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 violent relaxation in stellar systems

We discuss the statistical mechanics of violent relaxation in stellar systems following the pioneering work of Lynden-Bell (1967). The solutions of the gravitational Vlasov-Poisson system develop finer and finer filaments so that a statistical description is appropriate to smooth out the small-scales and describe the ``coarse-grained'' dynamics. In a coarse-grained sense, the system is expected to reach an equilibrium state of a Fermi-Dirac type within a few dynamical times. We describe in detail the equilibrium phase diagram and the nature of phase transitions which occur in self-gravitating systems. Then, we introduce a small-scale parametrization of the Vlasov equation and propose a set of relaxation equations for the coarse-grained dynamics. These relaxation equations, of a generalized Fokker-Planck type, are derived from a Maximum Entropy Production Principle (MEPP). We make a link with the quasilinear theory of the Vlasov-Poisson system and derive a truncated model appropriate to collisionless systems subject to tidal forces. With the aid of this kinetic theory, we qualitatively discuss the concept of ``incomplete relaxation'' and the limitations of Lynden-Bell's theory

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

Ultramafic vegetation and soils in the circumboreal region of the Northern Hemisphere

The paper summarizes literature on climate, soil chemistry, vegetation and metal accumulation by plants found on ultramafic substrata in the circumboreal zone (sensu Takhtajan, Floristic regions of the world, 1986) of the Northern Hemisphere. We present a list of 50 endemic species and 18 ecotypes obligate to ultramafic soils from the circumboreal region of Holarctic, as well as 30 and 2 species of Ni and Zn hyperaccumulators, respectively. The number of both endemics and hyperaccumulators are markedly lower compared to that of the Mediterranean and tropical regions. The diversity of plant communities on ultramafics soils of the circumboral region is also described. The underlying causes for the differences of ultramafic flora between arctic, cold, cool temperate and Mediterranean and tropical regions are also discussed. © 2018, The Ecological Society of Japan

An evolution criterion for gravitational systems

An evolution criterion is established for weakly-coupled gravitational systems without statistical inhomogeneities. Boltzmann's H decreases, without however approaching a limiting value. The evolution of the velocity distribution is towards a maxwellian, but the approach is deflected by an instability of the maxwellian distributions themselves. The velocity dispersion increases monotonically as new spatial correlations are created.Haggerty M. J., Severne G. An evolution criterion for gravitational systems. In: Bulletin de la Classe des sciences, tome 60, 1974. pp. 226-236

Correlation dynamics for the inhomogeneous anharmonic solid

Synopsis. — The correlation dynamics analysis for the inhomogeneous anharmonic solid is undertaken. The evolution equations for the reduced density matrices deriving from the von Neumann-Liouville equation are studied using a diagram technique. It is shown that the definition of the correlations depends upon the wavevector of the deformation field produced in the lattice. For the zero sound regime the usual cluster definition of the correlations applies. In the hydrodynamic limit of first sound, certain clusters are to be considered as vacuum states and the correlations must accordingly be redefined. The equations of evolution for the one-and two-phonon vacuum states are obtained to order λ2 for the zero and first sound regimes.Van Calck J., Severne G. Correlation dynamics for the inhomogeneous anharmonic solid. In: Bulletin de la Classe des sciences, tome 61, 1975. pp. 40-62