Mathematical Model Procedure Research Articles

Forecasting of Pavement Crack Performance with Adaptive Filter Model

The capability to forecast pavement crack performance has been identified as a critical pavement management system (PMS) need. In particular, crack performance forecasting can support proactive pavement management strategies. However, previous attempts at developing crack forecasting models have met with limited success. Because of the complexity of the pavement crack progression mechanism over time, a dynamic forecasting model could be more appropriate as opposed to static forecasting models. The results of a research effort to develop an adaptive filter model to forecast a pavement crack index for Florida’s highway network are summarized. The concept of the adaptive filter model is introduced along with its mathematical algorithm and modeling procedure. The adaptive filter model, which was developed with field data collected from Florida’s highway network, is able to dynamically forecast crack performance on the basis of historical crack performance data. For the purpose of model evaluation, the adaptive filter model was compared with the traditional autoregressive (AR) model. According to the comparison results, the adaptive filter model had significantly lower errors as compared with the AR model, demonstrating better forecasting capability. The adaptive filter model was more responsive to unexpected changes in pavement performance than the AR model. Given these advantages, it appears that such an adaptive filter model may have considerable potential for use in PMS applications.

Theoretical analysis for an air heater with a box-type absorber

The efficiency of the solar air collector can be enhanced by using metal vanes which are attached between the absorber and bottom plate of the collector. A mathematical model and solution procedure to study the effect of the metal vanes are presented. A method to select an optimal number of metal vanes, as well as an appropriate depth for the flowing air duct, has been developed. Moreover, a comparison between the performance of a collector having a box frame absorber and one having a finned plate absorber was carried out. The results show that a high efficiency can be achieved with the use of the metal vanes, particularly at smaller depths of the air duct.

Mathematical modeling of the migration process and prediction of the spread of contaminants from phosphogypsum wastes

Th potential and results of the procedure of mathematical modeling that we have developed for the spread of contaminants in the vicinity of harmful industrial wastes are addressed in a specific example of engineering practice.

96/01771 Thermal performance of solar air heaters: Mathematical model and solution procedure

96/01771 Thermal performance of solar air heaters: Mathematical model and solution procedure

Modelling of contaminant transport within a marshland environment

Since the early 1980s, leachate originating from the Alice and Fraser Municipal Landfill site, an active landfill site located near Pembroke, Ontario, has been discharged into a natural marshland system located some 300 m down-gradient from the waste disposal site. However, monitoring of the water quality within the marshland indicates that the contaminant level has not yet surpassed the background concentration values downstream from the main impacted area. A mathematical modelling procedure was developed in an attempt to predict the mobility of several contaminant species within the marshland environment. Parameters needed for the predictive model were gathered based on the physical configuration of the landfill and marshland as well as associated laboratory-derived data on the attenuation capacity of the marshland soil matrix. A multidimensional finite-difference model based on the Advection-Dispersion equation was used to predict migration of the contaminants. The model was adapted to the hydrologic characteristics of the marshland, emphasizing groundwater flow, dilution and the adsorption capacity of the organic soil. The surface water flow in the marshland was assumed to be at the marshland surface, i.e. only the groundwater flow in the organic soil layer was considered in this investigation. Modelling results indicate that marshland soil has the capacity to substantially retard the migration of several contaminant species typically found in landfill leachate.

Thermal performance of solar air heaters: mathematical model and solution procedure

A mathematical model and solution procedure for predicting the thermal performance of single-pass solar air collectors is presented. By omitting or providing a top glass cover over a plane absorber plate, or by providing a bottom plate under the absorber plate and circulating air over one or both of the air channels so formed, four common types of flat-plate solar air collector designs were considered. The surface temperatures of the walls surrounding the air streams were assumed uniform whereas the air temperatures were assumed to vary linearly along the collector. In the mathematical model, the solar collector was assumed sufficiently short for which the assumptions were valid. By considering a steady state heat transfer using the thermal network analysis procedure, a set of simultaneous equations for the mean temperature of the walls and the air streams were obtained. Instead of solving the simultaneous equations for mean temperatures explicitly, a matrix inversion method was employed using a standard sub-routine programme. Because heat transfer coefficients were temperature dependent, a set of mean temperatures was approximated which allowed the heat transfer coefficients to be evaluated as a first guess. An iterative process was then created that enabled the mean temperatures for the collector to be calculated. The newly-calculated mean temperatures were then compared with the initially-guessed temperatures. The iterative procedure was repeated until consecutive mean temperature values differed by less than 0.01°C. After this, another section of collector with a length equal to the previous one was added to the end of the first collector. The temperature conditions at the inlet of the second section were assumed equal to the outlet temperature conditions of the previous section. The iterative procedure to determine the mean temperatures was repeated for the next section. Additional sections were added until the required overall length of collector was considered. By this procedure, predictions of mean wall and air streams temperatures for a collector of any length could be obtained. Although only four, common single-pass types of flat-plate solar collectors are considered here, the solution procedure could be extended to encompass most other collector designs.

Thermal performance of solar air heaters: Mathematical model and solution procedure

A mathematical model and solution procedure for predicting the thermal performance of single-pass solar air collectors is presented. By omitting or providing a top glass cover over a plane absorber plate, or by providing a bottom plate under the absorber plate and circulating air over one or both of the air channels so formed, four common types of flat-plate solar air collector designs were considered. The surface temperatures of the walls surrounding the air streams were assumed uniform whereas the air temperatures were assumed to vary linearly along the collector. In the mathematical model, the solar collector was assumed sufficiently short for which the assumptions were valid. By considering a steady state heat transfer using the thermal network analysis procedure, a set of simultaneous equations for the mean temperature of the walls and the air streams were obtained. Instead of solving the simultaneous equations for mean temperatures explicitly, a matrix inversion method was employed using a standard sub-routine programme. Because heat transfer coefficients were temperature dependent, a set of mean temperatures was approximated which allowed the heat transfer coefficients to be evaluated as a first guess. An iterative process was then created that enabled the mean temperatures for the collector to be calculated. The newly-calculated mean temperatures were then compared with the initially-guessed temperatures. The iterative procedure was repeated until consecutive mean temperature values differed by less than 0.01°C. After this, another section of collector with a length equal to the previous one was added to the end of the first collector. The temperature conditions at the inlet of the second section were assumed equal to the outlet temperature conditions of the previous section. The iterative procedure to determine the mean temperatures was repeated for the next section. Additional sections were added until the required overall length of collector was considered. By this procedure, predictions of mean wall and air streams temperatures for a collector of any length could be obtained. Although only four, common single-pass types of flat-plate solar collectors are considered here, the solution procedure could be extended to encompass most other collector designs.

A Comparison of three mathematical modeling procedures for simulating fluid flow phenomena in bubble-stirred ladles

tribution between a FeS-Na2S flux and carbon-saturated liquid iron above 1200 ~ These researchers found that the distribution ratio increased with increasing FeS content in the matte and reached maximum at around FeS/ Na2S = 82/18. This trend is based on the fact that the activity of FeS in the matte increases significantly with increasing FeS content while the Ycu2s slightly increases. The temperature range of the present work is much lower than the preceding studies; however, the increase in equilibrium Cu2S content with increasing FeS content in the matte at a given temperature is similar to that of previous studies, lsl Reaction between copper and an FeS-NazS matte results in a high equilibrium Cu2S content which increases with temperature and starting FeS content. For a matte which has a starting composition of 82 wt pet FeS and 18 wt pet Na2S, the equilibrium concentration of CuzS is 52 wt pet at 1000 ~

Modelling and measurement of gas flow distribution in corrugated sheet structured packings

A mathematical model and calculation procedure are developed for the gas flow distribution in channels formed between tightly packed, corrugated, unperforated metal sheets. The model is a discrete cell model based on averaged mass, momentum and energy balance equations for each of numerous crossings of gas flow channels, with characteristic friction factors for gas inlet, bulk zone and wall zone as model parameters, which can be easily obtained from pressure drop measurements for each type and size of structured packing. The model enables prediction of velocity profiles leaving an element or packing layer consisting of segments of unperforated, structured packing. It is also suited for perforated packings which under operating (wetted) conditions function as a closed surface packing.

The Effect of Speed Versus Non-speed Training in Power Development

The objective of this research was to test the effect of a speed training versus strength training approach in power development. It was hypothesized that a speed-training program would be more efficient in power development than a strength program. Sixty-five football players participated in an off-season weight-training program. All players lifted three times per week and used the same program with one exception. Fifteen athletes performed a timed hip sled program, while the remaining 40 athletes performed a squat program designed to develop strength. The Margaraia-Kalamen (M-K) power test was used as a measure of power in watts. Baseline and follow-up weight/height2 (BMI), power clean, push press, squat and vertical jump measures were recorded. Using group comparison and paired t-tests, and analysis of covariance and ordinary least squares mathematical modeling procedures, no difference could be found between the two groups on any of the measures. Modeling was used to test the effect of the training group on power development while controlling for initial differences; no group differences in training effect were found. It was concluded that while speed training was not found to be superior to strength training, it could be an equivalent substitute. Future studies should evaluate a combined speed and strength approach for maximum efficiency in power development.

The Quantification of Pure-tone Audiograms and Auditory Brain Stem Evoked Responses Using Mathematical Modeling Procedures

The relationship between quantified pure-tone audiometric variables (namely, pure-tone audiometric slope and the degree of hearing loss) and the slope of the wave V L-I (latency-intensity) function of the ABR was investigated. The influence of loudness recruitment on the relationship between audiogram slope and the wave V L-I slope was also studied. Fifty-five ears were selected and divided into two groups (a positive Metz group consisting of 35 ears and a negative Metz group comprising 20 ears) for statistical analyses. The results of the study indicated no significant relationship between the audiogram variables and the slope of the wave V L-I function. However, a significant relationship emerged between the degree of hearing loss and the slope of the L-I function. The results also suggested that neither loudness recruitment nor audiometric configuration influenced the slope of the L-I function.

A graph partitioning procedure for machine assignment and cell formation in group technology†

SUMMARY This paper proposes a mathematical model and solution procedure for the group technology configuration problem—the grouping of individual machines into cells and the routing of components to machines within cells. Costs of inventory, machine depreciation, machine setup and material handling are first incorporated into a mathematical programming formulation. The formulation is then divided into two subproblems to facilitate solution. A heuristic graph partitioning procedure is then proposed for each subproblem. The first subproblem assigns components to specific machines. The second subproblem groups machines into cells. An approach for determining economic batch sizes in this environment is also included. Examples are included and the flexibility of the approach to various environments is discussed.

Age-related differences in the impact of spacing, lag, and retention interval.

An experiment is reported that examines age-related differences in the lag effect and its relation to retention interval. A total of 30 young and 30 older adults received both once-presented pairs and twice-presented pairs that were tested in a continuous cued-recall paradigm either after a short retention interval (2 pairs intervening between the last presentation of a pair and its test) or a long retention interval (20 pairs intervening between the last presentation of a pair and its test). In addition, the twice-presented pairs were separated by either 0, 1, 4, 8, or 20 intervening pairs. The results replicated the interaction between retention interval and lag that has been reported by Glenberg (1976, Journal of Verbal Learning and Verbal Behavior, 15, 1-16). Furthermore, although the older adults performed considerably lower than the younger adults in overall recall performance, their data were remarkably similar to the younger adults in the patterning of means. A mathematical modeling procedure was used to fit the data to Estes' stimulus fluctuation model. The results of this modeling procedure suggest that, compared with younger adults, older adults (a) encode less contextual information at a given point in time and (b) have a slower rate of contextual fluctuation across time.

The use of a mathematical modelling method to determine the optimal retrofitting option of an oil refinery steam system

In this paper, as a practical example, the use of mathematical modelling procedure to determine the optimal retrofitting option of an oil refinery steam system is presented. The basis for setting up a mathematical model is to use a network diagram to describe all potential practicable alternatives, therefore, in principle this method is appropriate to optimal design or optimal modification of any complex energy flow or material flow system. The nature of this model is a multi-objective zero-one linear mixed integer programming problem.

Correlation between electron capture and emission barriers of localized defects in mixed crystals

A mathematical model and experimental procedure for extraction of the local parameters of localized defects in mixed crystals from alloy fluctuations is proposed. The general procedure is illustrated using isothermal capacitance transient measurements.

A case study of silver exploration in parts of Idaho and Montana using mathematical modeling techniques

Mathematical modeling procedures were used to investigate the Butte, Dillon, Hamilton, and Elk City 2 degrees quadrangles in Idaho and Montana and to evaluate and predict areas for silver exploration. The modeling procedure consisted of digitizing a data base over cells, which were defined over the entire area, and using the data for predicting silver prospects for a maximum of 10 percent of the cells in each quadrangle. These predicted cells were further evaluated and confirmed by comparison with actual mining data and classified into first-, second-, and third-order prospects. Out of a total of 160 cells predicted, 61 were classified as first-order prospects, 76 as second-order prospects, and 23 as third-order prospects. The success and flexibility of the model in the trial area suggest its suitability as a generalizable model with potential to assist in mineral exploration and as a decision-making tool.

ChemInform Abstract: Electron‐rich Boranes and Related Molecules

The mathematical modelling procedure developed previously for predicting the structure of closo-BnHn2−, nido-BnHn4− and arachno-BnHn6− has been extended to the next two homologous series, for which the names eka-BnHn8− and dva-BnHn10− are proposed. Specific structural predictions are made for each of these molecules, most of which have yet to be synthesised. An atom—electron map is proposed that conveniently shows the relation between the boron hydrides and the hydrocarbons (and related species such as the polyphosphide and polysulfide ions).

Conversion of ecogram data to a mathematical equation of four dimensions

Mathematical modelling procedures were applied to previously published data presented in the form of ecograms. The information contained in the ecograms to express toxicity of Clostridium botulinum was transformed into a simple mathematical equation of the form: Y = β o[1 − e −β 1 (T − T o)] where Y = % toxicity; β 0, β 1, T 0 = regression coefficients as functions of NaCl and NaNO 2 concentrations; and T = storage temperature. This equation defined a new characteristic temperature, T 0, which was not indicated in the original ecograms. T 0 is the temperature below which no toxin is produced by Clostridium botulinum. It was proposed that the traditional way of studying food microbiology would benefit by the use of predictive modelling. Suggestions were made for other applications of mathematical modelling to problems of the preservation and safety of foods.

Electron-rich boranes and related molecules

The mathematical modelling procedure developed previously for predicting the structure of closo-B n H n 2−, nido-B n H n 4− and arachno-B n H n 6− has been extended to the next two homologous series, for which the names eka-B n H n 8− and dva-B n H n 10− are proposed. Specific structural predictions are made for each of these molecules, most of which have yet to be synthesised. An atom—electron map is proposed that conveniently shows the relation between the boron hydrides and the hydrocarbons (and related species such as the polyphosphide and polysulfide ions).

Resolution of steroid binding heterogeneity by fourier-derived affinity spectrum analysis (FASA)

A new mathematical method of analyzing radioreceptor assay data is presented. When there are many binding classes with different affinities, the probability-density function B( p) is described by the equation B( p) = ∫ −∞ ∞ q( k) f( p− k) dk, where q( k) is the affinity spectrum (density of a particular binding class as a function of affinity) and f( p− k) is a probability function (probability that dissociation constants will fall between k and p− k, where p is the free ligand concentration). This equation is solved for q( k) and evaluated explicitly by Fourier transformation, namely, q ̂ (w) = b ̂ (w) f ̂ (w) , where w is frequency. Since division by f ̂ (w) can amplify any high frequency noise present in the experimental data, a Gaussian smoothing function is introduced thus: q ̂ s (w) = q ̂ (w)e ( −w W 0 ) 2 , where W 0 is a constant. This produces an affinity spectrum defined as a plot of the number of binding sites, q s( k), versus their respective dissociation constants, k. Using a FORTRAN computer program, we verify this algorithm using simulated data. We also apply the procedure to resolve heterogenous populations of estrogen binders in human endometrium using [ 3H]estradiol as ligand. Two estrogen binder classes are revealed with dissociation constants approximately 2.5 natural logarithmic units apart. We identify one high-affinity ( K d = 0.18 n m)-low density (70 p m [or 72 fmol/mg protein]) subpopulation and one low affinity ( K d = 2.5 n m)-high density (101 p m [or 102 fmol/mg protein]) subpopulation of estradiol binders. The management of experimental error, sampling limitations, and nonspecific binding are discussed. This method directly transforms experimental data into an easily interpretable representation without mathematical modeling or statistical procedures.