Relaxation processes in one-dimensional self-gravitating many-body systems

Though one dimensional self-gravitating $N$-body systems have been studied for three decade, the nature of relaxation was still unclear. There were inconsistent results about relaxation time; some initial state relaxed in the time scale $T\sim N\,t_c$, but another state did not relax even after $T\sim N^2\,t_c$, where $t_c$ is the crossing time. The water-bag distribution was believed not to relax after $T\sim N^2\,t_c$. In our previous paper, however, we found there are two different relaxation times in the water-bag distribution;in the faster relaxation ( microscopic relaxation ) the equipartition of energy distribution is attains but the macroscopic distribution turns into the isothermal distribution in the later relaxation (macroscopic relaxation). In this paper, we investigated the properties of the two relaxation. We found that the microscopic relaxation time is $T\sim N\,t_c$, and the macroscopic relaxation time is proportional to $N\,t_c$, thus the water-bag does relax. We can see the inconsistency about the relaxation times is resolved as that we see the two different aspect of relaxations. Further, the physical mechanisms of the relaxations are presented.Comment: 11 pages, uuencoded, compressed Postscript, no figure, figures available at ftp://ferio.mtk.nao.ac.jp/pub/tsuchiya/Tsuchiya95.tar.g

Quasi-equilibria in one-dimensional self-gravitating many body systems

The microscopic dynamics of one-dimensional self-gravitating many-body systems is studied. We examine two courses of the evolution which has the isothermal and stationary water-bag distribution as initial conditions. We investigate the evolution of the systems toward thermal equilibrium. It is found that when the number of degrees of freedom of the system is increased, the water-bag distribution becomes a quasi-equilibrium, and also the stochasticity of the system reduces. This results suggest that the phase space of the system is effectively not ergodic and the system with large degreees of freedom approaches to the near-integrable one.Comment: 21pages + 7 figures (available upon request), revtex, submitted to Physical Review

Quasilinear theory of the 2D Euler equation

We develop a quasilinear theory of the 2D Euler equation and derive an integro-differential equation for the evolution of the coarse-grained vorticity. This equation respects all the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel. We show under which hypothesis we can derive a H-theorem for the Fermi-Dirac entropy and make the connection with statistical theories of 2D turbulence.Comment: 4 page

Gene transfer into hepatocytes using asialoglycoprotein receptor mediated endocytosis of DNA complexed with an artificial tetra-antennary galactose ligand

We have constructed an artificial ligand for the hepatocyte-specific asialoglycoprotein receptor for the purpose of generating a synthetic delivery system for DNA. This ligand has a tetra-antennary structure, containing four terminal galactose residues on a branched carrier peptide. The carbohydrate residues of this glycopeptide were introduced by reductive coupling of lactose to the alpha- and epsilon-amino groups of the two N-terminal lysines on the carrier peptide. The C-terminus of the peptide, containing a cysteine separated from the branched N-terminus by a 10 amino acid spacer sequence, was used for conjugation to 3-(2-pyridyldithio)propionate-modified polylysine via disulfide bond formation. Complexes containing plasmid DNA bound to these galactose-polylysine conjugates have been used for asialoglycoprotein receptor-mediated transfer of a luciferase gene into human (HepG2) and murine (BNL CL.2) hepatocyte cell lines. Gene transfer was strongly promoted when amphipathic peptides with pH-controlled membrane-disruption activity, derived from the N-terminal sequence of influenza virus hemagglutinin HA-2, were also present in these DNA complexes. Thus, we have essentially borrowed the small functional domains of two large proteins, asialoglycoprotein and hemagglutinin, and assembled them into a supramolecular complex to generate an efficient gene-transfer system

Statistical mechanics of two-dimensional vortices and stellar systems

The formation of large-scale vortices is an intriguing phenomenon in two-dimensional turbulence. Such organization is observed in large-scale oceanic or atmospheric flows, and can be reproduced in laboratory experiments and numerical simulations. A general explanation of this organization was first proposed by Onsager (1949) by considering the statistical mechanics for a set of point vortices in two-dimensional hydrodynamics. Similarly, the structure and the organization of stellar systems (globular clusters, elliptical galaxies,...) in astrophysics can be understood by developing a statistical mechanics for a system of particles in gravitational interaction as initiated by Chandrasekhar (1942). These statistical mechanics turn out to be relatively similar and present the same difficulties due to the unshielded long-range nature of the interaction. This analogy concerns not only the equilibrium states, i.e. the formation of large-scale structures, but also the relaxation towards equilibrium and the statistics of fluctuations. We will discuss these analogies in detail and also point out the specificities of each system.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002