Self-consistent nonlinear dynamics of Energetic Particle Modes, which are relevant for burning plasma conditions, are analyzed with respect to both saturation mechanisms and energetic particle transport. It is found that a “sensitive” parameter for Tokamak equilibria with hollow-q profiles is q at the minimum-q surface, higher q corresponding to larger particle transport. This fact has clear im...

We discuss the formation of graded morphogen profiles in a cell layer by nonlinear transport phenomena, important for patterning developing organisms. We focus on a process termed transcytosis, where morphogen transport results from the binding of ligands to receptors on the cell surface, incorporation into the cell, and subsequent externalization. Starting from a microscopic model, we derive e...

To improve our understanding of nonlinear elastic properties of soils, a method is proposed of estimation of stress-strain relations of soils in situ in strong ground motion based on vertical array data. Strong motion records provided by seismic vertical arrays allow estimation of nonlinear stressstrain relations in soil layers at different depths, from the surface down to the location of the d...

We introduce a maskless lithography tool and optically-initiated diffusive photopolymer that enable arbitrary two-dimensional gradient index (GRIN) polymer lens profiles. The lithography tool uses a pulse-width modulated deformable mirror device (DMD) to control the 8-bit gray-scale intensity pattern on the material. The custom polymer responds with a self-developing refractive index profile th...

Abstract—A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using th...

In this paper, the trellis representation of nonlinear codes is studied from a new perspective. We introduce the new concept of entropy/length profile (ELP). This profile can be considered as an extension of the dimension/length profile (DLP) to nonlinear codes. This elaboration of the DLP, the entropy/length profiles, appears to be suitable to the analysis of nonlinear codes. Additionally and ...

We study linear transmission and nonlinear soliton transport through quasiperiodic structures, where the lattice profiles are described by multiple modulation frequencies. We show that resonant scattering at mixed-frequency resonances limits transmission efficiency of localized wave packets, leading to radiation and possible trapping of solitons. We obtain an explicit analytical expression for ...

Spurious long-term solutions of a finite-difference method for a hyperbolic conservation law with a general nonlinear source term are studied. Results are contrasted with those that have been established for nonlinear ordinary differential equations. Various types of spurious behavior are examined, including spatially uniform equilibria that exist for arbitrarily small time-steps, nonsmooth ste...

We study nonlinear time-asymptotic stability of small–amplitude planar Lax shocks in a model consisting of a system of multi–dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is...

We study nonlinear asymptotic stability of small–amplitude Lax shocks in a model consisting of a system of multi–dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is based on th...