Namespace dom¶
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namespace
dom
¶ discrete orientation model for magnetic particles
Functions
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void
transition_matrix
(double *W, const double k, const double v, const double T, const double h, const double ms, const double alpha)¶ Compute the 2x2 transition matrix for a single particle.
Assumes uniaxial anisotropy and an applied field h<1 Only valid for large energy barriers: $(1-h)^2>>1$
- Parameters
W
: transition matrix [2x2]k
: anisotropy strength constant for the uniaxial anisotropyv
: volume of the particle in meter^3T
: temperature of environment in Kelvinh
: dimensionless applied field - normalised by \(H_k=\frac{2K}{\mu_0M_s}\)ms
: saturation magnetisationalpha
: dimensionless damping constant
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void
master_equation_with_update
(double *derivs, double *work, const double k, const double v, const double T, const double ms, const double alpha, const double t, const double *state_probabilities, const std::function<double(double)> applied_field)¶ Computes master equation for particle in time-dependent field.
Computes the applied field in the z-direction at time t. Uses the field value to compute the transition matrix and corresponding master equation derivatives for the single particle.
- Parameters
derivs
: master equation derivatives [length 2]work
: vector [length 4]k
: anisotropy strength constant for the uniaxial anisotropyv
: volume of the particle in meter^3T
: temperature of environment in Kelvinms
: saturation magnetisationalpha
: dimensionless damping constantt
: time at which to evaluate the external fieldstate_probabilities
: the current state probabilities for each of the 2 states (up and down) [length 2]applied_field
: a scalar function takes a double and returns a double. Given the current time should return normalised field \(h=(t)\) where the field is normalised by \(H_k\)
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double
single_transition_energy
(double K, double V, double h)¶ Compute the energy dissipated during one transition of the particle.
- Return
- the energy dissipated in one transition
- Parameters
K
: anisotropy constant of the particleV
: volume of the particleh
: applied field on the particle, reduced by the anisotropy field \(H_k=\frac{2K}{\mu_0M_s}\)
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void