This study proposes to use a method of nonlinear, nonstationary data processing and analysis, i.e., the Hilbert-Huang transform (HHT), to explore and characterize the signatures of soil nonlinearity and/or liquefaction from earthquake ground recordings. The paper first summarizes symptoms of soil nonlinearity and liquefaction shown in earthquake ground motion recordings. It then reviews the Fou...

– We have derived the local electric field inside graded metal-dielectric composite films with weak nonlinearity analytically, which further yields the effective linear dielectric constant and third-order nonlinear susceptibility of the graded structures. As a result, the composition-dependent gradation can produce a broad resonant plasmon band in the optical region, resulting in a large enhanc...

We show that electrons on liquid helium display intrinsic bistability of resonant intersubband absorption. The bistability occurs for comparatively weak microwave power. The underlying giant nonlinearity of the many-electron response results from the interplay of the strong short-range electron correlations, the long relaxation time, and the multisubband character of the electron energy spectrum.

The Landau-Lifshitz-Gilbert equation describes dynamics of ferromagnetism, where strong nonlinearity, nonconvexity are hard to tackle: so far, existing schemes to approximate weak solutions suffer from severe time-step restrictions. In this paper, we propose an implicit fully discrete scheme and verify unconditional convergence.

In this paper, we deal with a class of semilinear elliptic equation in a bounded domain Ω ⊂ R , N ≥ 3, with C boundary. Using a new fixed point result of the Krasnoselskii’s type for the sum of two operators, an existence principle of strong solutions is proved. We give two examples where the nonlinearity can be critical.

In this paper, we deal with the semilinear wave equation with strong damping. By choosing a suitable state space, we characterize the interpolation and extrapolation spaces of the operator matrix Aθ, analysis the criticality of the ε-regular nonlinearity with critical growth. Finally, we investigate the global existence of the ε-regular solutions which have bounded X ×X norms on their existence...

We find strong self-defocusing in bacteriorhodopsin films in the near IR with powers in the tens of milliwatts. The defocused beam acquires a ring pattern because of spatial self-phase modulation. We also demonstrate efficient four-wave mixing with phase-conjugate reflectivities of 26%. We discuss the origin of this high nonlinearity.