C++ main module for stochmagnet Package
1.0
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The software has been tested for some configuration of particles network
We applied an external \( H_{ext}=(1,0,0) \) to a magnetic particle with magnetic moment \( \mu=(0,1,0) \) and we study the evolution of \( \mu \) and E depending on the stochastic noise.
The deterministic case test is computed by the ito problem without any noise. The evolution of the deterministic trajectory is as follow
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evolution of mu | the energy evolution |
For the Ito stochastic model with constant noise \(\epsilon=0.1\), we obtain for the first simulation:
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evolution of mu | the energy evolution |
The mean of the total energies for the determinitic and stochastic models gives :
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evolution of means of E |
For the Ito stochastic model with inverse noise \(\epsilon=\frac{0.1}{1+t}\), we obtain for the first simulation:
![]() |
![]() |
evolution of mu | the energy evolution |
The mean of the total energies for the determinitic and stochastic models gives :
![]() |
evolution of means of E |
For the Stratanovich stochastic model, the magnetic moment \(\mu\) is not normalized in the algorithm but the norm of \(\mu\) in the Landau Lifschitz equation is explicitly set to 1.
For the this model with inverse noise \(\epsilon=\frac{0.1}{1+t}\), we obtain for the first simulation:
![]() |
![]() |
evolution of mu | the energy evolution |
The mean of the total energies for the determinitic and stochastic models gives :
![]() |
evolution of means of E |
For the this model with inverse noise \(\epsilon=\frac{0.1}{1+t}\), we obtain for the first simulation:
![]() |
![]() |
evolution of mu | the energy evolution |
The mean of the total energies for the determinitic and stochastic models gives :
![]() |
evolution of means of E |
We applied an external \(H_{ext}=(1,0,0)\) to two magnetic particles with initial magnetic moment \(\mu=(0,1,0)\). The distance between the 2 particles is 1 wheras the exchange coefficient is 1 ( \(J_{01}=J_{10}=1\) and \(J_{00}=J_{11}=-1\)).
We study the evolution of \(\mu\) and E depending on the stochastic noise.
The deterministic case test is computed by the ito problem without any noise. The evolution of the deterministic trajectory is as follow
![]() |
![]() |
![]() |
evolution of mu for particle 0 | evolution of mu for the particle 1 /td> | evolution of the energies |
For the Ito stochastic model with constant noise \(\epsilon=0.1\), we obtain for the first simulation:
![]() |
![]() |
![]() |
evolution of mu for particle 0 | evolution of mu for the particle 1 /td> | evolution of the energies |
![]() |
evolution of means of E |
For the Ito stochastic model with inverse noise \(\epsilon=\frac{0.1}{1+t}\), we obtain for the first simulation:
![]() |
![]() |
![]() |
evolution of mu for particle 0 | evolution of mu for the particle 1 /td> | evolution of the energies |
![]() |
evolution of means of E |
For the Stratonovich stochastic model with inverse noise \(\epsilon=\frac{0.1}{1+t}\), we obtain for the first simulation:
![]() |
![]() |
![]() |
evolution of mu for particle 0 | evolution of mu for the particle 1 /td> | evolution of the energies |
![]() |
evolution of means of E |
For the Normalized Stratonovich stochastic model with inverse noise \(\epsilon=\frac{0.1}{1+t}\), we obtain for the first simulation:
![]() |
![]() |
![]() |
evolution of mu for particle 0 | evolution of mu for the particle 1 /td> | evolution of the energies |
![]() |
evolution of means of E |
We applied an external \(H_{ext}=(1,0,0)\) to 20 magnetic particles located on a line with initial random magnetic moment. The distance between the 2 particles is 1 wheras the exchange coefficient is 1 ( \(J_{i,i+1}=J_{i+1,i}=1\) and \(J_{0,0}=J_{19,19}=-1\) and \(\forall i in {1,18}, J_{i,i}=-2\)).
We study the evolution of \(\mu\) and \(E\) depending on the stochastic noise.
The deterministic case test is computed by the ito problem without any noise. The evolution of the deterministic trajectory is as follow
![]() |
![]() |
![]() |
evolution of mu for all particles | evolution of mu for the particle 17 /td> | evolution of the energies |
Note that the Stratonovich model diverges for the coputing of \( mu\). So we chose to show only the Normalized Stratonovich system with inverse noise \(\varepsilon=\frac{0.1}{1+t} \),
![]() |
![]() |
![]() |
evolution of mu for all particles | evolution of mu for the particle 17 /td> | evolution of the energies |
We applied no external magnetic field to 5x5x1 magnetic particles located on a grid with initial magnetic moment \(\mu=(0,1,0)\) or \(\mu=(0,-1,0)\) in half of the domain. The step size of the grid is 1 in all directions. The Heissenberg operator is neglected.
We study the evolution of \(\mu\) and \(E\) depending on the stochastic noise.
The deterministic case test is computed by the ito problem without any noise. The evolution of the deterministic trajectory is as follow
![]() |
![]() |
evolution of mu for all particles | evolution of the energies |
Note that the Stratonovich model diverges for the coputing of \( mu\). So we chose to show only the Normalized Stratonovich system with inverse noise \(\varepsilon=\frac{0.1}{1+t} \),
![]() |
![]() |
evolution of mu for all particles | evolution of the energies |
We applied no external magnetic field to 5x5x1 magnetic particles located on a grid with initial magnetic moment \(\mu=(0,1,0)\) or \(\mu=(0,-1,0)\) in half of the domain. The step size of the grid is 1 in all directions and each particle is linked to all particles where its distance is less than 1 in each direction. he Heissenberg coefficient between 2 linked particles i and j verifies \(J_{ij}=1 \forall i \neq j \) and \(J_{ii}=-\sum_{j \neq i} J_{ij}\).
We study the evolution of \(\mu\) and \(E\) depending on the stochastic noise.
The deterministic case test is computed by the ito problem without any noise. The evolution of the deterministic trajectory is as follow
![]() |
![]() |
evolution of mu for all particles | evolution of the energies |
Note that the Stratonovich model diverges for the coputing of \( mu\). So we chose to show only the Normalized Stratonovich system with inverse noise \(\varepsilon=\frac{0.1}{1+t} \),
![]() |
![]() |
evolution of mu for all particles | evolution of the energies |