Narrow Results

Many physical systems are represented by Partial Differential Equations (PDEs), and the study of chaotic dynamics in these systems is interesting and challenging. In this paper, the Li–Yorke chaos of PDEs is studied, and the Li–Yorke chaos is observable in several classes of PDEs, including systems with or without energy injection. For the PDEs without energy injection, three kinds of PDEs are investigated revealing the existence of Li–Yorke chaos, including a type of transport equations, a class of wave equations, and a kind of Navier–Stokes equations. For the PDEs with energy injection, only dissipative type of PDEs are studied, including a model of sound variation of the drum with damping, a kind of reaction–diffusion equations, and a class of two-dimensional Navier–Stokes equations. It is shown that Li–Yorke chaos is well defined for the characterization of the complicated dynamics of these systems. In particular, a physical explanation about chaos in such PDEs is provided, which gives an interesting explanation of acoustic chaos.

In this paper, we introduce fractal interpolation functions (FIFs) and linear FIFs on a post critically finite (p.c.f. for short) self-similar set K. We present a sufficient condition such that linear FIFs have finite energy and prove that the solution of Dirichlet problem -Δ_μ u = f,u|_∂K = 0 is a linear FIF on K if f is a linear FIF.

Noise plays a major role in the behavior of various physical and biological systems, its effects being increasingly pronounced with decrease in system size. While it is jeopardizing the future development of several nanotechnologies, such as magnetic data storage, noise can also play a constructive role in many nonlinear systems, activating a resonance response. In this paper, it is proven that various hysteretic systems can exhibit such coherent behavior — a phenomenon that is generally known as coherence resonance when is solely induced by noise, and stochastic resonance when an external oscillatory signal is present. The quantity used to characterize the regularity of the stochastic output is the power spectrum, which displays a maximum at the resonance frequency. The calculation of the spectral densities for the outputs of hysteretic systems is performed in the framework of stochastic processes defined on graphs. The case of hysteretic systems described by rectangular loops is discussed and analytical expressions for the output power spectra are derived. These theoretical results suggest that hysteretic systems can be used by nanotechnology for concentrating the energy of a flat, noisy input into a short bandwidth frequency region.

In this paper, a new method for global interconnects optimization in nanoscale VLSI circuits using unequal repeater (buffer) partitioning technique is presented. The optimization is performed with the energy-delay product minimization at 65, 90, and 130 nm technology nodes and various loads, using the genetic algorithm (GA) of MATLAB. The results show more improvements of the total propagation delay with respect to the traditional equal buffer partitioning technique. This improvement is obvious for 90 and 130 nm, and with increasing capacitive load, the improvement will be achieved for 65 nm.

Regardless of the state of matter, such as solids, liquids, and gases, the smaller the matter size from bulk to nano-scale, especially in the quantum region, the more rapid is the energy increase. To this end, this study introduces the concept of a group system, in which atoms behave as one, and this system is reinterpreted as that comprising temperature–entropy (TS) energy in thermodynamic data. Based on this concept, water was passed through various mesh-like dissolved tubes, where the size and energy of the water group system were observed to change. Thereafter, as the scale and number of the meshes increased, the ozone, chlorine, and oxygen constituents, which are closely related to sterilization and washing, are generated, changing the basic water composition. Thus, this nano-size impact is not limited to solids and could facilitate in revolutionizing the future applications in fluids.