相关论文: Self-Assembly of Discrete Self-Similar Fractals

Winfree (1998) showed that discrete Sierpinski triangles can self-assemble in the Tile Assembly Model. A striking molecular realization of this self-assembly, using DNA tiles a few nanometers long and verifying the results by atomic-force…

Tile-based self-assembly systems are capable of universal computation and algorithmically-directed growth. Systems capable of such behavior typically make use of "glue cooperation" in which the glues on at least $2$ sides of a tile must…

In this article, fractal concepts were used to explore the thermally evaporated potassium bromide thin films of different thicknesses 200, 300, and 500 nm respectively; grown on aluminium substrates at room temperature. The self-affine or…

Self-assembly of granular particles is of great interest in both applied and basic research. It is commonly observed that when randomly packed into a container, granular particles form disordered structures like glass. As the particles are…

Much is known in the analysis of a finitely ramified self-similar fractal when the fractal has a harmonic structure: a Dirichlet form which respects the self-similarity of a fractal. What is still an open question is when such structure…

In geometrically frustrated assemblies, equilibrium self-limitation manifests in the form of a minimum in the free energy per subunit at a finite, multi-subunit size which results from the competition between the elastic costs of…

This papers briefly reviews the progress in studying the long-lived filamentary structures of a skeletal form (namely, tubules and cartwheels, and their simple combinations) in electric discharges in various fusion devices. These include…

We use numerical simulations to show how noninteracting hard particles binding to a deformable elastic shell may self-assemble into a variety of linear patterns. This is a result of the nontrivial elastic response to deformations of shells.…

We give a generalization of Lagarias' formula for diffraction by ideal crystals, and we apply it to the lattice case, in preparation for addressing the problem of quasicrystals and complex dimensions posed by Lapidus and van Frankenhuijsen…

We study Minkowski contents and fractal curvatures of arbitrary self-similar tilings (constructed on a feasible open set of an IFS) and the general relations to the corresponding functionals for self-similar sets. In particular, we…

The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion (SALR) potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk.…

We consider a special type of self-similar sets, called fractal squares, and give a brief review on recent results and unsolved issues with an emphasis on their topological properties.

We extend Falconer's 1988 landmark result on the dimensions of self-affine fractals to encompass the dimensions of their projections, showing furthermore that their families of exceptional projections contain algebraic varieties which are…

A new kind of composite were manufactured by densification of co-crumpled aluminium and tantalum thin foils using close die compression. It was shown by optical micrography that its microstructure is highly interlocked. The morphology was…

The 2-Handed Assembly Model (2HAM) is a tile-based self-assembly model in which, typically beginning from single tiles, arbitrarily large aggregations of static tiles combine in pairs to form structures. The Signal-passing Tile Assembly…

In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale…

We make a detailed experimental study of the threshold for the self-organization of thermal 87Rb atoms coupled to a high-finesse cavity over a range of atom numbers and cavity detunings. We investigate the difference between probing with a…

The molecular self-assembly of various structures such as micelles and vesicles has been the subject of comprehensive studies. Recently, a new approach to design these structures, the frame-guided assembly, has been developed to progress…

In previous papers by A. Kameyama and by J. Kigami distances on fractals have been discussed having two different but similar properties. One property is that the maps defining the fractal are Lipschitz of prescribed constants less than 1,…

Self-assembly kinetics is usually described by approaches which assume that the shape of the aggregates has a definite form (e.g., spherical, cylindrical, cubic, etc), however that is unlikely to be the case in many finite-sized…