scholarly journals Diffusion and propagation problems in some ramified domains with a fractal boundary

2006 ◽  
Vol 40 (4) ◽  
pp. 623-652 ◽  
Author(s):  
Yves Achdou ◽  
Christophe Sabot ◽  
Nicoletta Tchou
Keyword(s):  
Fractal Boundary

A biregular extension theorem from a fractal surface in

2011 ◽  
Vol 18 (1) ◽  
pp. 21-29
Author(s):  
Ricardo Abreu Blaya ◽  
Juan Bory Reyes ◽  
Tania Moreno García
Keyword(s):  
Continuous Function ◽  
Bounded Domain ◽  
Extension Theorem ◽  
Fractal Surface ◽  
Fractal Boundary ◽  
Hölder Continuous

Abstract The aim of this paper is to prove the characterization on a bounded domain of with fractal boundary and a Hölder continuous function on the boundary guaranteeing the biregular extendability of the later function throughout the domain.

Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System

2012 ◽  
Author(s):  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Fractal Boundary ◽  
Final State ◽  
Potential Wells ◽  
Mechanical Coupling ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.

scholarly journals On purely periodic beta-expansions of Pisot numbers

2002 ◽  
Vol 166 ◽  
pp. 183-207 ◽  
Author(s):  
Yuki Sano
Keyword(s):  
Natural Extension ◽  
Irreducible Polynomial ◽  
Main Tool ◽  
Pisot Number ◽  
Fractal Boundary ◽  
Pisot Numbers ◽  
Dimensional Domain

AbstractWe characterize numbers having purely periodic β-expansions where β is a Pisot number satisfying a certain irreducible polynomial. The main tool of the proof is to construct a natural extension on a d-dimensional domain with a fractal boundary.

scholarly journals The Effect of Indentation Angle of Koch Fractal Boundary on the Performance of Microstrip Antenna

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
P. Nageswara Rao ◽  
N. V. S. N. Sarma
Keyword(s):  
Resonant Frequency ◽  
Experimental Verification ◽  
Microstrip Antenna ◽  
Fractal Boundary ◽  
Triangular Patch ◽  
Resonant Behavior ◽  
Koch Fractal

The effect of indentation angle of Koch fractal boundary applied to a triangular patch on the resonant behavior and bandwidth is presented. It is shown that the resonant frequency can be controlled by changing the indentation angle of the boundary. With the experimental verification, it is established that for an indentation angle of more bandwidth is obtained compared to conventional .

A Multiscale Numerical Method for Poisson Problems in Some Ramified Domains with a Fractal Boundary

2006 ◽  
Vol 5 (3) ◽  
pp. 828-860 ◽  
Author(s):  
Yves Achdou ◽  
Christophe Sabot ◽  
Nicoletta Tchou
Keyword(s):  
Numerical Method ◽  
Fractal Boundary

ROUGHNESS EFFECT OF DIFFERENT GEOMETRIES ON MICRO GAS FLOWS BY LATTICE BOLTZMANN SIMULATION

2009 ◽  
Vol 20 (06) ◽  
pp. 953-966 ◽  
Author(s):  
CHAOFENG LIU ◽  
YUSHAN NI ◽  
YONG RAO
Keyword(s):  
Surface Roughness ◽  
Lattice Boltzmann ◽  
Experimental Studies ◽  
Resistance Coefficient ◽  
Lattice Boltzmann Model ◽  
Gas Flows ◽  
Fractal Boundary ◽  
Roughness Effects ◽  
Roughness Effect ◽  
Relative Roughness

The roughness effects of the gas flows of nitrogen and helium in microchannels with various relative roughnesses and different geometries are studied and analyzed by a lattice Boltzmann model. The shape of surface roughness is simulated to be square, sinusoidal, triangular, and fractal. Numerical computations compared with theoretical and experimental studies show that the roughness geometry is an important factor besides the relative roughness in the study of the effects of surface roughness. The fractal boundary presents a higher influence on the velocity field and the resistance coefficient than other regular boundaries at the same Knudsen number and relative roughness. In addition, the effects of rarefaction, compressibility, and roughness are strongly coupled, and the roughness effect should not be ignored in studying rarefaction and compressibility of the microchannel as the relative roughness increases.

Indeterminate sub-critical bifurcations in parametric resonance

1992 ◽  
Vol 438 (1904) ◽  
pp. 511-518 ◽  
Keyword(s):  
Parametric Resonance ◽  
Trivial Solution ◽  
Fractal Boundary ◽  
Parametrically Excited

In this paper we show that an indeterminate sub-critical bifurcation with an unpredictable outcome arises in typical parametrically excited systems. This occurs when the trivial solution is located on a fractal boundary as it loses its stability at a sub-critical bifurcation. Here, in the presence of even infinitesimal noise the outcome is indeterminate in the sense that we cannot predict on to which co-existing attractor the system will settle.

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