Speaker: JFR Archilla, T6 task coordinator (pdf slides color 240 Kb).
LOCNET midterm review. Mathematics Institute. University of Warwick, Warwick, UK, 21-22 September 2002.

Part A - Research Results

A.1 Scientific Highlights

T6 Randomness and nonlinearity

1. Spatial disorder in strict sense: Breather in disordered systems can be continued in some cases inside the linearised spectrum, and arbitrary weak nonlinearity was shown to allow energy transport [KA0a,KA0b]. The relation between breathers and Anderson modes is studied in a two-dimensional model [CAPR].
2. Spatial inhomogeneities due to impurities, shape or other causes: Properties of nonlinear impurity modes and their stability are studied in the generalized Schrödinger equation [SKBRC], and their effect on trapping in a Klein-Gordon model [CPAR-II]. Characteristic frequencies of breathers at bending points in curved alpha-helix proteins are found [AGCC]. Properties of moving breathers in FPU systems with segments of different masses are analyzed [BSS].
3. Temporal randomness, i.e., temperature: The survival of breather mobility across bending points in polymers with temperature is observed in [RSIT,IST,TIS]. The thermalization of standing phonons leading to transient DB is studied in [JMAK]. Work is still in progress on nonlinear conductivity of CDW materials by thermal nucleation of pairs of discommensurations (Baesens, MacKay, Floria & Sancho).
4. Application to DNA: Mobility of polarobreathers is observed to survive to weak diagonal and structural off-diagonal disorder in a 3D DNA model [HAA].

1. [KA0a] G Kopidakis (Heraklion), S Aubry (Saclay), Intraband discrete breathers in disordered nonlinear systems II: Localization, Physica D 139 (2000) 247-275.
2. [KA0b] G Kopidakis (Heraklion), S Aubry (Saclay), Discrete breathers and delocalization in nonlinear disordered systems, Phys. Rev. Lett. 84 (2000) 3236-3239.
3. [TIS] GP Tsironis (Heraklion), M Ibañes, JM Sancho (both Barcelona), Transport of localized vibrational energy in biopolymer models with rigidity, Europhysics Letters 57 (2002), 697-703.
4. [RSIT] R Reigada, JM Sancho, M Ibañnes (all Barcelona), GP Tsironis (Heraklion), Resonant motion of discrete breathers in curved nonlinear chains, J. Phys. A 34 (2001), 8465-8475.
5. [IST] M Ibañes, JM Sancho (Barcelona), GP Tsironis (Heraklion), Dynamical properties of discrete breathers in curved chains with first and second neighbors interactions, Phys. Rev. E (2002). In press.
6. [JMAK] M Johansson, AM Morgante (Saclay), S Aubry (Saclay) and G Kopidakis (Heraklion), Standing wave instabilities, breather formation and thermalization in Hamiltonian anharmonic lattices, Submitted to European Physical Journal, 2002.
7. [HAA] D Henning (Berlin), JFR Archilla (Sevilla) and J Agarwal (Berlin), Nonlinear charge transport mechanism in periodic and disordered DNA, submitted to Physica D, 2002.
8. [AGCC] JFR Archilla (Sevilla), Yu B Gaididei (Lyngby), PL Christiansen (Lyngby) and J Cuevas (Sevilla), Stationary and moving breathers in curved alpha-helix proteins, submitted to J. Phys. A, 2002.

1. [BSS] I Bena*, A Saxena and JM Sancho (all Barcelona), Interaction of a discrete breather with a lattice junction, Phys. Rev. E, in press.

1. [CAPR] J Cuevas, JFR Archilla, F Palmero, FR Romero (all Sevilla), Numerical study of two-dimensional disordered Klein-Gordon lattices with cubic soft anharmonicity, J. Phys. A 34-16 (2001), L221-L230.
2. [SKBRC] AA Sukhorukov, YS Kivshar, O Bang (Lyngby), J Juul Rasmussen and PL Christiansen (Lyngby), Nonlinearity and disorder: Classification and stability of nonlinear impurity modes, Phys. Rev. E 63 (2001),036601(1-18).
3. [CPAR-II] J Cuevas, F Palmero, JFR Archilla, FR Romero (all Sevilla), Moving discrete breathers in a Klein-Gordon chain with an impurity, Submitted to J. Phys. A, 2002.