Phase behavior and morphology of multicomponent liquid mixtures

Multicomponent systems are ubiquitous in nature and industry. While the physics of few-component liquid mixtures (i.e., binary and ternary ones) is well-understood and routinely taught in undergraduate courses, the thermodynamic and kinetic properties of $N$-component mixtures with $N>3$ have remained relatively unexplored. An example of such a mixture is provided by the intracellular fluid, in which protein-rich droplets phase separate into distinct membraneless organelles. In this work, we investigate equilibrium phase behavior and morphology of $N$-component liquid mixtures within the Flory-Huggins theory of regular solutions. In order to determine the number of coexisting phases and their compositions, we developed a new algorithm for constructing complete phase diagrams, based on numerical convexification of the discretized free energy landscape. Together with a Cahn-Hilliard approach for kinetics, we employ this method to study mixtures with $N=4$ and $5$ components. We report on both the coarsening behavior of such systems, as well as the resulting morphologies in three spatial dimensions. We discuss how the number of coexisting phases and their compositions can be extracted with Principal Component Analysis (PCA) and K-Means clustering algorithms. Finally, we discuss how one can reverse engineer the interaction parameters and volume fractions of components in order to achieve a range of desired packing structures, such as nested `Russian dolls' and encapsulated Janus droplets.Comment: 16 pages, 11 figures + hyperlinks to 7 video

A Latent Variable Approach to Multivariate Quantitative Trait Loci

A novel approach based on latent variable modelling is presented for the analysis of multivariate quantitative and qualitative trait loci. The approach is general in the sense that it enables the joint analysis of many kinds of quantitative and qualitative traits (including count data and censored traits) in a single modelling framework. In the framework, the observations are modelled as functions of latent variables, which are then affected by quantitative trait loci. Separating the analysis in this way means that measurement errors in the phenotypic observations can be included easily in the model, providing robust inferences. The performance of the method is illustrated using two real multivariate datasets, from barley and Scots pine

Experimental determination of the Berry phase in a superconducting charge pump

We present the first measurements of the Berry phase in a superconducting Cooper pair pump. A fixed amount of Berry phase is accumulated to the quantum-mechanical ground state in each adiabatic pumping cycle, which is determined by measuring the charge passing through the device. The dynamic and geometric phases are identified and measured quantitatively from their different response when pumping in opposite directions. Our observations, in particular, the dependencies of the dynamic and geometric effects on the superconducting phase bias across the pump, agree with the basic theoretical model of coherent Cooper pair pumping.Comment: 4 pages, 3 figure

37 GHz observations of a large sample of BL Lacertae objects

We present 37 GHz data obtained at Metsahovi Radio Observatory in 2001 December - 2005 April for a large sample of BL Lacertae objects. We also report the mean variability indices and radio spectral indices in frequency intervals 5 - 37 GHz and 37 - 90 GHz. Approximately 34 % of the sample was detected at 37 GHz, 136 BL Lacertae objects in all. A large majority of the detected sources were low-energy BL Lacs (LBLs). The variability index values of the sample were diverse, the mean fractional variability of the sample being \Delta S_2 = 0.31. The spectral indices also varied widely, but the average radio spectrum of the sample sources is flat. Our observations show that many of the high-energy BL Lacs (HBL), which are usually considered radio-quiet, can at times be detected at 37 GHz.Comment: 12 pages, 5 figures + 5 tables. Published in Astronomical Journa

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure