Performance Of Mathematical Model Research Articles

Automation and optimal design method of a wheeled vehicle operating over sloped weak sandy terrain

In this paper, a mathematical model of wheeled vehicle tractive or braking performance was developed and verified by experimental data. Then, various center of gravity and height of application force movement effects were analysed by simulation analysis. For a given set of vehicle dimensions and terrain wheel system constants, the simulation calculated effective tractive or braking effort and rear wheel sinkage, slip ratio or skid of a special designed wheeled robotic vehicle running over sloped weak sandy terrain for straight forward motion. For a 5.88 kN weight vehicle, the optimal eccentricity of center of gravity, the optimal application height and the maximum slope angle of terrain could be determined for rear-wheel drive (RWD), front-wheel drive (FWD), four-wheel drive (4WD) or rear-wheel brake (RWB), front-wheel brake (FWB), and four-wheel brake (4WB) travel systems.

Special issue on the workshop on Mathematical performance modeling and analysis (MAMA '99)

No abstract available.

A SIMPLE MODEL OF AXIAL FLOW CYCLONE PERFORMANCE UNDER LAMINAR FLOW CONDITIONS

Axial flow cyclones are particularly attractive in both gas cleaning and aerosol sampling due to the axial alignment between the inlet and outlet. In order to aid the development of suitable instruments for aerosol sampling, a mathematical model of axial flow cyclone performance under laminar flow conditions has been developed, using a number of simplifying assumptions. Aerosol penetration is considered separately through the vane section of the cyclone and its body, and the two models combined. Relating all dimensions to vane pitch, penetration as a function of Stokes’ number in the cyclone vanes is predicted to be dependent on vane outer radius, vane inner radius and the number of vane turns. Penetration in the cyclone body is predicted to depend on body length alone. Encouraging agreement is seen between published experimental data for aerosol sampling cyclones and predicted 50d ae values.

Selective catalytic reduction of NO x: a mathematical model for poison accumulation and conversion performance

A common control technique for limiting nitrogen oxide emissions is selective catalytic reduction (SCR) of NO x with NH 3. The lifetime of the catalyst, which has a critical role in overall SCR system economics, is, however, limited due to deactivation by poisoning. A two-dimensional model was developed to describe poison accumulation and activity of an SCR catalyst. The model that has no adjustable parameters accounts for simultaneous effects of internal and external diffusion and chemical kinetics in the SCR process. A validation of the model is accomplished by comparison with data from two different SCR plants. A comparison of different catalyst design variables is also made in terms of conversion after 2000 h operation in the presence of poisons. Simulations showed that it is possible to improve poison resistance of SCR catalyst monoliths by reconfiguration of their pore structure and channel diameter.

Performance limitations of free-space optical communication satellite networks due to vibrations: direct detection digital mode

Free-space optical communication between satellites net- worked together can permit high data rates between different places on Earth. The use of optical radiation as a carrier between the satellites permits very narrow beam divergence. Due to the narrow divergence and the large distance between the satellites, pointing from one satellite to another is difficult. The pointing task is further complicated by vibration of the pointing system caused by tracking noise and mechanical impacts. In this work we derive mathematical performance models for digital direct detection communication satellite networks as a function of the system parameters, the number of satellites, and the vibration amplitude. The optical intersatellite network model considered includes a transmitter sat- ellite, regenerative satellites, and a receiver satellite all networked to- gether. A comparison between three communication system modulation schemes—on-off keying (OOK), pulse position modulation (PPM), and pulse polarization binary modulation (PPBM)—is presented. These mod- els are the basis for optical communication tracking- and pointing-system design of appropriate complexity and performance to make the network as simple and inexpensive as possible. From the analysis it is clear that even low vibration amplitude of one satellite pointing system decreases the network performance dramatically. © 1997 Society of Photo-Optical Instru- mentation Engineers. (S0091-3286(97)01111-2)

Steady-State Performance of a Rotating Miniature Heat Pipe

The operating principle of a rotating miniature heat pipe (RMHP) with a grooved inner wall surface is addressed. A mathematical model of the hydrodynamic performance of RMHPs is developed. A simple correlation for the friction coefficient of axial liquid flow including a vapor drag effect is proposed, based on the numerical analysis of two-dimensional laminar liquid now in a groove. With the present model, the maximum performance and optimum liquid fill amount of RMHPs are predicted under various operating conditions. Influences of operating temperature, rotational speed, and liquid-vapor interfacial shear stress on the maximum performance and optimum liquid fill amount are discussed. Pressure drops of the axial liquid flow and vapor flow are demonstrated.

Knowledge-based fuzzy model for performance prediction of a rock-cutting trencher

A knowledge-based fuzzy model for performance prediction of a rock-cutting trencher has been developed. A trencher is a machine that uses a rotating cutting chain equipped with bits to excavate trenches in rock and soil. The performance of a trencher, and consequently the cost of a specific excavation project, is determined by its production rate and by the bit consumption (due to wear and breakage). Both these factors depend on the properties of the excavated rock material and on the trencher characteristics. Mathematical modeling of the trencher performance is difficult, since the interactions between the machine tool and the environment are dynamic, uncertain, and complex. The number of available measurements is too small to use statistical methods. Hence, an approach based on expert knowledge was applied to develop a rule-based fuzzy model. The use of fuzzy logic allows for smooth interfacing of the qualitative information involved in the rule base with the numerical input data. The developed model uses six input variables [rock strength, spacing of three joint (discontinuity) sets in the rock mass, joint orientation, and trench dimensions] to predict the production rate and bit consumption in terms of qualitative linguistic values. Numerical predictions are obtained by using a modified fuzzy-mean defuzzification which allows for straightforward adaptation of the consequent membership functions in order to fine-tune the model performance to the data. The expert knowledge is coded as if-then rules, hierarchically organized in four rule bases. The model was validated both qualitatively using dependency analysis and quantitatively using the available data. The results obtained so far are satisfactory.

A mathematical model of performance on a simple reaction time test.

A nonlinear function with components for learning and fatigue was used to model individual performance on a simple reaction time test. The relationships between the parameters of the model and the mean and variance of the reaction times are discussed. The function is used to analyze data from a field study of agricultural workers exposed to organophosphate pesticides. Exposure had a significant effect on the relationships between education level and initial performance, age and fatigue rate, and age and performance variability. Parameter estimates from the model were able to distinguish between effects that the mean and standard deviation of the reaction times were unable to distinguish.

Simulation of airlift bioreactors: Steady-state performance of continuous culture processes

A tanks-in-series model was applied for mathematical modeling of the steady-state performance of continuous cultures in an airlift bioreactor. In the present computational algorithm, non-linear algebraic equations for the material balances of micro-organism, substrate and dissolved oxygen around the hypothetical well-mixed stages with backflow in the riser and downcomer were solved simultaneously using the Newton-Raphson technique. The concentration profiles of micro-organism, substrate and dissolved oxygen in the airlift bioreactor for continuous cultures were obtained under the same specifications. The simulation results were discussed mainly from the viewpoint of mixing in the airlift bioreactor. The relationships between the micro-organism productivity and design parameters of the airlift bioreactor such as liquid recycle flow rate and downcomer configuration were examined. The effect of mixing on the washout was also discussed. Numerical examples indicate that the proposed simulation scheme is very flexible and useful for the design and operation studies of airlift bioreactors.

Performance Modeling of Parallel Algorithms for Solving Neutron Diffusion Problems

Neutron diffusion calculations are the most common computational methods used in the design, analysis, and operation of nuclear reactors and related activities. Here, mathematical performance models are developed for the parallel algorithm used to solve the neutron diffusion equation on message passing and shared memory multiprocessors represented by the Intel iPSC/860 and the Sequent Balance 8000, respectively. The performance models are validated through several test problems, and these models are used to estimate the performance of each of the two considered architectures in situations typical of practical applications, such as fine meshes and a large number of participating processors. While message passing computers are capable of producing speedup, the parallel efficiency deteriorates rapidly as the number of processors increases. Furthermore, the speedup fails to improve appreciably for massively parallel computers so that only small- to medium-sized message passing multiprocessors offer a reasonable platform for this algorithm. In contrast, the performance model for the shared memory architecture predicts very high efficiency over a wide range of number of processors reasonable for this architecture. Furthermore, the model efficiency of the Sequent remains superior to that of the hypercube if its model parameters are adjusted to make its processors as fast as thosemore » of the iPSC/860. It is concluded that shared memory computers are better suited for this parallel algorithm than message passing computers.« less

Scaleable parallel model development and performance analysis for MIMD molecular dynamics simulations

A scaleable parallel model developed specifically for molecular dynamics simulations is described. The description encompasses both hardware and software. It is mapped onto a transputer array, programmed, and used to verify concepts and gather experimental data. Simulations are run with sample sizes ranging from 1024 to 42,546 particles on arrays from 4 to 128 processors. Performance data is generated by fixing the sample size, changing the number of node processors used to run the simulation, and measuring execution speeds. The parallel implementation is dissected and used to develop a detailed mathematical performance model. The methodology for developing the mathematical model is described. Performance equations are derived for all computation and communication routines in the code, and combined to form a modular system performance estimator. Accuracy of the mathematical model is verified by comparing the measured baseline times against a set of performance estimation curves generated by the mathematical formulation. The computation and communication constraints to faster execution are identified and discussed, including the issues of load balancing, data partitioning strategy, and upper and lower limits on the number of processors that should be used for a simulation. Algorithm and architectural improvements are described, and their impact on performance predicted using the analytical tools developed.

Modeling road-cycling performance

This paper presents a complete set of equations for a "first principles" mathematical model of road-cycling performance, including corrections for the effect of winds, tire pressure and wheel radius, altitude, relative humidity, rotational kinetic energy, drafting, and changed drag. The relevant physiological, biophysical, and environmental variables were measured in 41 experienced cyclists completing a 26-km road time trial. The correlation between actual and predicted times was 0.89 (P < or = 0.0001), with a mean difference of 0.74 min (1.73% of mean performance time) and a mean absolute difference of 1.65 min (3.87%). Multiple simulations were performed where model inputs were randomly varied using a normal distribution about the measured values with a SD equivalent to the estimated day-to-day variability or technical error of measurement in each of the inputs. This analysis yielded 95% confidence limits for the predicted times. The model suggests that the main physiological factors contributing to road-cycling performance are maximal O2 consumption, fractional utilization of maximal O2 consumption, mechanical efficiency, and projected frontal area. The model is then applied to some practical problems in road cycling: the effect of drafting, the advantage of using smaller front wheels, the effects of added mass, the importance of rotational kinetic energy, the effect of changes in drag due to changes in bicycle configuration, the normalization of performances under different conditions, and the limits of human performance.

Effects of mismatch losses in photovoltaic arrays

Experimental and modeling results on the effects of mismatch losses in photovoltaic arrays are presented. Field tests conducted on each of the 192 modules are used to describe the variation in the properties of production run photovoltaic modules. Module specific estimates of a five-parameter module model are obtained by nonlinear regression. Mathematical models of four-module parallel string and series block photovoltaic array performance based on the five-parameter module model are developed and used to evaluate the variation in maximum output power and mismatch loss of arrays with random module orderings. Module maximum output power averaged 14% below the nameplate rating and exhibited a coefficient of variation of 2.1%. Mismatch losses were very small, never exceeding 0.53%. No differences between parallel string and series block arrays in array maximum output power were observed.

Free-space optical communication: detector array aperture for optical communication through thin clouds

Optical communication must contain clouds as parts of communication channels. Propagation of optical pulses through clouds causes widening in the spatial domain and attenuation of the pulse radiant power. These effects decrease the received signal and increase bit error rate (BER). One way to improve the BER of the communication system is by using adaptive methods to obtain more signal relative to noise power. Based on mathematical models of spatial widening of optical radiation derived by Monte Carlo simulation, a mathematical model for optimum performance of digital optical communication through clouds is developed. The purpose of the optimum adaptive communication system suggested here is to improve the BER by optimizing according to meterological conditions the spatial distribution of the detected radiation beam using a detector array where the external amplification of each detector is adaptable. Comparison and analysis of three models of communication systems in fog cloud channels are presented: (1) the optimum adaptive detector array aperture, (2) an ordinary single detector aperture of the same size, and (3) a small detector aperture. Improvement of more than four orders of magnitude in BER under certain conditions is possible with the new adaptive system model.

A Mathematical Model of Performance of Computer-Mediated Groups during Idea Generation

:As the use of computer-mediated systems for group work grows, the need for a better understanding of the impact of such systems becomes more important. Studies of non-computer-mediated group work have long been guided by mathematical models of group interaction and performance, but recent research suggests that these models do not fit the unique capabilities of computer-mediated systems. This article builds on previous group research to create a mathematical model of computer-mediated group performance which is then tested using data from two prior studies. This testing enabled us to conclude that models of computer-mediated groups run counter to the many guiding models of non-computer-mediated groups. We therefore discuss the implications of these differences in relation to users of this technology and to future developmental and empirical research.

Mathematical model of cycling performance.

A model of cycling performance is presented. The model is based on equating two expressions for the total amount of work performed. One expression is deduced from biomechanical principles deriving energy requirements from total resistance. The other models the energy available from aerobic and anaerobic energy systems, including the effect of oxygen uptake kinetics at the onset of exercise. The equation can then be solved for any of the variables. Empirically derived field and laboratory data were used to assess the accuracy of the model. Model estimates of 4,000-m individual pursuit performance times showed a correlation of 0.803 (P < or = 0.0001) with times measured in 18 high-performance track cyclists, with a mean difference (predicted--measured) of 4.6 s (1.3% of mean performance time). The model enables estimates of the performance impact of alterations in physiological, biomechanical, anthropometric, and environmental parameters.

Hydrolysis of Butteroil by Immobilized Lipase Using a Hollow-Fiber Reactor: Part VI. Multiresponse Analyses of Temperature and pH Effects

A lipase from Aspergillus niger, immobilized by physical adsorption on hydrophobic hollow fibers made of microporous polypropylene, was used to effect the hydrolysis of the glycerides of melted butterfat at 40, 50, 55, and 60°C (pH 7.0), and at pH 3.0, 4.0, 5.0, 7.0, 8.0, and 9.0 (40°C). McIlvane buffer and melted butterfat were pumped cocurrently through the hollow fiber reactor. The concentrations of ten different free fatty acids in the effluent oil stream were measured by HPLC. Multiresponse nonlinear regression methods were employed to fit the data to multisubstrate rate expressions derived from a Ping Pong Bi Bi mechanism in which the rate controlling step is deacylation of the enzyme. Thermal deactivation of the immobilized lipase was also included in the mathematical model of reactor performance. A postulated normal distribution of vmax with respect to the number of carbon atoms of the fatty acid residue (with an additive correction for the number of double bonds) was found to provide the best sta...

Mathematical modelling of a continuous, direct resistive heating furnace for the regeneration of activated carbon

A mathematical model of the steady-state performance of a continuous, direct resistive heating furnace (DRHF), used for regenerating granular activated carbon in gold-recovery circuits, has been developed. This mathematical model can be used as a design tool to predict the axial and radial temperature profiles, as well as the electrical potential and power requirements for a given set of carbon and steam flowrates, electrical current, and furnace dimensions. The validity of the model has been verified on a small-scale (up to about 3 kg/h) DRHF. The temperatures could mostly be predicted to within 20 K, while the electrical potential and power requirements were predicted correctly to within 10%. When the carbon's effective mean specific heat capacity was used as a fitting factor, it was concluded that the thermal decomposition of the carbon contributes about 300 J/(kg K) to the effective specific heat capacity of the sample of carbon used. Furthermore, it was concluded that carbon approaching the inlet is pre-heated by water vapour rising from the furnace, which condenses on the carbon, hence increasing its moisture content above the original moisture content of the carbon fed into the furnace hopper.

Monolithic reactors: mass transfer measurements under reacting conditions

By 1993 90% of all cars sold in the USA and the European Community will be fitted with catalytic converters. After light-off has taken place the performance of these units is controlled by mass transfer to the catalyst surface. An accurate knowledge of mass transfer coefficients is thus essential for mathematical modelling and prediction of performance. Existing correlations for mass transfer coefficients exhibit an order of magnitude discrepancy between respective predictions. The following correlation for the Sherwood number in monolithic reactors has been developed from novel sets of experiments made under reacting conditions and is valid for 0.8<(d/L Re Sc)<130. This range is typical conditions found in automobile exhaust gas cleaning applications. ▪

Hydrolysis of butteroil by immobilized lipase using a hollow‐fiber reactor: Part III. Multiresponse kinetic studies

A lipase from Aspergillus niger immobilized by adsorption on microporous, polypropylene hollow fibers was used to effect the continuous hydrolysis of the glycerides of butter oil at 40 degrees C and pH 7.0. The effluent concentrations of 10 different free fatty acid products were measured by high-performance liquid chromatography (HPLC). Multiresponse nonlinear regression methods were used to fit the data to a multisubstrate rate expression derived from a Ping Pong Bi Bi mechanism in which the rate-controlling step is deacylation of the lipase. Thermal deactivation of the enzyme was also included in the mathematical model of reactor performance. A postulated normal distribution of v(max) with respect to the chain length of the fatty acid (with an additive correction for the degree of unsaturation) was tested for statistical significance. The model is useful for predicting the free fatty acid profile of the lipolyzed butteroil product over a wide range of flow rates.