Modulational instability on triangular dynamical lattices with long-range interactions and dispersion

Investigations of vesicle gels by pulsed and modulated gradient NMR diffusion techniques

“…Gðt 0 Þdt 0 , which is determined by the effective gradient waveform G(t), and D k (u) is the spectrum of the VCF or the diffusion spectrum in the direction along the applied gradient. [26][27][28][29][30] While the PGSE method uses a single pair of spin labelling and de-labelling gradient pulses, the spin-labelling and de-labelling is repeated several times within the MGSE experiment. Thus, adequate signal attenuation can be achieved by using much lower gradient field strength compared to the PGSE approach.…”

“…The model for the restricted diffusion spectrum D(u) can be analytically derived in cases of simple geometries (planar, cylindrical and spherical). 30 Complex systems often consist of interconnected restricted environments or permeable pores, which define the long-range diffusivity D N . This is reflected in the diffusion spectrum as a finite component at zero frequency.…”

“…The coefficients a k and B k depend on the geometry under consideration. 30,33 As a rough model of our system we assume restrictions of spherical geometry. For a pore radius R, the coefficients a k and B k are given by…”

“…The VCF spectrum, also known as the diffusion spectrum, D(u), probed by the MGSE approach, is related to the mean square displacement which contains information about the sample morphology. 30 The zero frequency component of the diffusion spectrum corresponds to long range diffusion, while higher frequency components approach the bulk diffusion value. The MGSE approach is able to separate the effects of restricted diffusion from molecular migration across the interconnected porous structure.…”

Modulational Instability and Discrete Localized Modes in Two Coupled Atomic Chains with Next-Nearest-Neighbor Interactions

“…The eventual formulation of the soliton concept by Zabusky and Kruskal to elucidate on the recurrence phenomenon, triggered enormous interest in scientists around the world to investigate on this fascinating soliton entity [16]. Of particular interest is in discrete regimes, where the role and consequences of MI have been extensively studied within the frame work of discrete nonlinear Schrödinger (DNLS) amplitude equations [17][18][19][20][21][22][23][24][25]. This generally leads to the observation of discrete breathers, that were first identified by Takeno and Sievers in a perfect anharmonic lattice [26,27].…”