Veneziano Amplitudes, Spin Chains and String Models

In a series of recently published papers we reanalyzed the existing treatments of Veneziano and Veneziano-like amplitudes and the models associated with these amplitudes. In this work we demonstrate that the already obtained new partition function for these amplitudes can be exactly mapped into that for the Polychronakos-Frahm (P-F) spin chain model. This observation allows us to recover many of the existing string-theoretic models, including the most recent ones.Comment: 38 page

Entropically driven transition to a liquid-crystalline polymer globule

A self-consistent-field theory (SCFT) in the grand canonical ensemble formulation is used to study transitions in a helix-coil multiblock copolymer globule. The helices are modeled as stiff rods. In addition to the established coil-globule transition we show for the first time that, even without explicit rod-rod alignment interaction, the system undergoes a transition to a nematic liquid-crystalline (LC) globular state. The LC-globule formation is driven by the hydrophobic helical segment attraction and the anisotropy of the globule surface energy. The full phase diagram of the copolymer was calculated. It discriminates between an open chain, amorphous globule and LC-globule. This model provides a relatively simple example of the interplay between secondary and tertiary structures in homopolypeptides. Moreover, it gives a simple explanation for the formation of helix bundles in certain globular proteins.Comment: 5 pages, 5 figures, submitted to Europhys. Let

A transfer matrix approach to the enumeration of plane meanders

A closed plane meander of order $n$ is a closed self-avoiding curve intersecting an infinite line $2n$ times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on transfer matrix methods, for the enumeration of plane meanders. While the algorithm has exponential complexity, its rate of growth is much smaller than that of previous algorithms. The algorithm is easily modified to enumerate various systems of closed meanders, semi-meanders, open meanders and many other geometries.Comment: 13 pages, 9 eps figures, to appear in J. Phys.

Guest charges in an electrolyte: renormalized charge, long- and short-distance behavior of the electric potential and density profile

We complement a recent exact study by L. Samaj on the properties of a guest charge $Q$ immersed in a two-dimensional electrolyte with charges $+1/-1$. In particular, we are interested in the behavior of the density profiles and electric potential created by the charge and the electrolyte, and in the determination of the renormalized charge which is obtained from the long-distance asymptotics of the electric potential. In Samaj's previous work, exact results for arbitrary coulombic coupling $\beta$ were obtained for a system where all the charges are points, provided $\beta Q<2$ and $\beta < 2$. Here, we first focus on the mean field situation which we believe describes correctly the limit $\beta\to 0$ but $\beta Q$ large. In this limit we can study the case when the guest charge is a hard disk and its charge is above the collapse value $\beta Q>2$. We compare our results for the renormalized charge with the exact predictions and we test on a solid ground some conjectures of the previous study. Our study shows that the exact formulas obtained by Samaj for the renormalized charge are not valid for $\beta Q>2$, contrary to a hypothesis put forward by Samaj. We also determine the short-distance asymptotics of the density profiles of the coions and counterions near the guest charge, for arbitrary coulombic coupling. We show that the coion density profile exhibit a change of behavior if the guest charge becomes large enough ($\beta Q\geq 2-\beta$). This is interpreted as a first step of the counterion condensation (for large coulombic coupling), the second step taking place at the usual Manning--Oosawa threshold $\beta Q=2$

Bimodal distribution function of a 3d wormlike chain with a fixed orientation of one end

We study the distribution function of the three dimensional wormlike chain with a fixed orientation of one chain end using the exact representation of the distribution function in terms of the Green's function of the quantum rigid rotator in a homogeneous external field. The transverse 1d distribution function of the free chain end displays a bimodal shape in the intermediate range of the chain lengths ($1.3L_{p},...,3.5L_{p}$). We present also analytical results for short and long chains, which are in complete agreement with the results of previous studies obtained using different methods.Comment: 6 pages, 3 figure

Self- generated disorder and structural glass formation in homopolymer globules

We have investigated the interrelation between the spin glasses and the structural glasses. Spin glasses in this case are random magnets without reflection symmetry (e.g. $p$ - spin interaction spin glasses and Potts glasses) which contain quenched disorder, whereas the structural glasses are here exemplified by the homopolymeric globule, which can be viewed as a liquid of connected molecules on nano scales. It is argued that the homopolymeric globule problem can be mapped onto a disorder field theoretical model whose effective Hamiltonian resembles the corresponding one for the spin glass model. In this sense the disorder in the globule is self - generated (in contrast to spin glasses) and can be related with competitive interactions (virial coefficients of different signs) and the chain connectivity. The work is aimed at giving a quantitative description of this analogy. We have investigated the phase diagram of the homopolymeric globule where the transition line from the liquid to glassy globule is treated in terms of the replica symmetry breaking paradigm. The configurational entropy temperature dependence is also discussed.Comment: 22 pages, 4 figures, submitted to Phys. Rev.

Measurement of the K+→μ+νμγK^+\rightarrow{\mu^+}{\nu_{\mu}}{\gamma} decay form factors in the OKA experiment

A precise measurement of the vector and axial-vector form factors difference $F_V-F_A$ in the $K^+\rightarrow{\mu^+}{\nu_{\mu}}{\gamma}$ decay is presented. About 95K events of $K^+\rightarrow{\mu^+}{\nu_{\mu}}{\gamma}$ are selected in the OKA experiment. The result is $F_V-F_A=0.134\pm0.021(stat)\pm0.027(syst)$. Both errors are smaller than in the previous $F_V-F_A$ measurements.Comment: 9 pages, 8 figure