Stability Of Disks Research Articles

The Origin of Exponential Star-forming Disks

Abstract The disk components of galaxies generally show an exponential profile extending over several scale lengths, both in mass and star formation rate, but the physical origin is not well understood. We explore a physical model in which the galactic gas disk is viewed as a “modified accretion disk” in which coplanar gas inflow, driven by viscous stresses in the disk, provides the fuel for star formation, which progressively removes gas as it flows inward. We show that magnetic stresses from magneto-rotational instability are the most plausible source of the required viscosity, and construct a simple physical model to explore this. A key feature is to link the magnetic field strength to the local star formation surface density, B tot ∝ Σ SFR α . This provides a feedback loop between star formation and the flow of gas. We find that the model naturally produces stable steady-state exponential disks, as long as α ∼ 0.15, the value indicated from spatially resolved observations of nearby galaxies. The disk scale length h R is set by the rate at which the disk is fed, by the normalization of the B tot–ΣSFR relation and by the circular velocity of the halo. The angular momentum distribution of the gas and stars within the disk is a consequence of the transfer of angular momentum that is inherent to the operation of an accretion disk, rather than the initial angular momentum of the inflowing material. We suggest that magnetic stresses likely play a major role in establishing the stable exponential form of galactic disks.

Improving Aeroelastic Stability of Bladed Disks with Topologically Optimized Piezoelectric Materials and Intentionally Mistuned Shunt Capacitance.

It is well known that bladed disks with certain patterns of mistuning can have higher aeroelastic stability than their tuned counterparts. This requires small but accurate deviation of the mechanical properties on each blade sector, and currently it is difficult to realize by mechanical manufacturing. In this paper, we propose an adaptive strategy to realize the intentional mistuning for the improvement of aeroelastic stability. The basic idea is to bond or embed piezoelectric materials to each blade and use different shunt capacitance on each blade as the source of mistuning. When the shunt capacitance varies from zero (open-circuit, OC) to infinity (short-circuit, SC), the stiffness of each blade changes within a relatively small interval. In this way, the required small difference of stiffness among blades is altered into a relatively larger difference of the shunt capacitance. This provides a more feasible and robust way to implement the intentional mistuning, provided that the variation interval of blade stiffness between OC and SC contains the limits of required mistuning. Thus, it is critical to maximize the ability of changing the blade stiffness by shunt capacitance with limited amount of piezoelectric materials. To do so, a straightforward approach is proposed to get the best distribution of piezoelectric materials on the blade for the targeting mode. This approach is based on the FE model of the bladed disc, and the piezoelectric materials are introduced by replacing elements (if they are embedded) or adding an extra layer of elements (if they are bonded). An empirical balded disc with NASA-ROTOR37 profile is used as the example. With a proper design of the mistuning pattern and replace use piezoelectric materials of only 10% the blade mass, the proposed method can significantly improve the aeroelastic stability of bladed disks.

Dynamical interplay of disc thickness and interstellar gas: Implication for the longevity of spiral density waves

A typical galactic disc has a finite thickness. In addition to stars, it also contains a finite amount of interstellar gas. Here, we investigate the physical impact of the finite thickness of a galactic disc on the disc stability against the non-axisymmetric perturbations and on the longevity of the spiral density waves, with and without the presence of gas. The longevity is quantified via the group velocity of density wavepackets. The galactic disc is first modelled as a collisionless stellar disc with finite height and then more realistically as a gravitationally coupled stars plus gas system (with a different thickness for stars and gas). For each case, we derive the appropriate dispersion relation in the Wentzel-Kramers-Brillouin approximation and study the dynamical effect of the disc thickness on the life-time of spiral density waves via a parametric approach. We find the generic trend that the effective reduction in disc self-gravity due to disc thickness makes it more stable against the non-axisymmetric perturbations and shortens the life-span of the spiral density waves. Furthermore, interstellar gas and disc thickness are shown to have a mutually opposite dynamical effect on the disc stability as well as on the longevity of the spiral density waves. While the gas supports the non-axisymmetric features for a longer time, the disc thickness has an opposite, quenching effect. Consequently, the net change is set by the relative dominance of the opposite effects of the interstellar gas and the disc thickness.

Binary companions triggering fragmentation in self-gravitating discs

ABSTRACT Observations of systems hosting close-in (<1 au) giant planets and brown dwarfs (M ≳ 7 MJup) find an excess of binary-star companions, indicating that stellar multiplicity may play an important role in their formation. There is now increasing evidence that some of these objects may have formed via fragmentation in gravitationally unstable discs. We present a suite of 3D smoothed particle hydrodynamics simulations of binary-star systems with circumprimary self-gravitating discs, which include a realistic approximation to radiation transport, and extensively explore the companion’s orbital parameter space for configurations that may trigger fragmentation. We identify a ‘sweet spot’ where intermediate separation binary companions (100 au ≲ a ≲ 400 au) can cause a marginally stable disc to fragment. The exact range of ideal binary separations is a function of the companion’s eccentricity, inclination, and mass. Heating is balanced by efficient cooling, and fragmentation occurs inside a spiral mode driven by the companion. Short separation, disc-penetrating binary encounters (a ≲ 100 au) are prohibitive to fragmentation, as mass stripping and disc heating quench any instability. This is also true of binary companions with high orbital eccentricities (e ≳ 0.75). Wide separation companions (a ≳ 500 au) have little effect on the disc properties for the set-up parameters considered here. The sweet spot found is consistent with the range of binary separations that display an excess of close-in giant planets and brown dwarfs. Hence, we suggest that fragmentation triggered by a binary companion may contribute to the formation of these substellar objects.

Piv Planar Investigation for a Co-Flowing Air Interaction with a Liquid Spray Utilizing Air-Assisted Swirl Atomizer Centralized in a Disk Stabilizer

Piv Planar Investigation for a Co-Flowing Air Interaction with a Liquid Spray Utilizing Air-Assisted Swirl Atomizer Centralized in a Disk Stabilizer

Massive Molecular Gas as a Fuel Tank for Active Galactic Nuclei Feedback In Central Cluster Galaxies

Abstract Massive molecular gas has been discovered in giant elliptical galaxies at the centers of galaxy clusters. To reveal its role in active galactic nucleus (AGN) feedback in those galaxies, we construct a semianalytical model of gas circulation. This model especially focuses on the massive molecular gas (interstellar cold gas on a scale of ∼10 kpc) and the circumnuclear disk (≲0.5 kpc). We consider the destruction of the interstellar cold gas by star formation and the gravitational instability for the circumnuclear disk. Our model can reproduce the basic properties of the interstellar cold gas and the circumnuclear disk, such as their masses. We also find that the circumnuclear disk tends to stay at the boundary between stable and unstable states. This works as an “adjusting valve” that regulates mass accretion toward the supermassive black hole. On the other hand, the interstellar cold gas serves as a “fuel tank” in the AGN feedback. Even if the cooling of the galactic hot gas is prevented, the interstellar cold gas can sustain the AGN activity for ≳0.5 Gyr. We also confirm that the small entropy of hot gas (≲30 keV cm2) or the short cooling time (≲1 Gyr) is a critical condition for the existence of massive amounts of molecular gas in the galaxy. The dissipation time of the interstellar cold gas may be related to the critical cooling time. The galaxy behavior is described by a simple relation among the disk stability, the cloud dissipation time, and the gas cooling rate.

Spiral structure of the galactic disk and its influence on the rotational velocity curve

AbstractMost spiral galaxies have a flat rotational velocity curve, according to the different observational techniques used in several wavelengths domain. In this work, we show that nonlinear terms are able to balance the dispersive effect of the wave, thus reviving the observed rotational curve profiles without the inclusion of any other but baryonic matter concentrated in the bulge and disk. To prove that the considered model is able to restore a flat rotational curve, Milky Way has been chosen as the best‐mapped galaxy, to apply on. Using the gravitational N‐body simulations with up to particles, we test this dynamical model in the case of the Milky Way with two different approaches. Within the direct approach, as an input condition in the simulation runs, we set the spiral surface density distribution which is previously obtained as an explicit solution to nonlinear Schrödinger equation (instead of a widely used exponential disk approximation). In the evolutionary approach, we initialize the runs with different initial mass and rotational velocity distributions, in order to capture the natural formation of spiral arms and to determine their role in the disk evolution. In both cases, we are able to reproduce the stable and nonexpanding disk structures at the simulation end times of years, with no halo inclusion. Although the given model does not take into account the velocity dispersion of stars and finite disk thickness, the results presented here still imply that nonlinear effects can significantly alter the amount of dark matter which is required to keep the galactic disk in a stable configuration.

The Photometric and Spectroscopic Properties of Remnant and Restarted Radio Galaxies in the Lockman Hole Field

Radio galaxies are known to undergo phases of activity, where the stage after the jets have switched off is referred to as the remnant phase. This state can be followed by a restarted phase when the activity reignites. Remnant and restarted radio sources are important for testing models of the evolution of radio active galactic nuclei (AGN) and for understanding the impact the recurrent jet activity has on their host galaxies. Although we now have statistical samples of radio sources in various stages of their life cycle, how this intermittent radio activity is reflected in the optical properties in this sample has not yet been addressed, and is overall a much less studied aspect in the literature. In this work, we use the Wide-field Infrared Survey Explorer and the Sloan Digital Sky Survey (SDSS) photometry, and SDSS spectra to study these properties in a sample of the remnant, candidate restarted, and active radio galaxies selected using the LOw Frequency ARray at 150 MHz in the Lockman Hole extragalactic field. Within the range of radio luminosities and stellar masses studied in this work, we find no difference between the properties of the host galaxy and of the optical emission lines for objects in different phases of their radio life cycle. The vast majority of our radio sources (either remnant, candidate restarted, or comparison sample) are associated with radiatively inefficient optical AGN and red galaxies dominated by old stellar populations. Thus, the radio and emission-line AGN activity appears to be independent and regulated by different mechanisms. This suggests that, at least for the radio luminosities of our sample, the life cycle of the radio may depend on intrinsic reasons, such as the stability of the accretion disc, more than variation in the accretion rate and fuelling of the central black hole.

The Viscosity Parameter for Late-type Stable Be Stars

Abstract Using hydrodynamic principles we investigate the nature of the disk viscosity following the parameterization by Shakura & Sunyaev adopted for the viscous decretion model in classical Be stars. We consider a radial viscosity distribution including a constant value, a radially variable α assuming a power-law density distribution, and isothermal disks, for a late-B central star. We also extend our analysis by determining a self-consistent temperature disk distribution to model the late-type Be star 1 Delphini, which is thought to have a nonvariable, stable disk as evidenced by Hα emission profiles that have remained relatively unchanged for decades. Using standard angular momentum loss rates given by Granada et al., we find values of α of approximately 0.3. Adopting lower values of angular momentum loss rates, i.e., smaller mass loss rates, leads to smaller values of α. The values for α vary smoothly over the Hα emitting region and exhibit the biggest variations nearest the central star within about five stellar radii for the late-type, stable Be stars.

Physical conditions in the warped accretion disk of a massive star

Young massive stars warm up the large amount of gas and dust that condenses in their vicinity, exciting a forest of lines from different molecular species. Their line brightness is a diagnostic tool of the gas’s physical conditions locally, which we use to set constraints on the environment where massive stars form. We made use of the Atacama Large Millimeter/submillimeter Array at frequencies near 349 GHz, with an angular resolution of 0′′.1, to observe the methyl cyanide (CH3CN) emission which arises from the accretion disk of a young massive star. We sample the disk midplane with twelve distinct beams, where we get an independent measure of the gas’s (and dust’s) physical conditions. The accretion disk extends above the midplane, showing a double-armed spiral morphology projected onto the plane of the sky, which we sample with ten additional beams: Along these apparent spiral features, gas undergoes velocity gradients of about 1 km s−1 per 2000 au. The gas temperature (T) rises symmetrically along each side of the disk, from about 98 K at 3000 au to 289 K at 250 au, following a power law with radius R−0.43. The CH3CN column density (N) increases from 9.2 × 1015 cm−2 to 8.7 × 1017 cm−2 at the same radii, following a power law with radius R−1.8. In the framework of a circular gaseous disk observed approximately edge-on, we infer an H2 volume density in excess of 4.8 ×109 cm−3 at a distance of 250 au from the star. We study the disk stability against fragmentation following the methodology by Kratter et al. (2010, ApJ, 708, 1585), which is appropriate under rapid accretion, and we show that the disk is marginally prone to fragmentation along its whole extent.

From giant clumps to clouds – I. The impact of gas fraction evolution on the stability of galactic discs

ABSTRACT The morphology of gas-rich disc galaxies at redshift $\sim 1\!-\!3$ is dominated by a few massive clumps. The process of formation or assembly of these clumps and their relation to molecular clouds in contemporary spiral galaxies are still unknown. Using simulations of isolated disc galaxies, we study how the structure of the interstellar medium and the stability regime of the discs change when varying the gas fraction. In all galaxies, the stellar component is the main driver of instabilities. However, the molecular gas plays a non-negligible role in the interclump medium of gas-rich cases, and thus in the assembly of the massive clumps. At scales smaller than a few 100 pc, the Toomre-like disc instabilities are replaced by another regime, especially in the gas-rich galaxies. We find that galaxies at low gas fraction (10 per cent) stand apart from discs with more gas, which all share similar properties in virtually all aspects we explore. For gas fractions below $\approx 20{{\ \rm per\ cent}}$, the clump-scale regime of instabilities disappears, leaving only the large-scale disc-driven regime. Associating the change of gas fraction to the cosmic evolution of galaxies, this transition marks the end of the clumpy phase of disc galaxies, and allows for the onset of spiral structures, as commonly found in the local Universe.

Resolving local and global kinematic signatures of satellite mergers with billion particle simulations

ABSTRACT In this work, we present two new ∼109 particle self-consistent simulations of the merger of a Sagittarius-like dwarf galaxy with a Milky Way (MW)-like disc galaxy. One model is a violent merger creating a thick disc, and a Gaia–Enceladus/Sausage-like remnant. The other is a highly stable disc which we use to illustrate how the improved phase space resolution allows us to better examine the formation and evolution of structures that have been observed in small, local volumes in the MW, such as the z−vz phase spiral and clustering in the vR−vϕ plane when compared to previous works. The local z−vz phase spirals are clearly linked to the global asymmetry across the disc: we find both 2-armed and 1-armed phase spirals, which are related to breathing and bending behaviours, respectively. Hercules-like moving groups are common, clustered in vR−vϕ in local data samples in the simulation. These groups migrate outwards from the inner galaxy, matching observed metallicity trends even in the absence of a galactic bar. We currently release the best-fitting ‘present-day’ merger snapshots along with the unperturbed galaxies for comparison.

Hausdorff and packing dimensions and measures for nonlinear transversally non-conformal thin solenoids

AbstractWe extend the results of Hasselblatt and Schmeling [Dimension product structure of hyperbolic sets. Modern Dynamical Systems and Applications. Eds. B. Hasselblatt, M. Brin and Y. Pesin. Cambridge University Press, New York, 2004, pp. 331–345] and of Rams and Simon [Hausdorff and packing measure for solenoids. Ergod. Th. & Dynam. Sys.23 (2003), 273–292] for $C^{1+\varepsilon }$ hyperbolic, (partially) linear solenoids $\Lambda $ over the circle embedded in $\mathbb {R}^3$ non-conformally attracting in the stable discs $W^s$ direction, to nonlinear solenoids. Under the assumptions of transversality and on the Lyapunov exponents for an appropriate Gibbs measure imposing thinness, as well as the assumption that there is an invariant $C^{1+\varepsilon }$ strong stable foliation, we prove that Hausdorff dimension $\operatorname {\mathrm {HD}}(\Lambda \cap W^s)$ is the same quantity $t_0$ for all $W^s$ and else $\mathrm {HD}(\Lambda )=t_0+1$ . We prove also that for the packing measure, $0<\Pi _{t_0}(\Lambda \cap W^s)<\infty $ , but for Hausdorff measure, $\mathrm {HM}_{t_0}(\Lambda \cap W^s)=0$ for all $W^s$ . Also $0<\Pi _{1+t_0}(\Lambda ) <\infty $ and $\mathrm {HM}_{1+t_0}(\Lambda )=0$ . A technical part says that the holonomy along unstable foliation is locally Lipschitz, except for a set of unstable leaves whose intersection with every $W^s$ has measure $\mathrm {HM}_{t_0}$ equal to 0 and even Hausdorff dimension less than $t_0$ . The latter holds due to a large deviations phenomenon.

WALLABY Pre-Pilot Survey: the effects of angular momentum and environment on the H i gas and star formation properties of galaxies in the Eridanus supergroup

ABSTRACT We use high-resolution ASKAP observations of galaxies in the Eridanus supergroup to study their H i, angular momentum, and star formation properties, as part of the WALLABY pre-pilot survey efforts. The Eridanus supergroup is composed of three sub-groups in the process of merging to form a cluster. The main focus of this study is the Eridanus (or NGC 1395) sub-group. The baryonic specific angular momentum – baryonic mass (jb−Mb) relation for the Eridanus galaxies is observed to be an unbroken power law of the form $j_{\mathrm{b}} \propto M_{\mathrm{b}}^{0.57 \pm 0.05}$, with a scatter of ∼0.10 ± 0.01 dex, consistent with previous works. We examine the relation between the atomic gas fraction, fatm, and the integrated atomic disc stability parameter q (the fatm−q relation), and find that the Eridanus galaxies deviate significantly from the relation owing to environmental processes such as tidal interactions and ram pressure affecting their H i gas. We find that a majority of the Eridanus galaxies are H i deficient compared to normal star-forming galaxies in the field. We also find that the star formation among the Eridanus galaxies may be suppressed owing to their environment, thus hinting at significant levels of pre-processing within the Eridanus sub-group, even before the galaxies have entered a cluster-like environment.

Comparative study of different solid lubricants towards friction stability in a non-asbestos disc brake pad

Purpose This study aims to compare the influence of different solid lubricants on the friction stability of a non-asbestos disc brake pad. Design/methodology/approach Three brake pads were developed using three lubricants, namely, non-asbestos brake pad with sulfide mix (NASM), non-asbestos brake pad with bismuth sulfide (NABS) and non-asbestos brake pad with molybdenum disulfide (NAMO). Sulfide mix was indigenously developed by physically mixing friction modifiers, alkaline earth chemicals and various metallic sulfides homogeneously dispersed in graphite medium. The physical, chemical, mechanical and thermal properties of brake pads were characterized as per industrial standards. The tribological performances were studied using the Chase testing machine as SAE-J661-2012. The worn surface of the pads was studied using scanning electron microscope to analyze the dominating wear mechanism. Findings NASM was excellent in fade as well as wear resistance. NABS was better from a wear point of view, but fade resistance was moderate despite its higher cost. NAMO fared average in fade and wear despite its excellent dry lubricating properties. NASM was excellent in terms of fade as well as wear resistance. Originality/value Among the selected metal sulfides, the indigenously developed sulfide mix was better than the other two sulfides, which indicates that the synergetic effect of metal sulfides was always preferable to the individual sulfides.

New analysis of the ρ-class bursts, known as the “heartbeat” of GRS 1915+105: Pulse profile and spectral properties

Context. We present the results of a new analysis of three long Rossi-XTE observations of the microquasar GRS 1915+105 in the ρ class, performed in 1997, 1999, and 2000, and characterized by different peak profiles. The first data set, labeled G-1, is dominated by a single peak, while in the third observation (G-3), all bursts show a clearly detectable couple of peaks. The second observation (G-2) shows an intermediate structure with a single peak and an emerging shoulder on the decay side. Aims. We devised a new procedure to obtain mean burst profiles in every energy channel independently of the recurrence time intervals of the bursts, variable from 45 s to 53 s in the considered observations, with the aim of investigating the different features of peaks and the eventual spectral variations. Methods. All the bursts were aligned at a common time bin on the decaying portion of the bursts that is stable in simultaneous light curves at different energies. An averaging algorithm was then applied without modifying the statistical properties or scaling the burst lengths. We analyzed the peak amplitude ratios and the dependence of their delays on energy. The spectral distributions were evaluated for the various components: a stable multi-temperature disk plus a power law Comptonization component was used for the baseline emission and temperature differences of peak components were evaluated with the inclusion of an additional blackbody. Results. In addition to the well-observed double peak (P1 and P2) pattern, we detected a third small peak (P3) in the structured G-3 light curve. This peak, differently from the other two, exhibits a fast rising and a slower exponential decay, with a e-folding time constant of 1.32 s. The blackbody temperatures of P2 and P3 are higher than P1 and the power law spectrum of P3 is the flattest one. Conclusions. The time and spectral behavior of P3 is interpreted as a signature of a relatively hot plasma outflow from the disk into the corona and its duration is consistent with the crossing timescale of the particles through the corona where electrons radiate.

The role of gas fraction and feedback in the stability and evolution of galactic discs: implications for cosmological galaxy formation models

ABSTRACT High-redshift star-forming galaxies often have irregular morphologies with giant clumps containing up to 108−109 solar masses of gas and stars. The origin and evolution of giant clumps are debated both theoretically and observationally. In most cosmological simulations, high-redshift galaxies have regular spiral structures or short-lived clumps, in contradiction with many idealized high-redshift disc models. Here, we test whether this discrepancy can be explained by the low gas fractions of galaxies in cosmological simulations. We present a series of simulations with varying gas fractions, from 25 per cent, typical of galaxies in most cosmological simulations, to 50 per cent, typical of observed galaxies at 1.5 < z < 3. We find that gas-poor models have short-lived clumps, that are unbound and mostly destroyed by galactic shear, even with weak stellar feedback. In contrast, gas-rich models form long-lived clumps even with boosted stellar feedback. This shows that the gas mass fraction is the primary physical parameter driving violent disc instabilities and the evolution of giant clumps on ∼108 yr time-scales, with lower impact from the calibration of the stellar feedback. Many cosmological simulations of galaxy formation have relatively gas-poor galactic discs, which could explain why giant clumps are absent or short-lived in such models. Similar baryonic and dark matter mass distribution could produce clumpy galaxies with long-lived clumps at z ∼ 2 if the gas fraction was in better agreement with observations.

The outburst of a 60 min AM CVn reveals peculiar colour evolution: implications for outbursts in long-period double white dwarfs

ABSTRACT We report on multiwavelength observations during quiescence and of the first detected outburst of the ≈60 min orbital period AM CVn SDSS J113732+405458. Using X-ray and UV observations, we determined an upper limit duration of the event of about 1 yr. The amplitude of the outburst was remarkably small, of around 1 mag in r and 0.5 mag in g. We have also investigated the colour variations of SDSS J113732+405458 and other long-period AM CVns in outbursts and identified a track on the colour–magnitude diagram that is not compatible with the predictions of the disc instability model, suggesting that some outbursts in long-period AM CVns are caused by enhanced mass-transfer. To our knowledge, these are the first studies of the colour evolution in AM CVns. During quiescence we measured an X-ray luminosity for SDSS J113732+405458 of ≈3 × 1029 erg s−1 in the 0.5–10 keV band. This indicates a very low accretion rate, in agreement with the disc instability model for long-period systems. However, such a model predicts stable discs at somewhat long periods. The discovery of this system outburst, along with similarities to the long-period system SDSS J080710+485259 with a comparably long, weak outburst, indicates that these enhanced mass-transfer events may be more common in long-period AM CVns. A larger sample would be needed to determine empirically at what period, if any, the disc instability stops functioning entirely. Finally, we identified an infrared excess in the quiescence spectrum attributable to the donor. This makes SDSS J113732+405458 the second AM CVn to have a directly detected donor.

Bendy to the bone: Links between vertebral morphology and waterfall climbing in amphidromous gobioid fishes.

Locomotor force production imposes strong demands on organismal form. Thus, the evolution of novel locomotor modes is often associated with morphological adaptations that help to meet those demands. In the goby lineage of fishes, most species are marine and use their fused pelvic fins to facilitate station holding in wave-swept environments. However, several groups of gobies have evolved an amphidromous lifecycle, in which larvae develop in the ocean but juveniles migrate to freshwater for their adult phase. In many of these species, the pelvic fins have been co-opted to aid in climbing waterfalls during upstream migrations to adult habitats. During horizontal swimming, forces are produced by axial musculature pulling on the vertebral column. However, during vertical climbing, gravity also exerts forces along the length of the vertebral column. In this study, we searched for novel aspects of vertebral column form that might be associated with the distinctive locomotor strategies of climbing gobies. We predicted that stiffness would vary along the length of the vertebral column due to competing demands for stability of the suction disk anteriorly and flexibility for axial thrust production posteriorly. We also predicted that derived, climbing goby species would require stiffer backbones to aid in vertical thrust production compared to non-climbing species. To test these predictions, we used microcomputed tomography scans to compare vertebral anatomy (centrum length, centrum width, and intervertebral space) along the vertebral column for five gobioid species that differ in climbing ability. Our results support our second prediction, that gobies are more flexible in the posterior portion of the body. However, the main variation in vertebral column form associated with climbing ability was the presence of larger intervertebral spaces in Sicyopterus stimpsoni, a species that uses a distinctive inching behavior to climb. These results build on past kinematic studies of goby climbing performance and lend insights into how the underlying vertebral structure of these fishes may enable their novel locomotion.

Characteristic Orbits Of Charged Particles Around Charged Black Holes

We have considered Reissner-Nordstr¨om (RN) charged nonrotating black hole (BH).We have studied motion of charged particles around charged RN BH. It was found out that there are two boundary conditions for specific angular momentum of stable circular orbits corresponding to: innermost stable circular orbits (ISCO) and outermost stable circular orbits (OSCO) and accretion disk is originated between these two orbits. It was obtained the upper and lower limits for the value of particle’s charge which may exist in the accretion disk matter around the extreme charged Reissner Nordstr¨om black hole.