## Monte Carlo simulation of one dimensional harmonic...

I want to use maple2015 to perform a Monte-Carlo simulation of a one dimensional Harmonic Oscillator.

Consider a particle having displacements, x=na where n is an integer, i.e 0 plus minus one, etc.

The potential energy of the particle is given by U(x)= 1/2 kx^2 = 1/2 ka^2 n^2.

For this simulation will choose ka^2 = 0.01 k_B T where k_B is Boltzmann's constant, and T is the temprature in Kelvin.

So we should perform a Monte-Carlo simulation starting from x(0)=20a, and perfroming individual steps by selecting an attmept to move x=+-a ,with equal probability, and choose whether to make the actual step according to energy change expected in that step.

I need to draw particle's position and x(t), and particle's energy E(t).

After that I need to calculate and draw the autocorrelation functions \phi_x(t) and \phi_E(t).

I found some code that might help me, but I am nor sure how to implement the above two lines on maple; your help is appreciated.

http://pubs.acs.org/doi/suppl/10.1021/ed100414p/suppl_file/ed100414p_si_001.pdf

## Statistics monte carlo simulation question...

There is a horse a buggy ride around a small village which takes roughly 30 minutes.  Here is an example timing for 12 consecutive rides [34, 29, 32, 32, 28, 28, 27, 28, 39, 24, 27, 27].

How can I create a monte carlo simulation graph that would estimate the future times based on given data?  Do I randomly pick numbers from the given list for a simulation or generate random numbers based on mean and standard deviation generated from the data?

When would the best possible time to come back after 4 rides be?

## issues with angular displacement in given inverse ...

Hi,

I was playing around with the example "Simple Inverse Kinematic Problem" and found somethings to be odd:

the angular motion seems to be calculated from between pi and negative pi and this has some effects when using position block to move a joint.

the original angular displacement is graph below

the angular displacement after ik calculations have been performed:

if you run the simulation it seems to copy and mirror the input pendulum, however if you disable one of the IK solutions you see that infact its motion isn't like the input.

this becomes more prevailant when you use a position block to force rotation on a joint instead of using the 'prescribed rotation' blocks that comes with the example.

My question then:
why does this happen?
how do I work around this?

the importance that the motion is follow precisely becomes more prevailent when we want to extract other values such as vel, accel, torque. they are incorrect and very jumpy. Also simply put the angular displacement is wrong, how do I fix it?

(side note: I'm thinking  it has to do with the way arctan is calculated in maple limits it to stay in range -pi to pi
"For real arguments x, y, the two-argument function arctan(y, x), computes the principal value of the argument of the complex number x+Iy, so −π < arctan(y,x) ≤ π." from https://www.maplesoft.com/support/help/Maple/view.aspx?path=invtrig)

pjf

## Hourly simulation using iterative series of equati...

I am trying to do an hourly simulation of a solar-thermal system. The method I am using requires an inital guess for a value which is used in a series of equations. That variable is then back calculated, and checked against the initial guess. If it is too far off, the back calculated value is used as the new guess and so on...

My question is twofold. First, is there a way to create a sort of module that can execute a number of steps when called upon (i.e. the iterative process described above). Second, how can I run this for each hour of the year (the weather inputs for each hour will change) without manually executing each one, one at a time. So far my guess is to make a matrix with the weather inputs for each hour, and then have some sort of loop read the rows (hours) one at a time, pull the data from it, run the series of steps, and then store the output for that hour in a new matrix. Is this the best way to do this? If so, which functions/tools in Maple should I look into that can do this for me?

Thanks.

## Where is oscilloscope icon?...

where i can found oscilloscope icon for cisuit simulation?thanks

## Is Ising a package?...

Hi all

Is Ising a package?

for i = 1:12000

%while (1),

% Choose a random value between 0 and 1 for the interaction strength

J = rand()+1e-10;

% Perform a simulation

[M, N, E] = ising2(n_grid, J);

% Records the results

Ms = [Ms M/(n_grid^2)];

Es = [Es E/(n_grid^2)];

Ns = [Ns N];

Js = [Js J];

i = i+1;

## Theoretical Physics...

Hi,

I am a college student that is aspiring to become a theoretical theorist. I have postulates that are not in mathematical form yet, and I would like to use a program that can help with this process. I am new to the usage of Maple products, and I have questions. Is it possible to use Maple in this way, before getting to the difficult calculus steps? Can MapleSim or Maple Physics, perform simulations, or models of physics calculations?

Thank you,

Roi

How I can simulate control speed of car with sensor of speed, noise, feedback on maplesim?thanks

## How to model Moon tilt illusion?...

I never expected that the reflected light direction of sun from moon in the sky would be so dificult to imagine ...

at the following article mentioned :

we derive an equation for the magnitude of the moon tilt illusion that can be applied to all con gurations of sun and moon in the sky.

THE MOON TILT ILLUSION

since the calculations contains many steps and high level mathematical formula , there is no way rather to recourse to maple (powerful math assistant )

I hope there was adaptations between a lots of functions and predefined schema of maple and this problem so that the calculations and visualization facilitated several times ?

your effort will be a graet present for all the people of the world that look to the moon crescent everytime !

## Storage of the results of simulations...

Hello,

I have many tests to conduct on a MapleSim model. At each test simulations, I would like to change slightly some parameters.

As I have many tests to do (with different parameters), I would like to use a script so as to do like this :

Parameters test1
Store results of test 1

And so on ...

How can I do this kind of script ?

Is it possible to store the 3D animation results ?

Thank you for your help.

## Unusable simulation results for visualization...

Hello.

When I click to start simulation button maple start counting but after that don't open visualization. When I open visualization manually, there aren't results of simulation. Program don´t show any error. It does not work with my models and examples to. Thanks for your help.

## Probability of a situation occurance ...

I'm drawing a complete blank on this.

The probability of a branch breaking in a particular tree as someone climbs is 2%.  After the person has climbed over 40 branches, did any of them break?  I'm trying to set that up as a simulation in Maple but I'm not sure about how to do it.

I guess if I generate a random number and it falls under .02 it breaks, is that how I determine that?

randomize():

n := 0;
for i to 40 do
ran := evalf(rand()*10^(-12));
if ran < 0.2e-1 then n := n+1: end if:
end do:
print("Branch broke", n, "times")

I'm not sure I've got the probability right.

## MapleSim Crashing on Run...

When I run a simulation (i.e. Double Pendulum Example) MapleSim crashes with no errors or dialogues - completely shuts down. The simulation seems to compile ok, then as the plots are opening it crashes. My video card driver is up to date. Anyone know how to fix this?

Thanks.

## MapleSim for robotics simulation...

i click the web said USD99

but after click into it, academic version is USD1,555

there are commercial version, academic version , what are difference?

i see that there are self balance robot and humanoid walk robot

what are the specification of size, length of components are they?

if simulate robot hand which has a string make a tension to grip object

what kind of string is it? where can buy robots components which fit the simulations it do?

will maplesoft cooperate with 3D printer to fit the reality of robots?