Self-similar Model Research Articles

EVOLUTION OF SHOCKS AND TURBULENCE IN MAJOR CLUSTER MERGERS

We performed a set of cosmological simulations of major mergers in galaxy clusters to study the evolution of merger shocks and the subsequent injection of turbulence in the post-shock region and in the intra-cluster medium (ICM). The computations were done with the grid-based, adaptive mesh refinement hydro code Enzo, using an especially designed refinement criteria for refining turbulent flows in the vicinity of shocks. A substantial amount of turbulence energy is injected in the ICM due to major merger. Our simulations show that the shock launched after a major merger develops an ellipsoidal shape and gets broken by the interaction with the filamentary cosmic web around the merging cluster. The size of the post-shock region along the direction of shock propagation is about 300 kpc h^-1, and the turbulent velocity dispersion in this region is larger than 100 km s^-1. Scaling analysis of the turbulence energy with the cluster mass within our cluster sample is consistent with M^(5/3), i.e. the scaling law for the thermal energy in the self-similar cluster model. This clearly indicates the close relation between virialization and injection of turbulence in the cluster evolution. We found that the ratio of the turbulent to total pressure in the cluster core within 2 Gyr after the major merger is larger than 10%, and it takes about 4 Gyr to get relaxed, which is substantially longer than typically assumed in the turbulent re-acceleration models, invoked to explain the statistics of observed radio halos. Striking similarities in the morphology and other physical parameters between our simulations and the "symmetrical radio relics" found at the periphery of the merging cluster A3376 are finally discussed. In particular, the interaction between the merger shock and the filaments surrounding the cluster could explain the presence of "notch-like" features at the edges of the double relics.

Self-similar spherical collapse with tidal torque

$N$-body simulations have revealed a wealth of information about dark matter halos; however, their results are largely empirical. Using analytic means, we attempt to shed light on simulation results by generalizing the self-similar secondary infall model to include tidal torque. In this first of two papers, we describe our halo formation model and compare our results to empirical mass profiles inspired by $N$-body simulations. Each halo is determined by four parameters. One parameter sets the mass scale and the other three define how particles within a mass shell are torqued throughout evolution. We choose torque parameters motivated by tidal torque theory and $N$-body simulations and analytically calculate the structure of the halo in different radial regimes. We find that angular momentum plays an important role in determining the density profile at small radii. For cosmological initial conditions, the density profile on small scales is set by the time rate of change of the angular momentum of particles as well as the halo mass. On intermediate scales, however, $\ensuremath{\rho}\ensuremath{\propto}{r}^{\ensuremath{-}2}$, while $\ensuremath{\rho}\ensuremath{\propto}{r}^{\ensuremath{-}3}$ close to the virial radius.

Velocity structure of self-similar spherically collapsed halos

Using a generalized self-similar secondary infall model, which accounts for tidal torques acting on the halo, we analyze the velocity profiles of halos in order to gain intuition for N-body simulation results. We analytically calculate the asymptotic behavior of the internal radial and tangential kinetic energy profiles in different radial regimes. We then numerically compute the velocity anisotropy and pseudo-phase-space density profiles and compare them to recent N-body simulations. For cosmological initial conditions, we find both numerically and analytically that the anisotropy profile asymptotes at small radii to a constant set by model parameters. It rises on intermediate scales as the velocity dispersion becomes more radially dominated and then drops off at radii larger than the virial radius where the radial velocity dispersion vanishes in our model. The pseudo-phase-space density is universal on intermediate and large scales. However, its asymptotic slope on small scales depends on the halo mass and on how mass shells are torqued after turnaround. The results largely confirm N-body simulations but show some differences that are likely due to our assumption of a one-dimensional phase space manifold.

Relevance of jet emitting disc physics to microquasars: application to Cygnus X-1

The interpretation of the X-ray spectra of X-ray binaries during their hard states requires a hot, optically thin medium. There are several accretion disc models in the literature that account for this aspect. However, none is designed to simultaneously explain the presence of powerful jets detected during these states. A new quasi-keplerian hot accretion disc solution, a Jet Emitting disc (JED hereafter), which is part of a global disc-jet MHD structure producing stationary super-alfv\'enic ejection, is investigated here. Its radiative and energetic properties are then compared to the observational constraints found in Cygnus X-1. We solve the disc energy equation by balancing the local heating term with advection and cooling by synchrotron, bremsstrahlung and Comptonization processes. The heating term, disc density, accretion velocity and magnetic field amplitude were taken from published self-similar models of accretion-ejection structures. Both optically thin and thick regimes are considered in a one temperature gas supported disc. Three branches of solutions are found possible at a given radius but we investigate only the hot, optically thin and geometrically slim solutions. These solutions give simultaneously, and in a consistent way, the radiative and energetics properties of the disc-jet system. They are able to very well reproduce the accretion-ejection properties of Cygnus X-1, namely its X-ray spectral emission, jet power and jet velocity. About half of the released accretion power is used to produce two mildly relativistic (v/c~0.5) jets and for a luminosity of the order of 1\% of the Eddington luminosity, the JED temperature and optical depth are close to that observed in the hard state Cygnus X-1. The JEDs properties are in agreement with the observations of the prototypical black hole binary Cygnus X-1. and are likely to be relevant to the whole class of microquasars.

Relic proto-stellar discs and the origin of luminous circumstellar interaction in core-collapse supernovae

A small fraction of core collapse supernovae (SNe) show evidence that the outgoing blast wave has encountered a substantial mass ~ 1-10 M_sun of circumstellar matter (CSM) at radii ~100-1000 AU, much more than can nominally be explained by pre-explosion stellar winds. In extreme cases this interaction may power the most luminous, optically-energetic SNe yet discovered. Interpretations for the origin of the CSM have thus far centered on explosive eruptions from the star just ~ years to decades prior to the core collapse. Here we consider an alternative possibility that the inferred CSM is a relic disk left over from stellar birth. We investigate this hypothesis by calculating the evolution of proto-stellar disks around massive stars following their early embedded phase using a self-similar accretion model. We identify an initial gravitationally-unstable ("gravito-turbulent") phase, followed by a much longer period of irradiation-supported accretion during which less effective non-gravitational forms of angular momentum transport dominate. Although external influences, such as the presence of a wide binary companion, may preclude disk survival in many systems, we find that massive (~1-10 M_sun) disks can preferentially survive around the most massive stars. Reasons for this perhaps counterintuitive include (1) the shorter stellar lifetimes and (2) large photo-evaporation radii (~ 1000 AU) of very massive stars; (3) suppression of the magneto-rotational instability due to the shielding from external sources of ionization; and (4) relative invulnerability of massive disks to lower mass stellar collisions and luminous blue variable eruptions. Because very luminous SNe are rare, testing the relic disk model requires constraining the presence of long-lived disks around a small fraction of very massive stars.

MULTIRESOLUTION CONTROL OF CURVES AND SURFACES WITH A SELF-SIMILAR MODEL

This paper presents two self-similar models that allow the control of curves and surfaces. The first model is based on IFS (Iterated Function Systems) theory and the second on subdivision curve and surface theory. Both of these methods employ the detail concept as in the wavelet transform, and allow the multiresolution control of objects with control points at any resolution level.In the first model, the detail is inserted independently of control points, requiring it to be rotated when applying deformations. In contrast, the second method describes details relative to control points, allowing free control point deformations.Modeling examples of curves and surfaces are presented, showing manipulation facilities of the models.

Dead zones in protostellar discs: the case of jet emitting discs

Planet formation and migration in accretion discs is a very active topic. Among the many aspects related to that question, dead zones are of particular importance as they can influence both the formation and the migration of planetary embryos. The ionisation level in the disc is the key element in determining the existence and the location of the dead zone. This has been studied either within the Standard Accretion Disc (SAD) framework or using parametric discs. In this paper, we extend this study to the case of Jet Emitting Discs (JED), the structure of which strongly differ from SADs because of the new energy balance and angular momentum extraction imposed by the jets. We make use of the (r,z) density distributions provided by self-similar accretion-ejection models, along with the JED thermal structure derived in a previous paper, to create maps of the ionisation structure of JEDs. We compare the ionisation rates we obtain to the critical value required to trigger the magneto-rotational instability. It is found that JEDs have a much higher ionisation degree than SADs which renders very unlikely the presence of a dead zone in these discs. As JEDs are believed to occupy the inner regions of accretion discs, the extension of the dead zones published in the literature should be re-considered for systems in which a jet is present. Moreover, since JEDs require large scale magnetic fields close to equipartition, our findings raise again the question of magnetic field advection in circumstellar accretion discs.

OBSERVATIONAL PREDICTION OF HIGH MAGNETIC REYNOLDS NUMBER PRE-FLARE RECONNECTION EVENTS: AN APPLICATION OF NITTA'S SELF-SIMILAR RECONNECTION MODEL

We applied the evolutionary model of magnetic reconnection to simple pre-flare reconnection events driven by flux emergence as the first step in inspecting the realizability of the reconnection events predicted by this model. Previous works paid scant attention to the dependence of the magnetic Reynolds number (R*em) on reconnection events. We aim to clarify how the pre-flare phase of reconnection events in the high R*em range that is frequently encountered in astrophysical applications is observed. We clarify that (1) the time variation of the emission measure distribution strongly depends on R*em, (2) the expected light curve for sufficiently low R*em shows a long lifetime property while that for high R*em shows an impulsive property, and (3) in the case of recurrent small reconnection events on the same loop, the released magnetic energy scale is inversely correlated to the rear-end speed of the moving bright point along the loop. Note that other reconnection models cannot totally explain integration of these properties. If evidence of phenomena with these properties can be detected from, e.g., the Hinode observation, it strongly supports the validity of the self-similar reconnection model.

The observed growth of massive galaxy clusters - II. X-ray scaling relations

(Abridged) This is the second in a series of papers in which we derive simultaneous constraints on cosmology and X-ray scaling relations using observations of massive, X-ray flux-selected galaxy clusters. The data set consists of 238 clusters drawn from the ROSAT All-Sky Survey with 0.1-2.4 keV luminosities >2.5e44 erg/second, and incorporates extensive follow-up observations using the Chandra X-ray Observatory. Our analysis accounts self-consistently for all selection effects, covariances and systematic uncertainties. Here we describe the reduction of the follow-up X-ray observations, present results on the cluster scaling relations, and discuss their implications. Our constraints on the luminosity-mass and temperature-mass relations, measured within r_500, lead to three important results. First, the data support the conclusion that excess heating of the intracluster medium has altered its thermodynamic state from that expected in a simple, gravitationally dominated system; however, this excess heating is primarily limited to the central regions of clusters (r<0.15r_500). Second, the intrinsic scatter in the center-excised luminosity-mass relation is remarkably small, being undetected at the <10% level in current data; for the hot, massive clusters under investigation, this scatter is smaller than in either the temperature-mass or Y_X-mass relations (10-15%). Third, the evolution with redshift of the scaling relations is consistent with the predictions of simple, self-similar models of gravitational collapse, indicating that the mechanism responsible for heating the central regions of clusters was in operation before redshift 0.5 (the limit of our data) and that its effects on global cluster properties have not evolved strongly since then.

The universal galaxy cluster pressure profile from a representative sample of nearby systems (REXCESS) and theYSZ–M500relation

(abridged) We investigate the regularity of cluster pressure profiles with REXCESS, a representative sample of 33 local clusters observed with XMM-Newton. The sample spans a mass range of 10^14 M_sun <M_500<10^15 M_sun. We derive an average profile from observations scaled by mass and z according to the standard self-similar model, and find that the dispersion about the mean is remarkably low beyond 0.2R_500, but increases towards the centre. Deviations about the mean are related to both the mass and the thermo-dynamical state of the cluster. Unrelaxed systems have systematically shallower profiles while cooling core systems are more concentrated. The scaled profiles exhibit a residual mass dependence with a slope of about 0.12; however, the departure from standard scaling decreases with radius and is consistent with zero at R_500. The scatter in the core and departure from self-similar mass scaling is smaller compared to that of the entropy profiles, showing that the pressure is the quantity least affected by dynamical history and non-gravitational physics. Comparison with several state of the art numerical simulations shows good agreement outside the core. Combining the observational data below R_500 with simulation data above, we derive the universal pressure profile, that, in an analytical form, defines the physical pressure profile of clusters as a function of mass and z up to the cluster 'boundary'. Using this profile and the observed pressure profiles, we investigate the scaling properties of the integrated Compton parameter Y, considering both the spherically integrated quantity and the cylindrically integrated quantity, directly related to the Sunyaev-Zel'dovich (SZ) effect signal. We further derive the expected Y_SZ-M_500 and Y_SZ-L_X relations for any aperture.

Energy efficiency of consecutive fragmentation processes

Motivated by a problem arising in the mining industry, we present a first study of the energy required to reduce a unit mass fragment by consecutively using several devices. Two devices are considered, which we represent as different stochastic fragmentation processes. Following the self-similar energy model introduced in Bertoin and Martínez (2005), we compute the average energy required to attain a size η0 with this two-device procedure. We then asymptotically compare, as η0 goes to 0 or 1, its energy requirement with that of individual fragmentation processes. In particular, we show that, for a certain range of parameters of the fragmentation processes and of their energy cost functions, the consecutive use of two devices can be asymptotically more efficient than using each of them separately, or vice versa.

Energy efficiency of consecutive fragmentation processes

Motivated by a problem arising in the mining industry, we present a first study of the energy required to reduce a unit mass fragment by consecutively using several devices. Two devices are considered, which we represent as different stochastic fragmentation processes. Following the self-similar energy model introduced in Bertoin and Martínez (2005), we compute the average energy required to attain a size η0 with this two-device procedure. We then asymptotically compare, as η0 goes to 0 or 1, its energy requirement with that of individual fragmentation processes. In particular, we show that, for a certain range of parameters of the fragmentation processes and of their energy cost functions, the consecutive use of two devices can be asymptotically more efficient than using each of them separately, or vice versa.

Progress in the Self-Similar Turbulent Flame premixed combustion model

This paper is devoted to premixed combustion modeling in turbulent flow. First, we briefly remind the main features of the Self-Similar Turbulent Flame model that was more extensively developed in a former paper. Then, we carefully describe some improvements of the model. The determination of the turbulent flame velocity is based on the observed self-similarity of the turbulent flame and uses the local flame brush width as a fundamental parameter, which must be retrieved. With respect to the former version, we now derive more rigorously how the density variation has to be taken into account in the width retrieving function. We reformulate the diffusion term as a classical flux divergence term. We enforce the compatibility of the model for the limit of weak turbulence. We include a contracting effect of the source term, thus allowing to give a stationary mono-dimensional asymptotic solution with a finite width. We also include in a preliminary form, a stretch factor, which proves to be useful for controlling the flame behavior close to the flame holder and near the walls. The model implementation in the Star-CD CFD code is then tested on three different flame configurations. Finally, we shortly discuss the model improvements and the simulation results.

Self-similarity and scaling in forest communities

Ecological communities exhibit pervasive patterns and interrelationships between size, abundance, and the availability of resources. We use scaling ideas to develop a unified, model-independent framework for understanding the distribution of tree sizes, their energy use, and spatial distribution in tropical forests. We demonstrate that the scaling of the tree crown at the individual level drives the forest structure when resources are fully used. Our predictions match perfectly with the scaling behavior of an exactly solvable self-similar model of a forest and are in good accord with empirical data. The range, over which pure power law behavior is observed, depends on the available amount of resources. The scaling framework can be used for assessing the effects of natural and anthropogenic disturbances on ecosystem structure and functionality.

Accelerated cosmic expansion in a scalar-field universe

We consider here a spherically symmetric but inhomogeneous universe filled with a massless scalar field. The model obeys two constraints. The first one is that the gradient of the scalar field is timelike everywhere. The second constraint is that the radial coordinate basis vector is a unit vector field in the comoving coordinate system. We find that the resultant dynamical solutions compose a one-parameter family of self-similar models which is known as the Roberts solution. The solutions are divided into three classes. The first class consists of solutions with only one spacelike singularity in the synchronous-comoving chart. The second class consists of solutions with two singularities which are null and spacelike, respectively. The third class consists of solutions with two spacelike singularities which correspond to the big bang and big crunch, respectively. We see that, in the first case, a comoving volume exponentially expands as in an inflationary period; the fluid elements are accelerated outwards from the symmetry center, even though the strong energy condition is satisfied. This behavior is very different from that observed in the homogeneous and isotropic universe in which the fluid elements would move outwards with deceleration, if the strong energy conditions are satisfied. We are thus able to achieve the accelerated expansion of the universe for the models considered here, without a need to violate the energy conditions. The cosmological features of the models are examined in some detail.

A cross-layer design of wireless IP systems using effective bandwidth and MQAM adaptive modulation

In this paper, we introduce an effective bandwidth-based call admission control (CAC) with adaptive modulation technique to manage the traffic in a wireless IP-based network. Furthermore, in order to efficiently use the physical resources of the network, we take advantage of an adaptive MQAM (M-ary quadrature amplitude modulation) to match transmission rates to the time-varying channel conditions. This cross-layer architecture has been examined for the self-similar traffic model. The results show that by simultaneous implementation of the effective bandwidth algorithm in the data-link layer and adaptive modulation technique in the physical layer, the performance of the wireless network in terms of the number of rejected calls and system throughput improves.

CONSISTENT SELF-SIMILAR MAGNETOHYDRODYNAMICS EVOLUTION OF CORONAL TRANSIENTS

The self-similar model of coronal transients by B. C. Low is reconsidered. Due to a modification of the basic set of the initial assumptions of the model, a new class of more consistent solutions is found. The main advantage of these new solutions is that they do not contain areas with a physically inconsistent negative pressure. Instead, the novel solutions are derived on the basis of a special prescription for the thermal pressure of the transients that guarantees, by design, its positiveness throughout the whole evolution domain. The possible importance of these solutions for understanding the physics of the transient interplanetary coronal mass ejections (ICMEs; originating from the Sun), and magnetic clouds as a subclass of these, is discussed. A practical example is cited illustrating the application of our analytic results to describe some properties of real ICMEs. Some directions and scopes for further research are outlined.

A multivariate generalized long memory model

In this Note, we propose a new flexible multivariate long memory process which is a self-similar model with the ability to capture short-range dependence, seasonality and long-range dependence characteristics. Specifically, we extend the multivariate ARFIMA model proposed by Sowell (1989) [8], and investigate some of its statistical properties.

Properties of Self-similarity Networks

The self-similarity of complex networks has broad practical backgrounds. However, the properties of self-similar network have rarely studied so far. For this propose the self-similarity networks definition is captured firstly . Self-similarity model of complex networks is build based on information transfer, accounting to information transfer among nodes. Self-similarity of complex networks is researched based on the concept of fractal . Volume dimension is given to measure the self-similar network; besides, the shortage of volume dimension was also referred to. The information dimension was also proposed to study the self-similarity, which can reflect the similar objectively . Self-similarity of complex networks and simulation results is got from the data, finally further study is proposed.

A solvable model for homopolymers and self-similarity near the critical point

We consider a model for the distribution of a long homopolymer with an attractive zero-range potential at the origin in (polymer pinning and de-pinning). The distribution can be obtained as a limit of Gibbs distributions corresponding to properly normalized potentials concentrated in small neighborhoods of the origin as the size of the neighborhoods tends to zero. The distribution depends on the length T of the polymer and a parameter γ that corresponds, roughly speaking, to the difference between the inverse temperature in our model and the critical value of the inverse temperature. At the critical point γ cr = 0 the transition occurs from the globular phase (positive recurrent behavior of the polymer, γ &gt; 0) to the extended phase (Brownian type behavior, γ &lt; 0). The main result of the paper is a detailed analysis of the behavior of the polymer when γ is near γ cr . Our approach is based on analyzing the semigroups generated by the self-adjoint extensions ℒ γ of the Laplacian on parametrized by γ , which are related to the distribution of the polymer. The main technical tool of the paper is the explicit formula for the resolvent of the operator ℒ γ .