1. Analysis of growth models for batch kefir grain biomass production in RC1 reaction systemMarko Tramšek, Andreja Goršek, 2008, izvirni znanstveni članek Opis: This work describes the statistical analysis of three mathematical models, modified for describing the kefir grain biomass growth curve. Experimental data of time-dependent kefir grain mass increase were used. The propagation was performed in RC1 batch reaction system under optimal bioprocess parameters (temperature, rotational frequency of stirrer, glucose mass concentration) using traditional cultivation in fresh, high-temperature, pasteurized whole fat cow's milk. We compared values of biological parameters obtained by applying the nonlinear regression of experimental data in logistic, Gompertz and Richards models. The most statistically appropriate model was determined using the seven statistical indicators. We established that the kefir grain biomass growth curve during batch propagation under optimal bioprocess conditions can be most successfully described using the Gompertz growth model. Ključne besede: chemical processing, milk products, kefir grain growth, process parameters, design of experiments, modeling, mathematical models, Gompertz growth model, RC1 Objavljeno: 31.05.2012; Ogledov: 1918; Prenosov: 74 Povezava na celotno besedilo |
2. |
3. Analytical calculation of diffusion coefficients and other transport properties in binary mixturesJurij Avsec, Maks Oblak, 2006, izvirni znanstveni članek Opis: The note features the mathematical model of computing binary diffusion coefficient, thermal diffusion factor and viscosity in the real-gas region on the basis of nonequilibrium statistical mechanics. For the analytical calculation of transport properties, we have used the Kihara and Chapman-Cowling model up to the third order. In the presented note we calculated transport properties for mixtures between carbon monoxide and helium. We have developed the new mixing rules for the calculation of transport properties for mixtures. The analytical results obtained by statistical mechanics are compared with the experimental data and they show relatively good agreement. Ključne besede: thermodynamics, statistical thermodynamics, mathematical models, binary diffusion coefficient, thermal diffusivity, binary mixtures Objavljeno: 30.05.2012; Ogledov: 1339; Prenosov: 43 Povezava na celotno besedilo |
4. Reinforcing methods for composite timber frame-fiberboard wall panelsPeter Dobrila, Miroslav Premrov, 2003, izvirni znanstveni članek Opis: This paper presents different possibilities on how to reinforce timber frame wall panels, which are mainly used as load-carrying capacity elements in the construction of prefabricated timber structures. These walls can be treated as composite elements composed of a timber frame and fiber-plaster boards. As the boards are the weaker part of the system they need to be somehow reinforced in order to assure the resistance and ductility of the elements especially in multi-level buildings located in seismic or windy areas. The aim of this research is to determine the differences in resistance and ductility between elements, reinforced using two different methods. Whilst the first, using additional fiberboards, does not improve the resistance and especially the ductility in the contended sense, it is more convenient for finding a solution when inserting diagonal steel strips, which are fixed to the timber frame. Ključne besede: timber structures, stene, fiber-plaster boards, steel diagonals, mathematical models Objavljeno: 01.06.2012; Ogledov: 1383; Prenosov: 73 Povezava na celotno besedilo |
5. Calculation of thermophysical and thermochemical properties during hydrocarbon combustionJurij Avsec, Franc Zgaga, Milan Marčič, 2002, izvirni znanstveni članek Opis: A mathematical model is presented for computing the chemical and thermophysical properties in the process of combustion of natural gas. To identify the parameters of state of combustion products, their composition hasto be known, which may be determined from chemical equilibrium. The computation is performed with the use of chemical potentials and statistical thermodynamics, featuring all important molecular contributions (translation, rotation, vibration, and intermolecular potential energy). A thermal equation of state with two virial terms is used. The real gas mixture is treated as consisting of four components: carbon dioxide, nitrogen, carbon monoxide, and water. Virial coefficients are dependent on temperature and mole fractions of the real components. Mixed terms are taken into account. The caloric equation of state is based on statistical thermodynamics for an ideal gas. Corrections are made in accordance with the second law of thermodynamics and the thermal equation of state. As the whole computation is based on matrix algebra, increasing the number of components presents no problems. We tested our model in the high-pressure region (100 bar) and the low-pressure region (1 bar), in the temperature range 500 - 6000°K. Our model is compared with other analytical models presented in the literature and shows relatively good agreement. At the same time we tested the influence of real conditions on the chemical and thermophysical properties of combustion products. Ključne besede: statistical thermodynamics, thermodynamical properties, combustion of natural gas, mathematical models, thermodynamic functions of state, equation of state, virial coefficients Objavljeno: 01.06.2012; Ogledov: 1278; Prenosov: 79 Povezava na celotno besedilo |
6. MLC-kinase/phosphatase control of Ca[sup]2+ signal transduction in airway smooth musclesAleš Fajmut, Milan Brumen, 2008, izvirni znanstveni članek Opis: In airway smooth muscles, kinase/phosphatase-dependent phosphorylation and dephosphorylation of the myosin light chain (MLC) have been revealed by many authors as important steps in calcium ▫$(Ca^{2+})$▫ signalling pathway from the variation of ▫$Ca^{2+}$▫ concentration in cytosol to the force development. Here, a theoretical analysis of the control action of MLC-kinase (MLCK) and MLC-phosphatase (MLCP) in ▫$Ca^{2+}$▫ signalling is presented and related to the general control principles of these enzymes, which were previously studied by Reinhart Heinrich and his co-workers. The kinetic scheme of the mathematical model considers interactions among ▫$Ca^{2+}$▫, calmodulin (CaM) and MLCK and the well-known 4-state actomyosin latch bridge model, whereby a link between them is accomplished by the conservation relation of all species of MLCK. The mathematical model predicts the magnitude and velocity of isometric force in smooth muscles upon transient biphasic ▫$Ca^{2+}$▫ signal. The properties of signal transduction in the system such as the signalling time, signal duration and signal amplitude, which are reflected in the properties of force developed, are studied by the principles of the metabolic control theory. The analysis of our model predictions confirms as shown by Reinhart Heinrich and his co-workers that MLCK controls the amplitude of signal more than its duration, whereas MLCP controls both. Finally, the simulations of elevated total content of MLCK, a typical feature of bronchial muscles of asthmatic subjects and spontaneously hypertensive rats as well as potentiation of MLCP catalytic activity, are carried out and are discussed in view of an increase in the force magnitude. Ključne besede: cells, calcium, calcium oscillations, myosin light chains, enzyme activities, mathematical models Objavljeno: 07.06.2012; Ogledov: 1233; Prenosov: 9 Povezava na celotno besedilo |
7. Review of experimental models for confirmation of mathematical models of gearsBoris Aberšek, Jože Flašker, 2008, izvirni znanstveni članek Opis: In order to calculate the service life as precisely and reliably as possible we need good mathematical models for describing loading, geometry, properties of materials and fracture mechanics parameters. It can be established whether a mathematical model is precise and reliable only by comparison of results of the method such as analytical methods in case of simple problems and experiment when real complex structure are deal with. Since gears and gearing belong to the second group, by correctly selected and developed test pieces and carefully planned experiments we obtained results with which we confirmed and justified the mathematical model for calculating mentioned parameters. To this end we will show in this paper series of experimental methods and test pieces used on the gears. Ključne besede: machine elements, gears, mathematical models, testing, experimental methods, numerical analyses Objavljeno: 07.06.2012; Ogledov: 806; Prenosov: 36 Povezava na celotno besedilo |
8. Transition from Gaussian to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma gameMatjaž Perc, 2007, izvirni znanstveni članek Opis: We study the impact of stochastic payoff variations with different distributions on the evolution of cooperation in the spatial prisoner's dilemma game. We find that Gaussian-distributed payoff variations are most successful in promoting cooperation irrespective of the temptation to defect. In particular, the facilitative effect of noise on the evolution of cooperation decreases steadily as the frequency of rare events increases. Findings are explained via an analysis of local payoff ranking violations. The relevance of results for economics and sociology is discussed. Ključne besede: stochastic systems, spatial resonance, stochastic payoff variations, nonlinear systems, noise, spatial dynamics, mathematical models, prisoner's dilemma Objavljeno: 07.06.2012; Ogledov: 1212; Prenosov: 63 Povezava na celotno besedilo |
9. Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systemsMarko Gosak, Matjaž Perc, 2007, izvirni znanstveni članek Opis: We show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance. In particular, additive Gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner. Results obtained for the logistic map and the Lorenz equations suggest that the presented mechanism of coherence resonance is valid beyond particularities of individual systems. We attribute the findings to the increasing attraction of imminent periodic orbits and the ability of noise to anticipate their existence and use a modified wavelet analysis to support our arguments. Ključne besede: chaotic systems, spatial resonance, coherence resonance, nonlinear systems, noise, spatial dynamics, mathematical models, bifurcation diagrame Objavljeno: 07.06.2012; Ogledov: 1422; Prenosov: 65 Povezava na celotno besedilo |
10. Selective regulation of protein activity by complex Ca[sup]2+ oscillations : a theoretical studyBeate Knoke, Marko Marhl, Stefan Schuster, 2007, samostojni znanstveni sestavek ali poglavje v monografski publikaciji Opis: Calcium oscillations play an important role in intracellular signal transduction. As a second messenger, ▫$Ca^{2+}$▫ represents a link between several input signals and several target processes in the cell. Whereas the frequency of simple ▫$Ca^{2+}$▫ oscillations enables a selective activation of a specific protein and herewith a particular process, the question arises of how at the same time two or more classes of proteins can be specifically regulated. The question is general and concerns the problem of how one second messenger can transmit more than one signal simultaneously (bow-tie structure of signalling). To investigate whether a complex ▫$Ca^{2+}$▫ signal like bursting, a succession of low-peak and high-peak oscillatory phases, could selectively activate different proteins, several bursting patterns with simplified square pulses were applied in a theoretical model. The results indicate that bursting ▫$Ca^{2+}$▫ oscillations allow a differential regulation of two different calcium-binding proteins, and hence, perform the desired function. Ključne besede: biophysics, calcium oscillations, cellular dynamics, mathematical models, signalling, bow-tie structures, bursting, decoding Objavljeno: 07.06.2012; Ogledov: 1069; Prenosov: 10 Povezava na celotno besedilo |