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1 Archives of Control Sciences
1 International Journal of Applied Mathematics and Computer Science
1 Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych Politechniki Wrocławskiej. Studia i Materiały
1 Scientific Papers of The Institute of Electrical Machines, Drives and Measurements of the Wrocław University of Science and Technology Series: Studies and Research

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A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

Cherniha R., Stachowska-Piętka J., Waniewski J.

International Journal of Applied Mathematics and Computer Science

2014

Vol. 24, no. 4

837--851

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a three-component nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations as well as hydrostatic pressure. The model is developed in one spatial dimension approximation, and a governing equation for each of the variables is derived from physical principles. Under some assumptions the model can be simplified to obtain exact formulae for spatially non-uniform steady-state solutions. As a result, the exact formulae for fluid fluxes from blood to the tissue and across the tissue are constructed, together with two linear autonomous ODEs for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.

Steady-state analysis for a class of hyperbolic systems with boundary inputs

Bartecki K.

Archives of Control Sciences

2013

Vol. 23, no. 3

295--310

Results of a steady-state analysis performed for a class of distributed parameter systems described by hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of the system with two state variables and two boundary inputs, the analytical expressions for the steady-state distribution of the state variables are derived, both in the exponential and in the hyperbolic form. The influence of the location of the boundary inputs on the steady-state response is demonstrated. The considerations are illustrated with a practical example of a shell and tube heat exchanger operating in parallel- and countercurrent-flow modes.

Algorytm bezpośredniego określania stanów ustalonych w maszynach prądu przemiennego z uwzględnieniem równania ruchu

Sobczyk J.

Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych Politechniki Wrocławskiej. Studia i Materiały

2008

Vol. 62, nr 28

66-74

Praca prezentuje metodykę określania stanów ustalonych w maszynach prądu przemiennego w przypadkach gdy prędkość obrotowa maszyny nie jest stalą i zawiera składową okresową. Konieczne jest wówczas uwzględnianie równania ruchu mechanicznego, co napotyka na zasadnicze trudności, gdyż równania takiego układu elektromechanicznego mają nieliniowy charakter. W literaturze takie stany pracy wyznaczane są przez numeryczne całkowanie równań różniczkowych maszyny, łącznie z równaniem mechanicznym. W pracy przedstawiono algorytm, który umożliwia określenie rozwiązań ustalonych, zarówno jakościowe jak i ilościowe, poprzez bezpośrednie wyznaczenie widm Fouriera prądów oraz prędkości obrotowej.

The paper presents a methodology for determining steady-states in AC machines when angular veta ity is not constant and contain a periodic component. In such cases the motion equation should be taker into account what leads to essential troubles because such electromechanical equations are non-linear Usually such solutions are determined by numerical integration of differential equation of a machine both electrical and mechanical one. In the paper an algorithm is presented, which enables direct dctermii nation of the Fourier spectra of currents and mechanical values, such as angular velocity and rotary angle in steady-states, both qualitatively and quantitatively.