Mathematical Modelling

Mathematical Modelling

  • Ioannis Georgakakis added an answer:
    What are the limits of measurement in science?
    When I was in high school Bohr's atom of shells, s and p orbitals was introduced in chemistry. Realization was automatic that the world was explained according to theory that was verified by experiment. Through college and graduate school, looking for more complete explanation, theory is challanged but it is not brought to question "what is an electron or proton, if they have mass but are visible only in the sense that they emit light energy as photons that also have mass, "spots of light in orbit around nuclei?, the atom a solar system in minature"? Physicists will say this is not the picture they have evolved, but all that remains is the image of equations on a chalkboard, at best 'the image of things of a particle nature in alteration with things of a light nature'. Can a pieced-together stepwise reality of this nature be accepted? In the Feyman quote below pieces are added that can break any of the established laws "they are not directly observeable" or affect "causality". In this same meaning though neither electrons, protons, photons or atoms are observable and their causal effects are but a matter of humanly constructed theory and similarly based experimental apparatus. The possibility exists that theory and theory based apparatus entail one another and all that might be gotten is that the real universe is identical in this respect...i.e. existence entails the experienced universe and visa-verse.
    "You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c." These virtual photons, however, do not violate causality or special relativity, as they are not directly observable and information cannot be transmitted causally in the theory." (from "Varying c in quantum theory"
    Ioannis Georgakakis · Athens School of Fine Arts

    Please follow the results of our research. "ATMITO" is an answer we have for your question.

  • Aldo Dall'Osso added an answer:
    Why are physicists stuck with Fortran and not willing to move to Python with NumPy and Scipy?

    Nowadays all of the major Fortran related numerical calculus have exactly mapped equivalent libraries in more modern language framework like Numerical Python (NumPy) and Scientific Python (SciPy). 

    What keeps physicists stuck with Fortran?



    Scientific evidence?

    Aldo Dall'Osso · AREVA

    The purpose of Python and Fortran is not the same. Fortran is practical for programming mathematical and physical functions, whereas Python is practical for the definition of algorithms that use the above cited functions. For example, the french CEA is developing version 3 of the APOLLO code for neutronic analysis. The physical/mathematical functions are written in Fortran or C++. The calculation schemes that call these functions in order to perform design calculations are written in Python. In this way the time consuming functions take advantage of the high performance of Fortran, whereas the definition of the calculation schemes take advantage of the flexibility of the Python language. A description of this approach can be found in the following paper:
    H. Golfier et al, "APOLLO3: a common project of CEA, AREVA and EDF for the development of a new deterministic multi-purpose code for core physics analysis", M&C 2009, Saratoga Springs, New York, May 3-7, 2009.

  • Max Stanley Chartrand added an answer:
    Is the recombination rate for Helicobacter Pylori either constant and independent of the host or dependent on the environment?

    In my mathematical modeling of Helicobacter Pylori phenotype evolution there exist three constants that should be estimated- one of them is recombination rate- I need to know the exact value of the recombination rate for H. Pylori and also its unit.

    I have some experimental data as well, does fitting suit to find this constant?


    Max Stanley Chartrand · Northcentral University

    Ahmad, I can attest from a clinical viewpoint that Helicobacter Pylori is highly dependent upon its environment to exist and flourish. For we find clinically that such bacteria in the stomach when not treated by antibiotics virtually disappear in a matter of days when the acid barrier of the stomach is restored. I am attaching one of my short monographs on this topic here in case it can help spur a discussion on your excellent question.

  • Samir Kumbhar asked a question:
    Which is the best model to analyse the dynamic behavior of Magnetorhological Elastomer?

    I am in need of Mathematical model of MRE to study its dynamic behavior under varying magnetic field to design MRE based Dynamic vibration absorber

  • Yousef Hedayati added an answer:
    If we take the autocorrelation of a non-stationary signal, would the result be meaningful or misleading?
    Does it make sense to take the autocorrelation of a nonstationary signal or sequence? Or does it not matter in which case the interpretation will be affected (if at all)? Do we need to do some pre-processing before taking the autocorrelation of such a signal, or are the results as such valid?
    Yousef Hedayati · Iran University of Science and Technology

    Dear Laya Das,

    In some applications computing autocorrelation of a nonstationary signal iteratively(autocorrelation of the autocorrelation and so on) turns out to be more meaningful. This is called Recursive Autocorrelation. Check out this link:

    It might look irrelevant but it is worth considering since the idea is so attractive.

  • Efren Sandoval Mora added an answer:
    How to model mathematically plate and shell structural damage subject to blast and explosion loading?

    I find some paper for this topic in low-velocity dynamic loading on stiffened plate(like as grounding of ship bottom hull),but can not find in high-velocity range like explosion(internal or external). all of this re souls are in experimental or numerical method. How to model mathematically plate and shell structural damage subject to blast and explosion loading?

  • Robert Vichnevetsky added an answer:
    Can we calculate the direct wave element and reflect wave element at the same time use Parabolic Equation?

    I am now working about Parabolic equation to calculate the radio wave propagation over the sea surface. In the 2-D PE, the direct wave element and the reflect wave element by the sea surface are calculated at the same time, can we calculate the direct element and reflect element separately? I set the reflect coefficient of the surface to zero and obtained the direct element, but how could I get the reflect element? One way is to subtract the direct element from the total element, but I think it's not convenient. I wonder can we calculate the direct element and reflect element at the same time?

    Robert Vichnevetsky · Rutgers, The State University of New Jersey

    waves and parabolic equations have nothing in common

  • Marina Zharikova added an answer:
    What fire dynamic model is the most convenient for programming?

    Let me describe my task in short.

    I've created the electronic map of forestry, which includes a set of objects (polygons) of different nature, such as forest plants, roads, lakes etc. Each object is homogeneous. I have to write a program for mapping the dynamic of fire contour on the map. I’m going to use Rothermel’s model, because I have all input data for this model. But this model is good for homogeneous terrain, but my terrain is heterogeneous. I’m looking for the information, how Rothermel’s model can be adjusted to solve my task. Can anyone help me with the information on this question? Maybe there are other models, appropriate for programming... I would be grateful for any help.

    Marina Zharikova · Kherson National Technical University, Kherson, the Ukraine

    Alianna, I appreciate your kind help, thank you very much.

    I didn't manage to find Dr. Adler via ResearchGate and wrote him directly on his e-mail.

    Kindest regards,


  • Paul, D. added an answer:
    Does anyone have REFPROP FORTRAN source code for calculating the properties of Carbon dioxide?

    For the stability analysis of supercritical natural circulation loop i require the REFPROP FORTRAN source code for getting the properties of carbon dioxide. If anyone is having the code pl share it.

  • Behnam Farid added an answer:
    How can I get the mathematica package in this book?

    I read this book (Applied Laplace Transforms and z-Transforms for Scientists and Engineers(2004)).
    It is very good.
    Please ,can you help me, I need this mathematica package in your book to solve some problem in my work.

    With best regards

    You are welcome Ahmed.

  • Nour El Houda Tellache added an answer:
    How can we model disjoint constraints in linear programming?

    We have two constraints: xij- zuv >=0 , zij - xuv >=0  where xij , zuv, zij and  xuv are continuous variables. We would like that one of the two constraints will be satisfied, so how to model this disjoint constraints?

    Nour El Houda Tellache · University of Science and Technology Houari Boumediene

    Yes exactely,  I am using Cplex solver and I am traying also to use indecators. I got some results using M as small as possible,  so it is possible to compare now the two techniques in terme of execution time.

    Thank you a lot Sir Shahin Gelareh and José Barahona da Fonseca for your answers.

    Best regards,

  • Leonard Goeirmanto added an answer:
    Which open source software could be recommended for mathematical modelling of electronic systems ?
    Trying to develop a model for all to use, thus open source software.
    Leonard Goeirmanto · Universitas Mercu Buana

    open source software for mathematic: Octave, it is like Matlab

  • Dudley J Benton added an answer:
    How can I mathematically model the behaviour of the humans?

    Any suggestion/resources are appreciated.

    Dudley J Benton · McHale Performance

    On a more serious note, I have worked with some human data, and have been exposed to a lot of medical data. (Many of my father's medical publications are available on RG.) One thing I have noticed is that human-related data seems to be much more clumpy than the instrument readings (power plant data) that I work with on a daily basis, which is often normally distributed, with some skewing and perhaps dual peaks occasionally. Fitting a normal distribution to clumpy data is more difficult. We expect to be able to characterize data by averages and standard deviations, but maybe we shouldn't expect this for some types of data, and human-related data in particular. I've done a good bit of Monte Carlo simulations of various non-human systems, using distributed variables. Maybe we should consider models with variables that are not distributed, but rather clumpy. There are so many aspects of human behavior that can be divided into 2, 4, or 8 categories, which is why there are endless books and seminars based on this approach. There are always outliers in behavior, but more often than not, people follow a limited number of patterns. For instance our family likes to joke about people behaving like one of: lion, beaver, otter, or golden retriever (the 4 Myers-Briggs categories in familiar vernaculars). I add skunk, weasel, sloth, and border collie, as everyone knows at least one of them. Why not use integers for some variables and real numbers for others in a Monte Carlo simulation and keep track of the two separately?

  • Matthias Halisch added an answer:
    Any suggestions / hints for papers concerning (Euler) connectivity with application to Digital Rock Physics (DRP)?

    I am currently looking for some papers concerning Euler connectivity with specific application to Digital Rock Physics. (I am not looking for papers explaining the basics of this topic, but specifically for applications of this!)

    Does anyone have some good suggestions? Especially looking for sandstone related topics. Thanks in advance!

    Matthias Halisch · Leibniz-Institut für Angewandte Geophysik

    Well, the question was about Euler Conenctivity, not Hamiltonian Graph or Euler Graph Theory, sorry. :-/

    But maybe you can specify, what you exactely suggested?

  • J. Bocko added an answer:
    Related to Tensor double dot product: What is the double dot (A:B) product between tensors A(ij) and B(lm)?
    Referring to books on continuum mechanics, I see that the standards followed by text are very different. For example, author JN Reddy addresses A:B as A(ij)B(ji); while Holzapfel addresses A:B as A(ij)B(ij). Why are there such huge differences and which represents the actual scenario?
    J. Bocko · Technical University of Kosice - Technicka univerzita v Kosiciach

    Dear Govinda,

    there are two kinds of double dot scalar products:

    A..B :=  A(ij)B(ji)


    A:B :=  A(ij)B(ij)

    Problem is that in some old books (to have life more interesting and complicated :) ) you can find reverse definitions

    A:B := A(ij)B(ji)


    A..B := A(ij)B(ij)

    In case one of those tensors is symmetric the results is the same for both definitions.

  • Héctor Tuy added an answer:
    Can anyone suggest software to build causal loop diagrams for system analysis?
    I do a lot of modelling and system analysis. The best mean for that is paper, however, it would be handy to have a piece of software to build these diagrams on a computer for publication, presentations, or for teaching. Up until now I have used vector image software such as Inkscape or Adobe Illustrator.
    Héctor Tuy · Universidad Rafael Landívar

    Although not as powerful as STELLA, iThink, PowerSim or Vensim, you may also want to check SistemiTool:

  • Viktor Szabo added an answer:
    What boundary conditions should we use when modeling blood flow in coronary arteries?

    We are doing a one-dimensional modelling of coronary blood flow. Is there any publication referring to the boundary conditions we should use both on the inlet and on the outlet? Thank you very much for your help.

    Viktor Szabo · Budapest University of Technology and Economics

    Thank you very much, Alin for this useful material!

  • Joao A. N. Filipe added an answer:
    Does any have experience in modeling strategy of relaxation?

    Given a PDE model with some constraints restricting the range of values of model quantities, how does one apply the idea of relaxation to such a model? Any idea or references on relaxation idea of modelling, will be appreciated.

    Joao A. N. Filipe · University of Cambridge

    Following on your reply re ODEs of 19 days ago. I focus on a very simple form of relaxation by assuming that the logistic equation, du/dt = a*u*(k-u), is related to your problem because its solutions do not exceed k if it is initially below k. Here, a, k > 0 are parameters, k is often known as ‘carrying capacity’. If we add an extra term with time-varying per capita rate v(t), we can be recast the equation as a logistic model with time-varying carrying and a thus new long-term bound on u. Specifically: du/dt = a*u*(k-u)+v(t)*u, with v(t)>0. This can be rewritten as: du/dt = a*u*((k+v(t)/a)-u) = a*u(q(t)-u), where q(t)=k+v(t)/a is a time varying carrying capacity. Unlike the basic logistic, this ODE is not likely to have an exact solution (unless v(t) is special, such as a constant), but numerical solution should be straightforward. There are many options for the function v(t), depending on the specific application. Here is an article exploring the case where q(t) also obeys a logistic equation; in this case, there is a form of relaxation if q increases with time.

    P.S Meyer and JH Ausubel, Carrying Capacity: A Model with Logistically Varying Limits, Technological Forecasting and Social Change 61(3):209-214, 1999.

    This specific choice of v(t) incorporates a time scale parameter characterising the pace of the relaxation, which may be relevant. This is just a concrete example to illustrate a way of thinking about modelling relaxation; many other basic models and modifications thereof to incorporate relaxation would be possible.

  • Antonio Luiz Pacifico added an answer:
    What is the procedure of a distorted model in Buckingham pi theorem?

    I have a distorted model to a prototype. 

    Dimensional scale for thickness is not same as other geometrical dimensions. 

    I found that there is procedure to use distorted model to predict the prototype. 

    I searched in many papers and books about this issue but I did not find clear general procedure for this case. 

    Thanks in advance.

    Antonio Luiz Pacifico · University of São Paulo

    In these cases you have to know, previously, the phenomena you are studying/testing. This is necessary because in distorted models you will have to assume hypothesis that will take you to disregard some dimensionless groups. For example, in wind tunnel tests it is well known the hypothesis that in "in the absence of thermal and Coriolis effects and for a specified flow system, whose boundary conditions are expressed non dimensionally in terms of a characteristic length L and velocity U, the turbulent flow structure is similar at all sufficiently high Reynolds numbers" (Townsend, 1956, apud Snyder, W. H., Guideline for fluid modeling of atmospheric diffusion, EPA Report 600/8-81-009, April 1981). Thus under these conditions you can work with models doing analogy with others dimensionless groups but not Reynolds number. To do so, it is crucial to write all differential equations that govern your phenomena, normalize them and try to find the nondimensional groups involved. Then make a sensitivity test on these equations in order to find what could you disregard. It is not a easy task, it demands knowledge of the phenoma and, probably, several hypothesis testes.

  • Fateme Seihani Parashkouh added an answer:
    How can data envelopment analysis (DEA) theory be modeled in nonlinear instead of linear one?
    Is it possible to develop a model of DEA in nonlinear functions instead of linear?
    Fateme Seihani Parashkouh · Islamic Azad University

    I think you can use Charnes and Cooper  transformation (Tone 2001) in a reverse direction.

  • Joao A. N. Filipe added an answer:
    Does anyone know of any mathematical models for chickenpox with vaccination?
    A mathematical model for vaccination of chickenpox.
    Joao A. N. Filipe · University of Cambridge

    A text book explaining modelling approaches and with additional references: Keeling and Rohani, Modelling Infectious Diseases in humans and animals, Princeton Univ Press, Chapter 8.

  • Stefan Gross added an answer:
    How can I properly calculate Akaike information criterion for data with unclear sample size?

    The situation is as follows:

    An experiment measured the concentration of a certain chemical in cells at various times after exposure. The results were normalized by the concentration at time zero, so they are fractions. Millions of cells were combined together for the assay. The data points are means and SEMs based on several repeat experiments. I am interested to fit some models to these data and compare them by AIC, but am not sure how to calculate AIC properly because the sample size is unclear. I would appreciate suggestions from anyone interested!

    Stefan Gross · University of Greifswald

    see, bullet point 3) for the formula of AICc.

  • Mohammed Lamine Moussaoui added an answer:
    Any ideas about the stability of two solutions in a nonlinear system?
    Suppose a non linear system has at least 2 positive periodic solutions in a bounded domain. If one can show that the system is globally asymptotically stable, then is it a contradiction to the previous statement? If not, what can one say about the other solution? Can anybody suggest me any relevant references?
    Mohammed Lamine Moussaoui · University of Science and Technology Houari Boumediene

    Dear Santanu Biswas, 

    To be Convergent the Solution has to be Stable and Consistent (see lax theorem). The choice of the Discretization Step(s) defines a Domain of Stability this gives you several solutions for each choice. But the solution must be unique as it is stated by Fletcher in his book.

  • Samuel Alizon added an answer:
    Can someone assist me with some notes on modelling hiv vertical transmission?
    I am an MPhil student. I need material to understand the concepts better for my research. Papers and notes are welcome
  • Bilombo Raoul added an answer:
    What are the real world applications of Nondeterministic Finite Automata (NFA)?

    Can any one help me by giving some real life examples (Other than compiler design) where the idea of NFA can be implemented? If I can find the shortest string accepted by any NFA .. what kind of real life problems I can solve with it? 

    In the automated management, the research of the strategies to optimize the time
    or to optimize the energy is a fundamental question.
    It is about determining an optimal order corresponding to an optimal trajectory
    or to an optimal energy or at one optimal time.
    A simple example in the industry is the management of the train.
    One can determine the strategies to minimize the energy spent by the train in a journey.
    One can also minimize the length of a journey.
    Optimization of a system (train) in movement.
    Several examples can be observed in the industry.

  • Muthu Ramesh Babu added an answer:
    What is the difference between convex and non-convex optimization problems?
    How do we know whether a function is convex or not?
    What are the different commands used in matlab to solve these types of problems?
    Muthu Ramesh Babu · St. Joseph's College of Engineering, Chennai

    Convex problems have only one local optimum point, which is also the global optimum point. The point is maximum or minimum based on the second order derivative of that function. On the other hand, non convex problems have multiple optimum points.    

  • Jose A. Ramos added an answer:
    Mathematical model for identifying systems. What are the best indices of error behavior to validate the model by comparing data.
    For example Fit, VAF, MSE, RMSE: what is the best?
    Jose A. Ramos · Nova Southeastern University


    In my experience, FIT, VAF, RMSE/MSE in that order. MSE is problematic in the sense that two models with very different performance can give equal MSE.

  • Lawrence Margulies added an answer:
    Has anyone already applied a physiologically based pharmacokinetic two-compartment model for a single oral dose or i.p. injection of pristine SWCNT?
    I successfully implemented a two-compartment (gut-blood) mathematical model for a single oral dose (20 mg/kg) to simulate the SWCNT distribution in the blood using intestinal absorption constant (Ka = 0.033 min^-1/1.98 hrs^-1), volume of distribution ((Vd = D/C0), experimentally determined), and volume of the gut compartment (V1 = 82.5 ml/kg). The methodology might be further applied to build the two-compartment (peritoneum-blood) PBPK model for a single i.p. drug injection if the peritoneum-blood permeation constant is established.
    Lawrence Margulies · University of Guelph

    I haven't.

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