Related papers: The Water Puzzle and Marginal Utility Optimization
We consider a mathematical model for the classical Sudoku puzzle, which we call the primal problem and introduce a corresponding dual problem. Both problems are constraint satisfaction models and a duality relation between them is proved.…
In this paper the problem of optimal performance of a power system is considered. The problem is posed in various aspects within the frames of the theory of optimal control of stores. Mathematical models are presented by means of the…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…
A numerical method is presented to obtain approximate solutions to problems arising from sedimentation models. These processes are widely utilized in minery for recovering water from suspensions coming out of flotation processes. The main…
The response of inviscid incompressible unbounded fluid subject to a localized external perturbation is studed. The physically relevant hypotheses on the mode coupling mechanisma is justified by renormalization group method. The scaling…
It has long been a puzzle how to solve random multiplicative cascade structures analytically. We present an analytical solution found recently in the form of a simple pedagogical example of the general case.
The thermodynamic, dynamic and structural behavior of a water-like system confined in a matrix is analyzed for increasing confining geometries. The liquid is modeled by a two dimensional associating lattice gas model that exhibits density…
We consider an application of pooled stepped chutes where the transport in each pooled step is described by the shallow--water equations. Such systems can be found for example at large dams in order to release overflowing water. We analyze…
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…
The problem of Maxflow is a widely developed subject in modern mathematics. Efficient algorithms exist to solve this problem, that is why a good generalization may permit these algorithms to be understood as a particular instance of…
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time…
A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle…
Determining the maximum demand a water distribution network can satisfy is crucial for ensuring reliable supply and planning network expansion. This problem, typically formulated as a mixed-integer nonlinear program (MINLP), is…
Energy and water systems are highly interconnected. Energy is required to extract, transmit, and treat water and wastewater, and water is needed for cooling energy systems. There is a rapid increase in demand for energy and water due to…
We propose solving the power flow equations using monodromy. We prove the variety under consideration decomposes into trivial and nontrivial subvarieties and that the nontrivial subvariety is irreducible. We also show various symmetries in…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…