On the discrete Peyrard-Bishop model of DNA: stationary solutions and stability

As a first step in the search of an analytical study of mechanical denaturation of DNA in terms of the sequence, we study stable, stationary solutions in the discrete, finite and homogeneous Peyrard-Bishop DNA model. We find and classify all the stationary solutions of the model, as well as analytic approximations of them, both in the continuum and in the discrete limits. Our results explain the structure of the solutions reported by Theodorakopoulos {\em et al.} [Phys. Rev. Lett. {\bf 93}, 258101 (2004)] and provide a way to proceed to the analysis of the generalized version of the model incorporating the genetic information.Comment: 15 pages, 12 figure

Recursiveness, Switching, and Fluctuations in a Replicating Catalytic Network

A protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the path rate, the numbers of molecules and species, three phases are found: fast switching state without recursive production, recursive production, and itinerancy between the above two states. The number distributions of the molecules in the recursive states are shown to be log-normal except for those species that form a core hypercycle, and are explained with the help of a heuristic argument.Comment: 4 pages (with 7 figures (6 color)), submitted to PR

Skeleton and fractal scaling in complex networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in-silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.Comment: 4 pages, 2 figures, final version published in PR

The role of tank-treading motions in the transverse migration of a spheroidal vesicle in a shear flow

The behavior of a spheroidal vesicle, in a plane shear flow bounded from one side by a wall, is analysed when the distance from the wall is much larger than the spheroid radius. It is found that tank treading motions produce a transverse drift away from the wall, proportional to the spheroid eccentricity and the inverse square of the distance from the wall. This drift is independent of inertia, and is completely determined by the characteristics of the vesicle membrane. The relative strength of the contribution to drift from tank-treading motions and from the presence of inertial corrections, is discussed.Comment: 16 pages, 1 figure, Latex. To appear on J. Phys. A (Math. Gen.

Unifying CP violations of quark and lepton sectors

A preliminary determination of the Dirac phase in the PMNS matrix is \dell\approx -\frac{\pi}{2}. A rather accurately determined Jarlskog invariant $J$ in the CKM matrix is close to the maximum. Since the phases in the CKM and PMNS matrices will be accurately determined in the future, it is an interesting problem to relate these two phases. This can be achieved in a families-unified grand unification if the weak CP violation is introduced spontaneously {\it \`a la} Froggatt and Nielsen at a high energy scale, where only one meaningful Dirac CP phase appears.Comment: 10 pages with 3 figure

The Algorithmic Origins of Life

Although it has been notoriously difficult to pin down precisely what it is that makes life so distinctive and remarkable, there is general agreement that its informational aspect is one key property, perhaps the key property. The unique informational narrative of living systems suggests that life may be characterized by context-dependent causal influences, and in particular, that top-down (or downward) causation -- where higher-levels influence and constrain the dynamics of lower-levels in organizational hierarchies -- may be a major contributor to the hierarchal structure of living systems. Here we propose that the origin of life may correspond to a physical transition associated with a shift in causal structure, where information gains direct, and context-dependent causal efficacy over the matter it is instantiated in. Such a transition may be akin to more traditional physical transitions (e.g. thermodynamic phase transitions), with the crucial distinction that determining which phase (non-life or life) a given system is in requires dynamical information and therefore can only be inferred by identifying causal architecture. We discuss some potential novel research directions based on this hypothesis, including potential measures of such a transition that may be amenable to laboratory study, and how the proposed mechanism corresponds to the onset of the unique mode of (algorithmic) information processing characteristic of living systems.Comment: 13 pages, 1 tabl

Neutron Halo Isomers in Stable Nuclei and their Possible Application for the Production of Low Energy, Pulsed, Polarized Neutron Beams of High Intensity and High Brilliance

We propose to search for neutron halo isomers populated via $\gamma$-capture in stable nuclei with mass numbers of about A=140-180 or A=40-60, where the $4s_{1/2}$ or $3s_{1/2}$ neutron shell model state reaches zero binding energy. These halo nuclei can be produced for the first time with new $\gamma$-beams of high intensity and small band width ($\le$ 0.1%) achievable via Compton back-scattering off brilliant electron beams thus offering a promising perspective to selectively populate these isomers with small separation energies of 1 eV to a few keV. Similar to single-neutron halo states for very light, extremely neutron-rich, radioactive nuclei \cite{hansen95,tanihata96,aumann00}, the low neutron separation energy and short-range nuclear force allows the neutron to tunnel far out into free space much beyond the nuclear core radius. This results in prolonged half lives of the isomers for the $\gamma$-decay back to the ground state in the 100 ps-$\mu$s range. Similar to the treatment of photodisintegration of the deuteron, the neutron release from the neutron halo isomer via a second, low-energy, intense photon beam has a known much larger cross section with a typical energy threshold behavior. In the second step, the neutrons can be released as a low-energy, pulsed, polarized neutron beam of high intensity and high brilliance, possibly being much superior to presently existing beams from reactors or spallation neutron sources.Comment: accepted for publication in Applied Physics

The stochastic Gross-Pitaevskii equation II

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al. (J. Phys. B 35,1555,(2002). The derivation does not rely on the concept of local energy and momentum conservation, and is based on a quasi-classical Wigner function representation of a "high temperature" master equation for a Bose gas, which includes only modes below an energy cutoff E_R that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provide noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation, and by the feasibility of its numerical implementation.Comment: 24 pages of LaTeX, one figur

Banking union in historical perspective: the initiative of the European Commission in the 1960s-1970s

This article shows that planning for the organization of EU banking regulation and supervision did not just appear on the agenda in recent years with discussions over the creation of the eurozone banking union. It unveils a hitherto neglected initiative of the European Commission in the 1960s and early 1970s. Drawing on extensive archival work, this article explains that this initiative, however, rested on a number of different assumptions, and emerged in a much different context. It first explains that the Commission's initial project was not crisis-driven; that it articulated the link between monetary integration and banking regulation; and finally that it did not set out to move the supervisory framework to the supranational level, unlike present-day developments