pisces.math_utils.random_fields.generate_gaussian_cutoff_power_spectrum#

pisces.math_utils.random_fields.generate_gaussian_cutoff_power_spectrum(amplitude: float = 1.0, k0: float = 1.0, sigma: float = 1.0) → Callable[source]#

Generate a Gaussian-cutoff power spectrum function.

The Gaussian-cutoff spectrum is defined by

\[P(k) = A \exp\!\left[-\frac{1}{2} \left(\frac{k - k_0}{\sigma}\right)^2\right],\]

where \(A\) is the amplitude, \(k_0\) is the central wavenumber, and \(\sigma\) controls the width of the Gaussian. This spectrum is peaked around \(k_0\) and falls off rapidly away from the peak.

Parameters:

  • amplitude (float, optional) – Normalization amplitude \(A\). Default is 1.0.

  • k0 (float, optional) – Central wavenumber \(k_0\). Default is 1.0.

  • sigma (float, optional) – Width of the Gaussian \(\sigma\). Default is 1.0.

Returns:

A function P(kx, ky, ...) that takes arrays of wavenumber components and returns the Gaussian-cutoff spectrum.

Return type:

Callable

Examples

from pisces.math_utils.random_fields import generate_gaussian_cutoff_power_spectrum
L, n = 10.0, 256
k_grid = np.fft.fftfreq(n, d=L/n) * 2 * np.pi
k_mag = np.abs(k_grid)
power_spectrum = generate_gaussian_cutoff_power_spectrum(k0=5.0, sigma=2.0)
ps_array = power_spectrum(k_mag)

import matplotlib.pyplot as plt
plt.plot(k_mag, ps_array)
plt.xlabel('Wavenumber k')
plt.ylabel('Power Spectrum P(k)')
plt.title('Gaussian-Cutoff Spectrum')
plt.show()

(Source code, png, hires.png, pdf)

../_images/pisces-math_utils-random_fields-generate_gaussian_cutoff_power_spectrum-1.png