Showing posts with label mathematical models. Show all posts
Showing posts with label mathematical models. Show all posts

Sunday, 20 July 2025

The Analysis of Physical and Chemical Adsorption of Dysprosium Ions as Functions of the Temperature and Time in Terms of Boubaker Polynomials | Chapter 1 | Current Research Progress in Physical Science Vol. 3

 

In the present work, analytical solutions to the differential equation systems governing the kinetics of dysprosium adsorption within particular hosting edifices are presented. The chemical adsorption kinetics of rare earth elements inside regular crystalline materials such as ZnO are discussed. An approximate analytical expression of the non-steady-state doping concentrations is deduced by using the Boubaker polynomial expansion scheme (BPES). The results concerning the particular case of the dysprosium ion Dy3+ are discussed and evaluated in terms of temperature and time. In addition to an exponential parabolic time-dependent behavior, a notable temperature gradient is noted. Above a certain temperature limit, the reaction starts to occur and pertains to the energy needed to promote a 4f electron to the valence band.

 

Author(s) Details

A. Yumak
Department of Physics, Marmara University, Göztepe Kampus, 34722 Kadiköy, Istanbul, Turkey.

 

Please see the book here:- https://doi.org/10.9734/bpi/crpps/v3/467

Tuesday, 29 April 2025

Plant-Based Activated Carbons for Cobalt and Strontium Removal: Insights into Adsorption Mechanisms | Chapter 8 | Chemical and Materials Sciences: Research Findings Vol. 2

Aims: To investigate the adsorption behavior of Co(II) and Sr(II) ions on the surface of plant-based activated carbons (obtained from walnut shells (CA-N) and apple wood (CA-M), and modified by oxidation with nitric acid and nitric acid/urea mixture).

Methodology: Activated carbons were chemically modified using nitric acid (sample CA-Mox) and a nitric acid/urea mixture (samples CA-Mox-u, CA-Nox-u). Their physicochemical properties were characterized through nitrogen adsorption isotherms, SEM-EDX, FTIR spectroscopy, pH metric titrations, Boehm titration, and elemental analysis. Batch adsorption experiments were conducted to evaluate the removal efficiency of Co(II) and Sr(II) ions over a pH range of 2–10. Kinetic models (pseudo-first-order, pseudo-second-order, intraparticle diffusion) and isotherm models (Langmuir, Freundlich, Dubinin–Radushkevich, Temkin-Pyzhev) were applied to study adsorption mechanisms and estimate maximum adsorption capacities.

Results: On the surface of activated carbons the following functional groups have been identified: strongly acidic groups (CA-Mox, 0.95 meq/g; CA-Mox-u, 0.44 meq/g; CA-Nox-u, 0.32 meq/g) and weakly acidic and phenolic groups, while the pHpzc value of the studied activated carbons increase as follows:
CA-Mox (2.3) < CA-Mox-u (3.3) < CA-Nox-u (3.9) < CA-M (6.9) < CA-N (8.3).

The results of batch experiments indicate that maximum adsorption can be achieved in broad pH ranges: 4–8 for Co(II) and 4–10 for Sr(II). The maximum adsorption capacities of Co(II) and Sr(II) on oxidized activated carbons at pH = 4 are: CA-Mox, 0.085 and 0.076 mmol/g; CA-Mox-u, 0.056 and 0.041 mmol/g; and CA-Nox-u, 0.041 and 0.034 mmol/g, respectively.

The experimental data are best described by the pseudo-second kinetic model, suggesting that the adsorption of metal ions (cobalt(II) and strontium(II)) onto oxidized activated carbons is based on chemisorption. The constants determined for the Freundlich and Langmuir models and the energy values estimated by Dubinin–Radushkevich demonstrate that the adsorption process of strontium(II) and cobalt(II) ions onto oxidized activated carbons is favorable and dominated by chemisorption of the energetically homogenous surface in the modeled system.

Conclusion: The investigations highlight the important role of the solution pH, of the activated carbons' functional groups, and the pHpzc value for the adsorption process of cobalt(II) and strontium(II) ions. By summarizing the obtained results, the adsorption mechanisms of toxic metal ions on activated carbons were proposed.

 

 

Author (s) Details

Raisa Nastas
Institute of Chemistry of Moldova State University, 3, Academiei Str. Chisinau, MD-2028, Republic of Moldova.

 

Irina Ceban
Institute of Chemistry of Moldova State University, 3, Academiei Str. Chisinau, MD-2028, Republic of Moldova.

 

Tudor Lupascu
Institute of Chemistry of Moldova State University, 3, Academiei Str. Chisinau, MD-2028, Republic of Moldova.

 

Please see the book here:- https://doi.org/10.9734/bpi/cmsrf/v2/5160

 

Wednesday, 12 March 2025

The New Approaches in Mathematical Modeling of Grain Storage | Chapter 1 | Food Science and Agriculture: Research Highlights Vol. 1

After reviewing academic and technical literature it was found that traditional approaches are also significantly important for food security. According to this study, farmers are also adopting modern technology like hermetic storage and automated metal bins. The on-farm storage of grain like cover and plinth storage (CAP) technology also considerably improved since its inception as compared to heap storage of grain. After studying the surveys of agricultural extension, it was found that metal bins are maximum used due to their low cost, easy fabrication and use. For Animal feed storage like hay, the old traditional method of heap storage in the open or in go-downs is preferred by farmers. As a matter fact of these methodologies are basically based on traditional or local considerations. In terms of advancement only monitoring of environmental variables like temperature, breakage of grain, moisture etc are monitored in government godowns and research thrust is only for the use of these environment variables for preliminary design and fabrication of bins and silos. This paper emphasis on comprehensive control and maintenance of grain storage structure to monitor the health of grain through modern systems and technology like structural health monitoring(SHM) through piezoelectric energy, and computational fluid dynamics (CFD) to control environmental variables which is fed through the sensors and data loggers in the structure and Numerical methods like finite element method (FEM), boundary element method (BEM), discrete element method (DEM) etc. used for enhanced control and improvement of design of grain storage structures not restricting to bin and silos. This paper also highlights that low-cost underground grain storage is completely ignored by government agencies and communities due to its vulnerability to infestation of pests. This highlights the use of salt caverns if available as the best alternative to underground grain storage structures.

 

Author (s) Details

 

Sandeep Bhardwaj
Department of Civil Engineering, COAET, CCS Haryana Agricultural University, Hisar-125004, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/fsarh/v1/4219

Tuesday, 20 September 2022

Stability of Equilibria of Stochastically Perturbed Nonlinear Mathematical Models| Chapter 5 | Research Highlights in Mathematics and Computer Science Vol. 1

 The Smooth winged Sharpshooter's realized nonlinear numerical model is thought about. This model is believed to be impacted by stochastic bothers of the background noise, and these irritations are believed to be precisely corresponding to the framework state's deviation from the positive harmony. We get a vital and adequate condition for the harmony of the straight part of the nonlinear stochastic differential condition viable to have asympt-otic mean square steadiness. This need is likewise an adequate one for the likelihood based strength of the harmony of the underlying nonlinear condition. The outcomes are displayed in mathematical calculations and figures. It is noticed that the motivation behind this exploration isn't to concentrate on the solidness of a specific model. The proposed technique for strength examination can be applied to concentrate on steadiness of numerous other nonlinear conditions and frameworks of nonlinear conditions under stochastic annoyances.


Author(s) Details:

Leonid Shaikhet,
Department of Mathematics, Ariel University, Ariel 40700, Israel.


Please see the link here: https://stm.bookpi.org/RHMCS-V1/article/view/8244

Friday, 19 February 2021

Advanced Study on Drying Kinetics and Mathematical Modeling of Bottle Gourd | Chapter 2 | New Ideas Concerning Science and Technology Vol. 5

Objectives: Bottle gourd (Lagenaria siceraria L.) is an essential vegetable crop belonging to the Cucurbitaceae family in the tropical and subtropical regions of the world. It is most common in the sub-continent of Indo-Pakistan and is cultivated throughout India. The purpose of this analysis was to use a tray dryer to test the drying behavior of bottle gourd slices.

Style of the study: Bottle gourd slices were dried at 50, 55, 60, 65 and 70 + 1 °C in a tray dryer. Gravimetry assessed the moisture loss. Readings were taken within 30 minutes until constant weight was observed.

Location and Period of Study: In the Department of Food Science and Technology, MPKV Rahuri, experiments were conducted and completed within 12 months.

Methodology: Four separate drying models (Henderson, Logarithm, Page and Modified Page) were integrated into the drying curves, which are generally accepted for the modeling of drying agricultural materials. Based on the low RMSE, low χ2, and high R2, the best model describing the drying process was chosen. Results: Drying time at drying temperatures of 50, 55, 60, 65 and 70oC for bottle gourd slices was 630, 570, 450, 420 and 360 min, respectively. By comparing the time needed at temperatures of 50oC and 60oC and 60oC and 70oC, drying time was reduced by 28.57 percent and 20.00 percent, respectively. The moisture content of fresh bottle gourd was 92.09 percent (w.b.) at the beginning of the drying process, which is reduced to 7.08 percent (wb). As the drying time increased, the drying rate decreased. At 55oC, the drying rates were as high as 0.89 and at almost all temperatures, as low as 0.1. R2 values ranged from 0.788 to 0.954, R2 values were modified from 0.777 to 0.951, χ2 values ranged from 0.029 to 0.681, and RMSE values ranged from 0.0533 to 0.3742.

Conclusion: The drying time was shortened by an increase in the air drying temperature. In the falling rate era, drying mostly occurred. A better model for explaining the drying characteristics of bottle gourds at all temperatures was found to be the Henderson and Pabis model. At all temperatures, the product quality was found to be high.

Author (s) Details

Dr. Murlidhar Ingle
Krishi Vigyan Kendra, Badgaon-Balaghat, JNKVV, Jabalpur, 481115 (M.P.), India.

Dr. Ajay R. Tapre
Department of Food Processing Technology, A. D. Patel Institute of Technology (ADIT, Anand), India.

Radhika Nawkar
Krishi Vigyan Kendra, Badgaon-Balaghat, JNKVV, Jabalpur, 481115 (M.P.), India.

View Book :- https://stm.bookpi.org/NICST-V5/issue/view/22

Thursday, 24 September 2020

Research on the Existence and Uniqueness of Limit Cycles in a Class of Planar Differential Systems | Chapter 2 | Theory and Practice of Mathematics and Computer Science Vol.2

 

This article is an addition to the recent findings provided by M. In order to include other new classes, Sabatini addresses the nature and uniqueness of limit cycles of a certain type of planar differential systems. A concrete painting An example is given to illustrate the applicability of the outcome.

Author (s) Details

Khalil I. T. Al-Dosary
Department of Mathematics, College of Sciences, University of Sharjah, P.O. Box 27272, United Arab Emirates.

View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/271