Fractals from genomes: exact solutions of a biology-inspired problem

This is a review of a set of recent papers with some new data added. After a brief biological introduction a visualization scheme of the string composition of long DNA sequences, in particular, of bacterial complete genomes, will be described. This scheme leads to a class of self-similar and self-overlapping fractals in the limit of infinitely long constotuent strings. The calculation of their exact dimensions and the counting of true and redundant avoided strings at different string lengths turn out to be one and the same problem. We give exact solution of the problem using two independent methods: the Goulden-Jackson cluster method in combinatorics and the method of formal language theory.Comment: 24 pages, LaTeX, 5 PostScript figures (two in color), psfi

Dimensions of fractals related to languages defined by tagged strings in complete genomes

A representation of frequency of strings of length K in complete genomes of many organisms in a square has led to seemingly self-similar patterns when K increases. These patterns are caused by under-represented strings with a certain "tag"-string and they define some fractals when K tends to infinite. The Box and Hausdorff dimensions of the limit set are discussed. Although the method proposed by Mauldin and Williams to calculate Box and Hausdorff dimension is valid in our case, a different and simpler method is proposed in this paper.Comment: 9 pages with two figure

Condensation and Evaporation of Mutually Repelling Particles :Steady states and limit cycles

We study condensation and evaporation of particles which repel each other, using a simple set of rules on a square lattice. Different results are obtained for a mobile and an immobile surface layer.A two point limit cycle is observed for high temperature and low pressure in both cases. Here the coverage oscillates between a high and a low value without ever reaching a steady state. The results for the immobile case depend in addition on the initial coverage.Comment: 8 pages, 3 figure

Three-dimensional Isotropic Droplets in Rydberg-dressed Bose Gases

We predict a scheme for the creation of isotropic three-dimensional droplets in Rydbeg-dressed Bose gases, which contain both repulsive contact interactions and attractive van der Waals interactions causing the quantum fluctuation effect non-negligible. We present detailed beyond mean-field calculations with Lee-Huang-Yang correction and demonstrate the existence of isotropic droplets under realistic experimental conditions. Stable droplets possess flat-top density distribution, and their chemical potentials decrease with the particle number expansion towarding a critical value. We distinguish droplets from bright solitons through peak density, width of condensate and quantum depletion calculations. We summarize a phase diagram of realizing droplets, and subsequently highlight the stability of droplets by real time evolution as well as collisions. Our work provides a novel platform for investigating excitation spectrum and superfluid nature of droplets

CCP-WSI Blind Test Series 3: OpenFOAM Simulation of Focused Wave Interaction with a Simplified Wave Energy Converter

This paper presents a numerical study of a simplified wave energy converter (WEC) with and without a moon-pool under focused wave conditions and the work presented corresponds to a contribution to the CCP-WSI Blind Test Series 3. The numerical model applies the overset mesh technique in order to deal with large amplitude motions induced by the focused wave groups. The generation of the incident wave group is first examined through a mesh convergence test and by comparing with the experimental data. Simulations are then carried out with the presence of the WEC. In total three wave conditions are considered, each with the same wave period but different wave height. Non-linear effects on the WEC motion are clearly shown when the wave steepness increases and wave over-topping occurs. Furthermore, the effects of the moon pool on the dynamics and kinematics of the WEC including the damping effects on pitch response are also discussed, where the WEC motion is compared for the case with and without a moon-pool under the same wave conditions

Universal bifurcation property of two- or higher-dimensional dissipative systems in parameter space: Why does 1D symbolic dynamics work so well?

The universal bifurcation property of the H\'enon map in parameter space is studied with symbolic dynamics. The universal-$L$ region is defined to characterize the bifurcation universality. It is found that the universal-$L$ region for relative small $L$ is not restricted to very small $b$ values. These results show that it is also a universal phenomenon that universal sequences with short period can be found in many nonlinear dissipative systems.Comment: 10 pages, figures can be obtained from the author, will appeared in J. Phys.

Chlorido[(E)-2-hydr­oxy-6-(isonicotinoyl­hydrazonometh­yl)phen­yl]mercury(II) monohydrate

The asymmetric unit of the title compound, [Hg(C13H10N3O2)Cl]·H2O, contains two independent mercury(II) complexes with slightly different conformations, related via a pseudo-inversion centre, and two water mol­ecules. The HgII atoms show a typical linear geometry to a C atom of the benzene ring and to a Cl atom. A benzene C and the azomethine N atom chelate the HgII atoms with weak intra­molecular Hg⋯N bonding distances of 2.735 (3) and 2.739 (3) Å, respectively. The resulting five-membered metallacycles are nearly coplanar with the benzene rings [dihedral angles = 0.9 (1) and 0.7 (1)°], while the pyridine rings make dihedral angles with the benzene units of 58.17 (1) and 56.58 (1)°. In the crystal structure, the HgII complexes are linked by hydr­oxy donor and pyridine acceptor groups into chains along [010]. The water mol­ecules connect the complexes through inter­molecular O—H⋯Ocarbon­yl bonds in the a-axis direction, and the azomethine H atoms donate towards the water O atoms, forming a three-dimensional network of inter­molecular O—H⋯N, O—H⋯O and N—H⋯O hydrogen bonds