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J Neurosurg Sc 1977; 21: 243-246. Giulioni M, Ursino M. Impact of cerebral perfusion pressure and autoregulation on intracranial dynamics: A modeling study. Neurosurgery 1996; 39: 1005-1015. Juniewicz H, Kasprowicz M, Czosnyka M, Czosnyka Z, Gilewski S, Dzik M and Piccard JD. Analysis of intracranial pressure during and after the infusion test in patients with communicating hydrocephalus. Physiol Meas 2005; 26: 1039-1048. Lakin W, Stevans SA, Tranmer BI, Penar PL. A whole body mathematical model for intracranial pressure dynamics. J Math Biol 2003; 46: 347

References [1]. Radan, G. (2014). Micropiles axially loaded in karst terrain. Mathematical Modelling in Civil Engineering, Special Issue, Y.R.C. 2014, from . [2]. Seo, H. & Prezzi, M. (2008). Use of Micropiles for Foundations of Transportation Structures Final Report . Joint Transportation Research Program: Purdue University. [3]. Radan, G. (2015). Methods of foundation and stabilization of terrains with micropiles . Unpublished Doctoral Thesis, Technical

, 93-103. Angus, J.F., Cunningham, R.B., Moncur, M.W., Mackenzie, D.H. (1981). Phasic development in field crops. I. Thermal response in the seedling phase. Field Crops Research, 3, 365-378. Benech Arnold, R.L., Ghersa, C.M., Sanchez, R.A., Insausti, P. (1990). A mathematical model to predict Sorghum halepense (L.) Pers. seedling emergence in relation to soil temperature. Weed Research, 30, 91-99. Berge, N., Samaan, M., Juanole, G., Atamna J. (1994). Methodology for LAN modelling and analysis using Petri net based models. Proc. Int. Workshop on Modelling

, 347. Demir, V., Gunhan, T., Yagcioglu, A.K., Degirmencioglu, A. (2004). Mathematical modeling and the determination of some quality parameters of air-dried bay leaves. Biosystems Engineering, 88 (3), 325-335. Duttaroy, A.K., Jørgensen, A. (2004). Effects of kiwifruit consumption on platelet aggregation and plasma lipids in healthy human volunteers. Platelets, 15 (5), 287-292. Janowicz, M., Lenart A. (2007). Rozwój i znaczenie operacji wstępnych w suszeniu żywności. Właściwości Fizyczne Suszonych Surowców i Produktów Spożywczych , Komitet Agrofizyki PAN

model to predict seed dormancy loss in the field for Bromus tectorum L. Journal of Experimental Botany 49, 1235-1244. Benech Arnold, R.L., Ghersa, C.M., Sanchez, R.A., Insausti, P. (1990). A mathematical model to predict Sorghum halepense (L.) Pers. seedling emergence in relation to soil temperature. Weed Research, 30, 91-99. Berry, G.J., Cawood, R.J., Flood, R.G. (1988). Curve fitting of germination data using the Richards function. Plant, Cell & Environment, 11, 183–188. Bewley, J.D., Black, M. (1994). Seeds. Germination, Structure, and Composition. Springer

References Fic M., Ślesicki M., 2001. Wykorzystanie metod modelowania matematycznego do oceny oddziaływania wylewiska ścieków komunalnych na wody podziemne. (The use of mathematical modelling methods in evaluation of the effect of dumping site of municipal waste waters on ground waters). Zesz. Probl. Post. Nauk Rol. , 475: 415-429. Gutowska-Siwiec L., Ślesicki M., 2002. Mathematical modelling of contaminant flow and transport in ground waters. Env. Protect. Eng. , 28, 1: 43-48. Macioszczyk T., Rodzoch A., Frączek E., 1993. Projektowanie stref ochronnych źródeł

References Marchuk, G. I. (1982). Mathematical modelling in environmental problem . Moscow: Science. Marchuk, G. I. and Kondratyev, K. Y. (1992). Priorities of global ecology . Moscow: Science. Marchuk, G. I. (1973). Numerical solution of atmospheric and ocean dynamics problems. Moscow: Science. Jennifers, J. (1981). Introduction to system analysis: application for ecology. Moscow: World. Alekseyev, V. V., Kiselyeva, S. V., Lappo, S. S. (2005). Laboratory models of physical processes. Moscow: Science. Serdiutskaya, L. F. (2000). Study of mathematical

Mathematical modelling of wet oxidation of excess sludge

A mathematical model enabling a quantitative description of wet oxidation of excess sludge in continuous bubble columns is proposed. The model consists of mass and heat transfer kinetic equations and material and heat balance equations of gas and liquid phases flowing through the absorber. The equations of material and heat balance refer to a parallel, co- current flow of gas and liquid phase and take into account a complex chemical reaction in the liquid phase core. The proposed model was used in a numerical simulation of wet oxidation in a bubble absorber for different process conditions: flow rate and composition of the gas and liquid phase, temperature and pressure, and different heights and diameters of the column.


The paper presents a part of the work conducted in the first stage of a Research Grant called ”Hybrid micro-cogeneration group of high efficiency equipped with an electronically assisted ORC” acronym GRUCOHYB. The hybrid micro-cogeneration group is equipped with a four stroke Diesel engine having a maximum power of 40 kW. A mathematical model of the internal combustion engine is presented. The mathematical model is developed based on the Laws of Thermodynamics and takes into account the real, irreversible processes. Based on the mathematical model a computation program was developed. The results obtained were compared with those provided by the Diesel engine manufacturer. Results show a very high correlation between the manufacturer’s data and the simulation results for an engine running at 100% load. Future developments could involve using an exergetic analysis to show the ability of the ORC to generate electricity from recovered heat


The main aim of the current paper is to create a mathematical model for dual layer shell type recuperation system, which allows reducing the heat losses from the biomass digester and water amount in the biogas without any additional mechanical or chemical components. The idea of this system is to reduce the temperature of the outflowing gas by creating two-layered counter-flow heat exchanger around the walls of biogas digester, thus increasing a thermal resistance and the gas temperature, resulting in a condensation on a colder surface. Complex mathematical model, including surface condensation, is developed for this type of biogas dehumidifier and the parameter study is carried out for a wide range of parameters. The model is reduced to 1D case to make numerical calculations faster. It is shown that latent heat of condensation is very important for the total heat balance and the condensation rate is highly dependent on insulation between layers and outside temperature. Modelling results allow finding optimal geometrical parameters for the known gas flow and predicting the condensation rate for different system setups and seasons.