic properties of three-dimensional topological insulators. In the first part we investigate the non-equilibrium dynamics in closed quantum systems. Thanks to recent technologies, especially from the field of ultracold quantum gases, it is possible to realize such systems in the laboratory. The focus is on the influence of hydrodynamic slow modes on the thermalization process. Generic systems in equilibrium, either classical or quantum, in equilibrium are described by thermodynamics. This is characterized by an ensemble of maximal entropy, but constrained by macroscopically conserved quantities. We will show that these conservation laws slow down thermalization and the final equilibrium state can be approached only algebraically in time. When the conservation laws are violated thermalization takes place exponential in time. In a different study we calculate probability distributions of projective quantum measurements. Newly developed quantum microscopes provide the opportunity to realize new measurement protocols which go far beyond the conventional measurements of correlation functions. The second part of this thesis is dedicated to a new class of materials known as three-dimensional topological insulators. Also here new experimental techniques have made it possible to fabricate these materials to a high enough quality that their topological nature is revealed. However, their transport properties are not fully understood yet. Motivated by unusual experimental results in the optical conductivity we have investigated the formation and thermal destruction of spatially localized electron- and hole-doped regions. These are caused by charged impurities which are introduced into the material in order to make the bulk insulating. Our theoretical results are in agreement with the experiment and can explain the results semi-quantitatively. Furthermore, we study emergent lengthscales in the bulk as well as close to the conducting surface.

Multipartite entanglement in harmonic oscillators subjected to dissipative quantum dynamics

Una detallada descripción de la dinámica de bajas energías del entrelazamiento multipartito es proporcionada para sistemas armónicos en una gran variedad de escenarios disipativos. Sin hacer ninguna aproximación central, esta descripción yace principalmente sobre un conjunto razonable de hipótesis acerca del entorno e interacción entorno-sistema, ambas consistente con un análisis lineal de la dinámica disipativa. En la primera parte se deriva un criterio de inseparabilidad capaz de detectar el entrelazamiento k-partito de una extensa clase de estados gausianos y no-gausianos en sistemas de variable continua. Este criterio se emplea para monitorizar la dinámica transitiva del entrelazamiento, mostrando que los estados no-gausianos pueden ser tan robustos frente a los efectos disipativos como los gausianos. Especial atención se dedicada a la dinámica estacionaria del entrelazamiento entre tres osciladores interaccionando con el mismo entorno o diferentes entornos a distintas temperaturas. Este estudio contribuye a dilucidar el papel de las correlaciones cuánticas en el comportamiento de la corrientes energéticas.

Cross-correlation of excitation functions for different fragments and different scattering angles in Al-27(F-19, x)y reactions

Excitation functions have been measured for different projectile-like fragments produced in Al-27(F-19,x)y reactions at incident energies from 110.25 to 118.75 MeV in 250 keV steps. Strong cross section fluctuations of the excitation functions are observed. The cross- correlation coefficients of the excitation functions for different atomic number Z and for different scattering angle theta(cm) have been deduced. These coefficients are much larger than the statistical theoretical calculated ones. This indicates that there are strong correlations between different exit channels in the dissipative heavy ion Collision of Al-27(F-19,x)y.

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age. © 2004 Elsevier B.V. All rights reserved.

Avoidance of Long Mononucleotide Repeats in Codon Pair Usage

Protein is an essential component for life, and its synthesis is mediated by codons in any organisms on earth. While some codons encode the same amino acid, their usage is often highly biased. There are many factors that can cause the bias, but a potential effect of mononucleotide repeats, which are known to be highly mutable, on codon usage and codon pair preference is largely unknown. In this study we performed a genomic survey on the relationship between mononucleotide repeats and codon pair bias in 53 bacteria, 68 archaea, and 13 eukaryotes. By distinguishing the codon pair bias from the codon usage bias, four general patterns were revealed: strong avoidance of five or six mononucleotide repeats in codon pairs; lower observed/expected (o/e) ratio for codon pairs with C or G repeats (C/G pairs) than that with A or T repeats (A/T pairs); a negative correlation between genomic GC contents and the o/e ratios, particularly for C/G pairs; and avoidance of C/G pairs in highly conserved genes. These results support natural selection against long mononucleotide repeats, which could induce frameshift mutations in coding sequences. The fact that these patterns are found in all kingdoms of life suggests that this is a general phenomenon in living organisms. Thus, long mononucleotide repeats may play an important role in base composition and genetic stability of a gene and gene functions.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Multiscale analysis of protein functions and stochastic modelling of gene transcriptional regulatory networks

Genomic and proteomic analyses have attracted a great deal of interests in biological research in recent years. Many methods have been applied to discover useful information contained in the enormous databases of genomic sequences and amino acid sequences. The results of these investigations inspire further research in biological fields in return. These biological sequences, which may be considered as multiscale sequences, have some specific features which need further efforts to characterise using more refined methods. This project aims to study some of these biological challenges with multiscale analysis methods and stochastic modelling approach. The first part of the thesis aims to cluster some unknown proteins, and classify their families as well as their structural classes. A development in proteomic analysis is concerned with the determination of protein functions. The first step in this development is to classify proteins and predict their families. This motives us to study some unknown proteins from specific families, and to cluster them into families and structural classes. We select a large number of proteins from the same families or superfamilies, and link them to simulate some unknown large proteins from these families. We use multifractal analysis and the wavelet method to capture the characteristics of these linked proteins. The simulation results show that the method is valid for the classification of large proteins. The second part of the thesis aims to explore the relationship of proteins based on a layered comparison with their components. Many methods are based on homology of proteins because the resemblance at the protein sequence level normally indicates the similarity of functions and structures. However, some proteins may have similar functions with low sequential identity. We consider protein sequences at detail level to investigate the problem of comparison of proteins. The comparison is based on the empirical mode decomposition (EMD), and protein sequences are detected with the intrinsic mode functions. A measure of similarity is introduced with a new cross-correlation formula. The similarity results show that the EMD is useful for detection of functional relationships of proteins. The third part of the thesis aims to investigate the transcriptional regulatory network of yeast cell cycle via stochastic differential equations. As the investigation of genome-wide gene expressions has become a focus in genomic analysis, researchers have tried to understand the mechanisms of the yeast genome for many years. How cells control gene expressions still needs further investigation. We use a stochastic differential equation to model the expression profile of a target gene. We modify the model with a Gaussian membership function. For each target gene, a transcriptional rate is obtained, and the estimated transcriptional rate is also calculated with the information from five possible transcriptional regulators. Some regulators of these target genes are verified with the related references. With these results, we construct a transcriptional regulatory network for the genes from the yeast Saccharomyces cerevisiae. The construction of transcriptional regulatory network is useful for detecting more mechanisms of the yeast cell cycle.

Planar difference functions

In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop’s construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, x^3 is the only Alltop type function.