[m.2] Upd crosscorr hugo page (Closes #1130)

Merging branch 'm.2'  into 'main'.

See merge request !2957

hugo/content/ref/sample/roughness/interface.md

@@ -15,7 +15,8 @@ ba.LinearGrowthModel(...)
 ```
 
 These models define the behavior of autocorrelation function of roughness
-or, better to say, its Fourier spectrum in the full range of spatial frequencies from 0 to infinity.
+or, better to say, its Fourier spectrum in the full range of spatial
+frequencies from 0 to infinity.
 
 ##### Self-affine fractal model
 
@@ -24,8 +25,10 @@ ba.SelfAffineFractalModel(sigma, hurst, lateral_corr_length, max_spatial_freq=0.
 ```
 
 where
-- `sigma`, $\sigma$, is the root-mean-square amptitude of out-of-plane (transversal) fluctuation.
-- `hurst`, $H$, is a fractal exponent `H` with `0<H<1`. The smaller $H$ is, the more serrate the surface profile looks.
+- `sigma`, $\sigma$, is the root-mean-square amptitude of out-of-plane
+(transversal) fluctuation.
+- `hurst`, $H$, is a fractal exponent `H` with `0<H<1`.
+The smaller $H$ is, the more serrate the surface profile looks.
 - `lateral_corr_length`, $\xi$, is the lateral (in-plane) correlation length.
 - `max_spatial_freq`, $\nu_{max}$,  is a cut-off spatial frequency.
 
@@ -34,12 +37,15 @@ This is the K-correlation model of
 The autocorrelation spectrum is
 
 $$
-S(\nu)=\dfrac{4 \pi H \sigma^2\xi^2}{(1+(2\pi\nu)^2)^{1+H}} ,\quad  for \quad  \nu<\nu_{max}
+S(\nu)=\dfrac{4 \pi H \sigma^2\xi^2}{(1+(2\pi\nu)^2)^{1+H}} ,\quad
+for \quad  \nu<\nu_{max}
 $$
 
-In case there is no cut-off, the real-space roughness correlation function at the interface is expressed as: 
+In case there is no cut-off, the real-space roughness correlation
+function at the interface is expressed as: 
 $$
-< U(x, y) U(x', y')> = \sigma^2 \frac{2^{1-H}}{\Gamma(H)} \left( \frac{\tau}{ξ} \right)^H K_H \left( \frac{\tau}{ξ} \right),
+< U(x, y) U(x', y')> = \sigma^2 \frac{2^{1-H}}{\Gamma(H)} \left(
+\frac{\tau}{ξ} \right)^H K_H \left( \frac{\tau}{ξ} \right),
 \quad \tau=[(x-x')^2+(y-y')^2]^{\frac{1}{2}}
 $$
 
@@ -65,8 +71,10 @@ of underlying roughness and the growth of the new independent one,
 This is the model described by [Stearns 1993](https://doi.org/10.1063/1.109593)
 and extended by [Stearns and Gullikson 2000](https://doi.org/10.1016/S0921-4526(99)01897-9).
 
-The model describes the evolution of the roughness spectrum on the top surface of a growing film.
-Its autocorrelation spectrum depends not only on the model parameters but also on the film thickness
+The model describes the evolution of the roughness spectrum on
+the top surface of a growing film.
+Its autocorrelation spectrum depends not only on the model parameters
+but also on the film thickness
 and the spectrum of the underlying interface.
 Therefore, the model _cannot_ be applied directly to the substrate.
 

hugo/content/ref/sample/roughness/xcorr/_index.md

@@ -15,6 +15,12 @@ ba.SpatialFrequencyCrosscorrelation(base_crosscorr_depth, base_frequency, power)
 ba.CommonDepthCrosscorrelation(cross_corr_depth)
 ```
 
+Cross-correlation models determine interaction of the current interface with
+_underlying_ ones.
+
+If the interface is already using [linear growth model](../interface), the other
+cross-correlation settings are not needed.
+
 ### "Spatial frequency" model 
 
 ```python
@@ -27,12 +33,14 @@ $\nu_{base}$ between interfaces is damped by a factor $1/e$,
 - `base_frequency`, $\nu_{base}$, is a spatial frequency, for which the
 correlation of rougness spectrum between interfaces is damped by a factor
 $1/e$ at vertical distance $\xi\_{\perp base}$,
-- `power`, $p$, is a degree that determines the dependence of cross-correlation on spatial frequency.
+- `power`, $p$, is a degree that determines the dependence of cross-correlation
+on spatial frequency.
 
 Cross-correlation spectrum between interfaces $i$ and $j$ is
 
 $$
-S_{ij}(\nu)=\sqrt{S_i(\nu)S_j(\nu)} exp[-\dfrac{t}{\xi\_{\perp base}} \Big(\dfrac{\nu}{\nu_{base}}\Big)^p]
+S_{ij}(\nu)=\sqrt{S_i(\nu)S_j(\nu)} exp[-\dfrac{t}{\xi\_{\perp base}}
+\Big(\dfrac{\nu}{\nu_{base}}\Big)^p]
 $$
 
 where