相关论文: Self-Assembly of Discrete Self-Similar Fractals
In this paper we investigate $p$-adic self-similar sets and $p$-adic self-similar measures. We show that $p$-adic self-similar sets are $p$-adic path set fractals, and that the converse is not necessarily true. For $p$-adic self-similar…
We prove the computational weakness of a model of tile assembly that has so far resisted many attempts of formal analysis or positive constructions. Specifically, we prove that, in Winfree's abstract Tile Assembly Model, when restricted to…
The principle of fractal stiffness self-similarity is expanded to encompass structures with several differently-scaled contributors to the total stiffness matrix. The generalized principle is applied to solve the problem of a fractal…
Self-limiting assembly of particles represents the state-of-the-art controllability in nanomanufacturing processes where the assembly stops at a designated stage1,2, providing a desirable platform for applications requiring delicate…
In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of…
A crystal lattice, when confined to the surface of a cylinder, must have a periodic structure that is commensurate with the cylinder circumference. This constraint can frustrate the system, leading to oblique crystal lattices or to…
The self-assembly of particles into organized structures is a key feature of living organisms and a major engineering challenge. While it may proceed through the binding of perfectly matched, puzzle-pieces-like particles, many other…
Interaction between dipolar forces, such as permanent magnets, generally leads to the formation of one-dimensional chains and rings. We investigated whether it was possible to let dipoles self-assemble into three-dimensional structures by…
The possibility to align and organize faceted particles in the bulk offers intriguing possibilities for the design and discovery of materials and architectures exhibiting novel functional properties. The growth of ice crystals can be used…
We explore the use of templated self-assembly to facilitate the formation of complex target structures made from patchy particles. First, we consider the templating of high-symmetry shell structures around a spherical core particle. We find…
Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under…
Understanding protein self-assembly is important for many biological and industrial processes. Proteins can self-assemble into crystals, filaments, gels, and other amorphous aggregates. The final forms include virus capsids and condensed…
In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the…
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
We present ultra-shallow diffusion profiles performed by short-time diffusion of boron from the gas phase using controlled surface injection of self-interstitials and vacancies into the n-type Si(100) wafers. The diffusion profiles of this…
Au nanoparticles with near perfect monodispersity in shape and size self-assemble, very slowly and at room temperature, on polystyrene films for film thickness < 4R_{g}$, R_{g} being unperturbed polymer gyration radius. Nanoparticle shape…
Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…
Protein aggregation in the form of amyloid fibrils has important biological and technological implications. Although the self-assembly process is highly efficient, aggregates not in the fibrillar form would also occur and it is important to…
We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to…