Pathological element-based active device models and their application to symbolic analysis

This paper proposes new pathological element-based active device models which can be used in analysis tasks of linear(ized) analog circuits. Nullators and norators along with the voltage mirror-current mirror (VM-CM) pair (collectively known as pathological elements) are used to model the behavior of active devices in voltage-, current-, and mixed-mode, also considering parasitic elements. Since analog circuits are transformed to nullor-based equivalent circuits or VM-CM pairs or as a combination of both, standard nodal analysis can be used to formulate the admittance matrix. We present a formulation method in order to build the nodal admittance (NA) matrix of nullor-equivalent circuits, where the order of the matrix is given by the number of nodes minus the number of nullors. Since pathological elements are used to model the behavior of active devices, we introduce a more efficient formulation method in order to compute small-signal characteristics of pathological element-based equivalent circuits, where the order of the NA matrix is given by the number of nodes minus the number of pathological elements. Examples are discussed in order to illustrate the potential of the proposed pathological element-based active device models and the new formulation method in performing symbolic analysis of analog circuits. The improved formulation method is compared with traditional formulation methods, showing that the NA matrix is more compact and the generation of nonzero coefficients is reduced. As a consequence, the proposed formulation method is the most efficient one reported so far, since the CPU time and memory consumption is reduced when recursive determinant-expansion techniques are used to solve the NA matrix.Promep-Mexico UATLX-PTC-088Junta de Andalucía TIC-2532Ministerio de Educación y Ciencia TEC2007-67247, TEC2010-14825UC-MEXUS-CONACyT CN-09-31

Lie Markov models with purine/pyrimidine symmetry

Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to generalise it and allow for an inhomogeneous process, with time-dependent rates satisfying the same constraints. It is then useful to require that there exists a homogeneous average of this inhomogeneous process within the same model. This leads to the definition of "Lie Markov models", which are precisely the class of models where such an average exists. These models form Lie algebras and hence concepts from Lie group theory are central to their derivation. In this paper, we concentrate on applications to phylogenetics and nucleotide evolution, and derive the complete hierarchy of Lie Markov models that respect the grouping of nucleotides into purines and pyrimidines -- that is, models with purine/pyrimidine symmetry. We also discuss how to handle the subtleties of applying Lie group methods, most naturally defined over the complex field, to the stochastic case of a Markov process, where parameter values are restricted to be real and positive. In particular, we explore the geometric embedding of the cone of stochastic rate matrices within the ambient space of the associated complex Lie algebra. The whole list of Lie Markov models with purine/pyrimidine symmetry is available at http://www.pagines.ma1.upc.edu/~jfernandez/LMNR.pdf.Comment: 32 page

Transport dynamics of self-consistent, near-marginal drift-wave turbulence. I. Investigation of the ability of external flows to tune the non-diffusive dynamics

The reduction of turbulent transport across sheared flow regions has been known for a long time in magnetically confined toroidal plasmas. However, details of the dynamics are still unclear, in particular, in what refers to the changes caused by the flow on the nature of radial transport itself. In Paper II, we have shown in a simplified model of drift wave turbulence that, when the background profile is allowed to evolve self-consistently with fluctuations, a variety of transport regimes ranging from superdiffusive to subdiffusive open up depending on the properties of the underlying turbulence [D. Ogata et al., Phys. Plasmas 24, 052307 (2017)]. In this paper, we show that externally applied sheared flows can, under the proper conditions, cause the transport dynamics to be diffusive or subdiffusive.This work was supported by U.S. DOE Contract No. DE-FG02-04ER54741 with the University of Alaska Fairbanks and in part by a grant of HPC resources from the Arctic Region Supercomputing Center at the University of Alaska Fairbanks. This research was also sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2015-68265

Effects of the environment on galaxies in the Catalogue of Isolated Galaxies: physical satellites and large scale structure

We aim to identify and quantify the effects of the satellite distribution around a sample of galaxies in the Catalogue of Isolated Galaxies (CIG), as well as the effects of the Large Scale Structure (LSS) using the SDSS-DR9. To recover the physically bound galaxies we focus on the satellites which are within the escape speed of each CIG galaxy. We also propose a more conservative method using the stacked Gaussian distribution of the velocity difference of the neighbours. The tidal strengths affecting the primary galaxy are estimated to quantify the effects of the local and LSS environments. We also define the projected number density parameter at the 5$^{\rm th}$ nearest neighbour to characterise the LSS around the CIG galaxies. Out of the 386 CIG galaxies considered in this study, at least 340 (88\% of the sample) have no physically linked satellite. Out of the 386 CIG galaxies, 327 (85\% of the sample) have no physical companion within a projected distance of 0.3 Mpc. The CIG galaxies are distributed following the LSS of the local Universe, although presenting a large heterogeneity in their degree of connection with it. A clear segregation appears between early-type CIG galaxies with companions and isolated late-type CIG galaxies. Isolated galaxies are in general bluer, with likely younger stellar populations and rather high star formation with respect to older, redder CIG galaxies with companions. Reciprocally, the satellites are redder and with an older stellar populations around massive early-type CIG galaxies, while they have a younger stellar content around massive late-type CIG galaxies. This suggests that the CIG is composed of a heterogeneous population of galaxies, sampling from old to more recent, dynamical systems of galaxies.Comment: 19 pages, 10 figures, 1 table, accepted for publication in Astronomy & Astrophysic

Investigation of the interaction between competing types of nondiffusive transport in drift wave turbulence

Radial transport in turbulence dominated tokamak plasmas has been observed to deviate from classical diffusion in certain regimes relevant for magnetic confinement fusion. These situations at least include near-marginal turbulence, where radial transport becomes superdiffusive and mediated by elongated radial structures (or avalanches) and transport across radially sheared poloidal flows, where radial subdiffusion often ensues. In this paper, the interaction between very different physical ingredients responsible for these two types of nondiffusive dynamics (namely, turbulent profile relaxation close to a local threshold and the interaction with radially sheared zonal flows) is studied in detail in the context of a simple two-dimensional electrostatic plasma fluid turbulence model based on the dissipative trapped electron mode. It is shown that, depending on the relative relevance of each of these ingredients, which can be tuned in various ways, a variety of nondiffusive radial transport behaviors can be found in the system. The results also illustrate the fact that the classical diffusion paradigm is often insufficient to describe turbulent transport in systems with self-generated flows and turbulent profile relaxations. Published by AIP Publishing.This work was supported by U.S. DOE under Contract No. DE-FG02-04ER54741 with the University of Alaska Fairbanks and in part by a grant of HPC resources from the Arctic Region Supercomputing Center at the University of Alaska Fairbanks. This research was also sponsored in part by DGICT (Direccion General de Investigaciones Cientıficas y Tecnologicas) of Spain under Project No. ENE2015-68265

Conditional probability density functions of concentrations for mixing-controlled reactive transport in heterogeneous aquifers

This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes (and associated reaction rates) evolving in a randomly heterogeneous aquifer. Most existing approaches to solute transport in heterogeneous media focus on providing expressions for space–time moments of concentrations. In general, only low order moments (unconditional or conditional mean and covariance) are computed. In some cases, this allows for obtaining a confidence interval associated with predictions of local concentrations. Common applications, such as risk assessment and vulnerability practices, require the assessment of extreme (low or high) concentration values. We start from the well-known approach of deconstructing the reactive transport problem into the analysis of a conservative transport process followed by speciation to (a) provide a partial differential equation (PDE) for the (conditional) pdf of conservative aqueous species, and (b) derive expressions for the pdf of reactive species and the associated reaction rate. When transport at the local scale is described by an Advection Dispersion Equation (ADE), the equation satisfied by the pdf of conservative species is non-local in space and time. It is similar to an ADE and includes an additional source term. The latter involves the contribution of dilution effects that counteract dispersive fluxes. In general, the PDE we provide must be solved numerically, in a Monte Carlo framework. In some cases, an approximation can be obtained through suitable localization of the governing equation. We illustrate the methodology to depict key features of transport in randomly stratified media in the absence of transverse dispersion effects. In this case, all the pdfs can be explicitly obtained, and their evolution with space and time is discussed

A new simple proof for Lum-Chua's conjecture

The already proved Lum-Chua's conjecture says that a continuous planar piecewise linear differential system with two zones separated by a straight line has at most one limit cycle. In this paper, we provide a new proof by using a novel characterization for Poincar\'e half-maps in planar linear systems. This proof is very short and straightforward, because this characterization avoids the inherent flaws of the usual methods to study piecewise linear systems (the appearance of large case-by-case analysis due to the unnecessary discrimination between the different spectra of the involved matrices, to deal with transcendental equations forced by the implicit occurrence of flight time, ...). In addition, the application of the characterization allow us to prove that if a limit cycle exists, then it is hyperbolic and its stability is determined by a simple relationship between the parameters. To the best of our knowledge, the hyperbolicity of the limit cycle and this simple expression for its stability have not been pointed out before

A succinct characterization of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness

We close the problem of the existence of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness. In fact, a characterization for the existence of such objects is provided by means of a few basic operations on the parameters

Uniqueness and stability of limit cycles in planar piecewise linear differential systems without sliding region

In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential systems whose flow transversally crosses the switching line except for at most one point. In the research literature, many papers deal with the problem of determining the maximum number of limit cycles that these differential systems can have. This problem has been usually approached via large case-by-case analyses which distinguish the many different possibilities for the spectra of the matrices of the differential systems. Here, by using a novel integral characterization of Poincar\'e half-maps, we prove, without unnecessary distinctions of matrix spectra, that the optimal uniform upper bound for the number of limit cycles of these differential systems is one. In addition, it is proven that this limit cycle, if it exists, is hyperbolic and its stability is determined by a simple condition in terms of the parameters of the system. As a byproduct of our analysis, a condition for the existence of the limit cycle is also derived.Comment: To appear in Communications in Nonlinear Science and Numerical Simulatio

Transport dynamics of self-consistent, near-marginal drift-wave turbulence. II. Characterization of transport by means of passive scalars

From theoretical and modeling points of view, following Lagrangian trajectories is the most straightforward way to characterize the transport dynamics. In real plasmas, following Lagrangian trajectories is difficult or impossible. Using a blob of passive scalar (a tracer blob) allows a quasi-Lagrangian view of the dynamics. Using a simple two-dimensional electrostatic plasma turbulence model, this work demonstrates that the evolution of the tracers and the passive scalar field is equivalent between these two fluid transport viewpoints. When both the tracers and the passive scalar evolve in tandem and closely resemble stable distributions, namely, Gaussian distributions, the underlying turbulent transport character can be recovered from the temporal scaling of the second moments of both. This local transport approach corroborates the use of passive scalar as a turbulent transport measurement. The correspondence between the local transport character and the underlying transport is quantified for different transport regimes ranging from subdiffusive to superdiffusive. This correspondence is limited to the initial time periods of the spread of both the tracers and the passive scalar in the given transport regimes.This work was supported by U.S. DOE Contract No. DE-FG02-04ER54741 with the University of Alaska Fairbanks and in part by a grant of HPC resources from the Arctic Region Supercomputing Center at the University of Alaska Fairbanks. This research was also sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2015-68265