Related papers: The inverse problem for fractal curves solved with…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship…
This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to…
The paper deals with the mathematical - numerical analysis of the Mandelbrot equation extended by the dynamic continuous term. The possibilities of generation of fractal patterns with the mathematical form, defined in such a manner, were…
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…
Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness is studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a new boundary…
Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…
The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing…
We establish a correspondence between Pavlovian conditioning processes and fractals. The association strength at a training trial corresponds to a point in a disconnected set at a given iteration level. In this way, one can represent a…
We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…
We briefly review a number of important recent experimental and theoretical developments in the field of dynamic fracture. Topics include experimental validation of the equations of motion for straight tensile cracks (in both infinite media…
In this paper, we systematically review a series of effective methods for studying the qualitative properties of solutions to fractional equations. Beginning with the pioneering extension method and the method of moving planes in integral…
We study fractal measures on Euclidean space through the dynamics of "zooming in" on typical points. The resulting family of measures (the "scenery"), can be interpreted as an orbit in an appropriate dynamical system which often…
We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra…