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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What is the possible equation for this problem?

I am a programmer, I am in a situation that requires a mathematical equation. I just hope to know the final equation that solves the problem (step by step solution is not necessary). Of course I will ...
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59 views

What am I doing wrong? Deriving

I'm doing the same problem as the one on pg. 5 of this link: http://www.math.lsa.umich.edu/~pwn/01~ch1_solutions.pdf I got the same answer for my equation, although my approach was slightly ...
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86 views

Nondimensionalize an equation with logs

I have an equation with logs in it. Specifically the equation takes the form: $log(Y)=\alpha+\beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3$ Where $X_1$ through $X_3$ are variables. The trouble is that Y ...
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205 views

Mathematical modeling- oil spill?

An oil spill has fouled 200 miles of shoreline. The oil company responsible has been given 14 days to clean up the shoreline, after which a fine of $$10/day$ will be imposed. The local clean up crew ...
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91 views

How to Prove by definition, the given process is a Markov Process?

Define the process Xt by X0 = 1, and for t = 1, 2, . . . Xt = { uXt-1, with probability p, { vXt-1, with probability 1-p where 0 < v < 1 ...
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37 views

Assist me to obtain an equation please?

I have a plot which contain large number of points. I want to find an equation that calculates the percentage of a certain number of these points $(x,y)$, the ones having $x>5$ and $y>80$. In ...
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1answer
4k views

Mathematical model of Quadcopter?

I want to know how to make the mathematical model of Quadcopter? Is there any differential equation for quadcopter? I want to simulate quadcopter as a mathematical model so I want to know how can I ...
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89 views

Can you please help me model this curve?

I have no idea how to model this curve. Can someone please help?
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Question regarding the projective models of the anti-de-Sitter spaces and good online references for learning them from the scratch? (Specifics below)

As my title says above, I am trying to find answers to and also good online reference where I can find complete description of projective models of hyperbolic space, de-Sitter space and anti-de-Sitter ...
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50 views

Estimate parameters in $y=y_{0}(1-\frac{t}{\tau})e^{-\alpha t/\tau}$

Given the function $y(t)$ with two independent parameters $\tau$ and $\alpha$ $$ y=y_{0}\left(1-\frac{t}{\tau}\right)e^{-\alpha t/\tau}, $$ We have two data points (experimental data) $ ...
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274 views

Simple Non-Linear ODE - would like to find solution

In the modeling of the oscillation of a meniscus in a straw, the following non-linear ODE was derived. $$y'' = 1/y - 1$$ $y$ is a dimensionless displacement that is solely a function of time. The ...
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767 views

Intuitive meaning of right and left eigenvector

I am trying to get an intuitive understanding of the meanings of right and left eigenvectors. I guess the best thing you can do is to provide examples of application. (Examples from the field of ...
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196 views

Enlightening Mathematical Models

What is your favourite Mathematical Model? What features make it intuitive or elegant? This question is largely inspired by an example and a desire to find other's like it. Suppose we have two ...
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39 views

What kind of stochastic model shall I build for x(t) if $stdev(dx)$ is linear to $dx$?

I'm building a stochastic model for a process $x(t)$. I notice that daily $dx$ and spot standard deviation of $dx$ seem not related. By spot standard deviation of $dx$ means i take 30 days $dx$ ...
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3answers
73 views

How to model a doubling process with errors

An original document is duplicated. With probability $p_{err}$ a mistake is made in the copy (we will dub the resulting document the "wrong" document.) Both the original and the copy (right, or wrong) ...
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225 views

Finding the jacobian of a differential system with a piecewise function

My system: $$\frac{\mathrm{dx} }{\mathrm{d} t}=-ax^2+y^2-\gamma z$$ $$\frac{\mathrm{dy} }{\mathrm{d} t}=- h(y)-\beta y $$ $$\frac{\mathrm{dz} }{\mathrm{d} t}=x+h(y)-\beta z $$ where $h$ is the ...
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106 views

Differential Equations & Sinusoidal Functions

I am developing a model for sales forecasting, the basic premise of which is that the rate of change of sales is proportional to the number of possible buyers. In developing this model, I came up with ...
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91 views

I'm trying to understand the solution to this simple mathematical modelling question

This is an example from Gary Chartrand's "Introductory Graph Theory" (Page 8, Example 1.5). He provides an answer without actually showing the steps or working, and I am unable to figure it out. The ...
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100 views

Eigenvalue/eigenvector calculation for linearly changed matrices

I'm looking for a way to speed up my computation that involves solving a moderate size generalised eigenvalue problem (matrices 400x400) large number of times depending on the parameter $m$. The ...
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2answers
171 views

Summation notation problem

Any help is greatly appreciated! Outline: Hermione has been thinking about the imminent return of the Dark Lord, so she has been busy packing her bag with all the items required for her survival. ...
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1answer
262 views

Operations research - linear programming help appreciated.

George Weasley, the owner of Weasleys' Wizard Wheezes, recently found that his Skiving Snackboxes have become extremely popular amongst the students at Hogwarts School of Witchcraft and Wizardry, and ...
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14k views

How can I find the time constant of a first order system transfer function?

How can I obtain the time constant of the transfer function of a first order system, such as the example below? $$ \frac{C(s)}{R(s)} = \frac{2}{s + 3}$$ Where $C(s)$ is the output of the system and ...
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281 views

Interpretation of Phase Portrait

I have the following system $x'=f(X)$ of ODES: \begin{align} x_1'=& -4x_1^3(x_2-2)^2 \\ x_2'=& 2x_1^4(2-x_2) \end{align} Solving for equilibria: I got $1$ at $(0, 2)$. I plotted this and I am ...
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166 views

How to define a surface $z = f(x,y)$ with flat region at centre and sigmoidally tapering towards the edges?

How do we define a continuos function $f(x,y)$ within the bounded domain $x \in [a,b]$ and $y \in [c,d]$ so that $z=f(x,y)$ has a flat surface at the centre (flat means $f(x,y)= C$, $C$ being ...
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354 views

Classify the fixed points at the origin

Consider the linear system $$\frac{dx}{dt}= -3x+2y, \frac{dy}{dt}= ax+6y, a \neq -9$$ classify the fixed point at the origin? Is the correct approach to investigate the steady states and how these ...
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1answer
85 views

unit conversion doubt

Im a developer that likes maths, but dont have much experience, I had constructed a graphic that animates a bar that grows on the X axis according to a value. So, I have the values for the x ...
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2answers
197 views

Invert this function $y=(1-x)e^{-x}$

Consider the fucntion $f:\mathcal{R}\rightarrow \mathcal{R}$ given by the rule $ f(x)=(1-x)e^{-x} $ Now I want to invert this function(not just for fun but I have a data that seems to fit this ...
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1answer
167 views

Given average network diameter, how many nodes are three hops away.

The University of Milan found in 2011 that everyone on the Internet was, on average, 4.74 steps away from anyone else.. is that information sufficient to answer this question: What proportion of ...
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85 views

Closed-form solution

I wrote down this equation which is the mathematical model of a system. Is there any way to get $V_c(t)$ in a closed-form expression? $V_c(t+d) = V_s \cdot U\left(V_r ...
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139 views

How to solve the advection equation with spiral motion

The advection equation is : $$\frac{\partial f(x,y,t)}{\partial t} + \nabla_{(x,y)} \cdot (A f)= 0$$ With initial condition $f(x,y,0) = f_0(x,y)$. If the vector $A$ is constant, ie. $A = ...
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260 views

Euler angle in ellipsoid rotation

I am modeling an ellipsoid tumbling in a flow field. I have derived an expression for the Euler angle $\phi(t)$ of the rotation in the $x$-$y$ plane as a function of time, but its range is only $\pi$, ...
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47 views

How to visualize a function to aid in optimization?

I am working on minimization of a function with more than two parameters. I want to see variations, local extremes, saddle points, etc. of this function to get some idea of how is this function in ...
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1answer
38 views

Predicting time t given time t-n

..Hi, Everyone! I'm having a bit of trouble with a statistics/forecasting problem and I could use some help. I have temperature measurements for each hour of each day for the past 10 years. Given the ...
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23 views

simplifying equations from model

I'm using the community land model (CLM) to do some university work and I'm trying to understand some of the equations that go into the model, one example is: $$ ...
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41 views

Linear Fit Issue

Consider a quantity $Q$ that changes as a function of time. The function $Q(t)$ is not explicitly known. We know that $Q(t_{0})=Q_{0}$. Assume for $t-t_{0}\le\epsilon$, we have a method to estimate ...
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1answer
164 views

Statistics on three variables/factors

I have what is probably a simple problem. I'm trying to say something about sells of candy bars. I got data of sells for a population of children. There are three parameters (factors) to this data: ...
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110 views

Math model - constrain GDP given different growth rates of industries

ideas needed to model national GDP given different sector growth rates subject to some contraints Given: GDP equations for $n$ industries depend on growth rates and time i.e. $g(r_1,t), g(r_2, t), ...
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40 views

Regression model for a shearing process

30 Widgets are randomly assigned to a shearing process. There are 3 such processes, each getting 10 widgets. The lengths of each widget are recorded before undergoing the shearing. The amount that ...
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1answer
823 views

Python numerical solution for a nonlinear second order ODE with two boundary conditions

I want to solve numerical the next equation, in Python $$u''(x) = \left( a - \Big(b\big(u(x)^{2}\big)\Big) \right) \big(u'(x)\big)^{3}$$ it is a nonlinear second order $ODE$ with two $B.C$. ...
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58 views

is possible to deduce a formula for vaccination coverage from Whittle threshold theorem?

I am reading the article Application of Whittle’s stochastic threshold theorem to a chickenpox outbreak and I can't understand the meaning of the term "intensity" in the Whittle threshold theorem. In ...
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1answer
2k views

True Velocity and Heading

An airplane flies at $670$ MPH directly northwest. Wind blows at $70$ MPH from the west (i.e the wind is blowing towards the east). Determine the true velocity and heading of the plane. Steps: ...
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278 views

Pursuit curves and arc length question

I am studying pursuit curves where a fast pirate ship which pursues a heavily laden treasure ship which tracks along a straight line. The ratio of the speeds of the ships is r > 1 (which is fixed) and ...
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1answer
70 views

Acceleration of series convergence

everyone! I am currently struggling with following problem: compute the series $$ \sum\limits_{m=1}^{+\infty}\frac{1}{m}\sin(m\alpha)(\cos(m\beta_1) - \cos(m\beta_2)) $$ and $$ ...
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203 views

Sunk cost auction modeling.

Consider the following auction concept. I call it a "SUNK COST AUCTION" Each person bids, but you pay all of the money that you bid for every bid you make. So, if you bid \$1 that \$1 is gone, even if ...
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How to define an objective function that conveys the concept of selecting the best elements in a set

Consider a set of tasks $\mathcal{T} = \{t_1, \ldots, t_I\}$. Consider also a set of workers $\mathcal{W} = \{w^1, \ldots, w^J\}$, where each worker $w^j \in \mathcal{W}$ is associated with a value ...
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235 views

Water Systems: When can I use buckets of water to simulate an ODE.

It is quite common to use physical systems to perform calculations (see here and here). This is for a number of reasons: sometimes the physical system is efficient, sometimes it helps us understand ...
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642 views

Relationship between Turing bifurcation, saddle-node bifurcation, and Hopf bifurcation?

Quoting from http://jxshix.people.wm.edu/2009-harbin-course/mississippi-bifurcation-2.pdf a Turing bifurcation occurs when for an ODE and related PDE $u' = f(u,v), v' = g(u,v)$ $u_t = d_1 \nabla ...
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1answer
87 views

How do you set up a system of ODE's for this problem?

The problem is as follows: Black and White balls are being created inside an arbitrary volume at rates of $Q_{B}$ and $Q_{W}$. They also disappear from the volume at rates $\lambda_{B}$ and ...
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3answers
2k views

Calculating time of flight of object (Mechanics - horizontal elevated launch)

I need help with the following question: A smooth spherical object is projected horizontally from a point of vertical height H = 25.78 metres above horizontal ground with a launch speed of u = ...