Phase structure of NJL model with weak renormalization group

We analyze the chiral phase structure of the Nambu--Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential $V(\sigma;t)$ is given as a partial differential equation, where $\sigma:=\bar \psi\psi$ and $t$ is a dimensionless RG scale. When the dynamical chiral symmetry breaking (D$\chi$SB) occurs at a certain scale $t_c$, $V(\sigma;t)$ has singularities originated from the phase transitions, and then one cannot follow RG flows after $t_c$. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the D$\chi$SB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.Comment: 32 pages, 12 figures; Version published in Nuclear Physics

The Central Gas Systems of Early-Type Galaxies Traced by Dust Feature: Based on the HST WFPC2 Archival Images

We investigated the central gas systems of E/S0 galaxies by making use of the WFPC2 images of the Hubble Space Telescope archive. We searched the gas systems that were traced by the dust with a new method of making color excess images in F555W - F814W (V-I). Out of 25 sample galaxies, we detected gas system in 14 galaxies. The dust was newly detected in two galaxies that were thought to contain no dust based on single band, pre-refurbishment data. The full extents of the gas systems are 0.1 to 3.5 kpc, and the masses of the gas, log M(gas) [M(solar)], are 4.2 to 7.2. The AGN activity is well correlated with existence of the gas systems. None of galaxies without the gas systems show the AGN activity. On the other hand, some galaxies with the gas systems show the AGN activity; optical AGN activities are shown in 5 out of 11 galaxies of which AGNs are optically studied, and radio activities are shown in 6 out of 14 galaxies. This shows that the AGN activity is driven with the gas system.Comment: gzipped tarred file containing 7 files: Tomita.tex (main text, needs aaspp4.sty), Tomita.tab[1,2].tex (tables, need aj_pt4.sty), Tomita.fig [1a,1b,1c,2].ps (PS figures). To be appeared in AJ, Vol.120, No.1 (July 2000

Scaling Bubble Entrainment And Dispersion In Vertical Circular Plunging Jet Flows: Freshwater Versus Seawater

At a plunging jet, air entrainment may take place downstream of the impingement perimeter. This study investigates air entrainment and bubble dispersion at vertical circular plunging jets in freshwater, salty freshwater and seawater. The results show lesser air entrainment in seawater plunging jets for identical inflow conditions. The average pseudo-chord sizes are between 4 and 6 mm for all water solutions, although more fine bubbles were detected in seawater. It is believed that surfactants and bio-chemicals harden the induction trumpet at plunge point and diminish air entrapment at impingement in seawater

Acoustic Doppler Velocimetry (ADV) in a Small Estuarine System. Field Experience and "Despiking"

Estuarine mixing and dispersion are turbulent processes. Present understanding of estuary turbulence remains however limited, partly because long-duration studies of turbulent properties are difficult and rare. Herein, some long-duration turbulence data recorded at high frequency using acoustic Doppler velocimetry (ADV) are analysed. The data sets were collected in a small sub-tropical estuary. A new ADV data post-processing technique is developed for turbulence analysis of estuarine flows. The results show that acoustic Doppler velocimetry data cannot be used without suitable post-processing. Even classical "despiking" techniques are not simply applicable to natural unsteady estuary flows

Similitude of Air Bubble Entrainment and Dispersion in Vertical Circular Plunging Jet Flows. An Experimental Study with Freshwater, Salty Freshwater and Seawater

Air bubble entrainment at plunging jet takes place when the jet impact velocity exceeds a critical velocity Ve which is a function of the jet turbulence. Several researchers proposed an analogy between plunging jet flows and plunging breakers. Most works considered steady plunging jet results obtained with freshwater and there have been suggestions that air entrainment at breaking waves in the sea might be an entirely different process. This study investigates scale effects affecting air entrainment and bubble dispersion at vertical circular plunging jets. Three scale models were used and detailed air-water measurements were performed systematically for identical Froude numbers. For one scale, three water solutions were tested. All experimental results are presented in Appendices B and C. In freshwater, the results highlight significant scale effects when We1 = rw*V1 2*d1/s < 103 or V1/ur < 10. Identical experiments were performed with freshwater, salty freshwater and seawater. The results show lesser air entrainment in seawater plunging jets for identical inflow conditions. Results with saltwater are intermediate between freshwater and seawater results. Bubble chord times tch were also measured. The data were analysed in terms of pseudo-bubble chord length chab = V1*tch, which was found to overestimate real bubble chords by 10 to 30%. The data show that pseudo-bubble chord sizes range from less than 0.5 mm to more than 10 mm. The average pseudo-chord sizes are between 4 and 6 mm for all water solutions. Comparatively, however, more fine bubbles were detected in seawater than in freshwater. Fine bubbles (less than 0.5 mm) have a slower rise velocity and their underwater residence time is larger in seawater. They give a visual, misleading appearance to the air-water flow suggesting that very fine bubbles are predominantly entrained in seawater plunging jets. Overall the study contributes to a better understanding of air entrainment and bubble dispersion in vertical circular plunging jets. Differences in air entrainment mechanisms between freshwater and seawater are described. Scales effects are believed to occurs in laboratory wave flumes when the wave height at breaking is less than 0.25 to 0.35 m. Experimental results in seawater and saltwater suggest further that classical dimensional analysis of air entrainment is incomplete, and that further physical, chemical and biological fluid properties must be taken into account

Unsteady Air Bubble Entrainment and Detrainment at a Plunging Breaker: Dominant Time Scales and Similarity of Water Level Variations

At plunging breakers, air bubbles are entrained at the impingement of the water jet, formed at the top of the wave, with the water free surface in front. During the present study, air bubble entrainment at a pseudo-plunging breaker was investigated at near full-scale and further experimental work studied the bubble detrainment process. Experimental observations included the generation and propagation of waves downstream of the plunge point. Experimental results highlighted a number of unsteady air-water flow patterns and emphasise high levels of aeration: i.e., depth-averaged void fraction of more than 10% next to jet impact in shallow waters. Unsteady bubble injection experiments showed a strong vortical motion induced by the rising bubbles. Altogether, the results suggest that a dominant time scale is the bubble rise time d1/ur, which cannot be scaled properly with an undistorted Froude model. The study contributes to a better understanding of unsteady bubble entrainment at a pseudo-plunging breaker and the associated vortical circulation

Similitude of air entrainment at vertical circular plunging jets

Air bubble entrainment at plunging jet takes place when the jet impact velocity exceeds a critical velocity function of the inflow conditions. This study investigates scale effects affecting air entrainment and bubble dispersion at vertical circular plunging jets. Three scale models were used and detailed air-water measurements were performed systematically for identical Froude numbers. The results highlight significant scale effects when We1 < 1E+3 or V1/ur < 10. Bubble chord times were also measured and presented in terms of pseudo-bubble chord length which was found to overestimate real bubble chords by 10 to 30%. The data show pseudo-bubble chord sizes ranging from less than 0.5 mm to more than 10 mm. The average pseudo-chord sizes were between 5 and 7 mm

An Experimental Study of Tsunami Runup on Dry and Wet Horizontal Coastlines

Wave runup generated by a tsunami reaching the shoreline may induce devastating flood waves. When tsunami wave breaking is associated with a plunging jet, some energy dissipation at jet impact and the downstream propagation of the surge is characterised by a high initial momentum resulting from the plunging jet. New experiments were performed in a large-size facility (15-m long 0.8-m wide channel). The experimental data highlight a large wave celerity during the initial stage (i.e. x/do 30), the bore propagates at a speed similar to that predicted by the 'classical' analysis. The results highlight a reduced warning time downstream of plunging breaking wave