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Showing papers by "Polytechnic University of Catalonia published in 2005"


Journal ArticleDOI
TL;DR: A survey on theoretical results on ant colony optimization, which highlights some open questions with a certain interest of being solved in the near future and discusses relations between ant colonies optimization algorithms and other approximate methods for optimization.

2,093 citations


Journal ArticleDOI
17 Nov 2005-Nature
TL;DR: High-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel is demonstrated, showing that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions.
Abstract: Chaos is good, if you are looking to send encrypted information across a broadband optical network. The idea that the transmission of light-based signals embedded in chaos can provide privacy in data transmission has been demonstrated over short distances in the laboratory. Now it has been shown to work for real, across a commercial fibre-optic channel in the metropolitan area network of Athens, Greece. The results show that the technology is robust to perturbations and channel disturbances unavoidable under real-world conditions. Chaotic signals have been proposed as broadband information carriers with the potential of providing a high level of robustness and privacy in data transmission1,2. Laboratory demonstrations of chaos-based optical communications have already shown the potential of this technology3,4,5, but a field experiment using commercial optical networks has not been undertaken so far. Here we demonstrate high-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel. An optical carrier wave generated by a chaotic laser is used to encode a message for transmission over 120 km of optical fibre in the metropolitan area network of Athens, Greece. The message is decoded using an appropriate second laser which, by synchronizing with the chaotic carrier, allows for the separation of the carrier and the message. Transmission rates in the gigabit per second range are achieved, with corresponding bit-error rates below 10-7. The system uses matched pairs of semiconductor lasers as chaotic emitters and receivers, and off-the-shelf fibre-optic telecommunication components. Our results show that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions.

1,267 citations


Journal ArticleDOI
TL;DR: This work deals with the biological inspiration of ant colony optimization algorithms and shows how this biological inspiration can be transfered into an algorithm for discrete optimization, and presents some of the nowadays best-performing ant colonies optimization variants.

1,041 citations


Proceedings ArticleDOI
29 Jun 2005
TL;DR: The specification and goals of the task are introduced, the data sets and evaluation methods are described, and a general overview of the 19 systems that have contributed to the task is presented, providing a comparative description and results.
Abstract: In this paper we describe the CoNLL-2005 shared task on Semantic Role Labeling. We introduce the specification and goals of the task, describe the data sets and evaluation methods, and present a general overview of the 19 systems that have contributed to the task, providing a comparative description and results.

761 citations


Proceedings ArticleDOI
01 Dec 2005
TL;DR: In this paper, a novel wireless load sharing controller for islanding parallel inverters in an ac distributed system is proposed, where the resistive output impedance of the parallel-connected inverters is explored.
Abstract: In this paper, a novel wireless load-sharing controller for islanding parallel inverters in an ac distributed system is proposed. The paper explorers the resistive output impedance of the parallel-connected inverters in an island microgrid

718 citations


Journal ArticleDOI
TL;DR: In this article, an up-to-date survey of experimental and theoretical results in spatiotemporal optical solitons can be found, together with a review of the outstanding difficulties and open problems.
Abstract: In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.

717 citations


Journal ArticleDOI
TL;DR: This work proposes and analyzes a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices.
Abstract: Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k , respectively.

682 citations


Journal ArticleDOI
TL;DR: In this paper, a method to analyze grouped parts of a compositional vector through the adequate coordinates in an ad hoc orthonormal basis was proposed, and the study of balances of groups of parts (intergroup analysis) as an orthogonal projection similar to that used in standard subcompositional analysis (intra-group analysis).
Abstract: Amalgamation of parts of a composition has been extensively used as a technique of analysis to achieve reduced dimension, as was discussed during the CoDaWork'03 meeting (Girona, Spain, 2003). It was shown to be a non-linear operation in the simplex that does not preserve distances under perturbation. The discussion motivated the introduction in the present paper of concepts such as group of parts, balance between groups, and sequential binary partition, which are intended to provide tools of compositional data analysis for dimension reduction. Key concepts underlying this development are the established tools of subcomposition, coordinates in an orthogonal basis of the simplex, balancing element and, in general, the Aitchison geometry in the simplex. Main new results are: a method to analyze grouped parts of a compositional vector through the adequate coordinates in an ad hoc orthonormal basis; and the study of balances of groups of parts (inter-group analysis) as an orthogonal projection similar to that used in standard subcompositional analysis (intra-group analysis). A simulated example compares results when testing equal centers of two populations using amalgamated parts and balances; it shows that, in certain circumstances, results from both analysis can disagree.

534 citations


Journal ArticleDOI
TL;DR: It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data, proper accounting of uncertainty, etc.
Abstract: The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice.

505 citations


Journal ArticleDOI
TL;DR: The purpose of this paper is to provide a practical algorithm to evaluate numerically a general waterfilling solution, which includes the currently existingWaterfilling solutions and others that may possibly appear in future problems.
Abstract: Many engineering problems that can be formulated as constrained optimization problems result in solutions given by a waterfilling structure; the classical example is the capacity-achieving solution for a frequency-selective channel. For simple waterfilling solutions with a single waterlevel and a single constraint (typically, a power constraint), some algorithms have been proposed in the literature to compute the solutions numerically. However, some other optimization problems result in significantly more complicated waterfilling solutions that include multiple waterlevels and multiple constraints. For such cases, it may still be possible to obtain practical algorithms to evaluate the solutions numerically but only after a painstaking inspection of the specific waterfilling structure. In addition, a unified view of the different types of waterfilling solutions and the corresponding practical algorithms is missing. The purpose of this paper is twofold. On the one hand, it overviews the waterfilling results existing in the literature from a unified viewpoint. On the other hand, it bridges the gap between a wide family of waterfilling solutions and their efficient implementation in practice; to be more precise, it provides a practical algorithm to evaluate numerically a general waterfilling solution, which includes the currently existing waterfilling solutions and others that may possibly appear in future problems.

501 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns, showing that the growth of the epidemic prevalence is virtually instantaneous in all networks characterized by diverging degree fluctuations, independently of the structure of the connectivity correlation functions characterizing the population network.

Journal ArticleDOI
TL;DR: The orbital angular momentum spectra of a light beam can be used to image a variety of intrinsic and extrinsic properties encoded, e.g., in phase and amplitude gradients, dislocations or delays.
Abstract: A major application of optics is imaging all types of structural, physical, chemical and biological features of matter. Techniques based on most known properties of light have been developed over the years to remotely acquire information about such features. They include the spin angular momentum, encoded in the polarization, but not yet the orbital angular momentum encoded in its spiral spectrum. Here we put forward the potential of such spiral spectra. In particular, we use several canonical examples to show how the orbital angular momentum spectra of a light beam can be used to image a variety of intrinsic and extrinsic properties encoded, e.g., in phase and amplitude gradients, dislocations or delays.

Journal ArticleDOI
TL;DR: The main empirical results are the broad distributions of various quantities and the existence of weight-topology correlations which show that weights are relevant and that in general the modeling of complex networks must go beyond topology.
Abstract: We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network which are representatives of critical infrastructure and social system, respectively. The main empirical results are (i) the broad distributions of various quantities and (ii) the existence of weight-topology correlations. These measurements show that weights are relevant and that in general the modeling of complex networks must go beyond topology. We review a model which provides an explanation for the features observed in several real-world networks. This model of weighted network formation relies on the dynamical coupling between topology and weights, considering the rearrangement of new links are introduced in the system.

Journal ArticleDOI
TL;DR: In this article, the design and retrofit problem of a supply chain (SC) consisting of several production plants, warehouses and markets, and the associated distribution systems, is considered, where the problem objective is assessed by taking into account not only the profit over the time horizon, but also the resulting demand satisfaction.

Journal ArticleDOI
TL;DR: An uncompromisingly applied mathematical view, that the challenge of solving practical problems should motivate theoretical research; and that any new theory should be thoroughly investigated to see if it may provide answers to previously abandoned practical considerations.
Abstract: We take stock of the present position of compositional data analysis, of what has been achieved in the last 20 years, and then make suggestions as to what may be sensible avenues of future research. We take an uncompromisingly applied mathematical view, that the challenge of solving practical problems should motivate our theoretical research; and that any new theory should be thoroughly investigated to see if it may provide answers to previously abandoned practical considerations.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the existence of monotone solutions of the Peierls-Nabarro problem in a half-plane with dimension n = 2 and showed that the necessary and sufficient condition on the potential G has two, and only two, absolute minima in the interval [−1, 1], located at ±1.
Abstract: R n−1 are denoted by y = (y1, . . . , yn−1). Our main goal is to study bounded solutions of (1.1) that are monotone increasing, say from −1 to 1, in one of the y-variables. We call them layer solutions of (1.1), and we study their existence, uniqueness, symmetry, and variational properties, as well as their asymptotic behavior. The interest in such increasing solutions comes from some models of boundary phase transitions. When the nonlinearity f is given by f (u) = sin(cu) for some constant c, problem (1.1) in a half-plane is called the Peierls-Nabarro problem, and it appears as a model of dislocations in crystals (see [21, 36]). The Peierls-Nabarro problem is also central to the analysis of boundary vortices in the paper [28], which studies a model for soft thin films in micromagnetism recently derived by Kohn and Slastikov [26] (see also [27]). Our main result, Theorem 1.2, characterizes the nonlinearities f for which there exists a layer solution of (1.1) in dimension n = 2. We prove that the necessary and sufficient condition is that the potential G (defined by G ′ = − f ) has two, and only two, absolute minima in the interval [−1, 1], located at ±1. Under the additional hypothesis G ′′(±1) > 0, we also establish the uniqueness of a layer solution up to translations in the y-variable. The proofs of both the necessity and the sufficiency of the condition on G for existence use new ingredients, which we develop in this article. A first one is a nonlocal estimate, as well as a conserved or Hamiltonian quantity, satisfied by every layer solution in dimension 2 (see Theorem 1.3). The estimate can be seen as

Journal ArticleDOI
TL;DR: The results suggest that transport connectivity is much less sensitive to barriers, which control flow connectivity, and appears to be controlled by the existence of narrow, possibly discontinuous high-K paths.

Journal ArticleDOI
TL;DR: These amplitudes are quantified for two modulation strategies that use nearest vectors to the reference vector and will help for the calculation of the dc-link capacitors in a given specific application.
Abstract: The nearest vectors to the reference vector are commonly used in space-vector modulation (SVM) strategies. The main advantages of these modulation strategies are the low switching frequencies of the devices, the good output voltage spectra, and the low electromagnetic interference. However, when these techniques are applied to the three-level neutral-point (NP)-clamped inverter, low-frequency oscillations appear in the NP voltage for some operating conditions. As a result, the value of the dc-link capacitors must be increased in order to attenuate such oscillations. In this paper, these amplitudes are quantified for two modulation strategies that use nearest vectors to the reference vector. Owing to the nondimensional variables used in the analysis, the information provided will help for the calculation of the dc-link capacitors in a given specific application. Simulated and experimental examples are presented.

Book ChapterDOI
01 Jan 2005
TL;DR: This paper discuses some of the most critical aspects of the dynamic simulation of road networks, namely the heuristic dynamic assignment, the implied route choice models, and the validation methodology, a key issue to determine the degree of validity and significance of the simulation results.
Abstract: The deployment of ITS must be assisted by suitable tools to conduct the feasibility studies required for testing the designs and evaluating the expected impacts. Microscopic traffic simulation has proven to be the suitable methodological approach to achieve these goals. This paper discuses some of the most critical aspects of the dynamic simulation of road networks, namely the heuristic dynamic assignment, the implied route choice models, and the validation methodology, a key issue to determine the degree of validity and significance of the simulation results. The paper is structured in two parts, the first provides an overview on how the main features of microscopic simulation have been implemented in AIMSUN, and the second is devoted to discus in detail the heuristic dynamic assignment.

Book ChapterDOI
TL;DR: The authors offer concepts to model network structures and dynamics, focussing on approaches applicable across disciplines, and focus on networks that change their topology as in morphogenesis and self-organization.
Abstract: In this chapter we want to provide a review of the main results obtained in the modeling of epidemic spreading in scale-free networks. In particular, we want to show the different epidemiological framework originated by the lack of any epidemic threshold and how this feature is rooted in the extreme heterogeneity of the scale-free networks' connectivity pattern.

Journal ArticleDOI
TL;DR: In this paper, the formation and evolution of hydrogen-deficient post-AGB white dwarfs is studied in the context of a double-diffusive mixing-length theory of convection.
Abstract: We explore the formation and evolution of hydrogen-deficient post-AGB white dwarfs. To this end, we compute the complete evolution of an initially 2.7 Mstar from the zero-age main sequence through the thermally pulsing and mass-loss phases to the white dwarf stage. Particular attention is given to the chemical abundance changes during the whole evolution. A time-dependent scheme for the simultaneous treatment of abundance changes caused by nuclear reactions, diffusive overshoot- ing, salt fingers and convection is considered. We employed the double-diffusive mixing-length theory of convection for fluids with composition gradients. The study can therefore be considered as a test of its performance in low-mass stars. Also, time- dependent element diffusion for multicomponent gases is taken into account during the white dwarf evolution. The evolutionary stages corresponding to the last helium thermal pulse on the early white-dwarf cooling branch and the following born-again episode are carefully explored. Relevant aspects for PG 1159 stars and DB white dwarf evolution are studied in the framework of these new evolutionary models that take into account the history of the white dwarf progenitor. The scope of the calculations is extended to the domain of the helium-rich, carbon-contaminated DQ white dwarfs with the aim of exploring the plausibility of the evolutionary connection PG 1159-DB-DQ. In this regard, the implications for the double-layered chemical structure in pulsating DB white dwarfs is investigated. We examine the consequences of mass-loss episodes during the PG 1159 stage for the chemical stratification of the outer layer of DB and DQ white dwarfs.

Journal ArticleDOI
TL;DR: A novel approach for ship detection is proposed based on the analysis of SAR images by means of the discrete wavelet transform, which takes advantage of the difference of statistical behavior among the ships and the surrounding sea, interpreting the information through the wavelet coefficients in order to provide a more reliable detection.
Abstract: Carrying out an effective control of fishing activities is essential to guarantee a sustainable exploitation of sea resources. Nevertheless, as the regulated areas are extended, they are difficult and time consuming to monitor by means of traditional reconnaissance methods such as planes and patrol vessels. On the contrary, satellite-based synthetic aperture radar (SAR) provides a powerful surveillance capability allowing the observation of broad expanses, independently from weather effects and from the day and night cycle. Unfortunately, the automatic interpretation of SAR images is often complicated, even though undetected targets are sometimes visible by eye. Attending to these particular circumstances, a novel approach for ship detection is proposed based on the analysis of SAR images by means of the discrete wavelet transform. The exposed method takes advantage of the difference of statistical behavior among the ships and the surrounding sea, interpreting the information through the wavelet coefficients in order to provide a more reliable detection. The analysis of the detection performance over both simulated and real images confirms the robustness of the proposed algorithm.

Journal ArticleDOI
TL;DR: In this article, Alonso et al. used oedometer tests on an artificially prepared bentonite-sand mixture (80% bentonite by dry mass) to identify the most important features controlling soil behaviour.

Journal ArticleDOI
TL;DR: In this paper, the impact of the African dust on levels of atmospheric suspended particulate matter (SPM) and on wet deposition was evaluated in eastern Iberia for the period 1996-2002.
Abstract: [1] The impact of the African dust on levels of atmospheric suspended particulate matter (SPM) and on wet deposition was evaluated in eastern Iberia for the period 1996–2002. An effort was made to compile both the SPM and wet episodes. To this end, the time series of levels of TSP and PM10 in Levantine air quality monitoring stations were evaluated and complemented with the computation of back trajectories, satellite images, and meteorological analysis. Wet deposition frequency was obtained from weekly collected precipitation data at a rural background station in which the African chemical signature was identified (mainly pH and Ca 2+ concentrations). A number of African dust episodes (112) were identified (16 episodes per year). In 93 out of the 112 (13 episodes per year) the African dust influence caused high SPM levels. In 49 out of 112 (7 episodes per year), wet deposition was detected, and the chemistry was influenced by dust. There is a clear seasonal trend with higher frequency of dust outbreaks in May-August, with second modes in March and October. Wet events followed a different pattern, with a marked maximum in May. Except for one event, December was devoid of African air mass intrusions. On the basis of seasonal meteorological patterns affecting the Iberian Peninsula, an interpretation of the meteorological scenarios causing African dust transport over Iberia was carried out. Four scenarios were identified with a clear seasonal trend. The impact of the different dust outbreak scenarios on the levels of PM10 recorded at a rural site (Monagrega, Teruel, Spain) in the period 1996–2002 was also evaluated.

Journal ArticleDOI
TL;DR: The constitutive model presented in this work is built on a conceptual approach for unsaturated expansive soils in which the fundamental characteristic is the explicit consideration of two pore levels, and has been formulated considering concepts of classical and generalized plasticity theories.
Abstract: The constitutive model presented in this work is built on a conceptual approach for unsaturated expansive soils in which the fundamental characteristic is the explicit consideration of two pore levels. The distinction between the macro- and microstructure provides the opportunity to take into account the dominant phenomena that affect the behaviour of each structural level and the main interactions between them. The microstructure is associated with the active clay minerals, while the macrostructure accounts for the larger-scale structure of the material. The model has been formulated considering concepts of classical and generalized plasticity theories. The generalized stress-strain rate equations are derived within a framework of multidissipative materials, which provides a consistent and formal approach when there are several sources of energy dissipation. The model is formulated in the space of stresses, suction and temperature; and has been implemented in a finite element code. The approach has been applied to explaining and reproducing the behaviour of expansive soils in a variety of problems for which experimental data are available. Three application cases are presented in this paper. Of particular interest is the modelling of an accidental overheating, that took place in a large-scale heating test. This test allows the capabilities of the model to be checked when a complex thermo-hydro-mechanical (THM) path is followed.

Journal ArticleDOI
TL;DR: In this paper, an attempt to predict both landslide displacements and velocities was performed at Vallcebre by solving the momentum equation in which a viscous term (Bingham and power law) was added.
Abstract: In active landslides, the prediction of acceleration of movement is a crucial issue for the design and performance of warning systems. The landslide of Vallcebre in the Eastern Pyreenes, Spain, has been monitored since 1996 and data on rainfall, groundwater levels and ground displacements are measured on a regular basis. Displacements observed in borehole wire extensometers have shown an immediate response of the landslide to rainfall episodes. This rapid response is likely due to the presence of preferential drainage ways. The occurrence of nearly constant rates of displacement in coincidence with steady groundwater levels suggests the presence of viscous forces developed during the movement. An attempt to predict both landslide displacements and velocities was performed at Vallcebre by solving the momentum equation in which a viscous term (Bingham and power law) was added. Results show that, using similar rheological parameters for the entire landslide, computed displacements reproduce quite accurately the displacements observed at three selected wire extensometers. These results indicate that prediction of displacements from groundwater level changes is feasible.

Journal ArticleDOI
TL;DR: In this paper, the effect of hydraulic loading rate (HLR), aspect ratio, granular medium size and water depth on the removal of selected contaminants in horizontal subsurface flow constructed wetlands (SSF) over a period of three years was evaluated.

Journal ArticleDOI
TL;DR: In this article, the main contributors to recharge and discharge clearly differ from those in natural systems, and water can affect underground structures and infrastructure characteristics of cities such as basements, public transport services (trains, underground railways, etc.), and utility conduits.
Abstract: A number of specific factors must be considered when dealing with groundwater in urban areas. Urbanization significantly affects the natural water cycle, both in terms of quantity and quality. In particular, the main contributors to recharge and discharge clearly differ from those in natural systems. Moreover, water can affect underground structures and infrastructure characteristics of cities such as basements, public transport services (trains, underground railways, etc.), and utility conduits. As a result, urban groundwater is emerging as a distinct branch of hydrogeology. The objective of this paper is to review some of the topics that are specific to urban groundwater. These include (1) fluctuations in groundwater levels caused by changes in land and water uses; (2) pollution problems caused by point or non-point sources in urban areas; (3) characterization and quantification of the components contributing to groundwater recharge and discharge; (4) specific characteristics of groundwater flow and solute transport models in urban areas; and (5) integration of data for sustainable urban water management. Some of these issues are illustrated for the particular case of Barcelona, where a comprehensive hydrogeological study has been carried out during the last few years by both the public and the private sectors.

Journal ArticleDOI
TL;DR: The approach builds on the seminal results of Robertson and Seymour on Graph Minors, and as a result is much more powerful than the previous machinery of Alber et al. for exponential speedup on planar graphs.
Abstract: The (k, r)-center problem asks whether an input graph G has ≤k vertices (called centers) such that every vertex of G is within distance ≤r from some center. In this article, we prove that the (k, r)-center problem, parameterized by k and R, is fixed-parameter tractable (FPT) on planar graphs, i.e., it admits an algorithm of complexity f(k, r)nO(1) where the function f is independent of n. In particular, we show that f(k,r) = 2O(r log r) √k, where the exponent of the exponential term grows sublinearly in the number of centers. Moreover, we prove that the same type of FPT algorithms can be designed for the more general class of map graphs introduced by Chen, Grigni, and Papadimitriou. Our results combine dynamic-programming algorithms for graphs of small branchwidth and a graph-theoretic result bounding this parameter in terms of k and r. Finally, a byproduct of our algorithm is the existence of a PTAS for the r-domination problem in both planar graphs and map graphs.Our approach builds on the seminal results of Robertson and Seymour on Graph Minors, and as a result is much more powerful than the previous machinery of Alber et al. for exponential speedup on planar graphs. To demonstrate the versatility of our results, we show how our algorithms can be extended to general parameters that are “large” on grids. In addition, our use of branchwidth instead of the usual treewidth allows us to obtain much faster algorithms, and requires more complicated dynamic programming than the standard leaf/introduce/forget/join structure of nice tree decompositions. Our results are also unique in that they apply to classes of graphs that are not minor-closed, namely, constant powers of planar graphs and map graphs.

Journal ArticleDOI
TL;DR: In this paper, the authors present a procedure to solve groundwater reactive transport in the case of homogeneous and classical heterogeneous equilibrium reactions induced by mixing different waters, which can be used to test numerical codes by setting benchmark problems but also to derive closed-form analytical solutions whenever steps 2 and 3 are simple.
Abstract: [1] Modeling transport of reactive solutes is a challenging problem, necessary for understanding the fate of pollutants and geochemical processes occurring in aquifers, rivers, estuaries, and oceans. Geochemical processesinvolving multiple reactive species are generally analyzed using advanced numerical codes. The resulting complexity has inhibited the development of analytical solutions for multicomponent heterogeneous reactions such as precipitation/dissolution. We present a procedure to solve groundwater reactive transport in the case of homogeneous and classical heterogeneous equilibrium reactions induced by mixing different waters. The methodology consists of four steps: (1) defining conservative components to decouple the solution of chemical equilibrium equations from species mass balances, (2) solving the transport equations for the conservative components, (3) performing speciation calculations to obtain concentrations of aqueous species, and (4) substituting the latter into the transport equations to evaluate reaction rates. We then obtain the space-time distribution of concentrations and reaction rates. The key result is that when the equilibrium constant does not vary in space or time, the reaction rate is proportional to the rate of mixing, * T u D Vu, where u is the vector of conservative components concentrations and D is the dispersion tensor. The methodology can be used to test numerical codes by setting benchmark problems but also to derive closed-form analytical solutions whenever steps 2 and 3 are simple, as illustrated by the application to a binary system. This application clearly elucidates that in a three-dimensional problem both chemical and transport parameters are equally important in controlling the process.