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We study a non standard infinite horizon, infinite dimensional linear-quadratic control problem arising in the physics of non-stationary states (see e.g. \cite{BDGJL4,BertiniGabrielliLebowitz05}): finding the minimum energy to drive a given stationary state $\bar x=0$ (at time $t=-\infty$) into an arbitrary non-stationary state $x$ (at time $t=0$). This is the opposite to what is commonly studied in the literature on null controllability (where one drives a generic state $x$ into the equilibrium state $\bar x=0$). Consequently, the Algebraic Riccati Equation (ARE) associated to this problem is non-standard since the sign of the linear part is opposite to the usual one and since it is intrinsically unbounded. Hence the standard theory of AREs does not apply. The analogous finite horizon problem has been studied in the companion paper \cite{AcquistapaceGozzi17}. Here, similarly to such paper, we prove that the linear selfadjoint operator associated to the value function is a solution of the above mentioned ARE. Moreover, differently to \cite{AcquistapaceGozzi17}, we prove that such solution is the maximal one. The first main result (Theorem \ref{th:maximalARE}) is proved by approximating the problem with suitable auxiliary finite horizon problems (which are different from the one studied in \cite{AcquistapaceGozzi17}). Finally in the special case where the involved operators commute we characterize all solutions of the ARE (Theorem \ref{th:sol=proj}) and we apply this to the Landau-Ginzburg model., Comment: 31 pages, 0 figures

In this paper we address the problem of visualizing a set of individuals, which have attached a statistical value given as a proportion, and a dissimilarity measure. Each individual is represented as a region within the unit square, in such a way that the area of the regions represent the proportions and the distances between them represent the dissimilarities. To enhance the interpretability of the representation, the regions are required to satisfy two properties. First, they must form a partition of the unit square, namely, the portions in which it is divided must cover its area without overlapping. Second, the portions must be made of a connected union of rectangles which verify the so-called box-connectivity constraints, yielding a visualization map called Space-filling Box-connected Map (SBM). The construction of an SBM is formally stated as a mathematical optimization problem, which is solved heuristically by using the Large Neighborhood Search technique. The methodology proposed in this paper is applied to three real-world datasets: the first one concerning financial markets in Europe and Asia, the second one about the letters in the English alphabet, and finally the provinces of The Netherlands as a geographical application. HighlightsWe visualize the proportions and the dissimilarities attached to a set of individuals by using Space-filling Box-connected Maps (SBM), which are more flexible than the pie or fan charts.We propose a Mixed Integer Linear model to build SBMs.Large Neighborhood Search metaheuristic is shown to be capable of help visualizing complex sets.The methodology proposed in this paper is applicable to sets of different nature, as shown in our examples.

We study the existence and multiplicity of solutions for a class of fractional Schrodinger–Kirchhoff type equations with the Trudinger–Moser nonlinearity. More precisely, we consider M ( ‖ u ‖ N ∕ s ) ( − Δ ) N ∕ s s u + V ( x ) | u | N s − 1 u = f ( x , u ) + λ h ( x ) | u | p − 2 u in R N , ‖ u ‖ = ∬ R 2 N | u ( x ) − u ( y ) | N ∕ s | x − y | 2 N d x d y + ∫ R N V ( x ) | u | N ∕ s d x s ∕ N , where M : [ 0 , ∞ ] → [ 0 , ∞ ) is a continuous function, s ∈ ( 0 , 1 ) , N ≥ 2 , λ > 0 is a parameter, 1 p ∞ , ( − Δ ) N ∕ s s is the fractional N ∕ s -Laplacian, V : R N → ( 0 , ∞ ) is a continuous function, f : R N × R → R is a continuous function, and h : R N → [ 0 , ∞ ) is a measurable function. First, using the mountain pass theorem, a nonnegative solution is obtained when f satisfies exponential growth conditions and λ is large enough, and we prove that the solution converges to zero in W V s , N ∕ s ( R N ) as λ → ∞ . Then, using the Ekeland variational principle, a nonnegative nontrivial solution is obtained when λ is small enough, and we show that the solution converges to zero in W V s , N ∕ s ( R N ) as λ → 0 . Furthermore, using the genus theory, infinitely many solutions are obtained when M is a special function and λ is small enough. We note that our paper covers a novel feature of Kirchhoff problems, that is, the Kirchhoff function M ( 0 ) = 0 .

This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on the backstepping approach, which provides a systematic procedure to design an observer gain for systems with boundary measurement. If the output is not a boundary value of the state, the backstepping approach is not directly applicable to obtaining an observer gain that stabilizes the error dynamics. Therefore, we attempt to convert the error system into another system to which backstepping is applicable. The conversion is successfully achieved for a class of weighting functions, and the resultant observer realizes exponential convergence of the estimation error with an arbitrary decay rate in terms of the L 2 norm. In addition, an explicit expression of the observer gain is available in a special case. The effectiveness of the proposed observer is also confirmed by numerical simulations.

© 2017 The Author(s) Generating economical, high-resolution and high-quality computational grids for Large Eddy Simulation (LES) of wind flow and convective heat transfer (CHT) around surface-mounted obstacles is not straightforward. When the grid size is used as filter, LES grids should ideally consist of cubic cells, while CHT requires a very high near-wall resolution to resolve the thin viscous sublayer and buffer layer that represent the largest resistance to CHT. To avoid very high cell numbers and the need for excessive computational resources, non-conformal grids can be considered. This paper provides a detailed evaluation of the performance of non-conformal grids with cubic cells, for wind flow and CHT around a wall-mounted cubic obstacle. LES results on non-conformal versus conformal grids are compared with each other and with wind-tunnel measurements of wind speed and surface temperature. Moreover, sensitivity analysis is performed concerning the impact of overall grid resolution, subdomain size and grid refinement ratio. Average absolute deviations between LES on non-conformal versus conformal grids are about 0.9% (0.5 °C) for surface temperature on all cube surfaces. Comparison with experiments shows for the non-conformal grid an average and maximum absolute deviation for surface temperature of 2.0% (1.1 °C) and 7.6% (3.6 °C), respectively. The sensitivity analysis shows minor impact of subdomain size on convective heat transfer coefficients (CHTC) where, on average, absolute deviations of less than 2.2% are observed. This study shows that non-conformal grids can strongly reduce the total cell count (here by a factor up to 30.2) without significantly compromising the accuracy of results. ispartof: Building and Environment vol:119 pages:44-61 status: published

We solve the 3D controlled-source electromagnetic (CSEM) problem using the edge-based finite element method. The modeling domain is discretized using unstructured tetrahedral mesh. We adopt the total field formulation for the quasi-static variant of Maxwell's equation and the computation cost to calculate the primary field can be saved. We adopt a new boundary condition which approximate the total field on the boundary by the primary field corresponding to the layered earth approximation of the complicated conductivity model. The primary field on the modeling boundary is calculated using fast Hankel transform. By using this new type of boundary condition, the computation cost can be reduced significantly and the modeling accuracy can be improved. We consider that the conductivity can be anisotropic. We solve the finite element system of equations using a parallelized multifrontal solver which works efficiently for multiple source and large scale electromagnetic modeling. HighlightsThis paper develops an edge-based finite element method for 3D CSEM modeling.The algorithm is capable of dealing with anisotropic conductivity.We adopt a total field formulation and propose a new advanced boundary condition.We use a parallelized multifrontal method to solve the system of equations.The developed method is effective in modeling complex geometry such as bathymetry.

© 2017 Solving a multi-objective optimization problem yields an infinite set of points in which no objective can be improved without worsening at least another objective. This set is called the Pareto front. A Pareto front with adaptive resolution is a representation where the number of points at any segment of the Pareto front is directly proportional to the curvature of this segment. Such representations are attractive since steep segments, i.e., knees, are more significant to the decision maker as they have high trade-off level compared to the more flat segments of the solution curve. A simple way to obtain such representation is the a posteriori analysis of a dense Pareto front by a smart filter to keep only the points with significant trade-offs among them. However, this method suffers from the production of a large overhead of insignificant points as well as the absence of a clear criterion for determining the required density of the initial dense representation of the Pareto front. This paper's contribution is a novel algorithm for obtaining a Pareto front with adaptive resolution. The algorithm overcomes the pitfalls of the smart filter strategy by obtaining the Pareto points recursively while calculating the trade-off level between the obtained points before moving to a deeper recursive call. By using this approach, once a segment of trade-offs insignificant to the decision maker's needs is identified, the algorithm stops exploring it further. The improved speed of the proposed algorithm along with its intuitively simple solution process make it a more attractive route to solve multi-objective optimization problems in a way that better suits the decision maker's needs. ispartof: Computers & Chemical Engineering vol:106 pages:544-558 status: published

Combining lightweight characteristics with favourable noise and vibration behaviour, locally resonant metamaterials with vibro-acoustic stopband behaviour are gaining increasingly more attention. In view of applicability of metamaterials, this paper investigates the effects of curvature on stopband behaviour. Through derivation of curved unit cell models, dispersion curves for cylindrically curved infinite periodic structures are derived. The effect of curvature on metamaterials is investigated through both an academic example of an infinite cylindrically curved panel with added spring-mass systems and a realizable curved panel with resonant structures. It is shown that, whenever pure flexural motion exists in the host structure, the stopband mechanism can be applied to achieve flexural stopbands. ispartof: International Journal of Mechanical Sciences vol:127 pages:73-90 ispartof: location:SLOVENIA, Ljubljana status: published

© 2016 In contrast to classical experiment design methods, often based on alphabetic criteria, economic optimal experiment design assumes that our ultimate goal is to solve an optimization or optimal control problem. As the system parameters of physical models are in practice always estimated from measurements, they cannot be assumed to be exact. Thus, if we solve the model based optimization problem using the estimated, non-exact parameters, an inevitable loss of optimality is faced. The aim of economic optimal experiment design is precisely to plan an experiment in such a way that the expected loss of optimality in the optimization is minimized. This paper analyzes the question how to design economic experiments under the assumption that we have more than one candidate objective function. Here, we want to take measurements and estimate the parameters before we actually decide which objective we want to minimize. publisher: Elsevier articletitle: Multi-purpose economic optimal experiment design applied to model based optimal control journaltitle: Computers & Chemical Engineering articlelink: http://dx.doi.org/10.1016/j.compchemeng.2016.07.004 content_type: article copyright: © 2016 Published by Elsevier Ltd. ispartof: Computers & Chemical Engineering vol:94 pages:212-220 status: published

© 2015 Elsevier Ltd. All rights reserved. Many efficient exact branch and bound maximum clique solvers use approximate coloring to compute an upper bound on the clique number for every subproblem. This technique reasonably promises tight bounds on average, but never tighter than the chromatic number of the graph. Li and Quan, 2010, AAAI Conference, p. 128-133 describe a way to compute even tighter bounds by reducing each colored subproblem to maximum satisfiability problem (MaxSAT). Moreover they show empirically that the new bounds obtained may be lower than the chromatic number. Based on this idea this paper shows an efficient way to compute related >infra-chromatic> upper bounds without an explicit MaxSAT encoding. The reported results show some of the best times for a stand-alone computer over a number of instances from standard benchmarks., Pablo San Segundo is funded by the Spanish Ministry of Economy and Competitiveness (ARABOT: DPI 2010-21247-C02-01) and supervised by CACSA. Alexey Nikolaev and Mikhail Batsyn are supported by Russian Federation Grant 14-41-00039. The authors would like to thank Chu-Min Li and Zhe Quan for the source code of their MaxCLQ algorithm.

© 2015 Elsevier Ltd. All rights reserved. This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in general there is no one to one correspondence between the branches of the matrix Lambert W function and the characteristic roots of the system. Furthermore, it is shown that under mild conditions only two branches suffice to find the complete spectrum of the system, and that the principal branch can be used to find several roots, and not the dominant root only, as stated in previous works. The results are first presented analytically, and then verified by numerical experiments. publisher: Elsevier articletitle: Some special cases in the stability analysis of multi-dimensional time-delay systems using the matrix Lambert W function journaltitle: Automatica articlelink: http://dx.doi.org/10.1016/j.automatica.2015.01.016 content_type: article copyright: Copyright © 2015 Elsevier Ltd. All rights reserved. ispartof: Automatica vol:53 pages:339-345 status: published