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Questions tagged [mathematical-modeling]

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling.

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How to gain the exact solution of the partial discrete equation :$u(n,m+1)=u(n-1,m)+u(n,m)(u(n+1,m)-u(n-1,m))$

I made a mathematical discrete model of one dimensional flow. Then I achieved this equation: $u(n,m+1)=u(n-1,m)+u(n,m)(u(n+1,m)-u(n-1,m))$ Where n ,m are integer and $0\leq u \leq 1 $ for all n, m. ...
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What should I study in order to understand and develop “deformations”?

What should I study in order to understand and develop "deformations"? In order to describe how e.g. parts may deform? Intuitively deformation is solving DEs on some object meshes. However, I ...
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Biological/chemical modeling - two partners with multiple binding site interactions

I am wondering if there is any reported attempt to model the interaction of two multiple-sites molecules? I know that there is a lot of literature on how to model the binding of single molecules on ...
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1answer
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Proportionality for A-Level Maths

During the decay of a radioactive substance, the rate at which mass is lost is proportional to the mass present at the instant. Use $m$ for the mass of the substance in grams and $t$ for the time in ...
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Heat model of an initial liquid freezing

If i have a region $x>0$ that is initially liquid at constant temp $T_0$ above freezing temp $T_f$ (so $T_0 > T_f$). The surface at $x=0$ stays at $T_1$ below freezing temp (so $T_1<T_f<...
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1answer
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Heat Model Example for liquid and solid change in state

If i have a region $x>0$ that is initially liquid at constant temp $T_0$ above freezing temp $T_f$ (so $T_0 > T_f$). The surface at $x=0$ stays at $T_1$ below freezing temp (so $T_1<T_f<...
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Combustion Theory Book Recommendation

I am conducting research on highly volatile chemicals and have been recommended to read Mathematical Problems from CombustionTheory. I was wondering whether there is another book that could be ...
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48 views

Mathematical modeling of bacteria decay

If our mathematical model for the decay of a bacteria colony is: $100\left (\frac {1} {2} \right) ^ {n-1}$ =Number of Bacteria n is the number of the elapsed hours starting with 100 bacteria in a ...
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1answer
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Evaluate predictions by comparing to actual outcomes - but no categories to use

I have a dataset like so (left column produced by an estimation algorithm, right column being what happened in reality). [EDIT: Please note that every event is distinct (i.e., we are not repeatedly ...
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49 views

What would be a good mathematical model to measure the degree of homogeneity of a mixture?

At my current workplace, we are looking to quantify a batch to say how "similar/dissimilar" the items are. The problem can be stated like so (transformed for public posting): We have parts that can ...
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One opportunity, many stakeholders : which model to distribute one to many based on frequencies

I'm facing a situation where one sales opportunity can be the result of one or many stakeholders involved in its negotiations. I'm trying to model how much of an opportunity as unit/value has to be ...
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Mathematical Biology - Biochemical Reaction [closed]

I have the following system of reactions: \begin{align} M & \xrightarrow{\lambda(M,W)}M+M \\ W & \xrightarrow{\lambda(M,W)}W+W \\ M & \xrightarrow{\mu} \emptyset \\ W & \xrightarrow{\...
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1answer
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Mathematical modelling of elevator optimization problem

I have tried to model the following problem: "An elevator has a vertical acceleration $u(t)$ at time . Passengers would like to move from the ground level at $0$ altitude to the $16th$ floor at ...
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1answer
49 views

How can the shape in this picture be descibed mathematically?

I'm reading an article on Boltzmann that contains the following figure: It is obviously related to harmonic oscillators (since the article says so), but how could I describe this figure ...
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Meaning of these lines in terms of set notation? (with translation for AMPL) [closed]

I would like to know the meaning of these lines that belong to a mathematical model. Equations Where italic theta and epsilon are decision variables, and |I_DL| is the cardinality of a set. Edit: ...
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Mathematical set notation translation to AMPL/MILP code?

I am trying to run a model from an existing paper with the following mathematical model: and the following decision variables: I am unfamiliar with set notation and have tried to understand it, but ...
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1answer
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Οperational Research And linear Programming-The Houses Builder Problem

EXERCISE A builder has purchased $21,000$ square meters of land on which it is planned to build two types of houses, X(detached) and Y(a combination of town-house units), within an overall budget ...
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Bifurcation in a linear system with 2 equations and 1parameter

I have the following system $$\frac{dx}{dt} = ax+y$$ and $$\frac{dy}{dt} = -x+ay$$ By setting the derivative equals to $0$, we get the equilibrium point $(0,0)$. After drawing the phase portrait for ...
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2answers
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Improved model of a fishery: $\dot N=rN(1-\frac{N}{K})-H\frac{N}{A+N}$

Strogatz exercise $3.7.4.a:$ An improved model of a fishery is: $$\dot N=rN\left(1-\frac{N}{K}\right)-H\frac{N}{A+N}.$$ a) Give a biological interpretation of the parameter $A$; what does it ...
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1answer
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Predicting future values or modeling data

Suppose I know that this relationship exists y=(xb-b)+c+d if I had a table of y values for different values of x,b,c and d and I didnt know this relationship how would I go about finding this ...
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Describe QDA statistical model

I am trying to write the statistical model associated to the Quadratic Discriminant analysis framework with two classes. The observations are $(x_i,y_i)_{i = 1 \ldots n}$ where $x_i \in \mathbb{R}^{...
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Employee Scheduling Problem MIP

I am trying to create a mathematical model for employee scheduling. I have already got an idea on how I should model it but I do not know whether it is the best way to do it so. Take for example a ...
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unknown operator in homogenous model of heat application on plate.

I got the following assingment form my employer. Consider the following partial differential equation describing the heating of a two dimensional plate: $\rho(x,y)c(x,y)\frac{\partial T}{\partial t}(...
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1answer
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Expected number of rounds, adding $g$ rounds with probability $r$

This is closely related to the one on the link below, but I cannot really map it to mine... I play a game, with probability $r$ the game adds $g$ more rounds. What is the expected number of rounds ...
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How to model a stochastic process

If we consider a system having multiple functioning states, and the time to shift from the good state to one of the degrading states is a random variable (following a known distribution (not poisson, ...
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1answer
42 views

Solutions to the heat equation with a ring of coolant

I'm interested in solutions to the heat equation for the following problem $ \dfrac{\partial u}{\partial t} = c^2 \nabla^2 u $ on $ \left\{ (x,y) \vert x^2+y^2 \leq R^2 \right\} $ such ...
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Definition of the fitted values of a GLM?

I can't believe that I'm having to ask this, but it appears that neither my lecture notes nor Wikipedia comment on this, and even R's documentation seems unclear. So, plain and simply, what part of a ...
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13 views

Advection and diffusion for 2d sde

When looking at a 2d sde, for processes $Z_t=(X_t,Y_t)^T$. $dZ_t=f(X_t,Y_t)dt+g(X_t,Y_t)dB_t$ My textbook states that the diffusion is found by calculating $D=1/2\cdot g(X_t,Y_t)g(X_t,Y_t)^T$. For ...
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41 views

Including random variables in differential equations

I am having trouble finding information regarding the inclusion of random variables in differential equations. For example I have a simple model describing the growth of some population $X$ over time: ...
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phase portrait of a Lotka-Volterra competitive model with two species in octave

I need to make a phase portrait of a Lotka-Volterra competitive model with two species in GNU octave and I do not know how to do it. I manage to get to made the vector field. But I do not know how ...
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1answer
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Poisson adaptation of IRT model: how to interpret parameters?

for my work I made an assessment in which users have to stack blocks in a certain configuration in as few steps as possible. If the user does this in the minimally required number of steps, they get ...
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What is the way to go from point 1 to 2 while remaining in the region defined by half torus?

Basically this is a trajectory planning problem. As shown in figure below, how can I ensure that in moving from a point (x,y,z) to another point within torus, I don't get out of that torus region? go ...
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Required Practice Problems of Modelling Differential Equations?

Folks, In differential equations there are two things: 1. Modeling (form differential equation based on physical system or real life problem) 2. Solving differential equation Need help for first ...
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Explicit solutions of SDE

I am trying to use random variables to represent variation in population growth models such that growth rates can be represented as random variables themselves. In the simple exponential growth case ...
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How do I use an integer programmed mathematical modelling of TSP (travelling salesman problem)?

Okay, so I just finished my mathematical modelling of TSP using integer programming. Now, how do I use it? Now, I just want to know to use this model to solve a simple 5 vertices large graph. You ...
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1answer
43 views

Is there an accurate view on the distinction between “what mathematics can model” and what it cannot? [closed]

Is there an accurate view on the distinction between "what mathematics can model" and what it cannot? Not just in hard sciences. What about social, political questions? What's the accuracy of ...
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How is the Jacobian matrix computed in finite difference problems?

I have come across many papers which reference the Jacobian when solving certain finite difference inverse problems. And I have seen many articles and textbooks which discuss the mathematical ...
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1answer
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Model formulation: a conclusion about the model before solving it

I have found this simple model in a paper discussing robust optimization [1] $$\max \vec{c}^{T}\vec{x}$$ s.t. $$\sum_j a_{ij}x_j + \sum_j \tilde{a}_{ij}y_j \leq b_i \;\;\;\forall i$$ $$ -y_j \leq ...
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1answer
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Please correct my thinking about Ridge Regression

If ridge regression biases ALL beta coefficients of a regression model towards zero, wouldn't the model massively mispredict the y-variable? I know my logic must be wrong here, but I'd appreciate if ...
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1answer
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Partial Differential Equation Mathematical Modelling

Salutations, I have been trying to approach a modelling case about organism propagation which reproducing with velocity $\alpha$ spreading randomly according these equations: $$\frac{du(x,t)}{dt}=k\...
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Physical interpretation of mean squared divided by variance of a distribution

In chromatography, the signal is shaped like a Gaussian peak, and it is plotted against time vs. instrument's signal. https://en.wikipedia.org/wiki/Chromatography#/media/File:Rt_5_12.png Background: ...
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Given a system of functions, find a system of differential equations which describe that system

Inspired by modelling phenomena in biology, I'm wondering whether there has been mathematical study on the following question: Given some $\mathbf{X}(t) \in \mathbb{R}^n$, find $f = f(X_1, \dots, X_n)...
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Derivation of tau time-stepping in Gillespie algorithm?

I'm trying to find the derivation of tau ($\tau$) in the Gillespie algorithm. All the papers and chapters I've found simply say, without actually showing its derivation: "Tau is given by" $\tau = \...
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How to set up a lake pollution problem that can be modeled by a second order linear equation?

For my differential equations class, my assignment is to create a lake pollution problem that can be solved as both a second order ODE or as a system of first order ODEs. So my question is, how many ...
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Is python suitable for MCM/ICM? (Mathematical Contest In Modeling and Interdisciplinary Contest In Modeling)

I’m preparing for MCM/ICM 2019 and many resources show that Matlab is the best programming language for mathematical modeling competition. But I don’t think I have enough time to learn it from the ...
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Do you think mathematical optimal design has limitations in non-tech applications? What kind?

Do you think mathematical optimal design has limitations in non-tech applications? What kind? I know "mathematical optimization" or "mathematical modeling" is broad, but particularly in the context ...
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31 views

Production time optimization model

I have a problem where I have 2 different types of raw-material. These materials can be processed in two different production-lines which take different amount of time, depending on raw material. ...
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1answer
28 views

How to mathematically describe lag measured from cross correlation

In MATLAB, this is the function used to measure lag using cross-correlation: ...
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Modeling Cellular Motility Using Data

How would I model cellular motility from this format This is what my data looks like. t=48; % total time elapsed in hours C = [89.1 98.6 41.3751 124 54]; % cell density in cells/mm^2 C0= 12 * 10^...
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finding the nullclines of a two connected ODE's

so I've given the following problem: $dn_1/dt=N(t)n_1-n_1$ $dn_2/dt=N(t)n_2-4n_2$ $N(t)=25-6n_1-3n_2$ so I've found the fixed points of the 2 equations and got: [(0,0),(0,7),(4,0)] now I want to ...