In this work, the impact of a magnetic field on the onset of the Jeffrey fluid convection through a porous medium is investigated theoretically. The layer of Jeffrey fluid is heated from below and is operated by a consistent upright magnetic field. Using the normal mode procedure, a dispersion equation is obtained analytically and this dispersion relation is utilized to derive the critical conditions for the onset of stationary and oscillatory patterns of convection. The results reveal that the stability of the system diminished with the augmentation of the Jeffrey parameter, while an opposite result is obtained with magnetic field parameters (magnetic Chandrasekhar–Darcy number and magnetic Prandtl number). The size of convective cells decreases with Jeffrey and magnetic field parameters. It is also found that the existence of a magnetic field indicates the possibility of the survival of the oscillatory mode of convection.

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A double strand DNA has a double helical structure and it is modeled by a thin long twisted ribbon fixed at the both ends. A DNA-link is a topological model of such a DNA segment in the nuclear of a eukaryotic cell. In the cell cycle, the DNA is replicated and distributed into new cells. The complicated replication process follows the semi-conservative scheme in which each backbone string is preserved in the replicated DNA. This is interpreted in terms of splitting process of the DNA-link. In order to split the DNA-link, unknotting operations are required. This paper presents a recursive unknotting operations, which efficiently reduce the number of twistings.

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A DNA replicon is modeled by a special type of 2-component link, called a DNA-link, in which two circles form a double helix around a trivial center core curve. The DNA replication process is semi-conservative, which is interpreted as a splitting process of the DNA-link. To split this non-trivial link, the linking number must become zero, and thus an unknotting operation is necessary. Some families of enzymes act as the unknotting operation. The present paper considers two topological problems; one is to know how the linking number is reduced and the other, how the enzymes are allocated at appropriate places. For the first problem, we suggest a reduction system of the linking number of a DNA-link. From this system, the number of repetitions of the procedure is obtained and this could be reduced when the DNA is previously relaxed by type I topoisomerases. For the second problem, we propose a possible conformation of the DNA-link in which the unknotting operation does not change the knot type of the core curve but decreases the writhe. This conformation could allocate type II topoisomerases to appropriate places. These models suggest that the combination of type I and type II topoisomerases efficiently reduces the linking number and it is possible to allocate enzymes by the conformation of DNA strands.