All Questions
Tagged with mathematical-modeling applications
52 questions
0
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How to solve an ODE where the rate is directly proportional to two amounts?
Two chemicals in solution react together to form a compound: one unit of compound is formed from $a$ units of chemical $A$ and $b$ units of chemical $B$, with $a + b = 1$. Assume the concentration ...
- 5,245
2
votes
1
answer
98
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What is the probability that a marble from the urn has been picked up by exactly $n$ people?
An urn starts with $m$ marbles and is then approached by $p$ people, each of which picks up $k$ marbles, discarding one and returning the rest to the urn. The urn now has $m - p$ marbles remaining. ...
- 5,245
2
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0
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104
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Does the Buckingham PI theorem require base units?
When implementing the Buckingham PI theorem, it is common to use basis dimensions such as [MASS, LENGTH, TIME], where each is a base SI unit ...
- 25
0
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1
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166
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Does the Buckingham Pi theorem depend on rank, or quantity of units?
Does the Buckingham PI theorem require that k be the rank of the dimensional matrix or is it the quantity of base units; given ...
- 25
1
vote
1
answer
39
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Rate of progress relative to upper bound
Pardon the lack of rigor in my wording. I am looking for a way to quantify the rate of change of a function that compensates for the fact that this rate of change naturally slows down (in my example ...
- 185
3
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0
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65
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What are the applications of dynamical odometers?
Let $\mathbf{s} = (s_0, s_1, s_2, \ldots), s_i > 2$, be a sequence and let $\Delta_{\mathbf{s}}$ be the set of all sequences of nonnegative integers $\mathbf{a} = (a_0, a_1, a_2, \ldots)$ such that ...
- 494
3
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2
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326
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Can we clarify this "accumulated money flow" application of integration?
I read about this model/application in Calculus with Applications, 11th Edition by Lial, Greenwell, and Ritchey (example), where if you have a function $f(t)$ that models some revenue stream, the rate ...
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313
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Mathematical expression for physical forces in pendulum ODE
A 16 lb weight is suspended from a spring having a spring constant of 5 lb/ft. Assume that an external force given by
24 sin (10t) and a damping force with damping constant 4, are acting on the spring....
- 612
0
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1
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94
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How to read the surface plots?
I was reading this paper and I could not understand this figure. How do you read these kind of graphs? How to interpret the twists and folds; it's not like heat maps that are intuitive. Any help ...
- 39
4
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125
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Do repeated roots (and Real Jordan form) for ODE's come up in real world applications of ODE's
An equation like $y^{\prime \prime} + 2 y^{\prime} + y = 0$ has repeated roots: The characteristic polynomial is $r^2 + 2r + 1$ which has repeated roots $(-1,-1)$. Two basic solutions of the ODE are ...
- 727
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46
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Conceptual complex dynamics - Is it reasonable to perform bifurcation diagrams on PDE's?
I am working on a PDE model, the subject has been modeled with ODE's before. The articles usually have a bifurcation diagram, and to be able to validate my model, I want to compare my work with the ...
- 53
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115
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Which mathematics areas are important to be strong in for research in mathematical modelling of neuroscience/human psychology?
I’m guessing ODEs/PDEs would play a big role - I wonder exactly what methods from ODE/PDEs are used in this kind of research? I also wonder whether stochastic processes and stochastic differential ...
- 749
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48
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Find a function
It's a cuttout from Rempe article "A mathematical model of the sleep/wake cycle" about a function which I don't understand how to describe: $h(t)$ decays exponentially while the system is asleep
and ...
- 480
1
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1
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156
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Basic ODE story - tank with pumps
Full tank has $500$ liter of water containing $0.2\%$ of salt. One pipe pumps clear water in ($100$ liters per minute) and the other gets the mixture from the tank ($100$ liters per minute too). ...
- 2,200
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1
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48
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Epidemics and Mathematics, Literature Suggestions.
I am someone who has never studied Epidemics (or much applied mathematics), my background is probability theory, specifically McKean-Vlasov SDE. I was wondering if anyone in the area could suggest me ...
- 2,372
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47
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Could you please explain me the first term of second equation and third equation in the following model?
I have attached the image of the model. Could you please explain me the first term of second equation and third equation in the following model. (I didn't get the meaning of terms in bracket.)
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35
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Notation for a function/process that generates a set with unknown members?
Aside from some basic training in middle and high school many years ago, I'm new to sets (coming from the world of programming) and I'm trying to model a debugging process. I'm specifically trying to ...
- 11
-1
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1
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64
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Why do I keep seeing this equation in different fields?
I am a student studying mathematics at university. I have come across the expression $$1-\dfrac{1}{x}$$ in several different classes and I'm wondering about its significance.
The first place that I ...
- 3
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1
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1k
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Modeling Real World Situations / Trigonometric Functions
I got this question and it seemed to be tricky!
You are standing at a base of a Ferris Wheel which is 4 m above ground while your friend is riding. The Ferris Wheel is 8m in diameter. Describe how ...
1
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2
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383
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Simple Traffic Flow Problem - Interaction Probability (Heavy/Light Vehicle)
Suppose you have a section of road with two-way traffic, and some basic information about traffic volumes, for example:
Let $l_a$ be the number of light vehicles per hour that travel across this road ...
- 197
1
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22
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Dispersion of mid-air particles: scaling laws and similarity solutions of a function
I'm currently looking at some old questions from my undergraduate studies which I may not have fully understood but would like to understand now.
The initial stage of a dispersal process is very ...
- 6,433
2
votes
2
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255
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Probability density for velocity in mechanical energy
To be sure my basic physics isn't rusty...
Consider a 2-D bowled shaped classical potential well within which a classical particle of mass m is rolling.
In this system the conservation of energy ...
- 6,433
7
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996
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The Mathematics of Skateboarding Tricks.
This question is just for fun and I apologise if it's too broad or off topic.
The Details:
As anyone who has played the Tony Hawk games can tell you, skateboarding - at least in part - can be scored ...
- 47.2k
2
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81
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Question on modeling turbulence with Markov process vs high dimensional chaos
I basically asked this question over on Physics Stack Exchange, but that went nowhere and I've tried to refine my question to bring it here.
When numerically modeling a natural system with ...
- 143
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0
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133
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What are some good books of math applied to the military, warfare and combat.
Recently I've been interested in the math behind missiles, collisions, artilley, etc. I know topics like the parabolic course of a missile are in physics books, but I would like one that shows a ...
- 1,195
2
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1
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306
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Mathematical Problems of Climate Science?
Are there any interesting research-level mathematics problems that have come out of climate science specifically or that are abstractions of some of the issues and models pertaining to climate science?...
- 1,620
1
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1
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91
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Can evolutionary biology processes be mathematically described? [closed]
Action movies are full of violent combat, pursuiting and dangerous Scenarios. I think that the Evolution of mankind lead to such a behavior. It may be that selection processes have lead to the fact ...
- 2,920
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0
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1k
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Single Population Model with Harvesting: Mathematical Modelling
I'm hoping someone can just check if my solution is correct and if I understand the problem that is being asked. If any part of it is wrong or you don't understand me let me know. Thanks very much for ...
- 507
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1
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69
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Differences between models and theories [closed]
I'm trying to write about the differences between models and theories for academic writing (with no greek letters). I wonder if you agree with my text.
The differences between theories and models ...
- 2,275
2
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1
answer
91
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Heat Loss from a 1/2 Triaxial Ellipsoid (Tortoise)
BACKGROUND (TL;DR = How long does it take to chill a tortoise?)
I'm working on a simple(?) problem in reptile thermoregulation.
Tortoises (family Testudinidae) are common components of terrestrial ...
- 23
0
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1
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690
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How to perform non dimensionalization on a population model with predation?
So this problem is from my homework and I've been having some trouble with it. We have the following model of population growth where a and b are positive constants and r is a positive growth rate:
$...
- 21
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0
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97
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Does the "truncation function" $\langle a,b\rangle : \mathbb{R} \rightarrow \mathbb{R}$ have an accepted name or notation? [duplicate]
Given real numbers $a$ and $b$ satisfying $a \leq b$, define:
$$\langle a,b\rangle (x) = \mathrm{min}(b,\mathrm{max}(a,x)) = \mathrm{max}(a,\mathrm{min}(b,x))$$
(These numbers are equal because $a \...
- 68.7k
1
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1
answer
96
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Calculating remaining balance [Monthly compounding question with rate= 0.01]
Suzanne opens a line of credit at a local bank, and immediately borrows 1870 dollars. 6 months later, she repays 1060 dollars. 5 months after the repayment, she borrows 570 more dollars. 6 months ...
- 1,127
0
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2
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140
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Can car traffic be managed by mathematical formula? [closed]
How car traffic is managed? Is it managed by mathematical algorithm? Or by human(operator)? If it's by operator, can it be managed mathematically? Or is it by physics? By what theories/formula?
...
- 119
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1
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80
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Equilibrium and Stability of Nonlinear Interactions
Examine the nonlinear model:
$$\triangle x_t = rx_t(1-\frac{x_t}{K})-sx_ty_t$$
$$\triangle y_t = -dy_t+\epsilon x_ty_t$$
Find the equilibrium and their stability. Here all the parameters are ...
- 594
2
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0
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108
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Learning to Apply Mathematical Concepts ( i.e. function modelling, etc.)
Firsty, I want to state my situation clearly. I am one of those students who are incredibly good at absorbing mathematical concepts but without knowing how to apply them. I get A's but it is growing ...
- 321
1
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0
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97
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Is Principal Component Analysis applicable to this type of situation?
I'm trying to model the response of ant populations to pheromones in this way:
The ants are simulated as Self Propelled Particles with internal energy. They undergo acceleration due to their internal ...
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0
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1
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33
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A prove for information restoration with 2 schedules that delete information
What kind of mathematics or technique do I need to use the following?
Just pointing me in the right direction is also helpful as I love mathematics but I am not so good at it.
It's a problem I have ...
- 101
1
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0
answers
92
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Classifying growth as percent increase.
So I have been thinking about resource consumption a lot after watching the most important video you will ever see. It is pretty long so I will summarize it as follows, the professor makes a strong ...
1
vote
1
answer
263
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Including non-markovian processes in a birth-death process
Current model
I want to model a stochastic system with a birth-death (Markovian) model. I therefore have this kind of $n$ times $n$ (where $n$ is the number of possible states) transition matrix:
$$\...
- 1,625
1
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0
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65
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Math Algorithm Needed with Aggregated Percentages (Business Scenario)
I'm trying to figure out a math algorithm, but I'm having a hard time wrapping my head around the best way. Instead of defining a complex industry-specific process, I'll construct a simplified ...
- 111
1
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0
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147
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PDE modeling (heat conduction and flow)
The heat conduction is expressed by a classic heat equation like
$p(x) u_t + div (A(x) u) = f(x,t) $.
If I look at a porous medium like this (solid+gas) the heat equation should apply too (in a ...
- 31
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1
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364
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Bessell function of the first kind $J_v$ of the Bessel equation $x^2y''+xy'+(\lambda^2 x^2-v^2)y=0$
If we have an equation
$x^2y''+xy'+(x^2-v^2)y=0$
then the solution of the first kind $J_v(x)=x^v\sum_{m=0}^{\infty}\frac{(-1)^mx^{2m}}{2^{2m+v}m!(m+v)!}$.
Then how would you find the solution of ...
- 921
1
vote
1
answer
229
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Analyzing the stability of equilibria
There's a model with a condition $r>\mu$:
$$\begin{align}
S'&=r(S+I)-\beta SI-\mu S \\
I'&=\beta SI-(\mu +\alpha)I
\end{align}$$
I can easily see that the equilibria of the second ...
- 973
1
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1
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363
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Finding the basic reproduction number of a particular model
I have been reading a paper about a host-parasites models and for the model:
$$\begin{array}{rll}
\displaystyle{\frac{dx}{dt}}&=\lambda -dx -\beta v x & \text{Susceptible host} \\
\...
- 1,793
8
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2
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2k
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Differential vs difference equations in mathematical modeling
I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
- 1,793
2
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1
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348
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Relationship between Reproductive Ratio and Jacobian in Population Model
In class we defined the Reproductive Ratio, $R_0$ of a population modelled by SIR, SEIR,... as the average number of secondary infections caused by an average infected individual in an average ...
- 35.7k
1
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1
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369
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Real life scenario, probability model required for accidental vs supernatural causation.
A = HUMAN 1
B = HUMAN 2
A is related to B, specifically A is the father of B
A goes on holiday 5 years ago, staying in a hotel in popular tourist spot near Scotland (long way from home)
During ...
- 113
2
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2
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1k
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A model for the spruce budworm population
A model for the spruce budworm population $u(t)$ is governed by
$$\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\frac{u^2}{1+u^2}$$
where $r,q$ are positive dimensionless parameters. The nonzero stedy ...
- 1,793
4
votes
2
answers
2k
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Biology: Wright-Fisher model of genetic drift
In evolutionary biology (in population genetics to be more accurate) exists the concept of genetic drift. It describes how an allele (gene variant) (that has no advantage or disadvantage in terms of ...
- 1,625