• Korean Journal of Computational Design and Engineering
• /
• v.2 no.1
• /
• pp.11-18
• /
• 1997

Scientific volume visualization addresses the representation, manipulation, and rendering of volumetric data sets, providing mechanisms for looking closely into structures and understanding their complexity and dynamics. In the past several years, a tremendous amount of research and development has been directed toward algorithms and data modeling methods for a scientific data visualization. But there has been very little work on developing a mathematical volume model that feeds this visualization. Especially, in flow visualization, the volume model has long been required as a guidance to display the very large amounts of data resulting from numerical simulations. In this paper, we focus on the mathematical representation of volumetric data sets and the method of extracting meaningful information from the derived volume model. For this purpose, a B-spline volume is extended to a high dimensional trivariate model which is called as a flow visualization model in this paper. Two three-dimensional examples are presented to demonstrate the capabilities of this model.

• KSBB Journal
• /
• v.10 no.4
• /
• pp.358-369
• /
• 1995

A mathematical model using local thermodynamic equilibrium isotherms for adsorption in encapsulated adsorbent is proposed in order to optimize the design parameters in situ bioproduct separation process. The model accurately follows the experimental data on the adsorption of berberine, secondary metabolite produced in Thaictrum rugosum plant cell culture. The adsorption rate on encapsulated adsorbent is compared with that on alginate-entrapped adsorbent. The result shows that the higher loading capacity in encapsulated adsorbent is mainly due to the increase in the maximum solid phase concentration. Based on the adsorption rate and loading capacity, the encapsulated adsorbent would be more useful than the entrapped adsorbent when used in situ bioproduct separation process. Design parameters in situ bioproduct separation process, such as the size of the capsule, membrane thickness, the ratio of capsule volume to bulk volume, the ratio of single capsule volume to total capsule volume and the adsorbent content in the capsule, are evaluated by using the model. The ratio of single capsule volume to total capsule volume is the most effective parameter for adsorption of berberine on encapsulated adsorbent.

• Journal of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.885-897
• /
• 2006

A new mathematical model of pumping heart coupled to lumped compartments of blood circulation is presented. This lumped pulsatile cardiovascular model consists of eight compartments of the body that include pumping heart, the systemic circulation, and the pulmonary circulation. The governing equations for the pressure and volume in each vascular compartment are derived from the following equations: Ohm's law, conservation of volume, and the definition of compliances. The pumping heart is modeled by the time-dependent linear curves of compliances in the heart. We show that the numerical results in normal case are in agreement with corresponding data found in the literature. We extend the developed lumped model of circulation in normal case into a specific model for arrhythmia. These models provide valuable tools in examining and understanding cardiovascular diseases.

• IE interfaces
• /
• v.24 no.3
• /
• pp.241-247
• /
• 2011

This paper develops a mathematical model which searches an optimum lot size of a press line, and applies this model to the scheduling of the press line. This mathematical model is not a widely studied cost model but a model which considers the utilization of the press line under a lean production system. In this paper, the optimum lot size is a minimum lot size which does not exceed the total work time of the press line. A production volume and the priority of the production in the press line are adjusted using this optimum lot size. A mathematical model developed in this paper will allow determining the optimum lot size easily in case of variable production environments such as an introduction of a new product and a fluctuation of production volume of each item. Therefore, our model will make a better scheduling of the press line and will enhance the utilization of it.

• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.215-241
• /
• 2003

In this paper, solute transport in heterogeneous aquifers using a modified Fokker-Planck equation (MFPE) is investigated. This newly developed mathematical model is characterised with a time-, scale-dependent dispersivity. A two-dimensional finite volume quadrilateral mesh method (FVQMM) based on a quadrilateral background interpolation mesh is developed for analysing the model. The FVQMM transforms the coupled non-linear partial differential equations into a system of differential equations, which is solved using backward differentiation formulae of order one through five in order to advance the solution in time. Three examples are presented to demonstrate the model verification and utility. Henry's classic benchmark problem is used to show that the MFPE captures significant features of transport phenomena in heterogeneous porous media including enhanced transport of salt in the upper layer due to its parameters that represent the dependence of transport processes on scale and time. The time and scale effects are investigated. Numerical results are compared with published results on the some problems.

• Computers and Concrete
• /
• v.29 no.6
• /
• pp.361-374
• /
• 2022

On the premise of ensuring that the automatic and quantitative discharging function of concrete conveyors is met, the accuracy of the weight forecast by the mathematical model of the screw conveying volume is improved, and the error of the weight of the concrete parts and the accumulation thickness is reduced. In this paper, the discrete element method (DEM) is used to simulate the macroscopic flow of concrete. Using the concrete discrete element model, the size of the screw conveyor is set, and establish the response model between the influencing factors (process and structure) and the concrete mass flow rate according to the design points of the screw discharging experiment. The nonlinear data fitting method is used to obtain the volumetric efficiency function under the influence of process and structural factors, and the traditional screw conveying volume model is improved. The mass flow rate of concrete predicted by the improved mathematical model of screw conveying volume is consistent with the test results. The model can accurately describe the conveying process of concrete and achieve the purpose of improving the accuracy of forecasting the weight of discharged concrete.

• Water for future
• /
• v.17 no.2
• /
• pp.125-131
• /
• 1984

watershed Model by mathematical formulation is one of the powerful tool to analyze the hydrologic process in a watershed. The seasonal watershed model is one of the mathematial model from which the monthly streamflow can be simulated and forcasted for given precipitaion data. This model also enables us to compute the monthly runoff at each subbgasin when the basin is subdivided into several small subbasins. The computation of runoff volume makes a Prediction of the areal distirbution of runoff volume for a given precipitation data. Several basins in Han River basin were chosen to simulate the monthly runoff and compute the runoff at each subbasin. A simple logarithmic regression were conducted between runoff ratio and area ratio. The correlation was very high and the equation can be used for prediciting flood volume when flood at downstream gaging station is know.

• Journal of applied mathematics & informatics
• /
• v.9 no.2
• /
• pp.561-577
• /
• 2002

In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed.

• Journal of Pharmaceutical Investigation
• /
• v.10 no.1
• /
• pp.1-3
• /
• 1980

The model of an isolated organ system has been developed to simulate the kinetic behavior of drug levels in an acting organ or site. The model is developed from basic considerations of drug distribution with hemodynamical and pharmacokinetical meanings. Model: It is considered a situation in which non-metabolic drug substance is injected into the arterial inflow of an isolated organ at constant rate. The volume of distribution and the concentration of drug in the venous outflow can be mathematically expressed as a function of time.

• Geosystem Engineering
• /
• v.21 no.6
• /
• pp.335-343
• /
• 2018

Alkali-surfactant polymer flooding has become an important technique to improve oil recovery following the development of oil fields while the function of emulsification in enhanced oil recovery is rarely considered in the existing mathematical model for numerical simulation. In this paper, the mechanism of improving the recovery of the emulsification was analyzed in ASP flooding, and a relatively perfect mathematical model with deep filtration-theory was established, in which oil-water volume equation, saturation equation, viscosity equation, and permeability reduction equation are included. The new model is used to simulate the actual block of an oil field; the simulated results of the new model and an old model without considering the emulsification are compared with the actual well history. It is found that new model which is easy to be realized in numerical simulation has a high precision fitting, and the effect of adding oil and decreasing water is obvious. The sensitivity of emulsification was analyzed, and the results show that the water reducing funnel becomes wider and the rate of water cut decreases rapidly with the increase of emulsifying capacity, and then the rate of recovery slows down. The effect of increasing oil and decreasing water is better, and the degree of recovery increases. The emulsification of the ASP flooding is maintained at a moderate level, which corresponds to ${\Phi}=0.2$ in the new model, and the emulsification is applied to realize the general mathematical quantitative description, so as to better guide the oilfield development.