Study of Oscillating Flow of Viscoelastic Fluid With the Fractional Maxwell Model

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Jiu-hong Jia ◽  
Hong-xing Hua
Keyword(s):  
Exact Solution ◽  
Petroleum Chemistry ◽  
Viscoelastic Fluid ◽  
Maxwell Model ◽  
The Other ◽  
Oscillating Flow ◽  
Model Parameters ◽  
Series Approximation ◽  
Phase Lags ◽  
Annular Effect

The oscillating flow of the viscoelastic fluid in cylindrical pipes has been applied in many fields, such as industries of petroleum, chemistry, and bioengineering. It is studied using the fractional derivative Maxwell model in this paper. The exact solution is obtained utilizing a simpler and more reasonable technique. According to this velocity solution, the time-velocity profile of one kind of viscoelastic fluid is analyzed. From analysis, it is found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Moreover, two series approximations for the velocity are obtained and analyzed for different model parameters. In one series approximation, the velocity is parabolic in profile, while in the other series approximation, the velocity presents three characteristics: (1) it is independent of radius and at the centerline is smaller than that of steady Poiseuille flow, (2) the phase lags about 90deg with respect to the imposed pressure gradient, and (3) the Richardson annular effect is found near the wall.

Analysis of observability of model parameters for physical absorption of poorly soluble gases in packed beds

1982 ◽  
Vol 47 (10) ◽  
pp. 2639-2653 ◽  
Author(s):  
Pavel Moravec ◽  
Vladimír Staněk
Keyword(s):  
Transfer Functions ◽  
Plug Flow ◽  
Packed Bed ◽  
Model Parameters ◽  
Packed Bed Column ◽  
Interfacial Transport ◽  
Complex Arithmetic ◽  
Physical Absorption ◽  
Poorly Soluble ◽  
Phase Lags

Expressions have been derived for four possible transfer functions of a model of physical absorption of a poorly soluble gas in a packed bed column. The model has been based on axially dispersed flow of gas, plug flow of liquid through stagnant and dynamic regions and interfacial transport of the absorbed component. The obtained transfer functions have been transformed into the frequency domain and their amplitude ratios and phase lags have been evaluated using the complex arithmetic feature of the EC-1033 computer. Two of the derived transfer functions have been found directly applicable for processing of experimental data. Of the remaining two one is useable with the limitations to absorption on a shallow layer of packing, the other is entirely worthless for the case of poorly soluble gases.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

Simulation of the Film Blowing Process Using a Continuum Model for Crystallization in Polymers

2000 ◽  
Author(s):  
I. J. Rao
Keyword(s):  
Viscoelastic Fluid ◽  
Crystalline Phase ◽  
Elastic Solid ◽  
Second Law Of Thermodynamics ◽  
Maxwell Model ◽  
Polymer Processing ◽  
Solid Polymer ◽  
Crystalline Solid ◽  
Film Blowing ◽  
Anisotropic Elastic

Abstract In this paper we simulate the film blowing process using a model developed to study crystallization in polymers (see Rao (1999), Rao and Rajagopal (2000b)). The framework was developed to generate mathematical models in a consistent manner that are capable of simulating the crystallization process in polymers. During crystallization the polymer transitions from a fluid like state to a solid like state. This transformation usually takes place while the polymer undergoes simultaneous cooling and deformation, as in film blowing. Specific models are generated by choosing forms for the internal energy, entropy and the rate of dissipation. The second law of thermodynamics along with the assumption of maximization of dissipation is used to determine constitutive forms for the stress tensor and the rate of crystallization. The polymer melt is modeled as a rate type viscoelastic fluid and the crystalline solid polymer is modeled as an anisotropic elastic solid. The mixture region, where in the material transitions from a melt to a semi-crystalline solid, is modeled as a mixture of a viscoelastic fluid and an elastic solid. The anisotropy of the crystalline phase and consequently that of the final solid depends on the deformation in the melt during crystallization, a fact that has been known for a long time and has been exploited in polymer processing. The film blowing process is simulated using a generalized Maxwell model for the melt and an anisotropic elastic solid for the crystalline phase. The results of the simulation agree qualitatively with experimental observations and the methodology described provides a framework in which the film blowing problem can be analyzed.

scholarly journals Bird Species Identification Using Spectrogram Based on Multi-Channel Fusion of DCNNs

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1507
Author(s):  
Feiyu Zhang ◽  
Luyang Zhang ◽  
Hongxiang Chen ◽  
Jiangjian Xie
Keyword(s):  
Species Identification ◽  
Feature Fusion ◽  
Bird Species ◽  
The Other ◽  
Identification Accuracy ◽  
Mean Average Precision ◽  
Training Dataset ◽  
Model Parameters ◽  
Average Precision ◽  
Fusion Mode

Deep convolutional neural networks (DCNNs) have achieved breakthrough performance on bird species identification using a spectrogram of bird vocalization. Aiming at the imbalance of the bird vocalization dataset, a single feature identification model (SFIM) with residual blocks and modified, weighted, cross-entropy function was proposed. To further improve the identification accuracy, two multi-channel fusion methods were built with three SFIMs. One of these fused the outputs of the feature extraction parts of three SFIMs (feature fusion mode), the other fused the outputs of the classifiers of three SFIMs (result fusion mode). The SFIMs were trained with three different kinds of spectrograms, which were calculated through short-time Fourier transform, mel-frequency cepstrum transform and chirplet transform, respectively. To overcome the shortage of the huge number of trainable model parameters, transfer learning was used in the multi-channel models. Using our own vocalization dataset as a sample set, it is found that the result fusion mode model outperforms the other proposed models, the best mean average precision (MAP) reaches 0.914. Choosing three durations of spectrograms, 100 ms, 300 ms and 500 ms for comparison, the results reveal that the 300 ms duration is the best for our own dataset. The duration is suggested to be determined based on the duration distribution of bird syllables. As for the performance with the training dataset of BirdCLEF2019, the highest classification mean average precision (cmAP) reached 0.135, which means the proposed model has certain generalization ability.

scholarly journals Effectiveness of Information from Vehicles beyond Nearest Vehicle Ahead for Traffic Flow

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Hikaru Shimizu ◽  
Sho Nishiyama ◽  
Yukiko Wakita ◽  
Eisuke Kita
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Flow Simulation ◽  
The Other ◽  
Stable Region ◽  
Model Parameters ◽  
Model Stability ◽  
Acceleration Rate ◽  
Traffic Flow Simulation ◽  
Vehicle Acceleration

A driver usually controls the vehicle according to only the information from the nearest leader vehicle. If the information from the other leader vehicles is also available, the driver can control the vehicle more adequately. The aim of this study is to discuss the effectiveness of the information from the other leader vehicles than the nearest one for the traffic flow. For this purpose, the traffic flow is modeled by using the Chandler-type multi-vehicle-following model. This model changes the vehicle acceleration rate according to the velocity differences between the vehicle and its multileader vehicles. After the model stability analysis, the traffic flow simulation is performed. The results reveal that the stable region of the model parameters expands according to the increase of the number of the leader vehicles.

scholarly journals An Euler-Lagrange Equation only Depending on Derivatives of Caputo for Fractional Variational Problems with Classical Derivatives

2020 ◽  
Vol 8 (2) ◽  
pp. 590-601
Author(s):  
Melani Barrios ◽  
Gabriela Reyero
Keyword(s):  
Exact Solution ◽  
Variational Problem ◽  
Lagrange Equation ◽  
Integral Form ◽  
Variational Problems ◽  
The Other ◽  
Isoperimetric Problems ◽  
Caputo Derivatives ◽  
Fractional Variational Problems ◽  
Derivatives Of

In this paper we present advances in fractional variational problems with a Lagrangian depending on Caputofractional and classical derivatives. New formulations of the fractional Euler-Lagrange equation are shown for the basic and isoperimetric problems, one in an integral form, and the other that depends only on the Caputo derivatives. The advantage is that Caputo derivatives are more appropriate for modeling problems than the Riemann-Liouville derivatives and makes the calculations easier to solve because, in some cases, its behavior is similar to the behavior of classical derivatives. Finally, anew exact solution for a particular variational problem is obtained.

Co-Evolution of Communication and System Performance in Engineering Systems Design: A Stochastic Network-Behavior Dynamics Model

2021 ◽  
Author(s):  
Ashish M. Chaudhari ◽  
Erica L. Gralla ◽  
Zoe Szajnfarber ◽  
Jitesh H. Panchal
Keyword(s):  
System Design ◽  
System Performance ◽  
The Other ◽  
Model Parameters ◽  
Stochastic Network ◽  
Network Behavior ◽  
Dynamics Model ◽  
Behavior Dynamics ◽  
Technical Factors ◽  
Student Subjects

Abstract The socio-technical perspective on engineering system design emphasizes the mutual dynamics between interdisciplinary interactions and system design outcomes. How different disciplines interact with each other depends on technical factors such as design interdependence and system performance. On the other hand, the design outcomes are influenced by social factors such as the frequency of interactions and their distribution. Understanding this co-evolution can lead to not only better behavioral insights, but also efficient communication pathways. In this context, we investigate how to quantify the temporal influences of social and technical factors on interdisciplinary interactions and their influence on system performance. We present a stochastic network-behavior dynamics model that quantifies the design interdependence, discipline-specific interaction decisions, the evolution of system performance, as well as their mutual dynamics. We employ two datasets, one of student subjects designing an automotive engine and the other of NASA engineers designing a spacecraft. Then, we apply statistical Bayesian inference to estimate model parameters and compare insights across the two datasets. The results indicate that design interdependence and social network statistics both have strong positive effects on interdisciplinary interactions for the expert and student subjects alike. For the student subjects, an additional modulating effect of system performance on interactions is observed. Inversely, the total number of interactions, irrespective of their discipline-wise distribution, has a weak but statistically significant positive effect on system performance in both cases. However, excessive interactions mirrored with design interdependence and inflexible design space exploration reduce system performance. These insights support the case for open organizational boundaries as a way for increasing interactions and improving system performance.

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