scholarly journals Development of a mathematical model of vibratory non-lift movement of light seeds taking into account the aerodynamic forces and moments

2021 ◽  
Vol 3 (1 (111)) ◽  
pp. 70-78
Author(s):  
Аnton Nikiforov ◽  
Аlina Nykyforova ◽  
Roman Antoshchenkov ◽  
Vitalina Antoshchenkova ◽  
Sergey Diundik ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Aerodynamic Resistance ◽  
Euler Method ◽  
Dynamic Resistance ◽  
Algebraic Equations ◽  
Aerodynamic Forces ◽  
Tobacco Seeds ◽  
Fine Size ◽  
Lift Movement ◽  
The Impact

The modern practice of using vibratory machines when working with fine-size light-weight seeds is faced with such an undesirable phenomenon as the impact of aerodynamic forces and moments on the kinematics of vibrational movement of particles of the seed mixture fractions. According to the results of scientific studies devoted to the solution of this problem, only mathematical models of vibrational movement are used, where the aerodynamic factor is taken into account as taking the seeds by airflow. This is typical only for cleaning modes with the rebound of seeds from the vibrating surface. Aerodynamic forces and moments are present in them only as a force of aerodynamic resistance. The action of lateral aerodynamic forces and their moments are not taken into account. Their consideration allows to extend the range of action of the aerodynamic factor on the modes of vibration cleaning (vibroseparation) without rebound (but with sliding and rolling) which are of greater interest in terms of improving the efficiency of processing fine-size seeds. A mathematical model of seed vibration movement taking into account the action of a complete set of aerodynamic forces (dynamic resistance forces and lateral aerodynamic forces) and moments was proposed. This makes it possible to simulate non-lifting modes of vibrational movement of seeds. A system of algebraic equations that are linear with respect to the kinematic parameters of seed movement which was obtained by translating differential equations of movement into a finite-difference form was presented. The possibility of numerical solution of equations of movement by the Euler method was shown. The results of the evaluation of the model adequacy for the processes of vibration separation of tobacco seeds and false flax were presented. As shown by the results of calculations and experiments, the developed model provides an increase in the adequacy of the simulation results by 30 % in comparison with the model where the aerodynamic factor is not taken into account

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

Analyzing the Impact of Healthy Behavior on Weight Change with a Provable Mathematical Model (Preprint)

2020 ◽  
Author(s):  
Ayan Chatterjee ◽  
Ram Bajpai ◽  
Pankaj Khatiwada
Keyword(s):  
Physical Activity ◽  
Mathematical Model ◽  
Health Behavior ◽  
Weight Change ◽  
Simulated Data ◽  
Negative Behavior ◽  
Healthy Behavior ◽  
Healthy Habits ◽  
Lifestyle Diseases ◽  
The Impact

BACKGROUND Lifestyle diseases are the primary cause of death worldwide. The gradual growth of negative behavior in humans due to physical inactivity, unhealthy habit, and improper nutrition expedites lifestyle diseases. In this study, we develop a mathematical model to analyze the impact of regular physical activity, healthy habits, and a proper diet on weight change, targeting obesity as a case study. Followed by, we design an algorithm for the verification of the proposed mathematical model with simulated data of artificial participants. OBJECTIVE This study intends to analyze the effect of healthy behavior (physical activity, healthy habits, and proper dietary pattern) on weight change with a proposed mathematical model and its verification with an algorithm where personalized habits are designed to change dynamically based on the rule. METHODS We developed a weight-change mathematical model as a function of activity, habit, and nutrition with the first law of thermodynamics, basal metabolic rate (BMR), total daily energy expenditure (TDEE), and body-mass-index (BMI) to establish a relationship between health behavior and weight change. Followed by, we verified the model with simulated data. RESULTS The proposed provable mathematical model showed a strong relationship between health behavior and weight change. We verified the mathematical model with the proposed algorithm using simulated data following the necessary constraints. The adoption of BMR and TDEE calculation following Harris-Benedict’s equation has increased the model's accuracy under defined settings. CONCLUSIONS This study helped us understand the impact of healthy behavior on obesity and overweight with numeric implications and the importance of adopting a healthy lifestyle abstaining from negative behavior change.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

scholarly journals Modelling the impact of delaying vaccination against SARS-CoV-2 assuming unlimited vaccine supply

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Marcos Amaku ◽  
Dimas Tadeu Covas ◽  
Francisco Antonio Bezerra Coutinho ◽  
Raymundo Soares Azevedo ◽  
Eduardo Massad
Keyword(s):  
Mathematical Model ◽  
Vaccination Campaign ◽  
Vaccination Rate ◽  
Sao Paulo ◽  
The State ◽  
São Paulo ◽  
Health Authorities ◽  
The World ◽  
The Moment ◽  
The Impact

Abstract Background At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far. Methods We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations. Results The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole. Conclusions Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

scholarly journals Innovations in anaerobic digestion: a model-based study

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Karol Postawa ◽  
Jerzy Szczygieł ◽  
Marek Kułażyński
Keyword(s):  
Mathematical Model ◽  
Anaerobic Digestion ◽  
Production Efficiency ◽  
Biogas Production ◽  
Biogas Plant ◽  
Methane Content ◽  
Pig Manure ◽  
Pig Slurry ◽  
Production Chain ◽  
The Impact

Abstract Background Increasing the efficiency of the biogas production process is possible by modifying the technological installations of the biogas plant. In this study, specific solutions based on a mathematical model that lead to favorable results were proposed. Three configurations were considered: classical anaerobic digestion (AD) and its two modifications, two-phase AD (TPAD) and autogenerative high-pressure digestion (AHPD). The model has been validated based on measurements from a biogas plant located in Poland. Afterward, the TPAD and AHPD concepts were numerically tested for the same volume and feeding conditions. Results The TPAD system increased the overall biogas production from 9.06 to 9.59%, depending on the feedstock composition, while the content of methane was slightly lower in the whole production chain. On the other hand, the AHPD provided the best purity of the produced fuel, in which a methane content value of 82.13% was reached. At the same time, the overpressure leads to a decrease of around 7.5% in the volumetric production efficiency. The study indicated that the dilution of maize silage with pig manure, instead of water, can have significant benefits in the selected configurations. The content of pig slurry strengthens the impact of the selected process modifications—in the first case, by increasing the production efficiency, and in the second, by improving the methane content in the biogas. Conclusions The proposed mathematical model of the AD process proved to be a valuable tool for the description and design of biogas plant. The analysis shows that the overall impact of the presented process modifications is mutually opposite. The feedstock composition has a moderate and unsteady impact on the production profile, in the tested modifications. The dilution with pig manure, instead of water, leads to a slightly better efficiency in the classical configuration. For the TPAD process, the trend is very similar, but the AHPD biogas plant indicates a reverse tendency. Overall, the recommendation from this article is to use the AHPD concept if the composition of the biogas is the most important. In the case in which the performance is the most important factor, it is favorable to use the TPAD configuration.

scholarly journals Simulation Tests of a Cow Milking Machine—Analysis of Design Parameters

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1358
Author(s):  
Ewa Golisz ◽  
Adam Kupczyk ◽  
Maria Majkowska ◽  
Jędrzej Trajer
Keyword(s):  
Mathematical Model ◽  
Simplified Model ◽  
Design Parameters ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Local Loss ◽  
Linear Drag ◽  
Milking Machine ◽  
Machine Analysis ◽  
The Impact

The objective of this paper was to create a mathematical model of vacuum drops in a form that enables the testing of the impact of design parameters of a milking cluster on the values of vacuum drops in the claw. Simulation tests of the milking cluster were conducted, with the use of a simplified model of vacuum drops in the form of a fourth-degree polynomial. Sensitivity analysis and a simulation of a model with a simplified structure of vacuum drops in the claw were carried out. As a result, the impact of the milking machine’s design parameters on the milking process could be analysed. The results showed that a change in the local loss and linear drag coefficient in the long milk duct will have a lower impact on vacuum drops if a smaller flux of inlet air, a higher head of the air/liquid mix, and a higher diameter of the long milk tube are used.

scholarly journals Mathematical model of the feedback between global supply chain disruption and COVID-19 dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Xingyu Li ◽  
Amin Ghadami ◽  
John M. Drake ◽  
Pejman Rohani ◽  
Bogdan I. Epureanu
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Care Delivery ◽  
Global Supply Chain ◽  
Economic Losses ◽  
Chain Model ◽  
Supply Chain Disruption ◽  
Disease Networks ◽  
Resource Allocation Strategy ◽  
The Impact

AbstractThe pandemic of COVID-19 has become one of the greatest threats to human health, causing severe disruptions in the global supply chain, and compromising health care delivery worldwide. Although government authorities sought to contain the spread of SARS-CoV-2, by restricting travel and in-person activities, failure to deploy time-sensitive strategies in ramping-up of critical resource production exacerbated the outbreak. Here, we developed a mathematical model to analyze the effects of the interaction between supply chain disruption and infectious disease dynamics using coupled production and disease networks built on global data. Analysis of the supply chain model suggests that time-sensitive containment strategies could be created to balance objectives in pandemic control and economic losses, leading to a spatiotemporal separation of infection peaks that alleviates the societal impact of the disease. A lean resource allocation strategy can reduce the impact of supply chain shortages from 11.91 to 1.11% in North America. Our model highlights the importance of cross-sectoral coordination and region-wise collaboration to optimally contain a pandemic and provides a framework that could advance the containment and model-based decision making for future pandemics.

scholarly journals The Impact of Elongation on Change in Electrical Resistance of Electrically Conductive Yarns Woven into Fabric

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3390
Author(s):  
Željko Knezić ◽  
Željko Penava ◽  
Diana Šimić Penava ◽  
Dubravko Rogale
Keyword(s):  
Mathematical Model ◽  
Electrical Resistance ◽  
Electrically Conductive ◽  
Textile Materials ◽  
Measurement Results ◽  
Conductive Yarns ◽  
Yarn Count ◽  
As Relationship ◽  
The Impact ◽  
The Mathematical Model

Electrically conductive yarns (ECYs) are gaining increasing applications in woven textile materials, especially in woven sensors suitable for incorporation into clothing. In this paper, the effect of the yarn count of ECYs woven into fabric on values of electrical resistance is analyzed. We also observe how the direction of action of elongation force, considering the position of the woven ECY, effects the change in the electrical resistance of the electrically conductive fabric. The measurements were performed on nine different samples of fabric in a plain weave, into which were woven ECYs with three different yarn counts and three different directions. Relationship curves between values of elongation forces and elongation to break, as well as relationship curves between values of electrical resistance of fabrics with ECYs and elongation, were experimentally obtained. An analytical mathematical model was also established, and analysis was conducted, which determined the models of function of connection between force and elongation, and between electrical resistance and elongation. The connection between the measurement results and the mathematical model was confirmed. The connection between the mathematical model and the experimental results enables the design of ECY properties in woven materials, especially textile force and elongation sensors.

Study on Grinding Force in Two-Dimensional Ultrasonic Grinding Nano-Ceramics

2010 ◽  
Vol 42 ◽  
pp. 204-208 ◽  
Author(s):  
Xiang Dong Li ◽  
Quan Cai Wang
Keyword(s):  
Mathematical Model ◽  
Ultrasonic Vibration ◽  
Contact Time ◽  
Reaction Force ◽  
Grinding Force ◽  
Two Dimensional ◽  
Indentation Fracture ◽  
Ultrasonic Grinding ◽  
The Impact ◽  
Ultrasonic Vibration Assisted Grinding

In this paper, the characteristic of grinding force in two-dimensional ultrasonic vibration assisted grinding nano-ceramic was studied by experiment based on indentation fracture mechanics, and mathematical model of grinding force was established. The study shows that grinding force mainly result from the impact of the grains on the workpiece in ultrasonic grinding, and the pulse power is much larger than normal grinding force. The ultrasonic vibration frequency is so high and the contact time of grains with the workpiece is so short that the pulse force will be balanced by reaction force from workpiece. In grinding workpiece was loaded by the periodical stress field, which accelerates the fatigue fracture.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

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