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Air pockets can become trapped at high points in pipelines with irregular profiles, particularly during service interruptions. The resulting issues, primarily caused by peak pressures generated during pipeline filling, are a well-documented topic in the literature. However, it is surprising that this subject has not received comprehensive attention. Using a model developed by the authors, this paper identifies the key parameters that define the phenomenon, presenting equations in a dimensionless format. The main advantage of this study lies in the ability to easily compute pressure surges without the need to solve a complex system of differential and algebraic equations. Numerous cases of filling operations were analysed to obtain dimensionless charts that can be used by water utilities to compute pressure surges during filling operations. Additionally, it provides charts that facilitate the rapid and reasonably accurate estimation of peak pressures. Depending on their transient characteristics, pressure peaks are either slow or fast, with separate charts provided for each type. A practical application involving a water pipeline with an irregular profile demonstrates the model’s effectiveness, showing strong agreement between calculated and chart-predicted (proposed methodology) values. This research provides water utilities with the ability to select the appropriate pipe’s resistance class required for water distribution systems by calculating the pressure peak value that may occur during filling procedures.

Entrapped air pockets can cause failure in water distribution systems if air valves have not been appropriately designed for expelling air during filling manoeuvres performed by water utilities. One-dimensional mathematical models recently developed for studying this phenomenon do not consider the effect of blocking columns inside water pipelines. This research presents the development of a mathematical model for analysing the filling process in a pipeline with an undulating profile with various air valves, including blocking columns during starting-up water installations. The results show how different air pocket pressure peaks can be produced over transient events, which need to be analysed to ensure a successful procedure that guarantees pipeline safety during the pressure surge occurrence. In this study, an experimental set-up is analysed to observe the behaviour of two blocking columns during filling by comparing the air pocket pressure pulses.

A crucial, both from theoretical and practical points of view, problem in preference modelling is the number of questions to ask from the decision maker. We focus on incomplete pairwise comparison matrices based on graphs whose average degree is approximately 3 (or a bit more), i.e., each item is compared to three others in average. In the range of matrix sizes we considered, n=5,6,7,8,9,10, this requires from 1.4n to 1.8n edges, resulting in completion ratios between 33% (n=10) and 80% (n=5). We analyze several types of union of two spanning trees (three of them building on additional ordinal information on the ranking), 2-edge-connected random graphs and 3-(quasi-)regular graphs with minimal diameter (the length of the maximal shortest path between any two vertices). The weight vectors are calculated from the natural extensions, to the incomplete case, of the two most popular weighting methods, the eigenvector method and the logarithmic least squares. These weight vectors are compared to the ones calculated from the complete matrix, and their distances (Euclidean, Chebyshev and Manhattan), rank correlations (Kendall and Spearman) and similarity (Garuti, cosine and dice indices) are computed in order to have cardinal, ordinal and proximity views during the comparisons. Surprisingly enough, only the union of two star graphs centered at the best and the second best items perform well among the graphs using additional ordinal information on the ranking. The union of two edge-disjoint spanning trees is almost always the best among the analyzed graphs.

Quantum computing devices are believed to be powerful in solving hard computational tasks, in particular, combinatorial optimization problems. In the present work, we consider a particular type of the minimum bin packing problem, which can be used for solving the problem of filling spent nuclear fuel in deep-repository canisters that is relevant for atomic energy industry. We first redefine the aforementioned problem it in terms of quadratic unconstrained binary optimization. Such a representation is natively compatible with existing quantum annealing devices as well as quantum-inspired algorithms. We then present the results of the numerical comparison of quantum and quantum-inspired methods. Results of our study indicate on the possibility to solve industry-relevant problems of atomic energy industry using quantum and quantum-inspired optimization.

Recent droughts have severely threatened water security in many regions worldwide. Reservoirs, designed to combat droughts and secure water supply partially, are reported failing to fill up to the total capacity due to severe droughts. How bad is climate affecting reservoir filling up on a global scale? This issue has not been studied. We present a big picture of reservoirs in crisis using satellite altimetry. Thanks to the unique characteristics of CryoSat‐2, 525 reservoirs worldwide were investigated during 2010–2022. Results show that most reservoirs (93%) are found not fully filled up at least once. About 21% of reservoirs, which are mainly located in the Southern Hemisphere, show a significant decline in water levels. Moreover, about 20% of reservoirs with larger level fluctuations (>3 m) are located in less developed economies, indicating informed operation rules are needed. Further analyses indicate reservoirs are largely affected by extreme climate events, such as ENSO. Plain Language Summary A reservoir is an artificial lake where water is collected and stored for various purposes, such as flood control, irrigation, hydropower generation, industrial use, etc. In a changing climate, drought events can cause a decline in the natural flow of streams and rivers to the reservoirs. Consequently, many of the functions provided by the reservoir might be halted if the drought continues, just like the cases of Lake Powell and Lake Mead. The past decade saw several record‐breaking global annual temperatures. How have global reservoirs been affected in terms of the filling up? Leveraging more than a decade of CryoSat‐2 altimetry observations, we provided a global picture of this issue. We found that 93% of studied reservoirs have not been fully filled up at least once during 2010–2022. Our analyses revealed that droughts are the most probable culprits. About 86% of the 398 reservoirs with accessible SPEI data exhibited significant susceptibility to drought, while 43% of the 525 reservoirs demonstrated notable sensitivity to ENSO events. These findings have important implications for future reservoir operations to cope with more intensive drought events. It also means the benefits and costs of both existing and planned reservoirs need to be re‐assessed to take adaptation strategies. Key Points Water levels of reservoirs in the southern hemisphere show a declining trend About 93% of the 525 studied reservoirs have not been fully filled up at least once in the past 12 years Less developed economies need to develop informed reservoir operation rules to cope with climate change

In this paper, multi-dimensional global optimization problems are considered, where the objective function is supposed to be Lipschitz continuous, multiextremal, and without a known analytic expression. Two different approximations of Peano-Hilbert curve applied to reduce the problem to a univariate one satisfying the Hölder condition are discussed. The first of them, piecewise-linear approximation, is broadly used in global optimization and not only whereas the second one, non-univalent approximation, is less known. Multi-dimensional geometric algorithms employing these Peano curve approximations are introduced and their convergence conditions are established. Numerical experiments executed on 800 randomly generated test functions taken from the literature show a promising performance of algorithms employing Peano curve approximations w.r.t. their direct competitors.

In this paper, the problem of approximating and visualizing the solution set of systems of nonlinear inequalities is considered. It is supposed that left-hand parts of the inequalities can be multiextremal and non-differentiable. Thus, traditional local methods using gradients cannot be applied in these circumstances. Problems of this kind arise in many scientific applications, in particular, in finding working spaces of robots where it is necessary to determine not one but all the solutions of the system of nonlinear inequalities. Global optimization algorithms can be taken as an inspiration for developing methods for solving this problem. In this article, two new methods using two different approximations of Peano–Hilbert space-filling curves actively used in global optimization are proposed. Convergence conditions of the new methods are established. Numerical experiments executed on problems regarding finding the working spaces of several robots show a promising performance of the new algorithms.

Subsampling focuses on selecting a subsample that can efficiently sketch the information of the original data in terms of statistical inference. It provides a powerful tool in big data analysis and gains the attention of data scientists in recent years. In this review, some state-of-the-art subsampling methods inspired by statistical design are summarized. Three types of designs, namely optimal design, orthogonal design, and space filling design, have shown their great potential in subsampling for different objectives. The relationships between experimental designs and the related subsampling approaches are discussed. Specifically, two major families of design inspired subsampling techniques are presented. The first aims to select a subsample in accordance with some optimal design criteria. The second tries to find a subsample that meets some design requirements, including balancing, orthogonality, and uniformity. Simulated and real data examples are provided to compare these methods empirically.

Global optimization is a field of mathematical programming dealing with finding global (absolute) minima of multi-dimensional multiextremal functions. Problems of this kind where the objective function is non-differentiable, satisfies the Lipschitz condition with an unknown Lipschitz constant, and is given as a “black-box” are very often encountered in engineering optimization applications. Due to the presence of multiple local minima and the absence of differentiability, traditional optimization techniques using gradients and working with problems having only one minimum cannot be applied in this case. These real-life applied problems are attacked here by employing one of the mostly abstract mathematical objects—space-filling curves. A practical derivative-free deterministic method reducing the dimensionality of the problem by using space-filling curves and working simultaneously with all possible estimates of Lipschitz and Hölder constants is proposed. A smart adaptive balancing of local and global information collected during the search is performed at each iteration. Conditions ensuring convergence of the new method to the global minima are established. Results of numerical experiments on 1000 randomly generated test functions show a clear superiority of the new method w.r.t. the popular method DIRECT and other competitors.

In the area of computer simulation, Latin hypercube designs play an important role. In this paper the classes of maximin and Audze-Eglais Latin hypercube designs are considered. Up to now only several two-dimensional designs and a few higher dimensional designs for these classes have been published. Using periodic designs and the Enhanced Stochastic Evolutionary algorithm of Jin et al. (J. Stat. Plan. Interference 134(1):268–687, 2005 ), we obtain new results which we compare to existing results. We thus construct a database of approximate maximin and Audze-Eglais Latin hypercube designs for up to ten dimensions and for up to 300 design points. All these designs can be downloaded from the website http://www.spacefillingdesigns.nl .