Examining the growth and evolution of magnetic fields in clusters of galaxies: a numerical perspective

Magnetic fields are ubiquitous in galaxy cluster atmospheres and have a variety of astrophysical and cosmological consequences. Magnetic fields can contribute to the pressure support of clusters, affect thermal conduction, and modify the evolution of bubbles driven by active galactic nuclei. However, we currently do not fully understand the origin and evolution of these fields throughout cosmic time. Furthermore, we do not have a general understanding of the relationship between magnetic field strength and topology and other cluster properties, such as mass and X-ray luminosity. We can now begin to answer some of these questions using large-scale cosmological magnetohydrodynamic (MHD) simulations of the formation of galaxy clusters including the seeding and growth of magnetic fields. Using large-scale cosmological simulations with the FLASH code combined with a simplified model of the acceleration of cosmic rays responsible for the generation of radio halos, we find that the galaxy cluster frequency distribution and expected number counts of radio halos from upcoming low-frequency sur- veys are strongly dependent on the strength of magnetic fields. Thus, a more complete understanding of the origin and evolution of magnetic fields is necessary to understand and constrain models of diffuse synchrotron emission from clusters. One favored model for generating magnetic fields is through the amplification of weak seed fields in active galactic nuclei (AGN) accretion disks and their subsequent injection into cluster atmospheres via AGN-driven jets and bubbles. However, current large-scale cosmological simulations cannot directly include the physical processes associated with the accretion and feedback processes of AGN or the seeding and merging of the associated SMBHs. Thus, we must include these effects as subgrid models. In order to carefully study the growth of magnetic fields in clusters via AGN-driven outflows, we present a systematic study of SMBH and AGN subgrid models. Using dark-matter only cosmological simulations, we find that many important quantities, such as the relationship between SMBH mass and galactic bulge velocity dispersion and the merger rate of black holes, are highly sensitive to the subgrid model assumptions of SMBHs. In addition, using MHD calculations of an isolated cluster, we find that magnetic field strengths, extent, topology, and relationship to other gas quantities such as temperature and density are also highly dependent on the chosen model of accretion and feedback. We use these systematic studies of SMBHs and AGN inform and constrain our choice of subgrid models, and we use those results to outline a fully cosmological MHD simulation to study the injection and growth of magnetic fields in clusters of galaxies. This simulation will be the first to study the birth and evolution of magnetic fields using a fully closed accretion-feedback cycle, with as few assumptions as possible and a clearer understanding of the effects of the various parameter choices.

The SHIVir Survey: A Dynamical Catalogue of Virgo Cluster Galaxies and their Scaling Relations

By virtue of its proximity and richness, the Virgo galaxy cluster is a perfect testing ground to expand our understanding of structure formation in the Universe. Here, we present a comprehensive dynamical catalogue based on 190 Virgo cluster galaxies (VCGs) in the "Spectroscopy and H-band Imaging of the Virgo cluster" (SHIVir) survey, including kinematics and dynamical masses. Spectroscopy collected over a multi-year campaign on 4-8m telescopes was joined with optical and near-infrared imaging to create a cosmologically-representative overview of parameter distributions and scaling relations describing galaxy evolution in a rich cluster environment. The use of long-slit spectroscopy has allowed the extraction and systematic analysis of resolved kinematic profiles: Halpha rotation curves for late-type galaxies (LTGs), and velocity dispersion profiles for early-type galaxies (ETGs). The latter are shown to span a wide range of profile shapes which correlate with structural, morphological, and photometric parameters. A study of the distributions of surface brightnesses and circular velocities for ETGs and LTGs considered separately show them all to be strongly bimodal, hinting at the existence of dynamically unstable modes where the baryon and dark matter fractions may be comparable within the inner regions of galaxies. Both our Tully-Fisher relation for LTGs and Fundamental Plane analysis for ETGs exhibit the smallest scatter when a velocity metric probing the galaxy at larger radii (where the baryonic fraction becomes sub-dominant) is used: rotational velocity measured in the outer disc at the 23.5 i-mag arcsec^{-2} level, and velocity dispersion measured within an aperture of 2 effective radii, respectively. Dynamical estimates for gas-poor and gas-rich VCGs are merged into a joint analysis of the stellar-to-total mass relation (STMR), stellar TFR, and Mass-Size relation. These relations are all found to contain strong bimodalities or dichotomies between the ETG and LTG samples, alluding to a "mixed scenario'' evolutionary sequence between morphological/dynamical classes that involves both quenching and dry mergers. The unmistakable differentiation between these two galaxy classes appears robust against different classification schemes, and supports the notion that they are driven by different evolutionary histories. Future observations using integral field spectroscopy and including lower-mass galaxies should solidify this hypothesis.

Formulation and analysis of a diffusion-velocity particle model for transport-dispersion equations

The modelling of diffusive terms in particle methods is a delicate matter and several models were proposed in the literature to take such terms into account. The diffusion velocity method (DVM), originally designed for the diffusion of passive scalars, turns diffusive terms into convective ones by expressing them as a divergence involving a so-called diffusion velocity. In this paper, DVM is extended to the diffusion of vectorial quantities in the three-dimensional Navier–Stokes equations, in their incompressible, velocity–vorticity formulation. The integration of a large eddy simulation (LES) turbulence model is investigated and a DVM general formulation is proposed. Either with or without LES, a novel expression of the diffusion velocity is derived, which makes it easier to approximate and which highlights the analogy with the original formulation for scalar transport. From this statement, DVM is then analysed in one dimension, both analytically and numerically on test cases to point out its good behaviour.

Eddy diffusivity: A single dispersion analysis of high resolution drifters in a tidal shallow estuary

In an estuary, mixing and dispersion resulting from turbulence and small scale fluctuation has strong spatio-temporal variability which cannot be resolved in conventional hydrodynamic models while some models employs parameterizations large water bodies. This paper presents small scale diffusivity estimates from high resolution drifters sampled at 10 Hz for periods of about 4 hours to resolve turbulence and shear diffusivity within a tidal shallow estuary (depth < 3 m). Taylor's diffusion theorem forms the basis of a first order estimate for the diffusivity scale. Diffusivity varied between 0.001 – 0.02 m2/s during the flood tide experiment. The diffusivity showed strong dependence (R2 > 0.9) on the horizontal mean velocity within the channel. Enhanced diffusivity caused by shear dispersion resulting from the interaction of large scale flow with the boundary geometries was observed. Turbulence within the shallow channel showed some similarities with the boundary layer flow which include consistency with slope of 5/3 predicted by Kolmogorov's similarity hypothesis within the inertial subrange. The diffusivities scale locally by 4/3 power law following Okubo's scaling and the length scale scales as 3/2 power law of the time scale. The diffusivity scaling herein suggests that the modelling of small scale mixing within tidal shallow estuaries can be approached from classical turbulence scaling upon identifying pertinent parameters.

Strong nonlocalization induced by small scale parameter on terahertz flexural wave dispersion characteristics of a monolayer graphene

This paper presents the strong nonlocal scale effect on the flexural wave propagation in a monolayer graphene sheet. The graphene is modeled as an isotropic plate of one atom thick. Nonlocal governing equation of motion is derived and wave propagation analysis is performed using spectral analysis. The present analysis shows that the flexural wave dispersion in graphene obtained by local and nonlocal elasticity theories is quite different. The nonlocal elasticity calculation shows that the wavenumber escapes to infinite at certain frequency and the corresponding wave velocity tends to zero at that frequency indicating localization and stationary behavior. This behavior is captured in the spectrum and dispersion curves. The cut-off frequency of flexural wave not only depend on the axial wavenumber but also on the nonlocal scaling parameter. The effect of axial wavenumber on the wave behavior in graphene is also discussed in the present manuscript. (C) 2010 Elsevier B.V. All rights reserved.

Measurement of axial dispersion coefficient in a packed bed using X-ray

Dispersion of the liquid in a porous media is of great importance in many areas of engineering and has been studied by several researchers so far. A new experimental method has been developed to measure the dispersion coefficient. X-ray absorption technique provides a better understanding of dispersion that characterizes the mixing phenomenon in the packed beds. This is because the method is non-invasive and also it gives tracer concentration data at every point within the bed. The axial dispersion in a cylindrical bed of non-porous and non-wetting spherical particles has been measured for the flow of water. Aqueous barium chloride solution has been used a as tracer. X-ray images, recorded on a videocassette, have been analyzed using an image processing software to extract the local interstitial velocity and concentration data in the bed. Local dispersion coefficient has been determined with the help of aforementioned data. By using these data, the overall dispersion coefficient in a packed bed can also be estimated.

Dispersion and vaporization of biofuels and conventional fuels in a crossflow pre-mixer

In lean premixed pre-vaporized (LPP) combustion, controlled atomization, dispersion and vaporization of different types of liquid fuel in the premixer are the key factors required to stabilize the combustion process and improve the efficiency. The dispersion and vaporization process for biofuels and conventional fuels sprayed into a crossflow pre-mixer have been simulated and analyzed with respect to vaporization rate, degree of mixedness and homogeneity. Two major biofuels under investigation are Ethanol and Rapeseed Methyl Esters (RME), while conventional fuels are gasoline and jet-A. First, the numerical code is validated by comparing with the experimental data of single n-heptane and decane droplet evaporating under both moderate and high temperature convective air now. Next, the spray simulations were conducted with monodispersed droplets with an initial diameter of 80 mu m injected into a turbulent crossflow of air with a typical velocity of 10 m/s and temperature of around 800K. Vaporization time scales of different fuels are found to be very different. The droplet diameter reduction and surface temperature rise were found to be strongly dependent on the fuel properties. Gasoline droplet exhibited a much faster vaporization due a combination of higher vapor pressure and smaller latent heat of vaporization compared to other fuels. Mono-dispersed spray was adopted with the expectation of achieving more homogeneous fuel droplet size than poly-dispersed spray. However, the diameter histogram in the zone near the pre-mixer exit shows a large range of droplet diameter distributions for all the fuels. In order to improve the vaporization performance, fuels were pre-heated before injection. Results show that the Sauter mean diameter of ethanol improved from 52.8% of the initial injection size to 48.2%, while jet-A improved from 48.4% to 18.6% and RME improved from 63.5% to 31.3%. The diameter histogram showed improved vaporization performance of jet-A. (C) 2011 Elsevier Ltd. All rights reserved.

A Revisit to Capture the Entire Behavior of Ultrasonic Wave Dispersion Characteristics of Single Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory and Flugge Shell Model

In this paper, an ultrasonic wave propagation analysis in single-walled carbon nanotube (SWCNT) is re-studied using nonlocal elasticity theory, to capture the whole behaviour. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The revisited nonlocal elasticity calculation shows that the wavenumber tends to infinite at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. This frequency is termed as escape frequency. This behavior is observed only for axial and radial waves in SWCNT. It has been shown that the circumferential waves will propagate dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the explicit expressions of cut-off frequency depend on the nonlocal scaling parameter and the axial wavenumber. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTs is also discussed. The present results are compared with the corresponding results (for first mode) obtained from ab initio and 3-D elastodynamic continuum models. The acoustic phonon dispersion relation predicted by the present model is in good agreement with that obtained from literature. The results are new and can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

Ultrasonic Wave Dispersion Characteristics of Fluid-Filled Single-Walled Carbon Nanotubes Based on Nonclassical Shell Model

In this paper, ultrasonic wave propagation analysis in fluid filled single-walled carbon nanotube (SWCNT) is studied using nonlocal elasticity theory. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. The fluid inside the SWCNT is assumed as water. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The presence of fluid in SWCNT alters the ultrasonic wave dispersion behavior. The wavenumber and wave velocity are smaller in presence of fluid as compared to the empty SWCNT. The nonlocal elasticity calculation shows that the wavenumber tends to reach the continuum limit at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. It has been shown that the circumferential. waves will propagate non-dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the cut-off frequency depend on the nonlocal scaling parameter and also on the density of the fluid inside the SWCNT, and the axial wavenumber, as the fluid becomes denser the cut-off frequency decreases. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTS filled with water is also discussed.

SCALE EFFECTS ON ULTRASONIC WAVE DISPERSION CHARACTERISTICS OF MONOLAYER GRAPHENE EMBEDDED IN AN ELASTIC MEDIUM

Ultrasonic wave propagation in a graphene sheet, which is embedded in an elastic medium, is studied using nonlocal elasticity theory incorporating small-scale effects. The graphene sheet is modeled as an one-atom thick isotropic plate and the elastic medium/substrate is modeled as distributed springs. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. After that, an ultrasonic type of wave propagation model is also derived. The explicit expressions for the cut-off frequencies are also obtained as functions of the nonlocal scaling parameter and the y-directional wavenumber. Local elasticity shows that the wave will propagate even at higher frequencies. But nonlocal elasticity predicts that the waves can propagate only up to certain frequencies (called escape frequencies), after which the wave velocity becomes zero. The results also show that the escape frequencies are purely a function of the nonlocal scaling parameter. The effect of the elastic medium is captured in the wave dispersion analysis and this analysis is explained with respect to both local and nonlocal elasticity. The simulations show that the elastic medium affects only the flexural wave mode in the graphene sheet. The presence of the elastic matrix increases the band gap of the flexural mode. The present results can provide useful guidance for the design of next-generation nanodevices in which graphene-based composites act as a major element.

Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence

A scale-similarity model for Lagrangian two-point, two-time velocity correlations LVCs in isotropic turbulence is developed from the Kolmogorov similarity hypothesis. It is a second approximation to the isocontours of LVCs, while the Smith-Hay model is only a first approximation. This model expresses the LVC by its space correlation and a dispersion velocity. We derive the analytical expression for the dispersion velocity from the Navier-Stokes equations using the quasinormality assumption. The dispersion velocity is dependent on enstrophy spectra and shown to be smaller than the sweeping velocity for the Eulerian velocity correlation. Therefore, the Lagrangian decorrelation process is slower than the Eulerian decorrelation process. The data from direct numerical simulation of isotropic turbulence support the scale-similarity model: the LVCs for different space separations collapse into a universal form when plotted against the separation axis defined by the model.

Group velocity of probe light pulse in an open lambda system

The group velocity of the probe light pulse (GVPLP) propagating through an open Lambda-type atomic system with a spontaneously generated coherence is investigated when the weak probe and strong driving light fields have different frequencies. It is found that adjusting the detuning or Rabi frequency of the probe light field can realize switching of the GVPLP from subluminal to superluminal. Changing the relative phase between the probe and driving light. elds or atomic exit and injection rates can lead to GVPLP varying in a wider range, but cannot induce transformation of the property of the GVPLP. The absolute value of the GVPLP always increases with Rabi frequency of the driving light field increasing. For subluminal and superluminal propagation, the system always exhibits the probe absorption, and GVPLP is mainly determined by the slope of the steep dispersion.

Upper level and phase controlling group velocity in V-type system

With the external field coupling the two upper levels, we investigate the light pulse propagation properties with weak probe field in a V-type system. Due to the external upper level (UL) coupling field, the dispersion of the system has been influenced by the relative phase. It is shown that the UL field and the relative phase can be regarded as switches to manipulate light propagation between subluminal and superluminal. (c) 2007 Elsevier B.V. All rights reserved.

Controlling the group velocity in a five-level K-type atomic system

The properties of a five-level K-type system are investigated. With the controlling fields, the properties of the dispersion and absorption of the system are changed greatly. The system can produce anomalous dispersion regions with absorption and normal dispersion regions with absorption or transparency. Furthermore, the group velocity can be varied from subluminal to superluminal by varying the intensity of the controlling field and the probe detunings in principle. (C) 2008 Elsevier B.V. All rights reserved.

Longitudinal dispersion in laboratory and natural streams

This study concerns the longitudinal dispersion of fluid particles which are initially distributed uninformly over one cross section of a uniform, steady, turbulent open channel flow. The primary focus is on developing a method to predict the rate of dispersion in a natural stream.

Taylor's method of determining a dispersion coefficient, previously applied to flow in pipes and two-dimensional open channels, is extended to a class of three-dimensional flows which have large width-to-depth ratios, and in which the velocity varies continuously with lateral cross-sectional position. Most natural streams are included. The dispersion coefficient for a natural stream may be predicted from measurements of the channel cross-sectional geometry, the cross-sectional distribution of velocity, and the overall channel shear velocity. Tracer experiments are not required.

Large values of the dimensionless dispersion coefficient D/rU* are explained by lateral variations in downstream velocity. In effect, the characteristic length of the cross section is shown to be proportional to the width, rather than the hydraulic radius. The dimensionless dispersion coefficient depends approximately on the square of the width to depth ratio.

A numerical program is given which is capable of generating the entire dispersion pattern downstream from an instantaneous point or plane source of pollutant. The program is verified by the theory for two-dimensional flow, and gives results in good agreement with laboratory and field experiments.

Both laboratory and field experiments are described. Twenty-one laboratory experiments were conducted: thirteen in two-dimensional flows, over both smooth and roughened bottoms; and eight in three-dimensional flows, formed by adding extreme side roughness to produce lateral velocity variations. Four field experiments were conducted in the Green-Duwamish River, Washington.

Both laboratory and flume experiments prove that in three-dimensional flow the dominant mechanism for dispersion is lateral velocity variation. For instance, in one laboratory experiment the dimensionless dispersion coefficient D/rU* (where r is the hydraulic radius and U* the shear velocity) was increased by a factory of ten by roughening the channel banks. In three-dimensional laboratory flow, D/rU* varied from 190 to 640, a typical range for natural streams. For each experiment, the measured dispersion coefficient agreed with that predicted by the extension of Taylor's analysis within a maximum error of 15%. For the Green-Duwamish River, the average experimentally measured dispersion coefficient was within 5% of the prediction.