Mathematical Modelling

Mathematical Modelling

  • Agnes Schonbrunn added an answer:
    Does anyone have done a Co-IP for galpha protein with a GPCR?

    I cannot detect my galpha protein when I immunoprecipitate it with the receptor.

    Agnes Schonbrunn · University of Texas Medical School

    See lysis buffer and IP conditions in:

    Gu YZ, Schonbrunn A 1997 Coupling specificity between somatostatin receptor sst2A and G proteins: isolation of the receptor-G protein complex with a receptor antibody. Mol Endocrinol 11:527-537

  • Nkuba Nyerere added an answer:
    What is the physical interpretation of local and global stability of a disease free or endemic equilibrium in disease modelling?
    How can you explain the local and global stability of DFE or EE to a non-mathematician?
    Nkuba Nyerere · Sokoine University of Agriculture (SUA)

    Thank you Konstantin K. Avilov 

  • Michael Patriksson added an answer:
    Why the dualization algorithm are not much used in traffic assignment problem with the static demand ?

    I want to know why the direct methods are more qualified than the dual methods for solving the traffic assignment problem with the static demand

    I need advice, what direction I should take in my search?

    Michael Patriksson · Chalmers University of Technology

    Here is the local RG link: 

    https://www.researchgate.net/publication/262008873_Primal_convergence_from_dual_subgradient_methods_for_convex_optimization

  • Bin Jiang added an answer:
    How to check whether a system is Linear or Nonlinear?
    System is a black box.
    Bin Jiang · Högskolan i Gävle

    Very stimulating question!

    I would visualize it in order to see whether it is nonlinear or not, e.g., urban growth and evolution of social media.

    Jiang B. (2015), Head/tail breaks for visualization of city structure and dynamics, Cities, 43, 69-77, Preprint: http://arxiv.org/abs/1501.03046

    Jiang B. and Miao Y. (2014), The evolution of natural cities from the perspective of location-based social media, The Professional Geographer, xx(xx), xx-xx, DOI: 10.1080/00330124.2014.968886,  Preprint: http://arxiv.org/abs/1401.6756

  • Javad Khazaei added an answer:
    Does anyone know a good source on scaling-up models/techniques for chemical pilot plants to industrial scale?
    I am trying build a process model for a bioenergy system. In the literature, there are sufficient lab scale and pilot plant models for this process, but much less industrial (commercial) level data. I am looking for a book or a paper discussing what options we have to mathematically scale up a pilot plant model to industrial level. thanks!
    Javad Khazaei · University of Tehran

    hi there

    you think you could find some details on the book titled "Marco Zlokamik; Scale Up in Chemical Engineering".  more over there is another good as well as more complete on scale up, titled "Applied Dimensional Analysis and Modeling".  best

  • Waldemar W Koczkodaj added an answer:
    Do we need a new definition of fractals for big data? Or must fractals be based on power laws?

    So far definitions of fractals are mainly from mathematical point of view for the purpose of generating fractal sets or patterns, either strictly or statistically; see illustrations below (Figure 1 for strict fractals, while Figure 2 for statistical fractals; Fig. 4 for fractals emerged from big data):

    Big data are likely to show fractal because of the underlying heterogeneity and diversity. I re-defined fractal as a set or pattern in which the scaling pattern of far more small things than large ones recurs multiple times, at least twice with ht-index being 3. I show below how geographic forms or patterns generated from twitter geolocation data bear the same scaling property as the generative fractal snowflake.

    Jiang B. and Yin J. (2014), Ht-index for quantifying the fractal or scaling structure of geographic features, Annals of the Association of American Geographers, 104(3), 530–541, Preprint: http://arxiv.org/ftp/arxiv/papers/1305/1305.0883.pdf
    Jiang B. (2015), Head/tail breaks for visualization of city structure and dynamics, Cities, 43, 69-77, Preprint: http://arxiv.org/ftp/arxiv/papers/1501/1501.03046.pdf

    The new definition of fractals enables us to see the fractals emerged from big data. The answer to the question seems obvious. Yes, we need the new definition. BUT, some of my colleagues argued that the newly defined fractals are not fractal anymore, because they do not follow power laws.

  • Fudong Ge added an answer:
    How do I obtain the duality system of a Caputo fractional-order distributed parameter system?

    For integer-order distributed parameter system, we can get the dual system by utilizing the duality theory. However, for frational order distributed parameter system. the results is few

    Fudong Ge · University of California, Merced

    ok, Thanks very much .  Prof.Grabowski.   I will check them soon----

  • 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?
  • Luca Dimiccoli added an answer:
    Even when using regularization techniques in linear inverse problems is it recommendable to reduce the condition number previously?

    I found empirically that previous reduction of the condition number is useful even when using for instance Tikhonov-Philllips regularization, however I don't have theoretical backup on this. Has anyone a book or paper which can support this? Thank you in advance

    Luca Dimiccoli · Vrije Universiteit Brussel

    Try the other way around. Regularize first and then reduce the condition number. It makes more sense to me.

  • John Jupe 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" http://www.researchgate.net/go.Deref.html?url=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2FVariable_speed_of_light)
    John Jupe · Perceptual Awareness Centre

    Well here is another! I do think that this stuff strikes at the heart of the question.

    Vision-Space: The protagonists

    Working towards a relationship model of the dynamical systems governing human awareness 

    http://youtu.be/516mjrU3aC0

  • Bernd Schmeikal added an answer:
    How can I mathematically model the behaviour of the humans?

    Any suggestion/resources are appreciated.

    Bernd Schmeikal · University of Vienna

    Yes, you mention that. The problem is that in Nibhana noise can be meaningful.

  • Mats Jirstrand added an answer:
    Which is the most efficient algorithm/package to solve delay differential equations?

    I wish to know the methods of solving a system of equations that require, and those which don't require computer algebra. Is there a method, which is both theoretically and computationally efficient?

    Mats Jirstrand · Fraunhofer-Chalmers Centre

    I would suggest taking a look at the dde capabilities of Mathematica:

    http://www.wolfram.com/products/mathematica/newin7/content/DelayDifferentialEquations/
    http://reference.wolfram.com/language/tutorial/NDSolveDelayDifferentialEquations.html
    http://reference.wolfram.com/language/howto/SolveDelayDifferentialEquations.html
    http://www.wolfram.com/mathematica/new-in-10/enhanced-calculus-and-differential-equations/find-symbolic-solutions-for-delay-differential-equ.html

    Best regards,
    Mats

  • Klaus Thoeni added an answer:
    Which quadrature rule can be used in 3D BEM to evaluate hypersingular (1/r^2) Hadamard integrals?

    I am developing a 3D boundary element code for problems of elastostatics. This is not the focus of my research, I just need it as an instrument. I look  for a simple way of numerical evaluation of Hadamard finite part integrals, that occur in 3D fundamental solutions for tractions. These can be either evaluated on a triangular element or boiled down to 1D integrals of a kind: Integral from 0 to 1 f(x) dx / x^2. Papers on the topic that I've found seem to be messy and contradictory, nobody gives Gauss-like quadrature with points and weights. Any help is greatly appreciated. Thanks!  

    Klaus Thoeni · University of Newcastle

    There is no need to evaluate the hypersingular integral in order to get the stresses at the boundary. You can use a technique called "stress recovery". The method uses the nodal displacement tangential derivatives of a boundary element to determine the tangential strains at the point of interest. Then, by using Hooke’s law and the equilibrium condition at the boundary, the local stresses can be recovered which then have to be transformed back to the global coordinate system.

  • Zol Bahri Razali added an answer:
    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

    Zol Bahri Razali · Universiti Malaysia Perlis

    You can get the similar or apropriate answer by searching the keyword in the GOOGLE SCHOLAR page. Usually you will get the first paper similar to your keyword.

    From my experience, this way will help you a lot. If you still have a problem, do not hasitate to let me know.

    Kind regards, Dr ZOL BAHRI - Universiti Malaysia Perlis, MALAYSIA

  • Himanshu Kumar added an answer:
    What are the best ways to do the mathematical modelling of Notch and Wnt pathway?

    Need your opinion related to algorithms like Genetic Algorithm and others......

    Himanshu Kumar · Indian Institute of Information Technology Allahabad

    Thank You so much for informative discussions...

  • Mahtab Zadnoor added an answer:
    Is there any software to determine the number of codewords with fixed GC-content in DNA codes?
    If so where can I find it?
    Mahtab Zadnoor · Isfahan University of Technology

    hi again

    cloud you please help me with writting C-programming in order to compiling number of G and C, as you mentioned to me.

    I myself have problems by C-programming and cannot write a construction algorithm for compute direct content 01.

    best regards

    M.Zadnoor

  • Penny Rowe 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?

    Performance? 

    Portability?

    Scientific evidence?

    Penny Rowe · NorthWest Research Associates

    There is no need to convert old code into Python because you can call fortran code directly from Python using f2py.

  • Hanifa Taher 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.

    Hanifa Taher · United Arab Emirates University

    You can get the fluud propeetues from NIST chemistry webbook.

  • Victor Christianto added an answer:
    Can the ebola virus be considered as an epidemic in a scale-free network?

    Some researchers begin to consider epidemics in scale free network. Does the ebola virus belong to this situation? See Abramson (2001)

    And what are its implicatins for ebola spread prediction and modelling?

    Victor Christianto · University of New Mexico

    @Jimmy: thanks for your answer. Best wishes

  • Gugan Vignesh Selvaraj added an answer:
    What are the best tools for simulation and modelling?

    Hi,

    I wanted to know what are good tools for simulation and modelling and does it really need a tool? Can't we build our own software for out own system?

    I am new to this field only thing I know is there are two parts is such system 1) mathematical modelling 2) Graphical representation ( Its my perception need not be true).

    So can I implement mathematical modelling  using any object oriented language on my own and for graphical part  can use some tool to reduce efforts and time.

    Also suggest me some material that must be required to enter into field of simulation and modelling.

    Thank you.

    Gugan Vignesh Selvaraj · International Institute of Information Technology, Hyderabad

    Hey ! Just get hands on with python scripting : (For Following Reasons)

    - Open source

    - Has loads of freely available packages that does everything to you, just you need them get it installed

    - Easy to learn

    - Platform independent

    - High end scientific computing tool available in the market with fully loaded modern algorithms that can solve any type of problem in any domain

    - Gives awesome representations

    Easy way to get python is just google : anacoda python free download --- > Move on !!! by installing it 

    Some packages i would like you to google : 

    scipy

    numpy

    matplotlib

    sympy

    os

    pylab

    tkinter

    ipython

    All the Best :)

  • Joel Ndam added an answer:
    Why does limit of function not exist when right hand limit and left hand limit are different?

    If right hand limit and left hand limit exist, that means the limit 'exists'.

    But, this is wrong.... Why??

    Even in complex case, lim (z->0), (x^2y)/(x^4+y^2) does not exist... coz depending on the path, the values of limit changes.

    Why does that mean the limit does not exist?

    Joel Ndam · University of Jos

    The limit of a function at any given point is unique, hence it does not exist if left and right hand limits are not the same.

  • Vladimir Kadets added an answer:
    Is an explicit form of maximal ideals/homomorphism known of C-star algebra with almost periodic functions?

    Due to the Gelfand-Neumark Theorem algebra of almost periodic functions in the sense of Bohr is isometrically isomorphic to the algebra of complex continuous functions on the space of maximal ideals of the first algebra. This space is compact and is known as Bohr's compactification of the real line. I cannot find any explicite form of elements of this space; only abstract description, Hewitt, Ross monograph for example.

    Vladimir Kadets · V. N. Karazin Kharkiv National University

    You did not precise if you consider the algebra of CONTINUOUS almost periodic functions, as it is supposed usually. If so, I would suspect that a typical complex homomorphism, that is not an evaluation functional, reflects behavior of elements at infinity. Say, if one takes an arbitrary tending to infinity sequence tn  of reals, and an arbitrary ultrafilter U on N, then the functional F that maps every bounded almost periodic function f to the U-limit of f(tn) is a complex homomorphism. If the algebra that you consider contains also discontinuous functions, there will be also homomorphisms similar to "limit at a point": just take in the previous  example tn tending to some finite point.

  • Sándor F. Tóth 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?

    Sándor F. Tóth · University of Washington Seattle

    @Ed Klotz, good to know CPLEX is doing this on the fly to save us sloppy math programmers...

  • Ridha Djebali added an answer:
    Is it possible to solve a k-e turbulant model in comsol?

    Hi everyone! I need to numerically investigate turbulent regime of natural convection in closed rectangular area. So is it possible to solve k-e turbulence model of natural convection in a closed area in conjugate formulation in comsol? Or should I solve "manually" another turbulent model, which will be easier than k-e?

    Ridha Djebali · University of Jendouba, Tunisia

    Yes of course! but it is sometimes hard to handle it, you should know here that FEM (Comsol...)is designed for solid mechanics, however FVM (Fluent...) is well choice beacuse FVM is conservative for the transfer rates...

  • 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

    Hengky, thank you very much for your help. Very interesting papers, and useful for me.

    I'm developing web-oriented geoinformation system for protection against forest fires. I needed a mathematical model of forest fire dynamic, which I could program and include into my system for visual representation of fire behavior on a map of forestry. I can't use statistical mathematical methods, because I don't have enough data for them.  So, I dwelt on the Rothermel model.

  • Shelly Arora added an answer:
    How can I determine a boundary condition for vorticity at the entrance cavity?

    Hi everyone! I'm trying to solve a problem of force convection in square cavity. I'm using Boussinesq model in variables "stream function - vorticity". I'm having difficulty with the boundary conditions for vorticity at the entrance cavity. For stream function, I specify a gradient (dPsi/dn=1), for vorticity analogously as in Rouch "Computional hydrodynamic". But I get incorrect results. So I was convinced, that I set wrong boundary conditions for vorticity at the entrance cavity. Can someone suggest anything?

    Shelly Arora · Punjabi University, Patiala

    Hi Alexendre

    Sometimes, general finite difference schemes doesn't give good results for stiff problems. Instead of changing the boundary condition, try to change the numerical technique or use Shishkin meshes in your finite difference scheme. You will definitely get correct results.

  • Luis Antonio Aguirre added an answer:
    What do you think of model simplicity?
    People often use mathematical models to address a physical/biological problem. Likewise, they often claim their models are "simple" even when it is non-trivial to many readers. Any views on what you consider key features of a "simple model"? Is a mathematical model considered "simple" as a result of its ease of implementation within a specific program or does its simplicity have something to do with the number of estimable parameters, quantifiable variables, and few variables? I am curious what you think!
    Luis Antonio Aguirre · Federal University of Minas Gerais

    Nice point, Jimmy!

    Perhaps a relative answer to your question is more realistic than an absolute one. In that case we think of two models with comparable performance and then ask which of them is simpler.

    As for the general features, assuming the system being modelled is dynamic, features of DECREASING simplicity would be: static models (linear, then nonlinear), dynamic linear models, nonlinear models that are linear in the parameters, and nonlinear models that are not linear in the parameters. To these classes we might add time-invariant, and time-variant.

    Having established those general features of the model, then the number of parameters and number of inputs, as pointed out by Drs. Derbal and Tattersall, are good criteria. I particularly like the suggestion by Dr. Derbal that analytical approachability is an interesting criterion.

    The practial difficulty with this issue is that: 1) there is no general threshold above which a model is no longer simple, 2) we usually have to trade simplicity with performance. So in the end, it seems that simplicity must be addressed in relative terms... In fact, that is what is behind Ocam's razor principle. 

  • Igor Voloshyn added an answer:
    What conditions are needed in order for oscillatory solution of Volterra linear integral equation of convolution type to occur?

    I'm interested phenomena of appearance of oscillations when kernel and f(t) are non-periodic functions. This phenomena I observed studying behaviour of a solution of difference equations of Volterra type. And I'd like to get a submission of it through some theoretical continuous-time model. 

    Igor Voloshyn · Lviv Banking Institute of University of Banking (Kyiv)

    Dear Tarik,

    Thank you for your advice. I'm going to move this way. 

    Happy New Year!

    Best regards,

    Ihor

  • Farhad Tari added an answer:
    With contained lower-bound constraints of this form: Lj ≤xj, can an algorithm be suggested that could be used to solve efficiently the problem?

    Any suggestion/resources are appreciated.

    Farhad Tari · Sharif University of Technology

    I suggest you to explore the column generation procedure. It might help you to develop an efficient algorithm. Good luck.

  • Olga Zinovieva 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?
    Olga Zinovieva · Tomsk State University

    Thank you for this nice discussion. I've found great guidelines on the topic and would like to share it with you. Hope it will be helpful!

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