Linear Exponential Models Research Articles

Evaluation of the Condition of the Bottom of the Tanks for Petroleum Products-Forecast of the Remaining Operating Life

Corrosion rate measurements in the tank enable us to develop a new model for predicting the remaining operating period of the tank. The empirical model for the study of bottom plate thicknesses and corrosion pits is more conservative than the standard linear model, as it considers the autocatalytic nature of the corrosion process. We used the double exponential distribution of maximum values (Gumbel's) to evaluate the maximum depth of pits, and the double exponential distribution of minimum values to evaluate the minimum values of the plate thickness. A comparison of the values of the parameters obtained using linear extrapolation and exponential models indicates the unreliability of linear extrapolation, since disregarding dynamic processes underestimates the actual rate of corrosion.

Towards precise LET measurements based on energy deposition of therapeutic ions in Timepix3 detectors

Objective. There is an increasing interest in calculating and measuring linear energy transfer (LET) spectra in particle therapy in order to assess their impact in biological terms. As such, the accuracy of the particle fluence energy spectra becomes paramount. This study focuses on quantifying energy depositions of distinct proton, helium, carbon, and oxygen ion beams using a silicon pixel detector developed at CERN to determine LET spectra in silicon. Approach. While detection systems have been investigated in this pursuit, the scarcity of detectors capable of providing per-ion data with high spatial and temporal resolution remains an issue. This gap is where silicon pixel detector technology steps in, enabling online tracking of single-ion energy deposition. The used detector consisted of a 300 µm thick silicon sensor operated in partial depletion. Main results. During post-processing, artifacts in the acquired signals were identified and methods for their corrections were developed. Subsequently, a correlation between measured and Monte Carlo-based simulated energy deposition distributions was performed, relying on a two-step recalibration approach based on linear and saturating exponential models. Despite the observed saturation effects, deviations were confined below 7% across the entire investigated range of track-averaged LET values in silicon from 0.77 keV µm−1 to 93.16 keV µm−1. Significance. Simulated and measured mean energy depositions were found to be aligned within 7%, after applying artifact corrections. This extends the range of accessible LET spectra in silicon to clinically relevant values and validates the accuracy and reliability of the measurements. These findings pave the way towards LET-based dosimetry through an approach to translate these measurements to LET spectra in water. This will be addressed in a future study, extending functionality of treatment planning systems into clinical routine, with the potential of providing ion-beam therapy of utmost precision to cancer patients.

Evaluating pelvic tilt using the pelvic antero-posterior radiographs: A novel method.

Pelvic tilt (PT) is an important parameter for orthopedic surgeries involving hip and spine, typically determined from sagittal pelvic radiographs. However, various challenges can compromise the feasibility of measurement from sagittal imaging, including obscured landmarks, anatomical variations, hardware interference, and limited medical resources. Addressing these challenges and with the aim of reducing radiation exposure to patients, our study developed a novel method to estimate PT from antero-posterior (AP) radiographs, using vertical distances from the pelvic outlet and obturator foramen. We correlated these measurements with PT, defined both anatomically (anterior pelvic plane, PTa) and mechanically (centers of femoral heads and sacral plate, PTm). The study explored creating linear, exponential, and multivariate regression models based on twelve 3D CT-derived pelvic models (six men, six women), simulating AP radiograph projections with controlled PTs. We then validated these models against 105 pairs of patient stereoradiographs. Statistical analysis revealed that combined exponential-linear models yielded the most accurate results, with Pearson correlation coefficients of 0.75 for PTa and 0.77 for PTm, and mean absolute errors of 3.7° ± 2.6° for PTa and 4.5° ± 3.4° for PTm, showing excellent measurement reliability (all ICCs > 0.9) without significant gender discrepancies. In conclusion, this study presents a validated, simple, and accessible method for estimating PT using AP radiograph parameters, supported by the Supporting Information S1: Excel Tool, showing great potential for clinical application in hip and spine procedures.

Comparison between graph theory connectivity indices and landscape connectivity metrics for modeling river water quality in the southern Caspian sea basin

The maintenance of connectivity is critical to the proper functioning of an ecosystem. The present study was conducted with the aim of comparing graph theory connectivity indices and landscape connectivity metrics for the purpose of modeling river water quality. To conduct this study, a forest layer was extracted from land cover map and 25 large watersheds were selected. River water quality was then assessed from the perspective of 8 landscape connectivity metrics and 12 graph theory indices. We developed predictive models using stepwise linear regression, power, exponential, and logarithmic models to locate the best model form for each water quality parameter (dependent variable) we examined. The results indicated that models developed using graph theory connectivity indices resulted in higher coefficients of determination (R2) than models developed using landscape metrics. Only 5 independent variables from a potential set of 13 were significant in explaining the variation in water quality parameters. Also, the models with the highest R2 attempted to explain variations in CO3 (0.818), water discharge (0.733), and Ca levels (0.702). Therefore, the results of this study showed that graph theory connectivity indices had more significant correlation with water quality parameters compared to landscape connectivity metrics. This work also indicates that there exist nonlinear relationships among connectivity indices and water quality parameters.

Predicting Breast Reduction Resection Weights and Attainment of Insurance-Mandated Minimums.

Despite evidence that reduction mammaplasty alleviates macromastia symptoms independent of resection weights, resection minimums are commonly used to grant insurance coverage. Multiple formulas have been published to predict resection weights, but very few have evaluated predictive performance relative to attaining common insurance minimums. This was a retrospective single-center review of 268 patients from 2007 to 2020. Multiple linear regression and exponential models were created to predict resection weights and attainment of the Schnur, 350-g, and 500-g minimums. Accuracy was compared against published Appel, Descamps, and Galveston equations. Body mass index subgroup analyses were performed. The exponential model possessed the lowest resection weight prediction error overall (172.8 ± 211.5 g). All equations performed significantly better than surgeons in predicting attainment of the 500-g minimum. None performed better than the surgeons' predictive accuracy in attaining a 350-g minimum. Multiple linear regression and exponential models performed significantly better than surgeons in predicting attainment of the Schnur minimum. Only the exponential model performed significantly better than surgeons for both the Schnur (82% versus 71%; P < 0.01) and the 500-g minimums (89% versus 68%; P < 0.01). On body mass index subgroup analyses, all three minimums were biased in favor of obese women-the least egregious of these was the 350-g minimum. All minimums were biased against nonobese women. Our exponential model equation based on preoperative sternal notch-to-nipple and nipple-to-inframammary fold distances accurately predicts resection weights and improves on our surgeons' predictive accuracy in attaining the Schnur or 500-g minimums. This may prove useful in the preoperative setting to better counsel patients.

Impact of 3D conformal and Intensity Modulated Radiotherapy on secondary cancer risk for patients with early prostate cancer

Secondary cancer resulting from radiation exposure to normal tissues is always a concern. Thus, present study aimed to estimate this risk for patient receiving radiotherapy using advanced techniques like Intensity-modulated radiation therapy (IMRT) and Three-dimensional conformal radiotherapy (3DCRT). Ten prostate cancer cases were chosen, and CT images were acquired for each patient. 3DCRT and IMRT plans were generated and were compared with respect to several dosimetric parameters for Planning Target Volume (PTV) and for Organs at Risk (OARs). The second cancer risks were estimated by Excess absolute risk (EAR) for OARs. For prostate, the PTV dose coverage parameters were significantly improved in IMRT compared to 3DCRT. The rectum and bladder mean dose DMean, V50Gy, and V40Gy were significantly decreased with IMRT in comparison to 3DCRT. The maximum dose (DMax), DMean, V30Gy, and V20Gy for head of femurs significantly decreased with IMRT plans. However, the colon DMean significantly increased with IMRT compared with 3DCRT plans. Compared with the 3DCRT the IMRT plans decreased the organ equivalent dose (OED) in rectum based on the linear, plateau and linear-exponential models. The OED for the bladder also decreased with linear model in IMRT plan. While, the OED for the colon significantly increased in IMRT. The IMRT plans were decreased second cancer risk for the rectum by 10%, 26.6% and 19.5% for linear, plateau and linear-exponential dose-response models respectively. The bladder second cancer risk was decreased by 14% with linear dose-response model in comparison to 3DCRT plans. However, the second cancer risk for colon was significantly increased in average by 91.2% with IMRT plans. IMRT technique demonstrated a clear advantage in dose coverage, conformity, and homogeneity over 3DCRT and was superior in terms of OAR-sparing. The Second cancer risk for in field organs (rectum and bladder) was decreased with IMRT compared to 3DCRT plan.

Sex differences in audience effects on anogenital scent marking in the red-fronted lemur

How the presence of conspecifics affects scent mark deposition remains an understudied aspect of olfactory communication, even though scent marking occurs in different social contexts. Sex differences in scent-marking behaviour are common, and sex-specific effects of the audience could therefore be expected. We investigated sex differences in intra-group audience effects on anogenital scent marking in four groups of wild red-fronted lemurs (Eulemur rufifrons) by performing focal scent-marking observations. We observed a total of 327 events divided into 223 anogenital scent-marking events and 104 pass-by events (i.e. passage without scent marking). Using a combination of generalised linear mixed models and exponential random graph models, we found that scent marking in red-fronted lemurs is associated with some behavioural flexibility linked to the composition of the audience at the time of scent deposition. In particular, our study revealed sex differences in the audience effects, with males being overall more sensitive to their audience than females. Moreover, we show that these audience effects were dependent on the relative degree of social integration of the focal individual compared to that of individuals in the audience (difference in Composite Sociality Index) as well as the strength of the dyadic affiliative relationship (rank of Dyadic Composite Sociality Index within the group). The audience effects also varied as a function of the audience radius considered. Hence, we showed that scent marking in red-fronted lemurs is associated with some behavioural flexibility linked to the composition of the audience, ascribing red-fronted lemurs’ social competence in this context.

Modeling of Phosphorus Nutrition to Obtain Maximum Yield, High P Use Efficiency and Low P-Loss Risk for Wheat Grown in Sandy Calcareous Soils

Fertilization with high levels of phosphorus increases the risk of environmental pollution. Identification of critical values of P in soil (SOP) and in plant tissues (PiP) is essential for achieving the maximum wheat yield without P loss. The critical value is the value of P which gives the optimum yield; the response of crop yield to P fertilization above this value is not predictable or nil. Here, a 4-year field experiment was conducted to identify the SOP and PiP for achieving maximum yield of bread wheat using 11 rates of P fertilization (0, 15, 30, 45, 60, 75, 90, 105, 120, 135, and 150 kg P2O5 ha−1). The linear–linear and Mitscherlich exponential models were employed to estimate the PiP and SOP. The degree of phosphorus saturation (DPS) was used to assess the potential environmental risk; furthermore, phosphorus use efficiency (PUE) was also calculated under the studied fertilization levels. Phosphorus in soil and wheat plant was affected by the application rates and growing seasons. Increasing P fertilization rates led to gradual increases in soil and plant P. The SOP ranged between 21 and 32 mg kg−1, while the PiP ranged between 6.40 and 7.49 g kg−1. The critical values of P calculated from the Mitscherlich exponential models were 20% higher than those calculated from the linear–linear models. Adding levels of P fertilization ≥90 kg P2O5 ha−1 leads to higher potentials of P runoff and leaching, in addition, PUE decreased sharply under high P fertilization levels. The response of wheat yield to P fertilization in sandy calcareous soil is predictable below Olsen P values of 21 mg kg−1. Identification of critical P values for wheat production is of great importance to help policy makers improve P use efficiency and attain optimum wheat yield under eco-friendly environmental conditions by eliminating the accumulation of excess P fertilizers in soil and water.

Modelling and forecasting reservoir sedimentation of irrigation dams in the Guinea Savannah Ecological Zone of Ghana

Abstract Effective management of reservoir sedimentation requires models that can predict sedimentation of the reservoirs. In this study, linear regression, non-linear exponential regression and artificial neural network models have been developed for the forecasting of annual storage capacity loss of reservoirs in the Guinea Savannah Ecological Zone (GSEZ) of Ghana. Annual rainfall, inflows, trap efficiency and reservoir age were input parameters for the models whilst the output parameter was the annual sediment volume in the reservoirs. Twenty (20) years of reservoirs data with 70% data used for model training and 30% used for validation. The ANN model, the feed-forward, back-propagation algorithm Multi-Layer Perceptron model structure which best captured the pattern in the annual sediment volumes retained in the reservoirs ranged from 4-6-1 at Karni to 4-12-1 at Tono. The linear and nonlinear exponential regression models revealed that annual sediment volume retention increased with all four (4) input parameters whilst the rate of sedimentation in the reservoirs is a decreasing function of time. All the three (3) models developed were noted to be efficient and suitable for forecasting annual sedimentation of the studied reservoirs with accuracies above 76%. Forecasted sedimentation up to year 2038 (2019–2038) using the developed models revealed the total storage capacities of the reservoirs to be lost ranged from 13.83 to 50.07%, with 50% of the small and medium reservoirs filled with sediment deposits if no sedimentation control measures are taken to curb the phenomenon.

Choice of ideal sunshine hour based model to predict global solar radiation in India

Solar radiation is the key energy source for most of the energy conversion systems, whether it is biological or mechanical. It is also the most fundamental energy source for future energy demand. Like most of the developing countries, India also lacks sufficient instrument facilities to measure global solar radiation (GSR) at recommended spatial interval and alternative approaches must be used to generate GSR data. In the present study, six well known empirical models were tested to estimate the GSR over twelve major cities of India using long-term global solar radiation and bright sunshine hour data. The empirical coefficients have been calculated for all the models and each location using regression analysis method. Daily GSR are then calculated using those regression constants along with statistical analysis. Results reveal that all the models shows close estimation with low mean bias error (MBE), root mean square error (RMSE) and mean percentage error (MPE) values. Among all models, linear exponential and linear logarithmic models are highly recommended for prediction of GSR throughout the country, except Shillong, where Bakircilinear exponential model is recommended. Significance tests i.e., t-test also confirms that this two model produce most significant results than others.

Comparison between some meteorological elements measured by ECMWF and Earth stations in different regions in Iraq

The aim of this paper is to validate the data of three meteorological elements Air Temperature (Ta) , Relative Humidity (RH), Wind Speed (WS) from the European Center For-Medium Range Weather Forecasting (ECMWF) , against ground stations data using several Models at six stations well distributed in Iraq (Mosul, Kirkuk, Baghdad, Kut, Nasiriya, and Basra).&#x0D; Due to the difficulties which experienced by the ground climate stations in Iraq from a shortage of devices and equipment for measuring the various climatic elements, which led to a huge shortage of data throughout time for political, economic and natural disasters. It is found that researchers can adopt the data of satellite stations to monitor the climate because let’s found that there is a highly significance Correlations between the data of these stations and the data of the ground stations for climate monitoring&#x0D; Five Mathematical Models were used for that [Linear Models, Quadratic Models, Exponential Models, Logarithmic Models, and Power Models]. The performance of these models were evaluated by comparing the calculated (Ta, RH, WS) from earth stations.&#x0D; Those mathematical correlations help to be able to calculate the ground data in state of there is no ground climate stations data.&#x0D; Several statistical tests Correlation Coefficient (R), Coefficient of Determination (R2), Root Mean Square Error (RMSE), Mean Absolute Error (MAE) were used to control the validation and goodness of these Models.&#x0D; The R2 obtained from these Models were very high in all stations. This means that, there is a highly significance Correlations between (Ta, RH, WS) estimated and [Ta, RH, WS] measured in all station

Correlations Between Total Ozone Column and Some Metrological Elements in different regions in Iraq

Aluminium, The aim of this paper, is to find a correlation between Total Ozone Column[ TOC] and different meteorological elements [Ta, Rs, RH, WS ] at five stations well distributed in Iraq [Mosul, Kirkuk, Baghdad, Nasiriya, and Basra] using several Mathematical Models. Five Mathematical Models were used for that [Linear Models, Quadratic Models, Exponential Models, Logarithmic Models, and Power Models]. Several statistical tests [R, R2, MAE, and RMSE] were used to control these Models' validation and goodness. The quadratic model gave the highest R and R2 among the other models in all stations. The highest R and R2 means that there are a high significance Correlations between the measured Total Ozone Column (TOC) and the estimated (TOC) from the Models using [Ta, Rs, RH, WS] elements in all stations.

Optimal methionine plus cystine requirements in diets supplemented with L-methionine in starter, grower, and finisher broilers

Correct supplementation of dietary amino acids, such as methionine (Met) and cystine (Cys), is crucial to support the exponential growth of broilers. Historically, most available recommendations with regard to the optimal amount of Met plus Cys are based on studies wherein DL-Met was used as the Met source. Nowadays, L-Met is available as a registered feed additive, urging the need to establish the optimal L-Met plus Cys supplementation. The objective of this trial was to investigate these optimal L-Met plus Cys requirements of broilers in the starter (0–10 d), grower (11–23 d), and finisher (24–35 d) phase of life separately. A basal diet deficient in L-Met plus Cys was created along with 6 other diets with increasing L-Met concentrations for each phase. Birds were only included in one life phase and fed with a commercial diet before inclusion. The BW, daily weight gain, daily feed intake, and feed conversion ratio (gain-to-feed ratio) were measured for all birds. Slaughter parameters were determined for birds included in the finisher phase. At the end of each study period, significant differences (P < 0.05) were observed in all measured performance parameters. Birds fed with the deficient diets were characterized by a lower performance, whereas from some point, no gain in performance could be observed. Correct supplementation of L-Met plus Cys seemed more crucial in the starter and grower phase, which was characterized by bigger differences in performance between test diets compared with the finisher birds. The optimal L-Met plus Cys requirements were determined using linear broken line and exponential asymptotic models. The linear broken line model showed overall the best fit. The optimal L-Met plus Cys level was found to be 0.69, 0.66, and 0.62% for birds in the starter, grower, and finisher phase, respectively. From this study, it could be concluded that broilers have lower L-Met plus Cys requirements based on L-Met supplementation than the conventional requirements based on DL-Met. Nevertheless, further research is required to confirm these findings.

Network Analysis of the Social Environment Relative to Preference for and Tolerance of Exercise Intensity in CrossFit Gyms.

Known for its ability to improve fitness and health, high-intensity functional training (HIFT) focuses on functional movements completed at high intensities, often yielding outcomes superior to repetitive aerobic workouts. Preference for and tolerance of high-intensity exercise are associated with enjoyment of and adherence to HIFT. Similarly, the social environment present within CrossFit, a popular group-based HIFT modality, is important to the enjoyment of and adherence to HIFT. This study aimed to test whether preference and tolerance were related to social connections within CrossFit networks. Linear network autocorrelation models (LNAMs) and exponential random graph models (ERGMs) were computed on sociometric and attribute data from members of three CrossFit networks (n = 197). LNAMs showed the preference and tolerance scores of someone’s social connections were associated with their own in all three gyms, and ERGMs demonstrated preference and tolerance scores were associated with the presence of social ties within all networks. This study is the first to provide evidence for a relationship between social connections and preference and tolerance. Future longitudinal research is needed to determine if the social environment may influence and optimize a person’s preference of and tolerance for HIFT.

Temporal twilight zone and beyond: Timing mechanisms in consciously delayed actions.

Precise timing is essential for many kinds of human behavior. When a fastest response is not required, movements are initiated at the appropriate time requiring an anticipatory temporal component. Temporal mechanisms for movements with such an anticipatory component are not yet sufficiently understood; in particular, it is not known whether on the operational level for delayed movements distinct time windows are used or whether anticipatory control is characterized by continuous temporal processing. With a modified reaction-time paradigm, we asked participants to act with predefined time delays between 400 and 5000 ms; after each individual trial, a numerical feedback was provided which allowed correction of the response time for each next trial. Visual stimuli (Experiment 1) and auditory stimuli (Experiment 2) were used. In the statistical analyses, piecewise linear models and exponential decay models for the response variability of different delay times were compared. These analyses favored piecewise linear models; a decreasing variability with increasing delay of voluntary controlled actions was observed up to ~1 s, followed by close to constant variability beyond this delay. We suggest that precise temporal control of voluntary delayed movements is reached only after a "temporal twilight zone" of ~1 s, which apparently marks a temporal border between two different timing mechanisms.

Regression models for prediction of leaf area in purple ipe [Tabebuia impetiginosa (Mart.)

Besides its medicinal and ornamental use, Tabebuia impetiginosa is also very economically important. The achievement of accurate and easy-to-perform tools to determine its leaf area is fundamental for understanding the interaction between the plant and the environment. The objective of this work was to obtain regression equations by using several models that use allometric measurements of the fifth leaflet and to select the most accurate one to determine the leaf area of composite leaves of Tabebuia impetiginosa Mart. in a non-destructive way. By using the dimensions of the fifth leaflet such as - length (LFL in cm), maximum width (WFL in cm) and the product between LFL and WFL (LWFL) of leaf limb, the equations were estimated for linear, quadratic, potential and exponential linear models. The results showed that the determination of leaf area could be performed with excellent precision for leaves of different sizes of this species, using the product of the measurements of length and width of the fifth leaflet. The equation that best expresses the leaf area estimate of the composite leaf of Tabebuia impetiginosa is ELACL = 8.7772 + 2.3840 (LWFL).

Прогнозирование необходимого онлайн-школе числа преподавателей

The article describes an approach to forecasting the number of teachers to hire by an online English language school, based on an analysis of historical data on the lessons using linear regression and triple exponential smoothing models.

Tetranomial decompression sickness model using serious, mild, marginal, and non-event outcomes

Abstract Decompression sickness (DCS) is a condition resulting from reductions in ambient pressure, causing inert gas bubbles in tissues. This work focuses on hyperbaric exposures, specifically DCS resulting from underwater diving. Signs and symptoms of DCS can range from mild skin rashes and joint pain to serious neurological and cardiological malfunction, and even death. Marginal DCS is defined as symptoms associated with DCS that resolve spontaneously without recompression treatment. There are two categories of decompression modeling used to mitigate risk of DCS: deterministic and probabilistic; neither address DCS symptom severity. Symptom severity is important to U.S. Navy dive planning, as the Navy has different limits for the number allowable cases of mild-symptom DCS and more severe-symptom DCS for a given dive. In this work, a probabilistic model for predicting the tetranomial outcomes of serious, mild, marginal, and no DCS was developed, analyzed, and compared with trinomial and trinomial marginal models from our previous works. Six variants of exponential-exponential (EE1) and linear-exponential (LE1) models were calibrated with 3322 air and N2–O2 dive exposures detailed in the BIG292 empirical human dive trial data set. Two methods of symptom severity splitting were compared. The log likelihood difference test indicated the LE1 model using a previously-disclosed Type A/B splitting provided the best fit to the empirical dive data of all tetranomial models tested in this work. When comparing this tetranomial model to our previous trinomial and trinomial marginal models using the Pearson chi-squared statistic, we find that the tetranomial and trinomial marginal models’ predictions of marginal DCS are not aligned well with the incidence of marginal DCS in the data. Both the trinomial marginal model in our previous work and tetranomial model presented here are unable to accurately replicate the occurrence of marginal DCS events observed in the BIG292 dataset. These marginal DCS events may hinder model fit during calibration. We recommend the use of the trinomial model from our previous work, which simultaneously predicts the probability of mild, serious, and no DCS.

A portfolio approach to the optimal mix of funded and unfunded pensions

ABSTRACTIn this paper, we address the optimal funding of pensions by means of portfolio choice approach. Considering the unfunded (Paygo) pension system as a ‘quasi-asset’ with hedging and diversification properties, we derive the optimal portfolio mix of funded and Paygo systems within a mean variance and Bell linear exponential models. Our analysis involves both analytical computations and empirical estimations of optimal values using real long-term data for equity, bonds and the Paygo asset for several OECD countries and several time periods covering the time span 1897–2016. We find that in most cases a mix of both systems is desirable with a larger magnitude of Paygo system in the case of the Bell framework as we capture attitudes towards asymmetry and tail risks that are typical to equity markets.

Transient 3D finite element method for predicting extrudate swell of domains containing sharp edges

A new transient 3D finite element method for predicting extrudate swell of domains containing sharp edges is proposed. Here, the sharp edge is maintained over a large distance in the extrudate by describing the corner lines as material lines. The positions of these lines can be used to describe the transverse swelling of the 2D free surfaces and expand the domain over which a 2D height function on the free surfaces is applied. Solving the 2D height functions gives the positions of the free surfaces. First a 2D axisymmetric case was tested for comparison, using three different constitutive models. The Giesekus, linear Phan-Thien Tanner (PTT) and exponential PTT constitutive models all showed convergence upon mesh- and time-step refinement. It was found that convergence remains challenging due to the singularity at the die exit. The new method is validated by comparing the final volume change of the extrudate of a 3D cylinder to the final volume change of a reference mesh of the 2D axisymmetric case. Finally, simulations were performed for different, complex, die shapes for a viscous fluid and for viscoelastic fluids. The results compared favorably with literature. Viscoelastic results, using the Giesekus model and the exponential PTT model, were compared for different Weissenberg numbers and different values for the non-linear parameters of the constitutive models. It was found that the swell is highly dependent on the rheological parameters and the constitutive model used.