Vortices and chirality of magnetostatic modes in quasi-2D ferrite disk particles

In this paper we show that the vortex states can be created not only in magnetically soft "small" (with the dipolar and exchange energy competition) cylindrical dots, but also in magnetically saturated "big" (when the exchange is neglected) cylindrical dots. A property associated with a vortex structure becomes evident from an analysis of confinement phenomena of magnetic oscillations in a ferrite disk with a dominating role of magnetic-dipolar (non-exchange-interaction) spectra. In this case the scalar (magnetostatic-potential) wave functions may have a phase singularity in a center of a dot. A non-zero azimuth component of the flow velocity demonstrates the vortex structure. The vortices are guaranteed by the chiral edge states of magnetic-dipolar modes in a quasi-2D ferrite disk

Ribbon polymers in poor solvents: layering transitions in annular and tubular condensates

We study the structures of a ribbon or ladder polymer immersed in poor solvents. The anisotropic bending rigidity coupled with the surface tension leads ribbon polymers to spontaneous formation of highly anisotropic condensates in poor solvents. Unlike ordinary flexible polymers these condensates undergo a number of distinct layering transitions as a function of chain length or solvent quality, and the size of condensates becomes non-monotonic function of chain length. We show that the fluctuations of the condensates are in general small and these condensates are stable.Comment: 5 pages, 5 figures, visulaize missing figure number

Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro- and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q->infinity. It is shown that the highest power of the Kauffman invariant is correlated with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The obtained results are compared to the probability distribution of the minimum energy of a Potts system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references added

Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach

Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1, \quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, are discussed. For the semilinear heat equation $u_t= \Delta u+ u^p$, various blow-up patterns were under scrutiny since 1980s, while the case of higher-order diffusion was studied much less, regardless a wide range of its application.Comment: 41 pages, 27 figure

Kinetics and thermodynamics of salt-dependent T7 gene 2.5 protein binding to single- and double-stranded DNA

Bacteriophage T7 gene 2.5 protein (gp2.5) is a single-stranded DNA (ssDNA)-binding protein that has essential roles in DNA replication, recombination and repair. However, it differs from other ssDNA-binding proteins by its weaker binding to ssDNA and lack of cooperative ssDNA binding. By studying the rate-dependent DNA melting force in the presence of gp2.5 and its deletion mutant lacking 26 C-terminal residues, we probe the kinetics and thermodynamics of gp2.5 binding to ssDNA and double-stranded DNA (dsDNA). These force measurements allow us to determine the binding rate of both proteins to ssDNA, as well as their equilibrium association constants to dsDNA. The salt dependence of dsDNA binding parallels that of ssDNA binding. We attribute the four orders of magnitude salt-independent differences between ssDNA and dsDNA binding to nonelectrostatic interactions involved only in ssDNA binding, in contrast to T4 gene 32 protein, which achieves preferential ssDNA binding primarily through cooperative interactions. The results support a model in which dimerization interactions must be broken for DNA binding, and gp2.5 monomers search dsDNA by 1D diffusion to bind ssDNA. We also quantitatively compare the salt-dependent ssDNA- and dsDNA-binding properties of the T4 and T7 ssDNA-binding proteins for the first time