Modelling and characterization of a pneumatically actuated peristaltic micropump

There is an emerging class of microfluidic bioreactors which possess long-term, closed circuit perfusion under sterile conditions with in vivo-like flow parameters. Integrated into microfluidics, peristaltic-like pneumatically actuated displacement micropumps are able to meet these requirements. We present both a theoretical and experimental characterization of such pumps. In order to examine volume flow rate, we have developed a mathematical model describing membrane motion under external pressure. The viscoelasticity of the membrane and hydrodynamic resistance of the microfluidic channel have been taken into account. Unlike other models, the developed model includes only the physical parameters of the pump and allows the estimation of their impact on the resulting flow. The model has been validated experimentally.     

Mathematical modeling and study of the process of solidification in metal casting

The process of melting and solidification in metal casting is considered. The process is modeled by a three-dimensional two-phase initial-boundary value problem of the Stefan type. The mathematical formulation of the problem and its finite-difference approximation are given. A numerical algorithm is presented for solving the direct problem. The results are described and analyzed in detail. Primary attention is given to the evolution of the solidification front and to how it is affected by the parameters of the problem. Some of the results are illustrated by plots.     

Mathematical modeling of laser heating of metal. Dynamical problem

Institute of Mathematics and Information, Lithuanian Academy of Sciences. Translated from Litovskii Matematicheskii Sbornik (Lietyovs Matematikovs Rinkinys), Vol. 31, No. 4, pp. 687–699, October–December, 1991.     

Mathematical modeling of laser heating of metal. Spatial problem

Institute of Mathematics and Information, Lithuanian Academy of Sciences. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 4, pp. 700–707, October–December, 1991.     

Mathematical modeling of a reverse-process in a multibed catalytic reactor

An effective algorithm is presented for mathematical modeling of unsteady-state processes of heat and mass transfer in a multibed catalytic reactor that operates at periodic changes of the direction of the flow of an inlet gas.     

Mathematical modeling of church growth

The possibility of using mathematics to model church growth is investigated using ideas from population modeling. It is proposed that a major mechanism of growth is through contact between religious enthusiasts and unbelievers, where the enthusiasts are only enthusiastic for a limited period. After that period they remain church members but less effective in recruitment. This leads to the general epidemic model which is applied to a variety of church growth situations. Results show that even a simple model like this can help understand the way in which churches grow, particularly in times of religious revival.     

Mathematical modeling of plant morphogenesis

Current trends in biology call for analysis of the bulk information accumulated through mathematical simulations of biological processes aiming at revealing certain regularities and verifying hypotheses and predictions. Evolution of organisms is of special interest to mathematical modeling because it integrates a great body of different processes varying over time and over space. In this paper, models of biological processes as related to plant development are reviewed. The models are classified, and approaches to problems that are most intricate from the simulation standpoint, as well as relevant mathematical methods, are described.     

Mathematical modeling of infiltration metasomatism in a porous medium

We construct a mathematical model describing the processes of dissolution and redeposition of minerals in a medium with a nonhomogeneous distribution of acidity. The dynamics of extraction of a mineral from a leaching solutions is investigated. We show that filtration of solutions through reduced acidity regions induces deposition, increasing the concentration of the target mineral in the solid phase; in high pH regions, on the other hand, the mineral dissolves. The stratum may retain certain reserves of the target mineral after leaching depending on the size of the reduced pH region and its proximity to the extraction borehole. __________ Translated from Prikladnaya Matematika i Informatika, No. 26, pp. 5–17, 2007.     

Mathematical modeling of the temperature fields during the solidification of metal in molds of complicated profile

We present a computational model of the process of solidification of metal in molds of complicated configuration. The model is based on the theory of R-functions, which makes it possible to construct the normal equations of drawings and introduce additional parameters into these equations, by means of which one can assure the required behavior of the solution corresponding to the technological implementation of the process. Computational experiments were carried out using thePOLE system. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 59–65.     

Numerical investigation of a developmental pneumatically fed impact pulveriser

The current work has been carried out on a pneumatically fed impact pulveriser. A recent build of the proposed device, and early experiments have shown promising size reduction ratios and energy savings in comparison with conventional milling techniques.     

Mathematical modeling and computer simulation of a robotic rat pup

In this paper, we describe the mathematics and computer implementation of a robotic rat pup simulation. Our goal is to understand neurobehavioral principles in a mammalian model organism—the Norway rat pup (Rattus norvegicus). Our approach is unique in that animal, simulation, and robot studies occur in parallel and inform each other. Behavior is dependent on the nervous system, body morphology, physiology, environment, and the interactions among these elements. Autonomous robotics hardware models and their associated simulations allow the possibility of systematically manipulating variables in each of these elements in ways that would be impossible using live animals. Specifically, we describe the development and validation of a Newtonian-dynamics-based simulation of a robotic rat pup, including mathematical formulation and computer implementation. The computer simulation consists of three distinct components that interact to simulate robotic behavior: (1) dynamics of the robotic rat pup itself, including sensors and actuators, (2) environmental coupling dynamics of the robot arena with the robotic rat pup, and (3) the robot control algorithms as implemented on the physical robot. The mathematical formulation, software implementation, model identification, model validation, and an application example are all described.     

Mathematical modeling of multioscillator antennas located above a real Earth

A method is proposed for calculating the current distribution and the main electrical characteristics of arbitrarily oriented multioscillator antennas above a plane Earth. The boundary-value problem is reduced to a system of Gallen integral equations, which is solved by Galerkin's method with self-regularization. The saddle-point method is used to evaluate the Sommerfeld integrals for the far-zone field. Numerical results are presented.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 77–85.     

Mathematical modeling of spatial-temporal structures in a heterogeneous catalytic system

The article focuses on mathematical modeling of the spatial-temporal structures that appear in a heterogeneous catalytic reaction on the surface of a catalyst. A system of consistent mathematical models has been developed for a three-component reaction, describing self-organization phenomena on macro, meso, and micro levels. Qualitative analysis of the solutions of the ODE system (macro level) produces the existence regions of spatial-temporal structures of various types in distributed meso- and micro-level models. A point model is applied to predict the shape of traveling impulses and fronts; the switching direction in a bistable medium is determined analytically. Solutions constructed and investigated for a PDE multicomponent reaction-diffusion system describe trigger waves, single traveling impulses, phase and spiral waves. Spatial-temporal structures on the atomic level are investigated by the Monte Carlo method. Direct and inverse trigger waves are implemented, as well as single traveling impulses and spiral waves. The effect of internal fluctuations in the reaction system is investigated.     

Mathematical modeling of a steam generator for sensor fault detection

A dynamic model for a nuclear power plant steam generator (vertical, preheated, U-tube recirculation-type) is formulated as a sixth-order nonlinear system. The model integrates nodal mass and energy balances for the primary water, the U-tube metal and the secondary water and steam. The downcomer flow is determined by a static balance of momentum. The mathematical system is solved using transient input data from the Philippsburg 2 (FRG) nuclear power plant. The results of the calculation are compared with actual measured values. The proposed model provides a low-cost tool for the automatic control and simulation of the steam generating process. The “parity-space” algorithm is used to demonstrate the applicability of the mathematical model for sensor fault detection and identification purposes. This technique provides a powerful means of generating temporal analytic redundancy between sensor signals. It demonstrates good detection rates of sensor errors using relatively few steps of scanning time and allows the reconfiguration of faulty signals.     

Mathematical modeling of matter distribution in a circular cell ensemble

In this paper, a mathematical model describing substance transport in a circular cell ensemble is considered. The model is represented by an autonomous system of equations. With a parameter continuation model, it is shown that the stationary solutions may have various symmetry types represented by closed curves. The periodic solutions have the same property, where the components differ from each other by a simple shift.     

Mathematical modeling and fuzzy control of a flexible-link robot arm

In this paper, the Timoshenko theory is applied to investigate a new mathematical model for the “shoulder-elbow-like” single flexible-link robot arm with dampings. Detailed analysis and derivation are given to support the mathematical modeling of this particular flexible mechanism. A new design of a fuzzy-logic-based (PI + D)² control scheme is developed for both vibration suppression and set-point tracking. Computer simulation results for the modeling are performed to observe the significant vibration modes, and simulation results for the control scheme demonstrate that the controllers perform very well for the tracking based on this flexible-link model. A newly developed method for stability analysis using the “two-straight-lines” criterion is also presented.