Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Generic foundry model for InP-based photonics

Similarities and differences between photonic and microelectronic integration technology are discussed and a vision of the development of InP-based photonic integration in the coming decade is given

Mechanical and functional behavior of a Ni-rich Ni50.3Ti29.7Hf20Ni_{50.3}Ti_{29.7}Hf_{20} high temperature shape memory alloy

The mechanical and functional behaviors of a Ni-rich Ni50.3Ti29.7Hf20 high temperature shape memoryalloy were investigated through combined ex situ macroscopic experiments and in situ synchrotron X-raydiffraction. Isothermal tension and compression tests were conducted between room temperature and260 C, while isobaric thermomechanical cycling experiments were conducted at selected stresses up to700 MPa. Isothermal testing of the martensite phase revealed no plastic strain up to the test limit of1 GPa and near-perfect superelastic behavior up to 3% applied strain at temperatures above the austenitefinish. Excellent dimensional stability with greater than 2.5% actuation strain without accumulation ofnoticeable residual strains (at stresses less than or equal to 400 MPa) were observed during isobaricthermal cycling experiments. The absence of residual strain accumulation during thermomechanicalcycling was confirmed by the lattice strains, determined from X-ray spectra. Even in the untrainedcondition, the material exhibited little or no history or path dependence in behavior, consistent withmeasurements of the bulk texture after thermomechanical cycling using synchrotron X-ray diffraction.Post deformation cycling revealed the limited conditions under which a slight two-way shape memoryeffect (TWSME) was obtained, with a maximum of 0.34% two-way shape memory strain after thermomechanicalcycling under 700 MPa