Limitations of model-fitting methods for kinetic analysis: Polystyrene thermal degradation

In this paper, some clarifications regarding the use of model-fitting methods of kinetic analysis are provided in response to the lack of plot linearity and dispersion in the activation energy values for the thermal degradation of polystyrene found in the literature and some results proposing an nth order model as the most suitable one. In the present work, two model-fitting methods based on the differential and integral forms of the general kinetic equation are evaluated using both simulated and experimental data, showing that the differential method is recommended due to its higher discrimination power. Moreover, the intrinsic limitations of model-fitting methods are highlighted: the use of a limited set of kinetic models to fit experimental data and the ideal nature of such models. Finally, it is concluded that a chain scission model is more appropriate than first order.Junta de Andalucía TEP‐03002Ministerio de Economía y Competitividad CTQ2011‐2762

Limitations of model-fitting methods for kinetic analysis: Polystyrene thermal degradation

In this paper, some clarifications regarding the use of model-fitting methods of kinetic analysis are provided in response to the lack of plot linearity and dispersion in the activation energy values for the thermal degradation of polystyrene found in the literature and some results proposing an nth order model as the most suitable one. In the present work, two model-fitting methods based on the differential and integral forms of the general kinetic equation are evaluated using both simulated and experimental data, showing that the differential method is recommended due to its higher discrimination power. Moreover, the intrinsic limitations of model-fitting methods are highlighted: the use of a limited set of kinetic models to fit experimental data and the ideal nature of such models. Finally, it is concluded that a chain scission model is more appropriate than first order. © 2013 Elsevier B.V.Peer Reviewe

Scale Invariance in a Perturbed Einstein-de Sitter Cosmology

This paper seeks to check the validity of the "apparent fractal conjecture" (Ribeiro 2001ab: gr-qc/9909093, astro-ph/0104181), which states that the observed power-law behaviour for the average density of large-scale distribution of galaxies arises when some observational quantities, selected by their relevance in average density profile determination, are calculated along the past light cone. Implementing these conditions in the proposed set of observational relations profoundly changes the behaviour of many observables in the standard cosmological models. In particular, the average density becomes observationally inhomogeneous, even in the spatially homogeneous spacetime of standard cosmology, change which was already analysed by Ribeiro (1992b, 1993, 1994, 1995: astro-ph/9910145) for a non-perturbed model. Here we derive observational relations in a perturbed Einstein-de Sitter cosmology by means of the perturbation scheme proposed by Abdalla and Mohayaee (1999: astro-ph/9810146), where the scale factor is expanded in power series to yield perturbative terms. The differential equations derived in this perturbative context, and other observables necessary in our analysis, are solved numerically. The results show that our perturbed Einstein-de Sitter cosmology can be approximately described by a decaying power-law like average density profile, meaning that the dust distribution of this cosmology has a scaling behaviour compatible with the power-law profile of the density-distance correlation observed in the galaxy catalogues. These results show that, in the context of this work, the apparent fractal conjecture is correct.Comment: 18 pages, 1 figure, LaTeX. Final version (small changes in the figure plus some references update). Fortran code included with the LaTeX source. To be published in "Fractals

Quintessence Restrictions on Negative Power and Condensate Potentials

We study the cosmological evolution of scalar fields that arise from a phase transition at some energy scale \Lm_c. We focus on negative power potentials given by V=c\Lm_c^{4+n}\phi^{-n} and restrict the cosmological viable values of \Lm_c and $n$. We make a complete analysis of $V$ and impose $SN1a$ conditions on the different cosmological parameters. The cosmological observations ruled out models where the scalar field has reached its attractor solution. For models where this is not the case, the analytic approximated solutions are not good enough to determine whether a specific model is phenomenologically viable or not and the full differential equations must be numerically solved. The results are not fine tuned since a change of 45% on the initial conditions does not spoil the final results. We also determine the values of $N_c, N_f$ that give a condensation scale \Lm_c consistent with gauge coupling unification, leaving only four models that satisfy unification and SN1a constraints.Comment: 15 pages, LaTeX, 8 Figures. Minor changes in text, a discussion on initial conditions added (accepted in Phys.Rev.D

Impact of astrophysical effects on the dark matter mass constraint with 21cm intensity mapping

We present an innovative approach to constraining the non-cold dark matter model using a convolutional neural network (CNN). We perform a suite of hydrodynamic simulations with varying dark matter particle masses and generate mock 21cm radio intensity maps to trace the dark matter distribution. Our proposed method complements the traditional power spectrum analysis. We compare our CNN classification results with those from the power spectrum of the differential brightness temperature map of 21cm radiation, and find that the CNN outperforms the latter. Moreover, we investigate the impact of baryonic physics on the dark matter model constraint, including star formation, self-shielding of HI gas, and UV background model. We find that these effects may introduce some contamination in the dark matter constraint, but they are insignificant when compared to the realistic system noise of the SKA instruments.Comment: 17 pages, 12 figure

Dynamics of two coupled 4-DOF mechanical linear sliding systems with dry friction.

The paper introduces a model of two identical coupled 4-DOF mechanical linear sliding systems with dry friction coupled with each other by a linear torsional spring. The appropriate components (bodies) of the coupled systems are riding on two separated driving belts, which are driven at constant velocities, and stick-slip vibrations can be observed. In this case the physical interpretation of the considered model could be two rows of carriages laying on the guideways and coupled by an elastic shaft, which are moving at constant velocity with respect to the guideways as a foundation. From a mathematical point of view the analyzed problem is governed by eight nonlinear ordinary second order differential equations of motion yielded by the second kind Lagrange equations. Numerical analysis is performed in Mathematica software using the qualitative and quantitative theories of differential equations. Some interesting non-linear system dynamics are detected and reported using the phase portraits and the Poincaré maps. Next, power spectra obtained by the FFT technique are reported. The presented results show periodic, quasi-periodic, chaotic and hyperchaotic orbits. Moreover, synchronization effects between the coupled systems are also detected and studied

Implementation of hydrodynamic forces into the Moving Frame Method for analysis of multi-body wave energy converters

The aim of this research is to implement hydrodynamic forces into the Moving Frame Method (MFM) to enable time-dependent analysis of multi-body wave energy converters in irregular sea-states. The MFM leverages Lie Group Theory, Cartan’s concept of moving frames, and Frankel’s compact notation from the discipline of geometrical physics. Furthermore, it makes use of a coherent data structure founded in the Special Euclidean Group SE(3). Together these implementations maintain a notation which is consistent from 2D to 3D single bodies to multi-bodies, allowing for analysis which can be readily scaled up to include multiple links, bodies, and farms of devices, without increasing notational complexity and without loss of generality. This work models the three-float M4 WEC subject to irregular wave spectra using the MFM and linearization by Cummins’ equation. The impulse response function is pre-computed, and the hydrodynamic coefficients are taken from a WAMIT diffraction model. The power-take-off (PTO) is modelled as a linear damper. The system of second-order ordinary differential equations is advanced in time using the fourth order Runge-Kutta numerical method. Model-scale results are compared to earlier experimental work and show close agreement, with root-mean square errors of the time-series heave and surge responses less than 4×10^(-3) m. Power capture and θ_rms show close agreement across all peak periods with only a slight underprediction (<7%) of power at peak periods shorter than 1 s. Some discrepancies between the model-scale results and earlier experimental work are found and this is attributed to moments from the WAMIT diffraction model being generated about the centre of flotation and not the centre of mass, which is required in an MFM model. Full-scale results of annual energy yield for a wave site in Ireland show only a minor underprediction (<3%) compared to an earlier vectoral mechanics model. The results validate that hydrodynamic forces have been successfully implemented into the MFM model, opening for analysis of more complex wave energy converters with higher degrees of freedom, including other multi-body marine devices.Masteroppgave i havteknologiHTEK399MAMN-HTEK5MAMN-HTE

Empirical array quality weights in the analysis of microarray data

BACKGROUND: Assessment of array quality is an essential step in the analysis of data from microarray experiments. Once detected, less reliable arrays are typically excluded or "filtered" from further analysis to avoid misleading results. RESULTS: In this article, a graduated approach to array quality is considered based on empirical reproducibility of the gene expression measures from replicate arrays. Weights are assigned to each microarray by fitting a heteroscedastic linear model with shared array variance terms. A novel gene-by-gene update algorithm is used to efficiently estimate the array variances. The inverse variances are used as weights in the linear model analysis to identify differentially expressed genes. The method successfully assigns lower weights to less reproducible arrays from different experiments. Down-weighting the observations from suspect arrays increases the power to detect differential expression. In smaller experiments, this approach outperforms the usual method of filtering the data. The method is available in the limma software package which is implemented in the R software environment. CONCLUSION: This method complements existing normalisation and spot quality procedures, and allows poorer quality arrays, which would otherwise be discarded, to be included in an analysis. It is applicable to microarray data from experiments with some level of replication

A statistical analysis of X-ray variability in pre-main sequence objects of the Taurus Molecular Cloud

This work is part of a systematic X-ray survey of the Taurus star forming complex with XMM-Newton. We study the time series of all X-ray sources associated with Taurus members, to statistically characterize their X-ray variability, and compare the results to those for pre-main sequence stars in the Orion Nebula Cluster and to expectations arising from a model where all the X-ray emission is the result of a large number of stochastically occurring flares. We find that roughly half of the detected X-ray sources show variability above our sensitivity limit, and in ~ 26 % of the cases this variability is recognized as flares. Variability is more frequently detected at hard than at soft energies. The variability statistics of cTTS and wTTS are undistinguishable, suggesting a common (coronal) origin for their X-ray emission. We have for the first time applied a rigorous maximum likelihood method in the analysis of the number distribution of flare energies on pre-main sequence stars. In its differential form this distribution follows a power-law with index alpha = 2.4 +- 0.5, in the range typically observed on late-type stars and the Sun. The flare energy distribution is probably steep enough to explain the heating of stellar coronae by nano-flares (alpha > 2), albeit associated with a rather large uncertainty that leaves some doubt on this conclusion.Comment: accepted for publication in Astronomy & Astrophysics; to appear in a Special Section dedicated to the XMM-Newton Extended Survey of the Taurus Molecular Cloud (XEST

Global stabilization of a Korteweg-de Vries equation with saturating distributed control

This article deals with the design of saturated controls in the context of partial differential equations. It focuses on a Korteweg-de Vries equation, which is a nonlinear mathematical model of waves on shallow water surfaces. Two different types of saturated controls are considered. The well-posedness is proven applying a Banach fixed point theorem, using some estimates of this equation and some properties of the saturation function. The proof of the asymptotic stability of the closed-loop system is separated in two cases: i) when the control acts on all the domain, a Lyapunov function together with a sector condition describing the saturating input is used to conclude on the stability, ii) when the control is localized, we argue by contradiction. Some numerical simulations illustrate the stability of the closed-loop nonlinear partial differential equation. 1. Introduction. In recent decades, a great effort has been made to take into account input saturations in control designs (see e.g [39], [15] or more recently [17]). In most applications, actuators are limited due to some physical constraints and the control input has to be bounded. Neglecting the amplitude actuator limitation can be source of undesirable and catastrophic behaviors for the closed-loop system. The standard method to analyze the stability with such nonlinear controls follows a two steps design. First the design is carried out without taking into account the saturation. In a second step, a nonlinear analysis of the closed-loop system is made when adding the saturation. In this way, we often get local stabilization results. Tackling this particular nonlinearity in the case of finite dimensional systems is already a difficult problem. However, nowadays, numerous techniques are available (see e.g. [39, 41, 37]) and such systems can be analyzed with an appropriate Lyapunov function and a sector condition of the saturation map, as introduced in [39]. In the literature, there are few papers studying this topic in the infinite dimensional case. Among them, we can cite [18], [29], where a wave equation equipped with a saturated distributed actuator is studied, and [12], where a coupled PDE/ODE system modeling a switched power converter with a transmission line is considered. Due to some restrictions on the system, a saturated feedback has to be designed in the latter paper. There exist also some papers using the nonlinear semigroup theory and focusing on abstract systems ([20],[34],[36]). Let us note that in [36], [34] and [20], the study of a priori bounded controller is tackled using abstract nonlinear theory. To be more specific, for bounded ([36],[34]) and unbounded ([34]) control operators, some conditions are derived to deduce, from the asymptotic stability of an infinite-dimensional linear system in abstract form, the asymptotic stability when closing the loop with saturating controller. These articles use the nonlinear semigroup theory (see e.g. [24] or [1]). The Korteweg-de Vries equation (KdV for short)Comment: arXiv admin note: text overlap with arXiv:1609.0144