We introduce fractal liquids by generalizing classical liquids of integer dimensions d = 1, 2, 3 to a fractal dimension df . The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-integer dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid drop...

This paper considers fractal trees with self-similar side branching. The Tokunaga classification system for side branching is introduced, along with the Tokunaga self-similarity condition. Area filling (D = 2) and volume filling (D = 3) deterministic fractal tree constructions are introduced both with and without side branching. Applications to diffusion limited aggregation (DLA), actual draina...

nique for estimating the potential similarity of protein 3D shape is proposed. It is found tures of proteins are of self-similarity, such a phenomenon can be well described by imensions. We then adopt the size and the volume fractal dimensionality of proteins to the spatial complexity of the protein shape. Such quantitative measurement is helpful to earch space when we retrieve protein structur...

Fluctuations in the concentration of Brownian particles in one and two dimensions, or any reasonable measurement of the concentration such as in fluorescence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spectrum of the fluctuation S(omega) approximately omega-1/2 for diffusion in one dimension, approximately log omega in ...

The fractal antennas that have the multiband operation due to the self-similar property in fractal geometry, which plays a key role to create a fractal circular monopole patch antenna. The other important property that is, Space-filling property which actually determines the reduction in the size of the antenna. This property adds more electrical length in less volume which reduces the size of ...

in this present study, volume of fluid method in openfoam open source cfd package will be extended to consider phase change phenomena with modified model due to condensation and boiling processes. this model is suitable for the case in which both unsaturated phase and saturated phase are present and for beginning boiling and condensation process needn't initial interface. both phases (liqu...

Why does fractal image compression work? What properties must an image have for fractal block coders to work well? What is the implicit image model underlying fractal image compression? The behavior of fractal block coders is clear for deterministically self-similar structures. In this paper we examine the behavior of these coders on statistically self-similar structures. Speci cally, we examin...