Reentrant Condensation of DNA induced by Multivalent Counterions

A theory of condensation and resolubilization of a dilute DNA solution with growing concentration of multivalent cations, N is suggested. It is based on a new theory of screening of a macroion by multivalent cations, which shows that due to strong cation correlations at the surface of DNA the net charge of DNA changes sign at some small concentration of cations N_0. DNA condensation takes place in the vicinity of N_0, where absolute value of the DNA net charge is small and the correlation induced short range attraction dominates the Coulomb repulsion. At N > N_0 positive DNA should move in the oppisite direction in an electrophoresis experiment. From comparison of our theory with experimental values of condensation and resolubilization thresholds for DNA solution containing Spe$^{4+}$, we obtain that N_0 = 3.2 mM and that the energy of DNA condensation per nucleotide is $0.07 k_B T$.Comment: 8 pages, 4 figures, references correcte

Exploring Vacuum Structure around Identity-Based Solutions

We explore the vacuum structure in bosonic open string field theory expanded around an identity-based solution parameterized by $a(>=-1/2)$. Analyzing the expanded theory using level truncation approximation up to level 20, we find that the theory has the tachyon vacuum solution for $a>-1/2$. We also find that, at $a=-1/2$, there exists an unstable vacuum solution in the expanded theory and the solution is expected to be the perturbative open string vacuum. These results reasonably support the expectation that the identity-based solution is a trivial pure gauge configuration for $a>-1/2$, but it can be regarded as the tachyon vacuum solution at $a=-1/2$.Comment: 12 pages, 5 figures; new numerical data up to level (20,60) included; Contribution to the proceedings of "Second International Conference on String Field Theory and Related Aspects" (Steklov Mathematical Institute, Moscow, Russia, April 12-19, 2009

Symmetry approach in boundary value problems

The problem of construction of the boundary conditions for nonlinear equations is considered compatible with their higher symmetries. Boundary conditions for the sine-Gordon, Jiber-Shabat and KdV equations are discussed. New examples are found for the Jiber-Shabat equation.Comment: 7 pages, LaTe