How to find the distances between two adjacent maxima in a solution from NDSolve

I try to find a general approach to plot the time evolution of horizontal distances from maximum to maximum in a solution of PDE. The solution u[x,t] normally have multiple maximum and minimum in space x, which move in space x and evolve in time t.

Here is a simple example, in which the maxima and minima are periodic. But in my real problem they are not periodic and the distances between different pairs of adjacent max are different at a given t, also the distances between two adjacent max can change with t.

sol = NDSolve[{D[u[x, t], t] + u[x, t] D[u[x, t], x] + D[u[x, t], x, x] +  0.4*D[u[x, t], {x, 3}] + D[u[x, t], {x, 4}] == 0, u[-4 \[Pi], t] == u[4 \[Pi], t], u[x, 0] == 0.1*Sin[x]}, u, {t, 0, 20}, {x, -4 \[Pi], 4 \[Pi]}]  Plot3D[Evaluate[u[x, t] /. First[sol]], {t, 0, 10}, {x, -4 Pi, 4 Pi}, PlotRange -> All, PlotPoints -> 100] 

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I have tried to use Table[FindMaximum[Evaluate[u[x, t] /. First[sol]], {x, x0}][[2, 1, 2]], {t,0,tend,0.01}] with an initial position x0 to find a local maximum. But I don’t know how to find two adjacent maxima simultaneously in order to plot the time evolution of their distance.

FindRoot: unstable solution


a0 = 0;  A = ImplicitRegion[{-175 < x < 175, yc - 450 < y < yc, Cos[a] y - Sin[a] x > 0}, {x, y}];  B = {{-20, yc - 410, 16}, {0, yc - 410, 16}, {20, yc - 410, 16},         {-20, yc - 40, 16}, {20, yc - 40, 16}};  eqn = {Integrate[y, {x, y} \[Element] A] + 15 Pi/4 Total[B[[All, 2]] B[[All, 3]]^2],         Integrate[x y, {x, y} \[Element] A] + 15 Pi/4 Total[B[[All, 1]] B[[All, 2]] B[[All, 3]]^2],         Integrate[y^2, {x, y} \[Element] A] + 15 Pi/4 Total[B[[All, 2]]^2 B[[All, 3]]^2] - 100 10^6 yc/sc};  N[FindRoot[eqn == {0, 0, 0}, {{a, a0}, {yc, 225}, {sc, 15}}, WorkingPrecision -> 100], 10] 

I get:

{a -> 0, yc -> 113.2248453, sc -> 11.33863961}

which is what I expected (being an engineering problem, I know the solution).

Unfortunately, writing a0 = 10^-10 I get:

{a -> 1132.470809, yc -> 225.0000000, sc -> 12.19507508}

which is obviously incorrect. I suppose this is a problem of stability in the system of equations. How can it be solved in MMA? Thanks!

Dynamic programming algorithm with an O(n) performance that will give the optimal solution

I am currently learning the dynamic substructure and optimal solution for the coin change-making, and one of the questions given from my teacher is to describe an overall O(n) dynamic programming algorithm that will give the optimal solution and why is it O(n)? Can anyone help me to understand the question? Thank you!

IPS solution for a medium sized web application

As part of application security compliance we are supposed to implement an IPS on our application. The application is basically an educational web portal where students can enrol for course assessment. The assessment will be done in the backend by professionals and the certificate is issued to the students. This involves payment also. The application is hosted in Kubernetes in AWS cloud. 

We see that various levels of IPS are available in the market. Some includes threat intelligence models and SIEM modules. But for a small application like this, we don’t think SIEM is not necessary. Also, taking into consideration that we are running short of budget, we would like to opt for a basic IPS that can effectively protect the web application. 

I would like to invite suggestions. I am not looking for a specific tool recommendation, but rather a way of implementation.

What solution against ARP attacks in a University network?

I´m trying to protect my LAN (University campus) against ARP attacks using netcut.

I have 100 APs connected to my CISCO 2680. I used 8 VLANs and all of VLAN ports are connected to one gateway provided from a loadbalancer.

Even with this, I can detect some attackers.

Is there any solution to protect my LAN apart using VLANs in my L2?

Soon I’ll use WatchGuard as a firewall. Can this one deal with this kind of attacks?

Needing ideas for a business solution

Hello everyone,

I'm a university student in project management and our university has been having several organizational changes resulting in change of staff and way of doing things. We were given a task that me and my group are having issues resolving (since none of us know anything about the project and since our university advisers just came in they don't share anything with us). I thought it would be nice to ask for advice and more importantly ask for ideas, if you don't mind that is….

Needing ideas for a business solution

SharePoint Site url is not working for debugging a solution

For debugging a SharePoint solution I want to give test site URL in visual studio.

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but since web application URL is already access mapped

(http://example:2344 ->  

When I try to give URL in, it shows

“Remote SharePoint site connections are not supported “

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How can I use (Alternate Access Mapped Url) for debugging purpose since currently, I don’t have original URL (http://example:2344)?