Related Experiment Video
Updated: Mar 10, 2026

External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures
Published on: May 7, 2017
Patterning in systems driven by nonlocal external forces
L Luneville1, K Mallick2, V Pontikis3
1DEN-Service dÉtudes et de Recherche en Mathématique Appliquée, LRC CARMEN CEA-CNRS-ECP/SPMS, Université Paris-Saclay, F-91191, Gif-sur-Yvette, France.
Abstract:
This work focuses on systems displaying domain patterns resulting from competing external and internal dynamics. To this end, we introduce a Lyapunov functional capable of describing the steady states of systems subject to external forces, by adding nonlocal terms to the Landau Ginzburg free energy of the system. Thereby, we extend the existing methodology treating long-range order interactions, to the case of external nonlocal forces. By studying the quadratic term of this Lyapunov functional, we compute the phase diagram in the temperature versus external field and we determine all possible modulated phases (domain patterns) as a function of the external forces and the temperature. Finally, we investigate patterning in chemical reactive mixtures and binary mixtures under irradiation, and we show that the last case opens the path toward micro-structural engineering of materials.
Related Concept Videos
Classification of Systems-I
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Feedback control systems
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Internal and External Forces
Work Done on a System by External Force
In the presence of a non-conservative opposing force, like friction, some part of the work done...
Forced Oscillations
Mechanical Systems

