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#include "brains/SimInfo.hpp" |
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namespace OpenMD { |
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struct UniGradPars { |
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RealType a; |
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RealType b; |
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RealType c; |
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RealType alpha; |
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RealType beta; |
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}; |
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//! Applies a uniform electric field gradient to the system |
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/*! The gradient is applied as an external perturbation. The user specifies |
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\code{.unparsed} |
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uniformGradient = (a, b, c, alpha, beta); |
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uniformGradientStrength = c; |
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uniformGradientDirection1 = (a1, a2, a3) |
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uniformGradientDirection2 = (b1, b2, b3); |
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\endcode |
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in the .md file where the values of a, b, c, alpha, beta are in units of |
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\f$ V / \AA^2 \f$ |
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in the .md file where the two direction vectors, \f$ \mathbf{a} \f$ |
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and \f$ \mathbf{b} \f$ are unit vectors, and the value of \f$ g \f$ |
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is in units of \f$ V / \AA^2 \f$ |
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The electrostatic potential corresponding to this uniform gradient is |
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\f$ \phi(\mathbf{r}) = - a x y - b x z - c y z - \alpha x^2 / 2 - \beta y^2 / 2 + (\alpha + \beta) z^2 / 2 \f$ |
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\f$ \phi(\mathbf{r}) = - \frac{g}{2} \left[ |
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\left(a_1 b_1 - \frac{\cos\psi}{3}\right) x^2 |
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+ (a_1 b_2 + a_2 b_1) x y + (a_1 b_3 + a_3 b_1) x z + |
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+ (a_2 b_1 + a_1 b_2) y x |
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+ \left(a_2 b_2 - \frac{\cos\psi}{3}\right) y^2 |
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+ (a_2 b_3 + a_3 b_2) y z + (a_3 b_1 + a_1 b_3) z x |
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+ (a_3 b_2 + a_2 b_3) z y |
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+ \left(a_3 b_3 - \frac{\cos\psi}{3}\right) z^2 \right] \f$ |
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which grows unbounded and is not periodic. For these reasons, |
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where \f$ \cos \psi = \mathbf{a} \cdot \mathbf{b} \f$. Note that |
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this potential grows unbounded and is not periodic. For these reasons, |
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care should be taken in using a Uniform Gradient with point charges. |
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The corresponding field is: |
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\f$ \mathbf{E} = \left( \array{c} \alpha x + a y + b z \\ a x + \beta y + c z \\ b x + c y - (\alpha + \beta) z \end{array} \right) \f$ |
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\f$ \mathbf{E} = \frac{g}{2} \left( |
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2\left(a_1 b_1 - \frac{\cos\psi}{3}\right) x + (a_1 b_2 + a_2 b_1) y |
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+ (a_1 b_3 + a_3 b_1) z \\ |
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(a_2 b_1 + a_1 b_2) x + 2 \left(a_2 b_2 - \frac{\cos\psi}{3}\right) y |
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+ (a_2 b_3 + a_3 b_2) z \\ |
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(a_3 b_1 + a_1 b_3) x + (a_3 b_2 + a_2 b_3) y |
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+ 2 \left(a_3 b_3 - \frac{\cos\psi}{3}\right) z \end{array} \right) \f$ |
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The field also grows unbounded and is not periodic. For these reasons, |
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care should be taken in using a Uniform Gradient with point dipoles. |
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The corresponding field gradient is: |
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\f$ \nabla \mathbf{E} = \left( \array{ccc} \alpha & a & b \\ a & \beta & c \\ b & c & -(\alpha + \beta) \end{array} \right) \f$ |
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\f$ \nabla \mathbf{E} = \frac{g}{2} \left( \array{ccc} |
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2\left(a_1 b_1 - \frac{\cos\psi}{3}\right) & |
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(a_1 b_2 + a_2 b_1) & (a_1 b_3 + a_3 b_1) \\ |
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(a_2 b_1 + a_1 b_2) & 2 \left(a_2 b_2 - \frac{\cos\psi}{3}\right) & |
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(a_2 b_3 + a_3 b_2) \\ |
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(a_3 b_1 + a_1 b_3) & (a_3 b_2 + a_2 b_3) & |
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2 \left(a_3 b_3 - \frac{\cos\psi}{3}\right) \end{array} \right) \f$ |
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which is uniform everywhere. |
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bool doParticlePot; |
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Globals* simParams; |
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SimInfo* info_; |
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UniGradPars pars_; |
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Mat3x3d Grad_; |
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Vector3d v1_, v2_, v3_; |
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Vector3d a_, b_; |
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RealType g_, cpsi_; |
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}; |
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