What is Dynamics in Quantum Gravity?

The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen internal degree of freedom, the so called internal clock. We investigate the way in which the choice of internal clock determines the quantum dynamics and how much different quantum dynamics induced by different clocks are. We develop our method of comparison by extending the Hamilton-Jacobi theory of contact transformations to include a new type of transformations which transform both the canonical variables and the internal clock. We employ our method to study the quantum dynamics of the Friedmann-Lemaitre model and obtain semiclassical corrections to the classical dynamics, which depend on the choice of internal clock. For a unique quantisation map we find the abundance of inequivalent semiclassical corrections induced by quantum dynamics taking place in different internal clocks. It follows that the concepts like minimal volume, maximal curvature and the number of quantum bounces, often used to describe quantum effects in cosmological models, depend on the choice of internal clock.Comment: 14 pages, 6 figure

Dynamics of Internal Models in Game Players

A new approach for the study of social games and communications is proposed. Games are simulated between cognitive players who build the opponent's internal model and decide their next strategy from predictions based on the model. In this paper, internal models are constructed by the recurrent neural network (RNN), and the iterated prisoner's dilemma game is performed. The RNN allows us to express the internal model in a geometrical shape. The complicated transients of actions are observed before the stable mutually defecting equilibrium is reached. During the transients, the model shape also becomes complicated and often experiences chaotic changes. These new chaotic dynamics of internal models reflect the dynamical and high-dimensional rugged landscape of the internal model space.Comment: 19 pages, 6 figure

The Internal Dynamics of Globular Clusters

Galactic globular clusters are ancient building blocks of our Galaxy. They represent a very interesting family of stellar systems in which some fundamental dynamical processes have been taking place for more than 10 Gyr, but on time scales shorter than the age of the universe. In contrast with galaxies, these star clusters represent unique laboratories for learning about two-body relaxation, mass segregation from equipartition of energy, stellar collisions, stellar mergers, core collapse, and tidal disruption. This review briefly summarizes some of the tremendous developments that have taken place during the last two decades. It ends with some recent results on tidal tails around galactic globular clusters and on a very massive globular cluster in M31.Comment: An invited review (32 pages, 7 figures) in "The Chaotic Universe: Theory, Observations, Computer Experiments", Proceedings of the ICRA Rome-Pescara workshop, eds. V.G. Gurzadyan and R. Ruffini (Singapore: World Sci.), in pres

Mathematical modelling of internal HIV dynamics

We study a mathematical model for the viral dynamics of HIV in an infected individual in the presence of HAART. The paper starts with a literature review and then formulates the basic mathematical model. An expression for R0, the basic reproduction number of the virus under steady state application of HAART, is derived followed by an equilibrium and stability analysis. There is always a disease-free equilibrium (DFE) which is globally asymptotically stable for R0 1 then some simulations will die out whereas others will not. Stochastic simulations suggest that if R0 > 1 those which do not die out approach a stochastic quasi-equilibrium consisting of random uctuations about the non-trivial deterministic equilibrium levels, but the amplitude of these uctuations is so small that practically the system is at the non-trivial equilibrium. A brief discussion concludes the paper

Dynamics of active membranes with internal noise

We study the time-dependent height fluctuations of an active membrane containing energy-dissipating pumps that drive the membrane out of equilibrium. Unlike previous investigations based on models that neglect either curvature couplings or random fluctuations in pump activities, our formulation explores two new models that take both of these effects into account. In the first model, the magnitude of the nonequilibrium forces generated by the pumps is allowed to fluctuate temporally. In the second model, the pumps are allowed to switch between "on" and "off" states. We compute the mean squared displacement of a membrane point for both models, and show that they exhibit distinct dynamical behaviors from previous models, and in particular, a superdiffusive regime specifically arising from the shot noise.Comment: 7 pages, 4 figure

Solar neutrinos, helioseismology and the solar internal dynamics

Neutrinos are fundamental particles ubiquitous in the Universe. Their properties remain elusive despite more than 50 years of intense research activity. In this review we remind the reader of the noticeable properties of these particles and of the stakes of the solar neutrino puzzle. The Standard Solar Model triggered persistent efforts in fundamental Physics to predict the solar neutrino fluxes, and its constantly evolving predictions have been regularly compared to the detected neutrino signals. Anticipating that this standard model could not reproduce the internal solar dynamics, a SEismic Solar Model was developed which enriched theoretical neutrino flux predictions with in situ observation of acoustic waves propagating in the Sun. This review reminds the historical steps, from the pioneering Homestake detection, the GALLEX- SAGE captures of the first pp neutrinos and emphasizes the importance of the Superkamiokande and SNO detectors to demonstrate that the solar-emitted electronic neutrinos are partially transformed into other neutrino flavors before reaching the Earth. The success of BOREXINO in detecting the 7 Be neutrino signal justifies the building of a new generation of detectors to measure the entire solar neutrino spectrum. A coherent picture emerged from neutrino physics and helioseismology. Today, new paradigms take shape: determining the masses of neutrinos and the research on the Sun is focusing on the dynamical aspects and on signature of dark matter. The third part of the review is dedicated to this prospect. The understanding of the crucial role of both rotation and magnetism in solar physics benefit from SoHO, SDO, and PICARD space observations. For now, the particle and stellar challenges seem decoupled, but this is only a superficial appearance. The development of asteroseismology shows the far-reaching impact of Neutrino and Stellar Astronomy.Comment: 60 pages, 12 figures Invited review in press in Report on Progress in Physic

Diversity, Stability, Recursivity, and Rule Generation in Biological System: Intra-inter Dynamics Approach

Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for the differentiation provides the diversity and stability of cell society. Relevance of the theory to cell biology is discussed.Comment: 19 pages, Int.J. Mod. Phes. B (in press

Internal dynamics around static-deformation FEM states

Constant velocity or constant force FEM solutions are static-deformation states, where the elastic deformation is stationary. These are the typical operation conditions. Time-dependence, or fluctuations, of the static-deformation states are treated as perturbations, leading to a fast-converging expansion, for typical operation conditions, in which the time-scale of the input force is slower than the internal dynamics

Internal dynamics of the galaxy cluster Abell 959

The connection of cluster mergers with the presence of extended, diffuse radio sources in galaxy clusters is still being debated. In this paper we aim to obtain new insights into the internal dynamics of Abell 959, showing evidence of a diffuse radio source, analyzing velocities and positions of member galaxies. Our analysis is based on redshift data for 107 galaxies in the cluster field acquired at the Telescopio Nazionale Galileo. We also use photometric data from the Sloan Digital Sky Survey (Data Release 6). We combine galaxy velocities and positions to select 81 galaxies recognized as cluster members and determine global dynamical properties. We analyze the cluster searching for substructures by using several statistical methods. We also study the 2D galaxy distribution in the field of the cluster. We compare our results with those from X-ray and gravitational lensing analyses. We estimate a cluster redshift of z=0.2883 +/- 0.0004. We detect an NE high velocity group at 5' from the cluster center with a relative line--of--sight (LOS) velocity of ~ +1900 km/s with respect to the main system. We also detect a central, dense structure elongated along the SE--NW direction likely connected with the two dominant galaxies and their surrounding cores. This elongated central structure is probably the trace of an old cluster merger. The LOS velocity dispersion of galaxies is very high (1025 (-75/+104) km/s). The virial mass is M(<R=1.48 Mpc)= 1.15 (-0.19/+0.25) Msun. Our results suggest that this cluster is forming along two main directions of mass accretion and show the typical characteristics of radio clusters; i.e., it is very massive and shows a young dynamical state. However, deeper radio observations are needed to clarify the nature of the diffuse radio emission in Abell 959.Comment: 12 pages, 13 figures, 3 tables. Accepted for publication on Astronomy and Astrophysic

Symmetric Space Sigma-model Dynamics: Internal Metric Formalism

For the symmetric space sigma model in the internal metric formalism we explicitly construct the lagrangian in terms of the axions and the dilatons of the solvable Lie algebra gauge and then we exactly derive the axion-dilaton field equations.Comment: 10 page