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# Mathematical Models - Science topic

Explore the latest questions and answers in Mathematical Models, and find Mathematical Models experts.
Questions related to Mathematical Models
Question
How can I get horizontal planes of voxels in tomography using topography area?
Or more precisely, what procedure can be considered to make this mode have its own mathematical model so that I can intersect the rays with its mathematical model?
Although I wrote the mathematics of the two x-ray anodes to make resection and intersection back in 1978, I am not an expert in CT mathematical modeling. Therefore, if you know each voxel's x, y, and z coordinates, then a horizontal section is to pick up all voxels with the same z-value. A profile section picks up all voxels with the same y-value, and a cross-section picks up all voxels with the same x-value. If you need a higher resolution than the voxel size, you make more sections around the location of interest and do interpolation.
Question
Dear Esteemed Researchers,
I have a mathematical model of a Plant. I want to implement two different controllers and see the response of system in tracking a specific reference. I would like to analyze the transient time response of the system for both the controllers. I don't mean to just check the response in simulation I want technical analysis using tools such as eigenvalue analysis. What tool can help me build up the evidence for best transient time response.
Thank you.
Question
I have developed a mathematical model for modeling and optimizing process design. Now there are measurable input data available to compute other parameters via the model. I need suggestions on Open Source software and applications that are user friending that I can use to write my mathematical model equations to automatically calculate the measurable inputs are keyed in.
Software outside the usual programing and coding using MatLab and Python interface.
There are several open-source software and applications that you can use to write your mathematical model equations and automatically calculate the measurable inputs as they are keyed in. Here are a few options:
1. Jupyter Notebook: a web-based interactive environment for creating documents that contain live code, equations, visualizations, and narrative text. It supports many programming languages including Python, R, and Julia.
2. RStudio: a free and open-source integrated development environment (IDE) for R. It provides a user-friendly interface for writing and running code, as well as visualizing and analyzing data.
3. Scilab: a free and open-source software for numerical computation. It has a user-friendly interface and supports a wide range of mathematical functions, including optimization and control systems.
4. Maxima: a free and open-source computer algebra system that can manipulate symbolic expressions and perform numerical calculations. It has a command-line interface, but there are also several graphical user interfaces (GUIs) available for it, such as wxMaxima.
5. Geogebra: a dynamic mathematics software for learning and teaching math, science, and engineering. It has a user-friendly interface and supports a wide range of mathematical functions, including optimization and control systems.
These are just a few examples, there are many other options available. It depends on the specific requirements of your project and your personal preference.
Question
I am looking for study material (books, articles, codes or even YouTube videos) on parameter estimation of differential equation models (using any method but preferably least squares). I would like to calibrate some mathematical models in the form of ODEs and PDEs; I have a time series data set for the dependent variables. I could simply Google but I would like material that has demonstrations for easy learning.
Use particle swarm optimization (PSO) or other metaheuristic algorithms for finding the optimal parameters of a system of ordinary differential equations (SODE) by minimizing the error (e.g. mean absolute percentage error or MAPE) between data and the model's solution. In Matlab, you can use ode45 package to solve the SODE. The step is:
0. Suppose you want to estimate the parameters in region interval I.
1. Generate m random vectors X in I, these vectors act as the initial guess of parameters.
2. Solve the SODE using ode45 for each vectors value. Then calculate the MAPE between SODE's solution with the data.
3. Find the minimum of the obtained MAPE. The vector vapue X* which gives the minimum of MAPE will act as the initial optimal parameters.
4. Next, you use the updating formula in the PSO to update the previous vectors X (you can find this in many books or article).
5. Redo the process 2-4 using the new vectors X.
6. At the desire stopping criteria, for example maximum iteration, you will get the estimated parameters value of your model.
Feel free to contact me for more detail explanation. I can help you.
Question
We, as humans, use myths, stories, and spiritual thoughts to interoperating the world around us. However, most of our thoughts are compromised by biases. Mathematical models are helping us to create a consensus among the different segments of society. Are these models have alternatives?
Mathematical models don't always create consensus, because pragmatic considerations come into play in the adoption of a model. For example, folks may disagree about which geometry is best for representing or interpreting certain theoretical posits or observations, a question which cannot always be settled conclusively.
Question
The SEIR model is famous as some countries such as Malaysia use it to predict emerging infectious diseases such as COVID-19? What makes it famous among other mathematical models, agent-based model etc.?
kindly tell me the scope of research in computer virus model with stochastic term and what are the limitation.
Question
what is the scope of research in the field of mathematical biology or mathematical model
kindly send me the scope of research of computer virus propagation with stochastic term
Question
Please, I need, if available, some important research papers which relate the theory of dynamical systems to climate change. Also, in general, I know there are a lot of published research articles that relate dynamical systems to many applications. But, are there papers that research centers and governments depend on that before taking any procedures? I mean, are there papers, especially on climate change and the environment, which are not only in theory but have practical applications?
Fellow researcher,
Chaos theory, which is a branch of dynamical systems was founded by the study of the Lorenz attractor (butterfly diagram). Edward Lorenz was a meteorologist and this attractor was introduced by him as a consequence of its simplified mathematical model for atmospheric convection. So yes, climate study and dynamical systems are interlinked since the beginning and I recommend Strogatz's "Nonlinear Dynamics And Chaos" for a overview with applications to climate change or "Nonlinear Dynamics in Weather and Climate" for a more specialized text. It is worth to mention that climate change also involve stochastic processes so consulting also works like "Stochastic resonance in climatic change" is important for you repertoire.
Which you have fun and have success in your studies.
Question
The Mandelbrot set is related to the Feigenbaum cascades, which are found in lots of mathematical models of real-life phenomena. But does the Mandelbrot set have have any real-world use, either on its own or in connection with Feigenbaum cascades? Or is it purely aesthetic?
you can look below this source for your question:
My regards,
Question
I already have the GHI from the weather station are there any equations to calculate the GTI or only It can be accurately measured by a pyranometer installed at the same tilt
angle as the PV panels ?
Dudley J Benton thank you very much for your answer I already concluded that I need to measure it. most of the formulas need more parameters than I already have.
Question
Hello world,
I am performing dynamic analysis on the rotating cantilever beam. With the help of mathematical model I have calculated the natural frequency for axial and two transverse direction that seems to vary with the rotating speed of the beam. The attached file show the variation of natural frequency .
I am clueless with the physics behind the variation?
Is it necessary to decrease axial natural frequency with increase in speed and increase of other two directional frequencies ??
Help me to draw the conclusion.
If you have included damping in your model, then it will be the damped natural frequency.
I am not yet 100% sure but I think the Coriolis force is considered while taking into account the gyroscopic effect. I have not yet through this topic so at present I am unable to account for their effects. I will update the answer if I learn/find anything regarding it.
Regards,
Jatin
Question
If the geodetic coordinates (φ,λ,h) of the ground station (e.g., GPS station) is known, how can the pressure, temperature, and relative humidity of this station be predicted at different times?. I'm looking for a mathematical model+modeling data, not instruments (equipment) used. If you have any information about this, please share it here.
You might be biased against measurements because you feel you cannot afford them. But often there are meteorological networks nearby - based on stations, weather radar, lidar, GPS dual frequency electron density, meteorological satellites, and many amateur networks. One measurement is sometimes worth 10 supercomputer's. You did not say what you are trying to do, or where. The location matters a lot - for the complexity of the modeled region, for the sparsity or abundance of continuous data stream, and for the possibility of others working on the same place.
I found that many of the seismic stations are recording meteorological data. Because when you work at parts per million or parts per billion problems the atmospheric variations are often one of the largest variations. Sometimes simple correlations remove or identify the the big variations. But I found that imaging arrays ultimately are needed.
I am sorry I cannot answer you more clearly. You don't say your restraints in terms of computing resources. If you have 10 supercomputer nodes, there are one set of options. If you have only a Raspberry Pi, then something else is needed.
I am sitting here listening to a lightning storm passing over the area. It reminds me of all the electromagnetic sensor methods for monitoring weather in 3D and quantitatively. You did not say how long your project related to the question might be. If it is a casual "I wonder?" or "a ten year plan", the methods are different.
I see you are working with geopotential. The daily variations of the gradient of the potential are easily measurable. After subtracting the sun moon portion of that, the largest component is the local atmosphere. I mentioned the seismic stations measuring temperature, pressure, humidity, acoustic. That is because the acceleration is correlated with atmospheric events and properties.
The most cost effective way to get good estimates for different locations is to use a combination of all the available continuous data streams and their correlations, then use algorithms that can run on low cost equipment. But all that is set by what you are trying to accomplish.
Atomic clocks are "direct geopotential sensors". You might want to look more closely at gravimeters and gravity gradiometers. Again, I cannot tell what you are trying to do, so I cannot be more specific. But generally the gravimeter networks are more sensitive to meteorological changes. I am trying to set up gravitational imaging arrays to 3D image the atmosphere for cities that also have 3D weather radar and climate models at sufficient resolution - for correlations. The less expensive gravitational sensors, once calibrated, are not bound by electromagnetic noise or weather conditions as much.
You seem to be assuming "I can get some data more easily by running a model". But often the best models are proprietary or horribly difficult to run. Then your best bet is to locate places on the Internet where the data is served continuously. The European Space Agency has a rather large project on global climate change that has to estimate global climate at any location over long time periods. Their model outputs are available. They keep moving things around, but you might try looking here - https://spacedata.copernicus.eu/ just to get some sense of what is going on. Brian Bramanto link is good. But the global climate model community is large and varied, and has many applications.
All their models, and any model you find will have to have been calibrated using real data, to be of any use. So whether you tap the raw data, or they do it and feed you the processed results - you are ultimately looking at measurements by someone. Usually many someones.
Looks like you and I are in the same project. You might want to take a closer look at Mossbauer methods for measuring the geopotential. That is the first absolute gravitational potential measurement. Also, the neutrino and cosmic ray networks are getting to the level of sensitivity and temporal resolution they can pick up daily and hourly variations driven by local pressure temperature humidity. Their results depend on the local atmospheric density.
Rather than TPH, you might want to think more in terms of mass density variations. PV = nRT is really very useful. n(i) = ParticlesPerCubicMeter(i) = MassDensity * AvagadrosNumber/ MolecularWeight(i) for sets of molecular and atomic species. i is the index for the species. It might seem trivial, but if you have to use it a million times and it gets embedded in thousands of different models, it is good to bring it out explicitly to be able to combine results from many groups.
Richard Collins, The Internet Foundation
Question
Hello everyone, I am looking for a good MPC quadratic optimization mathematical model to optimize a cost function or performance index, for a battery energy storage state space model. Would anybody suggest a good research paper or post a formulation that contains a good mathematical model for quadratic optimization? An objective function with viable constraints, which can be possible to implement in function solvers such as quadprog or cplex would be ideal. Thank you
Dear Giovanni Ponce,
I suggest you see the links and attached file on the topic.
Best regards
Question
I have plenty of data from leaves, but is there a way to calculate their photosynthesis rate?
I count with:
• Leaf temperature
• Leaf VPD
• Stomatal conductance and density (stomata/cm2) and their % aperture
• RH & Temperature from the environment
• Irradiation from the sun (W/m2)
• PAR Light
I know that the best way to obtain photosynthesis rate is with a enclosed chamber and measure the decrease of CO2, but is there a way to calculate it with some of the data that I already have?
I have been searching for a mathematical model or any kind of coupled equations, but I haven't found any info.
There may not be direct to the point, however, I advice you read the following articles.
Thank you!
Question
Dear colleagues!
Tell me, please, why does the velocity of nerve impulse conduction along the nerve decrease when the nerve is stretched?
Maybe there are some mathematical models that describe this effect?
I see what you mean by making nodes of Ranvier "longer": that is a possibility; but this would have to be compared with possible elongation of myelin sheaths as well (i.e. the signal could be slowed down in longer nodes of Ranvier, but at the same time make longer "jumps").
I also thought about another possible explanation of the phenomenon that you observe: could it be that the axon diameter is decreased as you stretch it? We know that the propagation velocity is proportional to the (square root of the) axon diameter, so if the diameter is decreased, so will be the velocity.
I think it is important, in any case, to know what is happening to the myelin sheath: is it stretching as well? Is it by any chance getting thinner? A thinner myelin sheath could also imply a smaller membrane resistance...
I don't know what in particular you want to focus on in your model, but it could be relevant for you to consider time and length constants (see for instance https://nba.uth.tmc.edu/neuroscience/m/s1/chapter03.html).
Hope this is useful! :-)
Question
Dear fellows,
Maybe you have done interesting measurements to test some model?
I can always use such data to use as examples and tests for my regression analysis software, and it's a win-win, since I might give you a second opinion on your research.
It's important that I also get the imprecision (measurement error/confidence interval) on the independent and dependent variables. At this moment, my software only handles one of each, but I'm planning to expand it for more independent variables.
Koen Van de Moortel Data modeling (data modeling) is the process of developing a data model for storing data in a database. This data model is a conceptual representation of data objects, data object connections, and data object rules.
Question
i need it to do a simulation for a building
In order to simulate a building within TRNSYS, you have to use TRNBuild which is a EnergyPlus engine based add-on; you may need to take a look at the energyplus documentation to get a general idea on how different objects (i.e thermal zones, spaces..) are definded. Moreover, if the simulation of the building in question include HVAC and Energy management system (EMS), i would then suggest you to use either OpenStudio Application or OpenStudio SDK, who gives a complete and intuitive access to EnergyPlus along with a suite of applications including a Parametric Analysis Tool (PAT). Also all those tools are free and open source.
Question
The traditional way of deriving the mathematical model of any dc-dc converter is by using the volt and charge second balance to find the average model of the converter. However, is there any other way to derive the model of a converter that also accurately represents its dynamics?
Hi,
Multiple methods are available. You can perturb the voltage, current, or control parameters during CCM or DCM in a linearized model. Else, average model is a good alternative.
Thanks
Question
Need help with this kindly message me or let me here on the discussion for the clear description of the this I need the on paper Mathematical model of the Interleaved boost converter...
Question
Hello All,
How to mathematically model creativity?
Can we use deep learning models to predict creativity?
Kindly suggest.
Thanks.
Kindly check also the following useful RG link:
Question
Design of experiment helps to estimate the percentage contribution of factors and significant factors affecting the process. Interaction plots and mathematical models can also be arrived at.
Dear Mr. Ravi Chate,
Yes, there are many ways, including method, analysis of variance (ANOVA), complete factorial designs, bacterial foraging technique, and fuzzy logic and etc which you choose depending on your test conditions.
Good luck.
Zohreh SHAKERI.
Question
It has been observed that different incidents rates like bilinear, standard, saturated have used. My query is where to use which incidence rate? (For any particular disease? Or any other criteria?)
Question
I am an undergrad student at UET Lahore, I am studying Near field PV energy conversion, I have developed the mathematical model for the system on MATLAB, but it seems that it can't be solved, since the solution involves sqrt of iota which cant be integrated to find current density, I really need help on this, thank you.
An explanation would help me.
Since I haven't found a completely solved model anywhere. All the papers just had the mathematical overview followed by results.
Question
For example, a simple 1D porous flow problem in a reservoir. On the left of the model, there is a production well. So how should I deal with this production well? Adding a Neumann boundary condition at the left? Will it change the physical problem that I am trying to simulate? since if there is a production or injection well, it should be a source term in the mathematical model.
Follow
Question
Please, present a list of references, which describes the interaction of the subatomic particles.
You could consult Quantum Mechanics by Leonard Schiff ( a book)
One of the later chapters deals with Quantization of Fields, as far as the electromagnetic field. This leads to Photons. It is fairly understandable in this reference.
The idea is that quatizing fields leads to particles.(However particle physics is far broader than this) It uses creation and destruction of photons.
Second quantization starts when think of many particles and use the wave fnction as operator, rather than just function. I guess it is a small subset of QFT or particle physics.
Question
Dear researchers
As a research team, we intend to work on various fractional mathematical models in which fixed point theory and fractional calculus play an important role. I invite interested researchers to work on numerical techniques and simulations. If you are familiar with numerical techniques and MATLAB software, please contact me.
Thank you very much.
Best regards
Sina
Dear friends
Thank you very much for your kind messages. I will contact with you soon. Thanks.
Question
Hello everyone,
I wanted to know when we perform in vitro drug release experiments and fit them into various mathematical models:
1. How do we choose the best model based on the graph or the R-square value or something else?
2. the n value is supposed to be calculated only for the Korsmeyer-Peppas model or for all the models?
Hello,
I am not an expert in your area but when I read your question I Googled a bit and have found the article "Application of Mathematical Models in Drug Release Kinetics of Carbidopa and Levodopa ER Tablets" by Radhakant Gouda, Himankar Baishya and Zhao Qing in the Journal of Developing Drugs 2017, 6-2. It can be downloaded from here:
Good luck
Question
Hi~
There is an amide reaction (-COOH + -NH2 to -N-C=O) at the interface of molten PA6 and silane coupling agent film. How to evaluate the influence of temperature on reaction rate quantitatively?
Any suggestions or reference recommendations would be appreciated.
Thanks a lot.
Since that is a reaction with several intermediates, that is not a trivial thing.
Mathematical models: I suppose you know about TST? You can in principle use DFT and a reaction dynamics package to generate a full model. However, since you have a non-trivial heterogenous system, this will be hard to get right. In the homogenous case that was shown e.g. here:
When you have measured temperature-dependent product formation rates, you can set up a mechanism with the individual steps and try fitting the product formation rate using Eley-Rideal, Langmuir-Hinshelwood or some sort of intermediate mechanism. However, if you can only measure the rate of the amide formation itself and not the side products, the fit will probably be overdefined.
Question
Background of the problem for people non familiar with transfusion:
Every day, hospital transfusion services must guarantee they have enough blood to meet patient transfusion demand. This is very like managing a food stock in a refrigerator but even easier (just one product, one expiration date).
Assumptions:
- RBC (red blood cell) units are kept on a refrigerator with enough capacity
- Maximum expiration date for RBC is 42 days.
- We make a routine order to the blood bank provider (our grocery store) every day from Monday to Friday. We can make additional orders if we run out of stock.
- We practice first in first out.
The model should satisfy the following targets:
- Minimize the expiration rate (the number of RBC units expiring every certain time)
- The less time on the refrigerator the better (eat fresh)
- Avoid extraordinary orders as much as possible (some extraordinary order might be considered to cope with transfusion peaks of demand)
- Note: I have purposely simplified the problem (no considerations of ABO group distribution, crossmatched reserved units, or reduced expiration date of the irradiated blood…).
Non controlled external factors:
- Transfusion rate
- Average remaining time to expiration of the received blood.
What we are looking for is the optimal number of RBC units we must order on a routine basis (M-F) which is the only factor we can adjust to optimize the equation. Resulting figure must be recalculated when transfusion rate or average expiration date of the received units change.
Intuitively, I see how the number of extraordinary orders and RBC freshness are at opposite sides of a balance, because if a higher number of extraordinary orders is tolerated, then it should result in a smaller but fresher RBC inventory. On the other hand, in order to avoid extraordinary orders, you need a greater inventory thus increasing the average age of your products and the risk of expiration.
Any idea or suggestion? Any available script on Excel/SPSS/Stata/R/SQL? Any related bibliography?
I can provide raw data for simulations on demand if someone want to make a collaboration.
good work
Interested
best of luck
Question
Hi,
I am trying to write the motivation part for linearization of a non-linear mathematical formulation. I claim the mathematical model will be more simple and easier to solve. But, of course, I need a reference for that! Any suggested book chapters or articles that discuss this point please?
Zak
Linearization is one amongst most important problem solving methods, in science.
Thanks
Question
Hi Good Day, I am working on finding trim point using a non linear aircraft mathematical Model. The optimization algorithm (Nelder-Mead) can search for minimum cost function to trim the aircraft for conventional controls. Now when in addition to aileron, rudder and elevator, Differential elevator is another variable available, I get multiple trim solutions based upon starting point. How can I specify any other constraint so that I get the minimum deflections for trim. My solution is that the deflections which cause minimum drag or throttle deflection is the global minimum in this case but how can i implement it in the objective function. Has anyone attempted this earlier. Regards
Dear Farhat,
I am sorry for my late response and thank you for your interest in my publications.
The constraints can be added to the objective function as a penalty term.
You can use the penalty or the barrier method to solve constrained problems.
I advise you to read Chapter 17 of the Numerical Optimization book by Jorge Nocedal and Stephen Wright.
If you have written the code in MATLAB, I can help you to edit the code.
Regards
Murat Millidere
Question
Can the Runge-Kutta method solve the governing equation in the attached article? the mathematical model is a plate includes both geometric nonlinearity and nonlinear stiffness, which teacher can explain? Are there any similar examples?
if you want to solve the Eq (21) or Eq(22), you could use conventional forth order RK with tiny time step.
However, by experience, Implicit versions of RK get more accurate results than forth-order RK, in less cpu time(for linear and nonlinear dynamic systems).
Question
Can the Runge-Kutta method solve the governing equation in the attached article? the mathematical model is a plate includes both geometric nonlinearity and nonlinear stiffness, which teacher can explain? Are there any similar examples?
Runge-Kutta methods of various orders are derived based on Taylor Series expansions of various orders. There are explicit or implicit RK methods. The explicit single step methods are used to solve systems of first order IVPs (of non-stiff ODEs). The implicit methods are more suitable for stiff differential equations (due to occurrence of numerical instabilities). There are also explicit or implicit multi-step methods, and semi-implicit methods. [Search references!]
Higher order differential equations are transformed into systems of first order ODEs (IVPs) and the above (implicit / explicit) methods are applied based on the type of the ODEs (stiff / non-stiff). Infact, there are other methods...
Many Thanks!
Question
How can i draw and make a mathematical model for a different shape for a metal foam matrix, I have a numerical program for fluid flow through cupper foam matrix with sensible heat transfer, so I need to insert the foam matrix in the numerical program to complete the simulation program.
Greeting
My target it to build a model for the metal foam matrix as shown in the attachment file
with my respect
Question
A mathematical model to analyze the combined effects of interest and inflationary rates on inventory systems (World Bank World Economic Indicators database 2019)
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Hello everyone,
I need to know the methods used to calculate β and γ in the mathematical model of infectious diseases (S.I.R).
Zerouali Bilel lots of thanks bro.
Question
Dear colleagues,
Does anyone know a method for predicting (with more or less uncertainty) the contribution of organisms (community, species, functionnal group...) to a function/process?
I'm not a mathematical modeler and I don't pretend to create something robust. Rather, I am in an exploratory process to enable a better understanding among stakeholders.
For the moment I have found a few publications on plants that can help me (below) but I wonder if there are any others publications, on others organisms, ecosystems?
Best regards,
Kevin Hoeffner
References:
-Garnier, E., Cortez, J., Billès, G., Navas, M. L., Roumet, C., Debussche, M., ... & Toussaint, J. P. (2004). Plant functional markers capture ecosystem properties during secondary succession. Ecology, 85(9), 2630-2637.
-Suding, K. N., Lavorel, S., Chapin Iii, F. S., Cornelissen, J. H., DIAz, S., Garnier, E., ... & Navas, M. L. (2008). Scaling environmental change through the community‐level: A trait‐based response‐and‐effect framework for plants. Global Change Biology, 14(5), 1125-1140.
-Zwart, J. A., Solomon, C. T., & Jones, S. E. (2015). Phytoplankton traits predict ecosystem function in a global set of lakes. Ecology, 96(8), 2257-2264.
Hello Kevin,
I think you can use trait-based apporach to understanding the contribution of organism to function
Question
Scientists and engineers solve physical and mathematical models containing tens and hundreds of SI variables, and take into account a larger number of potential effects of interaction between them, using super-powerful computers and developed advanced mathematical methods. But this requires significant time and financial resources. In addition, with the current rapid development of science, the situation with the identification of truly revolutionary discoveries is complicated by the complexity of their identification (the idea of ​​incommensurability of scientific theories): supporters of each paradigm see the world in their own way because of their scientific training and previous experience. They use a different conceptual framework and different ideas about scientific standards.
Is there a limit to our knowledge?
Your remark : " A tool is only as good as the person using it."
For me it is difficult not agree with you.
At the same time, I would like to put your attention once more on ONE point:
Person (scientist, engineer, observer, he or she) formulates his vision of the physical pnenomena basing on his knowledge, life experience and intuition - one can say - phylosophical opinion.
As a physical-mathematical tool for formulating a model, he uses different variables from any system of units (SI, SGS, Plank system and so on.). There is no other way.
My problem (and I try to convince scientific society) is:
If any system of units consists of the finite number of variables (read my articles) and a model includes the finite amount information (read Del Santo, F., & Gisin, N. (2019) Physics without determinism: Alternative interpretations of classical physics. Phys. Rev. A, 100, 1–9.
there is the initial inevitable blurring of the object that is being studied by the observer.
This explains the impracticability of achieving infinite precision!
Do you agree with this ???
Question
Inter-facial Tension (IFT), Combined Chemical (CC), Mathematical Model (MM)
Much chemical process modelling and/or simulation work can be done with the widely-used Microsoft’s Excel.
Application example ― Simulations carried in Excel 5.0 with Visual Basic for Applications (VBA) macros ― The recursive least squares algorithm (RLS) allows for (real-time) dynamical application of least squares regression to time series. Years ago, while investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS algorithm with forgetting factor (RLS-FF) to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, while giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The power dissipated by agitation was accessed by a torque meter (pilot plant). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
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how Silvaco solves the mathematical model. Is it using Finite Element Methods or Finite Difference Methods?
your can use either of them, but FDM is good for your model.
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If we could find a mathematical model for each optimization problem, could mathematical programming replace meta-heuristic algorithms?
I am not sure I understand the premise of the question.
(1) If one does not have a mathematical model of an optimization problem, can we actually call it that? and
(2) How would meta-heuristics help in this case?
I imagine that to use a meta-heuristic for optimization, one would need at the very least a black-box, which takes values from some set and produces elements in a totally ordered set. In mathematical language, such black box is a function, and I would call this a mathematical model of one's problem. There are optimization algorithms that rely only on function values; see for example the relevant chapter in Nocedal&Wright's textbook ( ).
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We use many mathematical models and state-space models in digital control systems. Before applying these concepts in real life scenarios, how useful (or less useful) it is to do a simulation in MATLAB?
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I have predictions from mathematical models in the systems biology field, not yet confirmed experimentally. However, I would like to publish in pee-review journals free from publication charges.
Web of Science Master Journal List - WoS MJL by Clarivate:
Question
In the 21st century, we can safely say that absolutely all modern achievements in the field of science are based on the successes of modeling theory, on the basis of which practical recommendations are given that are useful in physics, technology, biology, sociology, etc., are extracted. In addition, this is due to the fact that the application of the principles of the theory of measurements in determining the fundamental constants allows us to check the consistency and correctness of the basic physical theories. In addition to the above, the quantitative predictions of the main physical theories depend on the numerical values ​​of the constants included in these theories: each new sign can lead to the detection of a previously unknown inconsistency or, conversely, can eliminate the existing inconsistency in our description of the physical world. At the same time, scientists have come to a clear understanding of the limitations of our efforts to achieve very high measurement accuracy.
The very act of measurement already presupposes the presence of a physical and mathematical model that describes the phenomenon under study. Simulation theory focuses on the process of measuring the experimental determination of values ​​using special equipment called measuring instruments. This theory covers only aspects of data analysis and the procedure for measuring the observed quantity or after the formulation of a mathematical model. Thus, the problem of uncertainty before experimental or computer simulations caused by the limited number of quantities recorded in the mathematical model is usually ignored in measurement theory.
No, dear Boris. :) "Fast" in this case is not "great". "Great" is the content.
I also gave the following comment under this my preprint:
"If you have at least a basic mathematical education, you are able to understand the elementary essence of this preprint, as the first simplest, shortest and most obvious proof of Fermat's Last Theorem, FLT. There are some questions or suspicions about the reasons for the almost 400-year (at least) inability to present this proof. But, more on that later ... If you are reading these lines and, if it is not difficult for you, please recommend this preprint and share this link with friends , acquaintances and colleagues. "
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I have created a 2 dimensional mathematical model for a UAV in matlab. I also created a programmatic GUI for the UAV flight simulation. However, i now need to create a clock which displays the time for the flight of the UAV. How can i do this
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Hai. I'm a young researcher. Just want to ask how can I verify my mathematical model if the model that I propose is based on the real problem. For example, I propose a mathematical model for a staff rostering based on real-problem, so how can I verify my model? and second question, how can I compare the result. If I make comparisons with the real result that is from the manual rostering, maybe it's like a bias because might be the result from my model can produce a better solution.
Dear Mohamad Norizal AbdullahThe answer to your first question is partially given in your second question. A way to validate your model could be comparing its results to a real ones. This will give an idea on the accuracy of your model and can inform on its validation, depending on the biais between the real and modeled problems.
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Is it possible to mathematically model a binary variable using continuous variables in the optimization problems?
For example, assume that 'X' is {0,1}. Can I define it as 0<=X<=1 in my problem and impose some additional constraints instead to force X to become only '0' or '1'?
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I need to do further modeling on the voltage source inverter (VSI). Can anyone please tell me how to define the mathematical model of a voltage source inverter? Where can I find the transfer function for a VSI?
Does this paper provide the type of model you are looking for?
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Growth of vapour bubbles occurs in a superheated liquid during the non equilibrium between vapour and superheated liquid. How to build the mathematical model?
Dr. Salahuddin
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My question is that what are the main steps needed to mathematically model a process e.g (natural process, evolutionary process, physical or chemical,.. and so on) to develop a novel optimization algorithm that is able to tackle real-world problems?
Bahaa El-Din Helmy, the general framework that I have learned and used for modelling is a five step process descripted bellow:
1. Definition of objectives: "Simply" define the focus of the model; what are you planning on having as inputs and outputs? what are the boundaries of the model (what is and is not considered)? etc.
2. Identification and/or development of theoretical/experimental models: When developing a mathematical model, it is necessary to identify what equations you will use to represent your system (natural, chemical, biological processes, etc.). This can be done through the literature and based on fundamental knowledge (e.g. Newton's laws, Maxwell's equations, Bernoulli's equations, etc.). However, in some cases, it is possible that these relationships are not known, or that they are not understood to the extent needed, in which case it can be necessary to develop that knowledge yourself. This can be done either through experimental work or theoretical exploration, though I will not get into the differences between inductive and deductive modelling.
If this isn't fully clear, you can look at this review for an example based on composting modelling (my primary field of knowledge):
As an example, composting relates physical, chemical and biological phenomenon, so each of these have their associated models/equations that come together to form a composting model (e.g. energy and mass balances, biodegradation kinetics, chemical reactions, etc.). Step 2 is the identification of which equations are used for each one of these processes/phenomena/steps. Therefore, to build my composting model, I need to identify what equations I will use for heat balance (e.g. Fourier's law for conduction, Netwon's law for convection), biological kinetics (e.g. first-order equations, Monod degradation model), and so on.
3. Implementation and numerical solution: Knowing what equations your mathematical model is based on, you must now make this function numerically (most likely on a computer). This comes down to determining what software/language you use (Excel, Matlab, Python, C, etc.) and programming your equations into said software/language (parameters, variables, functions, relationships, etc.).
4. Identification and collection of required data: It is necessary to have the data to run your model, especially for parameters. For example, the gravitational constant of Earth or the universal gas constant are well known, but the reproductive rate of a specific species might not be. Note, though, that this might come beforehand. It is possible that you are constrained with what data you can use, in which case you would have to define your objectives (step 1) around this reality.
5. Application, calibration and validation: The final step for model development should be the application of your model. Depending on what you are modelling, it can be very unlikely that your model will be accurate on the first try. In these situations, it is important to focus on trends. Are you seeing a hint of what you would expect? Is the model reacting to certain stimulus? Is it overreacting or underreacting? This is where calibration becomes important; finding the parameters that best allow your model to represent reality and get as close to real data as possible. It is very possible to have a model that should make complete theoretical sense that provides outputs that are completely off, and sometimes this is just due to a parameter having an extra decimal point or being slightly off. Once the model is calibrated, you can then validate it with real case studies, after which you can be confident about how your model works, what it does well, and what are its weaknesses.
NOTE: I have presented this pathway as being rather linear, but model development is always intrinsically iterative. It is normal that, as you grow and gain understanding of what you are modelling, you will redefine your objectives, change your equations, implement the model in a variety of different manners, etc.
I hope this helps!!
Cheers,
Eric
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Residence time distribution for a tubular reactor follows semi empirical model, I want to know how can I use this RTD for predicting conversion of my system using mass balance equation for the tubular reactor( like axial dispersion model which consider reaction happening in the system as well as axial dispersion).
Prajakta Gajbhiye, In my opinion, you cannot "incorperate" E(t) into any mass balance equation. However, you can try to modify the mass balance taking into account, apart from longitudinal dispersion, e.g. radial dispersion. The model can also be extended with the dynamics of the catalyst grain. But that's just a guess.
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I am working on particular research work and there is a need for a mathematical model to be used on Convolutional Neural Network.
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A mathematical model of temperature-dependent sex determination
of crocodile eggs
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Gaze tracking technologies are used in a wide variety of applications. Most gaze tracking systems require a personal calibration process where the user is instructed to gaze at certain points before the system can be used. I focus on the relationship between the eye, camera, and light sources.
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Can a mathematical model be added to a paper on bean genetic and diseases manuscript?
Dear Ahasan Ullah Khan The application of mathematics to biological problems dates back to 1865 when Gregor Mendel deduced inhertance of biological characters mathematically in his pea plants. Nowadays, almost all biological research papers carry statistical analyses in the result's section. Yes, mathematical model can be applied to account for the problems related to bean genetics and disease resistance.
Thanks!
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I read in many articles a statement that best proximity point theory has applications in the field of Economics, game theory, biological science. But I want to see some physical problem that was mathematically modeled and then solved by using best proximity point theory or fixed point theory.
Please se my recent paper, "Approximation of fixed points and best proximity points of relatively nonexpansive mappings".
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I need to have some mathematical models to predict rust creation and its growing rate on different commercial available steels in different atmospheric conditions. I consider temperature, humidity, distance from coast or salinity of air as input of the mathematical model. Other parameters can be considered
Dear Dr. Saverio Debernardis,
I suggest you to have a look at the following paper regarding the corrosion models that become increasingly relevant toward simulations, lifetime predictions, and the optimization of corrosion prevention:
-Atmospheric corrosion modeling
Hans Simillion,Olga Dolgikh,Herman Terryn, Johan Deconinck
CORROSION REVIEWS, 32(3-4) (2014)
Regarding the corrosive aspect, there are some mathematical models that, depending on the different weather parameters, give an indication of the content of particles (aerosols) containing particularly aggressive ions such as Cl- ions (... and we are already entering already in a not simple field) in particular areas but with regard to the degree of damage to a material the variables, besides the environment, are so many that I do not know models validated and used "concretely".
Very often, since structures that have a life of several years are generally considered, the problem is addressed with exposures of different materials, protected or not, in particular marine stations, in conditions carefully monitored according to international regulations, considering exposures that can last even 5 years. If you think you need to know more about this topic, you can find some papers related to the GEMS (Genoa Experimental Marine Station) of the CNR-IAS that are present on my RG page.
I personally work on "Corrosion and Protection of Materials" and therefore I am available for any information and / or clarifications.
Best regards, Pierluigi Traverso
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Dear experts,
Can we do mathematical modeling related to the predictions of our dreams?
If yes, then what will be the significance of such modeling, and if not, then what are the problems in such prediction modeling?
The answer is no. Most of the dreams coming are actually the thoughts we hve in mind after thinking hard on it when we are awake. There are some credible claims of mathematicians whose contributions originated in dreams, example: Descartes and Ramanujan . Considering your question at face value, it would depend on the dream, how deeply the problem has taken root in one’s thoughts, and one’s talent at analysis related to the problem.
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Hi everyone, i am making optimization for energy management system of EV charging station. I established the mathematical model objective function (minimization of electricity cost) and constraints then i made a Python simulation. In the simulation results, i got the charging station load profile (power profile and energy profile) the energy charged in the car is discharged later on in the charging station and i got in the end 0 cars charged. Anyone can help with ideas on how i limit the energy discharged to be equal only to the initial amount of the car and not every EV charged it discharge later. Thank you.
Energy is equal to a half of capacity time square of its voltage
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I need transfer function for the mathematical model of solute and fluid transport in human kidney for the simulation purpose.
Mathematical Modeling of Kidney Transport
By: Anita T. Layton
Modeling transport in the kidney: investigating function and dysfunction
By: Aurélie Edwards
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I need plants with unknown terms in the mathematical model. Systems can be linear or nonlinear.
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My mathematical model is giving results on single variable entry. I have a total of 250 variables and need to evaluate the results from the same model. Instead of putting values one by one, is it possible to import the 250 variables data in bulk and at the end get the separate results through one single model?
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We want to connect different disciplinınary with TIME SCALE,
Which equation, mathematical model or differential equation is interested in electrical car battery ?
I suggest you review the attached papers and conclude some more simulation via MATLAB :
May be sufficient for your starting Thesis.
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I wanna analyze forces between an ExoSuit and a Human for improving its design in terms of efficient actuation and safe interaction with the user. so I should derive a mathematical model. but:
• how I can validate the results?
• I know it is possible to use software like OpenSim, but they have just a human skeleton model and I need to define its coupled model with ExoSuit. can you share a contribution to this kind of problem?
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I would be grateful for suggestions to solve the following problem.
The task is to fit a mechanistically-motivated nonlinear mathematical model (4-6 parameters, depending on version of assumptions used in the model) to a relatively small and noisy data set (35 observations, some likely to be outliers) with a continuous numerical response variable. The model formula contains integrals that cannot be solved analytically, only numerically. My questions are:
1. What optimization algorithms (probably with stochasticity) would be useful in this case to estimate the parameters?
2. Are there reasonable options for the function to be optimized except sum of squared errors?
Dear;
You can solve the integrals manually or by a software.
Regards
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is there any reference or published report can help me to make mathematical model? i do not have any experience in this object..
Dear;
You start with building an intuition of the process as below, and you consider an idealized situation with one organic molecule and another maybe ionized molecule, after you explore how they interact chemically ,electrically and physically.
Regards.
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In 2018,
Which are the latest trends in studies of parameter tuning and control metaheuristics?
- Comparisons,
- Frameworks,
- Mathematical models,
- Demonstrations,
- Tools,
- Etc
Dear;
Title of the article : Autonomous search and tracking of objects using model predictive control of unmanned aerial vehicle and gimbal: Hardware-in-the-loop simulation of payload and avionics.
Regards
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Hello researchers.,
I am trying to find a simple mathematical model for getting the Tumor size variation during chemotherapy treatments. All most all of the models have been trained with the mice models. What are the simple mathematical models available to show the tumor size variation which can be also validated with the real clinical data?
I am afraid that you cannot replace diagnostic imaging with a mathematical model. At least that is the situation in real life patients.
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Since the unfortunate appearance of COVID-19, there has been a massive number of mathematical models based on the SIR or SEIR models. A perusal of these has shown that the models are mainly numerical simulations to predict the course of the outbreak under varying conditions. Would an understanding of the disease dynamics be improved if equilibria or bifurcation analysis was incorporated?
Nice discussion...👍
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we have three vehicles V1, V2, V3
V2, V3 in the same direction, while V3 is coming from the opposite direction
Three given speed s1, s2, s3 respectively . uniform speed.
The distance between V1 and V3 = D is also given.
The meeting point of V1, V3 is given.
d1 is the distance from V1 to the meeting point given.
d2 is the distance from V3 to the meeting point given.
d1+d2=D
The distance between V1 and V2= L1, given.
The parking distance L2 is the distance of V1 from V2 after the overtaking is given to m1+m2+10, m1, m2 are given which are the length of V1,V2.
How to mathematically calculate the safety distance (d) for safety overtaking?