Related Experiment Video
Updated: Aug 8, 2025
07:44
Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems
Published on: April 28, 2016
15.1K
Non-reciprocity induces resonances in a two-field Cahn-Hilliard model
Tobias Frohoff-Hülsmann1, Uwe Thiele1,2, Len M Pismen3
1Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, Münster 48149, Germany.
Summary
This study analyzes a non-reciprocally coupled Cahn-Hilliard system, revealing identical instability thresholds to reaction-diffusion systems. Weakly nonlinear analysis and simulations explore oscillatory behavior and pattern formation dynamics.
Area of Science:
- Nonlinear dynamics
- Pattern formation
- Materials science
Background:
- Cahn-Hilliard systems are crucial for modeling phase separation.
- Non-reciprocal coupling introduces complex dynamics like oscillations.
- Understanding pattern formation is key in materials science and biology.
Purpose of the Study:
- To investigate the linear stability and nonlinear dynamics of a non-reciprocally coupled two-field Cahn-Hilliard system.
- To analyze oscillatory behavior and coarsening suppression.
- To compare weakly nonlinear results with fully nonlinear simulations.
Main Methods:
- Linear stability analysis of steady uniform states.
- Weakly nonlinear analysis to derive amplitude equations for Hopf-Turing resonance.
- Fully nonlinear simulations using a conserved amended FitzHugh-Nagumo system.
Main Results:
- Instability thresholds match those of two-species reaction-diffusion systems.
- Identified a 'Hopf-Turing' resonance mechanism.
- Weakly nonlinear predictions were validated by fully nonlinear simulations.
Conclusions:
- The non-reciprocally coupled Cahn-Hilliard system exhibits rich dynamics, including oscillations and suppressed coarsening.
- The weakly nonlinear approach provides valuable insights but has limitations.
- Further research into nonlinear dynamics of extended systems is warranted.
Keywords:
Hopf–Turing resonanceactive matterconserved FitzHugh–Nagumo modelnon-reciprocal Cahn–Hilliard modelpattern formationweakly nonlinear analysisMore Related Videos
Related Concept Videos
01:12Double Resonance Techniques: Overview
255
Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
Spin decoupling is usually achieved by...
255
01:05Atomic Nuclei: Magnetic Resonance
714
The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
714
01:14Sound Waves: Resonance
2.6K
Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
2.6K
01:23Atomic Nuclei: Nuclear Relaxation Processes
696
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis.
696
01:23Parallel Resonance
246
The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:
246
01:26Resonance in an AC Circuit
2.1K
The property of an inductor makes it resist any change in the current passing through it, while the property of a capacitor is to build up the charge across its terminals. Hence, if an inductor and capacitor are connected in series, they have opposite effects on the relative phase between current and voltage. The current through the circuit undergoes forced oscillation at the frequency of the source. The resistance term in an R-L-C circuit acts as a damping term because power is dissipated...
2.1K