38 research outputs found

    COST-S: a new methodology and tools for sewerage asset management based on whole life costs

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    This is the final version of the article. Freely available from IWA Publishing via the link in this record.This paper discusses the development of a methodology and software tools aimed at assisting management decisions in order to provide acceptable performance at a minimum cost over the whole life of the sewerage system. Whole Life Costing (WLC) approaches have been shown to offer an ideal platform to provide investment and operational management tools that take account of the timing of interventions, system behaviour and performance all within a sensible economic and engineering framework. The need for such a methodology and the requirements for its useful implementation are introduced first. The paper then describes how research collaboration between the UK Water Industry and two UK research centres (Centre for Water Systems at Exeter University and Pennine Water Group at Universities of Sheffield and Bradford), and supported by the UK Engineering and Physical Sciences Research Council grant, resulted in an innovative, practical and auditable methodology with associated tools for better proactive management of ageing and rapidly deteriorating sewerage systems.The authors would like to acknowledge the generous support of EPSRC (Project No.GR/M16122/01 and GR/R98617/01) as well as that of the industrial collaborators;AWG, Northumbrian Water,Thames Water Services,United Utilities and Yorkshire Water Services

    Conservation laws for self-adjoint first order evolution equations

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    In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physic

    Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties

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    [EN] In this paper we study random non-autonomous second order linear differential equations by taking advantage of the powerful theory of random difference equations. The coefficients are assumed to be stochastic processes, and the initial conditions are random variables both defined in a common underlying complete probability space. Under appropriate assumptions established on the data stochastic processes and on the random initial conditions, and using key results on difference equations, we prove the existence of an analytic stochastic process solution in the random mean square sense. Truncating the random series that defines the solution process, we are able to approximate the main statistical properties of the solution, such as the expectation and the variance. We also obtain error a priori bounds to construct reliable approximations of both statistical moments. We include a set of numerical examples to illustrate the main theoretical results established throughout the paper. We finish with an example where our findings are combined with Monte Carlo simulations to model uncertainty using real data.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M.; Villafuerte, L. (2018). Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Advances in Difference Equations. (3):1-29. https://doi.org/10.1186/s13662-018-1848-8S1293Apostol, T.M.: Mathematical Analysis, 2nd edn. Pearson, New York (1976)Boyce, W.E.: Probabilistic Methods in Applied Mathematics I. Academic Press, New York (1968)Calbo, G., Cortés, J.C., Jódar, L.: Random Hermite differential equations: mean square power series solutions and statistical properties. Appl. Math. Comput. 218(7), 3654–3666 (2011)Calbo, G., Cortés, J.C., Jódar, L., Villafuerte, L.: Solving the random Legendre differential equation: mean square power series solution and its statistical functions. Comput. Math. Appl. 61(9), 2782–2792 (2011)Casabán, M.C., Cortés, J.C., Navarro-Quiles, A., Romero, J.V., Roselló, M.D., Villanueva, R.J.: Computing probabilistic solutions of the Bernoulli random differential equation. J. Comput. Appl. Math. 309, 396–407 (2017)Casabán, M.C., Cortés, J.C., Romero, J.V., Roselló, M.D.: Solving random homogeneous linear second-order differential equations: a full probabilistic description. Mediterr. J. Math. 13(6), 3817–3836 (2016)Cortés, J.C., Jódar, L., Camacho, J., Villafuerte, L.: Random Airy type differential equations: mean square exact and numerical solutions. Comput. Math. Appl. 60(5), 1237–1244 (2010)Cortés, J.C., Jódar, L., Company, R., Villafuerte, L.: Laguerre random polynomials: definition, differential and statistical properties. Util. Math. 98, 283–295 (2015)Cortés, J.C., Jódar, L., Villafuerte, L.: Random linear-quadratic mathematical models: computing explicit solutions and applications. Math. Comput. Simul. 79(7), 2076–2090 (2009)Cortés, J.C., Jódar, L., Villafuerte, L.: Mean square solution of Bessel differential equation with uncertainties. J. Comput. Appl. Math. 309(1), 383–395 (2017)Cortés, J.C., Sevilla-Peris, P., Jódar, L.: Analytic-numerical approximating processes of diffusion equation with data uncertainty. Comput. Math. Appl. 49(7–8), 1255–1266 (2005)Díaz-Infante, S., Jerez, S.: Convergence and asymptotic stability of the explicit Steklov method for stochastic differential equations. J. Comput. Appl. Math. 291(1), 36–47 (2016)Dorini, F., Cunha, M.: Statistical moments of the random linear transport equation. J. Comput. Phys. 227(19), 8541–8550 (2008)Dorini, F.A., Cecconello, M.S., Dorini, M.B.: On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Commun. Nonlinear Sci. Numer. Simul. 33, 160–173 (2016)Golmankhaneh, A.K., Porghoveh, N.A., Baleanu, D.: Mean square solutions of second-order random differential equations by using homotopy analysis method. Rom. Rep. Phys. 65(2), 350–362 (2013)Grimmett, G.R., Stirzaker, D.R.: Probability and Random Processes. Clarendon Press, Oxford (2000)Henderson, D., Plaschko, P.: Stochastic Differential Equations in Science and Engineering. Cambridge Texts in Applied Mathematics. World Scientific, Singapore (2006)Hussein, A., Selim, M.M.: A developed solution of the stochastic Milne problem using probabilistic transformations. Appl. Math. Comput. 216(10), 2910–2919 (2009)Hussein, A., Selim, M.M.: Solution of the stochastic transport equation of neutral particles with anisotropic scattering using RVT technique. Appl. Math. Comput. 213(1), 250–261 (2009)Hussein, A., Selim, M.M.: Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Appl. Math. Comput. 218(13), 7193–7203 (2012)Khodabin, M., Maleknejad, K., Rostami, M., Nouri, M.: Numerical solution of stochastic differential equations by second order Runge–Kutta methods. Math. Comput. Model. 53(9–10), 1910–1920 (2011)Khodabin, M., Rostami, M.: Mean square numerical solution of stochastic differential equations by fourth order Runge–Kutta method and its application in the electric circuits with noise. Adv. Differ. Equ. 2015, 62 (2015)Khudair, A.K., Ameen, A.A., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using Adomian decomposition method. Appl. Math. Sci. 51(5), 2521–2535 (2011)Khudair, A.K., Haddad, S.A.M., Khalaf, S.L.: Mean square solutions of second-order random differential equations by using the differential transformation method. Open J. Appl. Sci. 6, 287–297 (2016)Lesaffre, E., Lawson, A.B.: Bayesian Biostatistics. Statistics in Practice. Wiley, New York (2012)Li, X., Fu, X.: Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks. J. Comput. Appl. Math. 234(2), 407–417 (2010)Licea, J.A., Villafuerte, L., Chen-Charpentier, B.M.: Analytic and numerical solutions of a Riccati differential equation with random coefficients. J. Comput. Appl. Math. 309(1), 208–219 (2013)Liu, S., Debbouche, A., Wang, J.: On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths. J. Comput. Appl. Math. 312, 47–57 (2017)Loève, M.: Probability Theory. Vol. I. Springer, Mineola (1977)Lord, G.J., Powell, C.E., Shardlow, T.: An Introduction to Computational Stochastic PDEs. Cambridge Texts in Applied Mathematics. Dover, New York (2014)Nouri, K., Ranjbar, H.: Mean square convergence of the numerical solution of random differential equations. Mediterr. J. Math. 12(3), 1123–1140 (2015)Rencher, A.C., Schaalje, G.B.: Linear Models in Statistics, 2nd edn. Wiley, New York (2008)Santos, L.T., Dorini, F.A., Cunha, M.C.C.: The probability density function to the random linear transport equation. Appl. Math. Comput. 216(5), 1524–1530 (2010)Seber, G.A.F., Wild, C.J.: Nonlinear Regression. Cambridge Texts in Applied Mathematics. Wiley, New York (2003)Smith, R.C.: Uncertainty Quantification: Theory, Implementation, and Applications. SIAM, Philadelphia (2014)Soheili, A.R., Toutounian, F., Soleymani, F.: A fast convergent numerical method for matrix sign function with application in SDEs (Stochastic Differential Equations). J. Comput. Appl. Math. 282, 167–178 (2015)Soong, T.T.: Random Differential Equations in Science and Engineering. Academic Press, New York (1973)Villafuerte, L., Braumann, C.A., Cortés, J.C., Jódar, L.: Random differential operational calculus: theory and applications. Comput. Math. Appl. 59(1), 115–125 (2010)Xiu, D.: Numerical Methods for Stochastic Computations. A Spectral Method Approach. Cambridge Texts in Applied Mathematics. Princeton University Press, New York (2010

    CONCENTRATIONS OF LEAD, MERCURY AND CADMIUM IN TWO SPECIES OF FRESHWATER FISH RAISED IN TEMPERATURE-CONTROLLED WATER TANKS: IMPLICATIONS FOR HUMAN DIET.

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    It is known that the bioaccumulation process in fish is influenced by temperature, water-hardness and diet. Particularly, the use of warm water such as that coming from a power station plant after cooling in vapour condensers, besides enhancing the growth of fish, could facilitate accumulation process of xenobiotics with increasing health hazard for human consumers. The concentrations of three heavy metals (Pb, Hg and Cd) were determined in two species of freshwater fishes, the sturgeon (Acipenser naccarii) and the carp (Cyprinus carpio) raised in thermal aquaculture using water from the river Po. One hundred fishes with an initial weight of about 80 g each fed on wet pellets (3% of live weight) and bred for two years at a temperature ranging form a minimum of 15 \ub0C in the winter and a max of 25 \ub0C in the summer. Every three months five fishes were sacrificed and the three elements were determined by AAS in muscle samples. After 24 months of breeding, the following mean levels (mg/kg dry weight) of heavy metals were detected in the muscles of the sturgeon and the carp, respectively: 1.89 +- 1.2 and 1.52 +- 0.6 of Pb; 0.73 +- 0.3 and 0.41 +- 0.2 Hg; 0.26 +- 0.1 and 0.10 +- 0.06 of Cd. Interestingly, the metal concentrations found in these fishes were about ten times lower than in wild ones living of the river Po, in spite of the same aquatic environment. Therefore, the results suggest that the use of the cooling water form thermoelectric plant for aquaculture is a highly efficient system. In fact, it allows considerable fish growth in short time but reducing the bioaccumulation of the heavy metals, so that the raised fish can be considered suitable for human consumption

    An efficient algorithm for sensor placement in water distribution systems

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    The objective of this paper is to present an optimal sensor placement methodology to assist in the effective and efficient detection of accidental and/or intentional contaminant intrusion(s) in water distribution systems. The work presented here is done in response to call for papers for the Battle of the Water Sensors Networks (BWSN), at the Water Distribution Systems Analysis Symposium (2006). The above problem is formulated and solved as a constrained multiobjective optimisation problem. The four objectives are: (1) minimisation of the expected time of detection, (2) minimisation of the expected population affected prior to detection, (3) minimisation of the expected demand of contaminated water prior to detection and (4) maximisation of the detection likelihood. The constraint modelled is the pre-specified number of detection sensors used in the sampling design. Decision variables are the sensor network locations. The solution methodology proposed is based on the novel Noisy Cross-Entropy Sensor Locator (nCESL) algorithm. This algorithm is applied to the two competition networks under four base contamination scenarios (A, B, C and D) and two different numbers of sensors available (5 and 20). The results obtained demonstrate the effectiveness and efficiency of the sensor placement methodology proposed. Copyright ASCE 2006

    Energy Consumption Forecast of Photo-Voltaic Comfort Cooling using UPPAAL Stratego

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