Related papers: On Intersecting IFS Fractals with Lines
Time-like linear dilaton backgrounds admit a classical solution that describes a closed folded string that is created at an instant. We refer to such strings as Instant Folded Strings (IFS). We study an exact worldsheet CFT description of…
Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…
Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…
Hadrons are composite objects made of quarks and gluons, and during a collision one can have several elementary interactions between the constituents. These elementary interactions, using an appropriate theoretical framework, can be related…
We discuss the problem of bounding the Fourier transforms of stationary measures of iterated function systems (IFSs) and how the pseudo-randomness of the IFS either due to arithmetic, algebraic or geometric reasons is reflected in the…
Motility-induced phase separation (MIPS) is a purely non-equilibrium phenomenon in which self-propelled particles phase separate without any attractive interactions. One surprising feature of MIPS is the emergence of polar, nematic, and…
Several important conjectures in Fractal Geometry can be summarised as follows: If the dimension of a self-similar measure in $\mathbb{R}$ does not equal its expected value, then the underlying iterated function system contains an exact…
This research focuses on the discovery and localization of hidden objects in the wild and serves unmanned systems. Through empirical analysis, infrared and visible image fusion (IVIF) enables hard-to-find objects apparent, whereas…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
For an even set of points in the plane, choose a max-sum matching, that is, a perfect matching maximizing the sum of Euclidean distances of its edges. For each edge of the max-sum matching, consider the ellipse with foci at the edge's…
The fitting of spectral lines is a common step in the analysis of line observations and simulations. However, the observational noise, the presence of multiple velocity components, and potentially large data sets make it a non-trivial task.…
Accurate frictional contact is critical in simulating the assembly of rod-like structures in the practical world, such as knots, hairs, flagella, and more. Due to their high geometric nonlinearity and elasticity, rod-on-rod contact remains…
This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…
We derive the effective potential for composite fields in a class of (quasi-) planar models with long-range interactions. This class of models can be relevant for high temperature superconductors and graphite. The fractal structure of the…
Strong collisional shocks in multi-ion plasmas are featured in many high-energy-density environments, including Inertial Confinement Fusion (ICF) implosions. However, their basic structure and its dependence on key parameters (e.g., the…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
This paper investigates proppant flow and transport in intersected fractures at angles typical for intersections of pre-existing and new hydraulic fractures. Proppant is small granular material, which is placed into hydraulic fractures…
This paper provides an alternative description for the fixed points of the fractal operator associated with a mixed possibly infinite iterated function system via a canonical projection type function. Some visual aspects of our results are…
In computer graphics, simplifying a polygonal mesh surface~$\mathcal{M}$ into a geometric proxy that maintains close conformity to~$\mathcal{M}$ is crucial, as it can significantly reduce computational demands in various applications. In…
Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act…