Related Experiment Video
Updated: Jul 30, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
Roughening and super-roughening in the ordered and random two-dimensional sine-gordon models
1Grupo Interdisciplinar de Sistemas Complicados (GISC), Departamento de Matematicas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganes, Madrid, Spain.
Abstract:
We present a comparative numerical study of the ordered and the random two-dimensional sine-Gordon models on a lattice. We analytically compute the main features of the expected high-temperature phase of both models, described by the Edwards-Wilkinson equation. We then use those results to locate the transition temperatures of both models in our Langevin dynamics simulations. We show that our results reconcile previous contradictory numerical works concerning the super-roughening transition in the random sine-Gordon model. We also find evidence supporting the existence of two different low-temperature phases for the disordered model. We discuss our results in view of the different analytical predictions available and comment on the nature of these two putative phases.
Related Concept Videos
Graphical and Analytic Representation of Sinusoids
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
Second Order systems I
By reinterpreting the system, one can derive the closed-loop transfer function, which...
Second Order systems II
If ζ...
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Shape and Texture of Coarse Aggregate
Limits with Oscillating Discontinuities

