Global transposable characteristics in the yeast complete DNA sequence

Global transposable characteristics in the complete DNA sequence of the Saccharomyces cevevisiae yeast is determined by using the metric representation and recurrence plot methods. In the form of the correlation distance of nucleotide strings, 16 chromosome sequences of the yeast, which are divided into 5 groups, display 4 kinds of the fundamental transposable characteristics: a short period increasing, a long quasi-period increasing, a long major value and hardly relevant.Comment: 19 pages, 5 figures, 5 table

Periodic correlation structures in bacterial and archaeal complete genomes

The periodic transference of nucleotide strings in bacterial and archaeal complete genomes is investigated by using the metric representation and the recurrence plot method. The generated periodic correlation structures exhibit four kinds of fundamental transferring characteristics: a single increasing period, several increasing periods, an increasing quasi-period and almost noincreasing period. The mechanism of the periodic transference is further analyzed by determining all long periodic nucleotide strings in the bacterial and archaeal complete genomes and is explained as follows: both the repetition of basic periodic nucleotide strings and the transference of non-periodic nucleotide strings would form the periodic correlation structures with approximately the same increasing periods.Comment: 23 pages, 6 figures, 2 table

Terminal thermocapillary migration of a droplet at small Reynolds numbers and large Marangoni numbers

In this paper, the overall steady-state momentum and energy balances in the thermocapillary migration of a droplet at small Reynolds numbers and large Marangoni numbers are investigated to confirm the quasi-steady state assumption of the system. The droplet is assumed to have a slight axisymmetric deformation from a sphere shape. It is shown that under the quasi-steady state assumption, the total momentum of the thermocapillary droplet migration system at small Reynolds numbers is conservative. The general solution of the steady momentum equations can be determined with its parameters depending on the temperature fields. However, a nonconservative integral thermal flux across the interface for the steady thermocapillary migration of the droplet at small Reynolds numbers and large Marangoni numbers is identified. The nonconservative integral thermal flux indicates that no solutions of the temperature fields exist for the steady energy equations. The terminal thermocapillary migration of the droplet at small Reynolds numbers and large Marangoni numbers cannot reach a steady state and is thus in an unsteady process

Terminal states of thermocapillary migration of a planar droplet at moderate and large Marangoni numbers

In this paper, thermocapillary migration of a planar droplet at moderate and large Marangoni numbers is investigated analytically and numerically. By using the dimension-analysis method, the thermal diffusion time scale is determined as the controlling one of the thermocapillary droplet migration system. During this time, the whole thermocapillary migration process is fully developed. By using the front-tracking method, the steady/unsteady states as the terminal ones at moderate/large Marangoni numbers are captured in a longer time scale than the thermal diffusion time scale. In the terminal states, the instantaneous velocity fields in the unsteady migration process at large Marangoni numbers have the forms of the steady ones at moderate Marangoni numbers. However, in view of the former instantaneous temperature fields, the surface tension of the top surface of the droplet gradually becomes the main component of the driving force on the droplet after the inflection point appears. It is different from that the surface tension of the bottom surface of the droplet is the main component of the driving force on the droplet for the latter ones. The physical mechanism of thermocapillary droplet migration can be described as the significance of the thermal convection around the droplet is higher than/just as the thermal conduction across the droplet at large/moderate Marangoni numbers.Comment: 8 pages, 6 figure

Extension Of Bertrand's Theorem And Factorization Of The Radial Schr\"odinger Equation

The Bertrand's theorem is extended, i.e. closed orbits still may exist for other central potentials than the power law Coulomb potential and isotropic harmonic oscillator. It is shown that for the combined potential $V(r)=W(r)+b/r^2$ ($W(r)=ar^{\nu}$), when (and only when) $W(r)$ is the Coulomb potential or isotropic harmonic oscillator, closed orbits still exist for suitable angular momentum. The correspondence between the closeness of classical orbits and the existence of raising and lowering operators derived from the factorization of the radial Schr\"odinger equation is investigated.Comment: 4 pages, 1 figug

Analysis of correlation structures in the Synechocystis PCC6803 genome

Transfer of nucleotide strings in the Synechocystis sp. PCC6803 genome is investigated to exhibit periodic and non-periodic correlation structures by using the recurrence plot method and the phase space reconstruction technique. The periodic correlation structures are generated by periodic transfer of several substrings in long periodic or non-periodic nucleotide strings embedded in the coding regions of genes. The non-periodic correlation structures are generated by non-periodic transfer of several substrings covering or overlapping with the coding regions of genes. In the periodic and non-periodic transfer, some gaps divide the long nucleotide strings into the substrings and prevent their global transfer. Most of the gaps are either the replacement of one base or the insertion/reduction of one base. In the reconstructed phase space, the points generated from two or three steps for the continuous iterative transfer via the second maximal distance can be fitted by two lines. It partly reveals an intrinsic dynamics in the transfer of nucleotide strings. Due to the comparison of the relative positions and lengths, the substrings concerned with the non-periodic correlation structures are almost identical to the mobile elements annotated in the genome. The mobile elements are thus endowed with the basic results on the correlation structures.Comment: 29 pages, 6 figure