Computational Schemes for Optimizing Domains of Attraction in Dynamical Systems

In this paper, several computational schemes are presented for the optimal tuning of the global behavior of nonlinear dynamical sys- tems. Specifically, the maximization of the size of domains of attraction associated with invariants in parametrized dynamical sys- tems is addressed. Cell Mapping (CM) tech- niques are used to estimate the size of the domains, and such size is then maximized via different optimization tools. First, a ge- netic algorithm is tested whose performance shows to be good for determining global maxima at the expense of high computa- tional cost. Secondly, an iterative scheme based on a Stochastic Approximation proce- dure (the Kiefer-Wolfowitz algorithm) is eval- uated showing acceptable performance at low cost. Finally, several schemes combining neu- ral network based estimations and optimiza- tion procedures are addressed with promising results. The performance of the methods is illus- trated with two applications: first on the well-known van der Pol equation with stan- dard parametrization, and second the tuning of a controller for saturated systems.

On the efficiency of a dedicated LMA for multicast traffic distribution in PMIPv6 domains

IP multicast allows the efficient support of group communication services by reducing the number of IP flows needed for such communication. The increasing generalization in the use of multicast has also triggered the need for supporting IP multicast in mobile environments. Proxy Mobile IPv6 (PMIPv6) is a network-based mobility management solution, where the functionality to support the terminal movement resides in the network. Recently, a baseline solution has been adopted for multicast support in PMIPv6. Such base solution has inefficiencies in multicast routing because it may require multiple copies of a single stream to be received by the same access gateway. Nevertheless, there is an alternative solution to support multicast in PMIPv6 that avoids this issue. This paper evaluates by simulation the scalability of both solutions under realistic conditions, and provides an analysis of the sensitivity of the two proposals against a number of parameters.

Improving abstract interpretations by combining domains

This article considers static analysis based on abstract interpretation of logic programs over combined domains. It is known that analyses over combined domains provide more information potentially than obtained by the independent analyses. However, the construction of a combined analysis often requires redefining the basic operations for the combined domain. A practical approach to maintain precision in combined analyses of logic programs which reuses the individual analyses and does not redefine the basic operations is illustrated. The advantages of the approach are that proofs of correctness for the new domains are not required and implementations can be reused. The approach is demonstrated by showing that a combined sharing analysis — constructed from "old" proposals — compares well with other "new" proposals suggested in recent literature both from the point of view of efficiency and accuracy.

Treatment of singularities in 2-D domains using BIEM

The singularities which arise when there is a sudden change of boundary conditions are modelled using spectral shape interpolation functions. The procedure can be used for elasticity as well as potential theory and to any degree of accuracy with respect to the smooth part of the curve.

First passages in bounded domains: When is the mean first passage time meaningful?

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(ω) distribution of the random variable ω=τ1/(τ1+τ2), which is a measure for how similar the first passage times τ1 and τ2 are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(ω) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(ω), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.

Functional, structural and phylogenetic analysis of domains underlying the Al sensitivity of the aluminum-activated malate/anion transporter, TaALMT1.

Triticum aestivum aluminum-activated malate transporter (TaALMT1) is the founding member of a unique gene family of anion transporters (ALMTs) that mediate the efflux of organic acids. A small sub-group of root-localized ALMTs, including TaALMT1, is physiologically associated with in planta aluminum (Al) resistance. TaALMT1 exhibits significant enhancement of transport activity in response to extracellular Al. In this study, we integrated structure–function analyses of structurally altered TaALMT1 proteins expressed in Xenopus oocytes with phylogenic analyses of the ALMT family. Our aim is to re-examine the role of protein domains in terms of their potential involvement in the Al-dependent enhancement (i.e. Al-responsiveness) of TaALMT1 transport activity, as well as the roles of all its 43 negatively charged amino acid residues. Our results indicate that the N-domain, which is predicted to form the conductive pathway, mediates ion transport even in the absence of the C-domain. However, segments in both domains are involved in Al3+ sensing. We identified two regions, one at the N-terminus and a hydrophobic region at the C-terminus, that jointly contribute to the Al-response phenotype. Interestingly, the characteristic motif at the N-terminus appears to be specific for Al-responsive ALMTs. Our study highlights the need to include a comprehensive phylogenetic analysis when drawing inferences from structure–function analyses, as a significant proportion of the functional changes observed for TaALMT1 are most likely the result of alterations in the overall structural integrity of ALMT family proteins rather than modifications of specific sites involved in Al3+ sensing.

Assessment of damage domains of the High-Temperature Engineering Test Reactor (HTTR)

This paper presents an assessment analysis of damage domains of the 30 MWth prototype High-Temperature Engineering Test Reactor (HTTR) operated by the Japan Atomic Energy Agency (JAEA). For this purpose, an in-house deterministic risk assessment computational tool was developed based on the Theory of Stimulated Dynamics (TSD). To illustrate the methodology and applicability of the developed modelling approach, assessment results of a control rod (CR) withdrawal accident during subcritical conditions are presented and compared with those obtained by the JAEA.

Analysis of the damage domains of sbo sequences with rcp passive thermal shutdown

The integrated Safety Assessment (ISA) methodology, developed by the Spanish Nuclear Safety Council (CSN), has been applied to a thermal-hydraulic analysis of PWR Station Blackout (SBO) sequences in the context of the IDPSA (Integrated Deterministic-Probabilistic Safety Assessment) network objectives. The ISA methodology allows obtaining the damage domain (the region of the uncertain parameters space where the damage limit is exceeded) for each sequence of interest as a function of the operator actuations times. Given a particular safety limit or damage limit, several data of every sequence are necessary in order to obtain the exceedance frequency of that limit. In this application these data are obtained from the results of the simulations performed with MAAP code transients inside each damage domain and the time-density probability distributions of the manual actions. Damage limits that have been taken into account within this analysis are: local cladding damage (PCT>1477 K); local fuel melting (T>2499 K); fuel relocation in lower plenum and vessel failure. Therefore, to every one of these damage variables corresponds a different damage domain. The operation of the new passive thermal shutdown seals developed by several companies since Fukushima accident is considered in the paper. The results show the capability and necessity of the ISA methodology, or similar, in order to obtain accurate results that take into account time uncertainties.

Flow around a hemisphere-cylinder at high angle of attack and low Reynolds number. Part II: POD and DMD applied to reduced domains

Three-dimensional direct numerical simulations (DNS) have been performed on a finite-size hemispherecylinder model at angle of attack AoA = 20◦ and Reynolds numbers Re = 350 and 1000. Under these conditions, massive separation exists on the nose and lee-side of the cylinder, and at both Reynolds numbers the flow is found to be unsteady. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are employed in order to study the primary instability that triggers unsteadiness at Re = 350. The dominant coherent flow structures identified at the lower Reynolds number are also found to exist at Re = 1000; the question is then posed whether the flow oscillations and structures found at the two Reynolds numbers are related. POD and DMD computations are performed using different subdomains of the DNS computational domain. Besides reducing the computational cost of the analyses, this also permits to isolate spatially localized oscillatory structures from other, more energetic structures present in the flow. It is found that POD and DMD are in general sensitive to domain truncation and noneducated choices of the subdomain may lead to inconsistent results. Analyses at Re = 350 show that the primary instability is related to the counter rotating vortex pair conforming the three-dimensional afterbody wake, and characterized by the frequency St ≈ 0.11, in line with results in the literature. At Re = 1000, vortex-shedding is present in the wake with an associated broadband spectrum centered around the same frequency. The horn/leeward vortices at the cylinder lee-side, upstream of the cylinder base, also present finite amplitude oscillations at the higher Reynolds number. The spatial structure of these oscillations, described by the POD modes, is easily differentiated from that of the wake oscillations. Additionally, the frequency spectra associated with the lee-side vortices presents well defined peaks, corresponding to St ≈ 0.11 and its few harmonics, as opposed to the broadband spectrum found at the wake.