2.12 Thursday, September 24, 2020

2.12.1 Top new questions this week
2.12.2 Greatest hits from previous weeks
2.12.3 Can you answer these questions?

2.12.1 Top new questions this week

Solving the Lotka-McKendrick model with NDSolve
Nonlinear dispersal equation modeling insect aggregation
Making a faster alternative for PatternSequence
How can I get material property data past what’s provided via ElementData?
DSolve does not return solution to simple system of second order PDEs
Build the following symmetric array
Evaluate section by button click

Solving the Lotka-McKendrick model with NDSolve

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230366

The Lotka-McKendrick model is a demographic model that represents the way a population changes over time due to fertility and mortality. For an age-specific population density \( u(a, t) \), and a total ...

asked by Pillsy https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=531 12 votes

answered by Chris K https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=6358 9 votes

Nonlinear dispersal equation modeling insect aggregation

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230429

I’m a newbie with Mathematica, I know it’s a basic answer, but I can’t solve the problem on my own. I have the following equation reflecting insect aggregation at low population densities (taken from ...

asked by Vefhug https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=74729 10 votes

answered by xzczd https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1871 17 votes

Making a faster alternative for PatternSequence

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230622

I need to improve a pattern or switch an approach. It is best described by an example For a hierarchy/order given by a list e.g.:

order = {1, 2, 3}

and a list:

asked by Kuba https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5478 9 votes

answered by Leonid Shifrin https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=81 9 votes

How can I get material property data past what’s provided via ElementData?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230484

Background Let’s say I want information (e.g. bulk modulus or space group) on an element or chemical compound that isn’t available via e.g. ElementData[]

asked by Sterling https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=61736 6 votes

answered by Sterling https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=61736 6 votes

DSolve does not return solution to simple system of second order PDEs

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230383

I’m trying to solve a simple system of second order PDEs with Mathematica 11.1. Here is the system:

asked by C. B. https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=74734 6 votes

answered by bbgodfrey https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1063 3 votes

Build the following symmetric array

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230650

My mind is a bit cloudy and I can’t quite pinpoint the pattern here that will allow me to write an elegant piece of code to build the following symmetric matrix of for a given size ...

asked by QuantumDot https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2048 5 votes

answered by kglr https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=125 4 votes

Evaluate section by button click

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230613

I have a section in my notebook devoted to unit testing, since I’m not comfortable to use the built-in system. I’d like to evaluate the entire section by button click. But I get lost in the notebook ...

asked by infinitezero https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=31036 5 votes

answered by Kuba https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5478 5 votes

2.12.2 Greatest hits from previous weeks

Assign the results from a Solve to variable(s)
Finding unit tangent, normal, and binormal vectors for a given r(t)
Multivariable Taylor expansion does not work as expected
xkcd-style Plots
What’s the most difficult multidimensional integral that Mathematica has solved?
Drawing a square root spiral
Get a "step-by-step" evaluation in Mathematica

Assign the results from a Solve to variable(s)

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=6669

I understand Mathematica can’t assign the results of a Solve to the unknowns because there may be more than 1 solution. How can I assign the 4 values of following result to variables?

asked by stevenvh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1450 56 votes

answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 34 votes

Finding unit tangent, normal, and binormal vectors for a given r(t)

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=18598

For my Calc III class, I need to find \(T(t), N(t)\), and \(B(t)\) for \(t=1, 2\), and \(-1\), given \(r(t)=\{t,t^2,t^3\}\).

I’ve got Mathematica, but I’ve never used it before and I’m not sure how to coerce ...

asked by a98 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5605 30 votes

answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 43 votes

Multivariable Taylor expansion does not work as expected

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=15023

The basic multivariable Taylor expansion formula around a point is as follows:

\[ f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac {1}{2!}(\mathbf a \cdot \nabla ) \]

asked by matheorem https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4742 58 votes

answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 65 votes

xkcd-style Plots

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=11350

I received an email to which I wanted to respond with a xkcd-style graph, but I couldn’t manage it. Everything I drew looked perfect, and I don’t have enough command over ...

asked by Amatya https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=2039 615 votes

answered by Simon Woods https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=862 474 votes

What’s the most difficult multidimensional integral that Mathematica has solved?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=222184

I am interested in benchmarking numerical integration methods and am trying to develop a wider set of difficult multivariate examples. For my particular methods, I only want to look at non-negative-...

asked by ben18785 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=19278 6 votes

Drawing a square root spiral

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=66969

Here is a start. I’m looking for a nice way to draw it.

asked by matrix89 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=5379 24 votes

answered by Bob Hanlon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=9362 21 votes

Get a "step-by-step" evaluation in Mathematica

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=148

Is it possible in Mathematica to get a step-by-step evaluation of some functions; that’s to say, outputting not only the result but all the stages that have led to it? If so, how does one do it?

asked by Cydonia7 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=44 125 votes

answered by J. M.’s discontentment https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=50 105 votes

2.12.3 Can you answer these questions?

How can I make NDSolve aware of vectorial nature of an ODE?
NDsolve Boundary Condition is a Function of the Solution
Optimizing a graph-theoretic piece of code

How can I make NDSolve aware of vectorial nature of an ODE?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230550

I am trying to solve the equilibrium equation \(\text {DIV } \mathbf P(\textbf {u}(x,y)) = \mathbf {f}\), where \(\mathbf P\) is the stress tensor defined by \[ \mathbf P = \mathbf F + (1-\det \mathbf F) \] asked by rmk236 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=74782 1 vote

NDsolve Boundary Condition is a Function of the Solution

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230520

I am trying to solve something like Fick’s Law using NDSolve

\[\frac {\partial \varphi }{\partial t}=\frac {\partial ^2 \varphi }{\partial r^2}+F(r,t)\] Subject to a ...

asked by UranylTrioxide https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=74775 1 vote

Optimizing a graph-theoretic piece of code

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=230425

I have written the following piece of code:

asked by Mr. Mister https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=74745 2 votes