Outer Mass Research Articles

The Bartnik–Bray Outer Mass of Small Metric Spheres in Time-Symmetric 3-Slices

Given a sphere with Bartnik data close to that of a round sphere in Euclidean 3-space, we compute its Bartnik-Bray outer mass to first order in the data's deviation from the standard sphere. The Hawking mass gives a well-known lower bound, and an upper bound is obtained by estimating the mass of a static vacuum extension. As an application we confirm that in a time-symmetric slice concentric geodesic balls shrinking to a point have mass-to-volume ratio converging to the energy density at their center, in accord with physical expectation and the behavior of other quasilocal masses. For balls shrinking to a flat point we can also compute the outer mass to fifth order in the radius---the term is proportional to the Laplacian of the scalar curvature at the center---but our estimate is not refined enough to identify this term at a point which is merely scalar flat. In particular it cannot discern gravitational contributions to the mass.

The Double Galaxy Cluster A2465. III. X-Ray and Weak-lensing Observations∗

Abstract We report Chandra X-ray observations and optical weak-lensing measurements from Subaru/Suprime-Cam images of the double galaxy cluster A2465 (z = 0.245). The X-ray brightness data are fit to a β model to obtain the radial gas density profiles of the northeast (NE) and southwest (SW) subcomponents, which are seen to differ in structure. We determine core radii, central temperatures, the gas masses within r 500c, and the total masses for the broader NE and sharper SW components assuming hydrostatic equilibrium. There is no large X-ray excess between the two components. The central entropy of the NE subcluster is about two times higher than the SW. Along with its structural properties and an apparent radio halo that is a sign of a merger, this suggests that the NE component has undergone merging on its own. The weak-lensing analysis gives virial masses for each substructure, which compare well with earlier dynamical results. The derived outer mass contours of the SW sub-component from weak lensing are more irregular and extended than those of the NE. Although there is a weak enhancement and small offsets between X-ray gas and mass centers from weak lensing, the lack of large amounts of gas between the two subclusters indicates that A2465 is in a pre-merger state. We discuss star formation enhancement in this system resulting from its dynamics and shock-induced star formation scenarios. A dynamical model that is consistent with the observed cluster data, based on the FLASH program and the radial infall model, is constructed, where the subclusters currently separated by ∼1.2 Mpc are approaching each other at ∼2000 km s−1 and will meet in ∼0.4 Gyr.

Wide bandwidth 2-DoF electromagnetic MEMS energy harvester for low g applications

This paper presents the design of a 2-DoF electromagnetic MEMS energy harvester, optimized to be realized using commercially available microfabrication processes. The proposed 2-DoF system consists of two inter-connected vibrating masses to achieve dynamically amplified displacement amplitude, at low-frequency and low-g vibrations with wide operational bandwidth. The vibrating microstructure, with sputtered NdFeB magnets, is designed considering microfabrication constraints of MetalMUMPs process. The stationary planar microcoils are designed using 0.35 μm CMOS MIMOS process. The vibrating microstructure and stationary planar microcoils are bonded together using photoresist with thickness of 30 μm. The magnets are arranged in a Halbach array configuration to concentrate the magnetic field on the stationary microcoils side while cancelling the field nearly zero on the other side. The input acceleration value with respect to overall damping is optimized, for a structurally limited gap of 160 μm between the inner and outer mass of the 2-DoF vibrating system, using design of experiments (DOE) based response surface models. For the proposed design, two resonant frequencies of 40.7 and 89.6 Hz are obtained with an operational bandwidth of 49 Hz. With an input acceleration value of 0.442g, an induced voltage of 18 mV and output power of 0.82 nW is btained at the first resonant frequency while an induced voltage of 14 mV and output power of 0.54 nW is obtained at the second resonant frequency. The normalized power density of the proposed energy harvester design is 7.94 ? 10ź7 (W/cm3/g2) at 40.7 Hz, with an overall device volume of 0.0058 cm3.

On the migration-induced formation of the 9:7 mean motion resonance

We study formation of 9:7 mean motion resonance (MMR) as a result of convergent migration of two planets embedded in a disc. Depending on the migration parameters, initial orbits and planets' masses the system may pass through the resonance or enter it (permanently or temporarily). We illustrate that a stable equilibrium of the averaged system (a periodic orbit of the N-body model) is surrounded by the region of permanent resonance capture, whose size depends on the migration parameters and the planets mass ratio. A system located inside this region tends towards the equilibrium (the capture is permanent), while a system located outside the region evolves away from the equilibrium and leaves the resonance. We verify recent results of Delisle et al. and Xu & Lai where they show that for $m_1 \lesssim m_2$ ($m_1, m_2$ are the inner and outer planets' masses) the equilibrium is unstable when the migration is added, so the capture cannot be permanent. We show that for particular migration parameters the situation may be reversed (the equilibria are unstable for $m_1 \gtrsim m_2$). We illustrate that 9:7 MMR consists of two modes separated with a separatrix. The inner one is centred at the equilibrium and the outer one has no equilibrium in its centre. A system located outside the region of stable capture evolves from the inner into the outer mode. The evolution occurs along families of periodic orbits of the averaged system, that play a crucial role in the dynamics after the resonance capture.

Migration of planets into and out of mean motion resonances in protoplanetary discs: analytical theory of second-order resonances

Recent observations of Kepler multi-planet systems have revealed a number of systems with planets very close to second-order mean motion resonances (MMRs, with period ratio $1:3$, $3:5$, etc.) We present an analytic study of resonance capture and its stability for planets migrating in gaseous disks. Resonance capture requires slow convergent migration of the planets, with sufficiently large eccentricity damping timescale $T_e$ and small pre-resonance eccentricities. We quantify these requirements and find that they can be satisfied for super-Earths under protoplanetary disk conditions. For planets captured into resonance, an equilibrium state can be reached, in which eccentricity excitation due to resonant planet-planet interaction balances eccentricity damping due to planet-disk interaction. We show that this "captured" equilibrium can be overstable, leading to partial or permanent escape of the planets from the resonance. In general, the stability of the captured state depends on the inner to outer planet mass ratio $q=m_1/m_2$ and the ratio of the eccentricity damping times. The overstability growth time is of order $T_e$, but can be much larger for systems close to the stability threshold. For low-mass planets undergoing type I (non-gap opening) migration, convergent migration requires $q \lesssim 1$, while the stability of the capture requires $q\gtrsim 1$. These results suggest that planet pairs stably captured into second-order MMRs have comparable masses. This is in contrast to first-order MMRs, where a larger parameter space exists for stable resonance capture. We confirm and extend our analytical results with $N$-body simulations, and show that for overstable capture, the escape time from the MMR can be comparable to the time the planets spend migrating between resonances.

High pressure-low flow remodeling of the rat saphenous vein wall.

Objective To better understand factors that may play a role in the development of varicosities. Methods We induced combined flow-pressure disturbance in the saphenous system of the rat by performing chronic partial clipping of the main branch. Biomechanical and quantitative histological testing was undertaken. Results A rich microvenous network developed. Bloodflow decreased to 0.65 ± 0.18 µl/s (control side, 3.5 ± 1.4 µl/s) and pressure elevated to 6.8 ± 0.7 mmHg (control side, 2.3 ± 0.2 mmHg, p < 0.05). Involution of the wall and lumen was observed (16.5%, 28.7% and 35.5% reduction in outer diameter, wall thickness and wall mass respectively, p < 0.05). Elevated macrophage (CD68) and cell division (Ki67) activity was observed. Elastic tissue and smooth muscle actin became less concentrated in the inner medial layers. Conclusions Low-flow induced morphological shrinking of the lumen in veins may override pressure-induced morphological distension. Loosening of the force-bearing elements during flow-induced wall remodeling may be an important pathological component in varicosity.

Mass estimates for very cold (&lt;8 K) gas in molecular cloud cores

The mass of prestellar cores is an essential ingredient to understand the onset of star formation in the core. The low level of emission from cold dust may keep parts of it hidden from observation. We aim to determine the fraction of core mass in the temperature range < 8 K that can be expected for typical low- and high-mass star formation regions. We calculate the dust temperature within standard spherically symmetric prestellar cores for a grid of density powerlaws in the outer core regions, core masses, and variation in the external multi-component radiation field. The dust is assumed to be composed of amorphous silicate and carbon, and variations of its optical properties are discussed. As measure for the distribution of cores and clumps, we use core mass functions derived for various environments. In view of the high densities in very cold central regions, dust and gas temperatures are assumed to be equal. We find that the fraction of mass with temperatures < 8 K in typical low- and high-mass cores is < 20\%. It is possible to obtain higher fractions of very cold gas by placing intermediate- or high-mass cores in a typical low-mass star formation environment. We show that the mass uncertainty arising from FIR to mm modeling of very cold dust emission is smaller than the mass uncertainty due to the unknown dust opacities.

Bifurcation structure of the special class of nonstationary regimes emerging in the 2D inertially coupled, unit-cell model: Analytical study

Present work is devoted to the analytical investigation of the bifurcation structure of special class of nonstationary low-energy regimes emerging in the locally resonant unit-cell model. System under consideration comprises an outer mass with internal rotator and subject to the 2D, nonlinear local potential. These regimes are characterized by the slow, purely rotational motion of the rotator synchronized with the periodic energy beats between the axial and the lateral vibrations of the outer element. Thus the angular speed of the rotator and the beating frequency of the outer element satisfy the 1:2 resonance condition. In the present study these regimes are referred to as regimes of synchronous nonlinear beats (RSNB). Using the regular muti-scale analysis in the limit of low energy excitation we derive the slow-flow model. To showcase the evolution of RSNBs we used the special Poincaré map technique applied on the slow-flow model. Results of the Poincaré sections unveiled some interesting local bifurcations undergone by these regimes. Further analysis of the slow-flow model enabled us to describe the RSNBs analytically as well as exposed their entire bifurcation structure. The bifurcation analysis has shown the coexistence of several branches of RSNBs corresponding to the regimes of weak and strong, two-dimensional, recurrent energy channeling. We substantiate the results of the analytical study with numerical simulations of the full model and find them to be in the very good agreement.

A UNIFORM CATALOG OF MOLECULAR CLOUDS IN THE MILKY WAY

ABSTRACT The all-Galaxy CO survey of Dame et al. is by far the most uniform, large-scale Galactic CO survey. Using a dendrogram-based decomposition of this survey, we present a catalog of 1064 massive molecular clouds throughout the Galactic plane. This catalog contains 2.5 × 108 solar masses, or 25 − 5.8 + 10.7 % of the Milky Way's estimated H2 mass. We track clouds in some spiral arms through multiple quadrants. The power index of Larson's first law, the size-linewidth relation, is consistent with 0.5 in all regions—possibly due to an observational bias—but clouds in the inner Galaxy systematically have significantly (∼30%) higher linewidths at a given size, indicating that their linewidths are set in part by the Galactic environment. The mass functions of clouds in the inner Galaxy versus the outer Galaxy are both qualitatively and quantitatively distinct. The inner Galaxy mass spectrum is best described by a truncated power law with a power index of γ = −1.6 ± 0.1 and an upper truncation mass of M 0 = (1.0 ± 0.2) × 107 M ⊙, while the outer Galaxy mass spectrum is better described by a non-truncating power law with γ = −2.2 ± 0.1 and an upper mass of M 0 = (1.5 ± 0.5) × 106 M ⊙, indicating that the inner Galaxy is able to form and host substantially more massive GMCs than the outer Galaxy. Additionally, we have simulated how the Milky Way would appear in CO from extragalactic perspectives, for comparison with CO maps of other galaxies.

Kozai–Lidov cycles towards the limit of circumbinary planets

Abstract In this Letter, we answer a simple question: Can a misaligned circumbinary planet induce Kozai–Lidov cycles on an inner stellar binary? We use known analytic equations to analyse the behaviour of the Kozai–Lidov effect as the outer mass is made small. We demonstrate a significant departure from the traditional symmetry, critical angles and amplitude of the effect. Aside from massive planets on near-polar orbits, circumbinary planetary systems are devoid of Kozai–Lidov cycles. This has positive implications for the existence of highly misaligned circumbinary planets: an observationally unexplored and theoretically important parameter space.

Sarcoidosis. Debut as orbital pseudotumour

Case report78-Year-old female patient being investigated for a left orbital pseudotumour of 17 days onset. She had proptosis, pain, with no limitation of eye movements, periorbital edema, and upper eyelid ptosis, compatible with an orbital pseudotumour. The MRI showed an upper outer left orbital mass adjacent to the side of eyeball and an increase in soft tissue at the level of lacrimal gland. The histopathology study of an eyelid lesion demonstrated the presence of non-caseating granulomas. DiscussionA definitive diagnosis of orbital sarcoidosis was made. Oral treatment with corticosteroids and methotrexate achieved gradual control of the disease.

Integrated damping systems for tall buildings: tuned mass damper/double skin facade damping interaction system

Summary As today's tall buildings become ever taller and more slender, wind-induced vibration is a serious design issue. This paper presents integrated damping systems for tall buildings. An emphasis is placed on investigating the potential of double skin facades (DSF) as an integrated damping system for tall buildings. In the first scheme, the connectors between the inner and outer skins of the DSF system are designed to have low axial stiffness with a damping mechanism. Through this design, vibration of the primary building structure can be substantially reduced. However, excessive movements of the DSF outer skin masses are a design limitation. In the second scheme, the tuned mass damper (TMD) and DSF damping (DSFD) interaction system is studied to mitigate the design limitation of the first scheme and to resolve other TMD-related design issues. TMDs are usually very large and located near the top of tall buildings for their effective performance. As a result, very valuable occupiable space near the top of tall buildings is sacrificed to contain large TMDs. In addition, installing TMD systems means adding additional masses to tall buildings. Through the TMD/DSFD interaction system, these issues can also be substantially addressed. Compared with the conventional TMD system, the TMD/DSFD interaction system requires a significantly reduced TMD mass ratio to achieve the same target damping ratio. Compared with the first scheme only with the DSFD mechanism, movements of the DSF outer skins can be better controlled in the TMD/DSFD interaction system. Copyright © 2015 John Wiley & Sons, Ltd.

Antibubbles and fine cylindrical sheets of air

Drops impacting at low velocities onto a pool surface can stretch out thin hemispherical sheets of air between the drop and the pool. These air sheets can remain intact until they reach submicron thicknesses, at which point they rupture to form a myriad of microbubbles. By impacting a higher-viscosity drop onto a lower-viscosity pool, we have explored new geometries of such air films. In this way we are able to maintain stable air layers which can wrap around the entire drop to form repeatable antibubbles, i.e. spherical air layers bounded by inner and outer liquid masses. Furthermore, for the most viscous drops they enter the pool trailing a viscous thread reaching all the way to the pinch-off nozzle. The air sheet can also wrap around this thread and remain stable over an extended period of time to form a cylindrical air sheet. We study the parameter regime where these structures appear and their subsequent breakup. The stability of these thin cylindrical air sheets is inconsistent with inviscid stability theory, suggesting stabilization by lubrication forces within the submicron air layer. We use interferometry to measure the air-layer thickness versus depth along the cylindrical air sheet and around the drop. The air film is thickest above the equator of the drop, but thinner below the drop and up along the air cylinder. Based on microbubble volumes, the thickness of the cylindrical air layer becomes less than 100 nm before it ruptures.

Sarcoidosis. Comienzo como pseudotumor orbitario

Case report78 year-old female patient being investigated for a left orbital pseudotumour of 17 days onset. She had proptosis, pain, with no limitation of eye movements, periorbital oedema, and upper eyelid ptosis, compatible with an orbital pseudotumour. The MRI showed an upper outer left orbital mass adjacent to the side of eyeball and an increase in soft tissue at the level of lacrimal gland. The histopathology study of an eyelid lesion demonstrated the presence of non-caseating granulomas. DiscussionA definitive diagnosis of orbital sarcoidosis was made. Oral treatment with corticosteroids and methotrexate achieved gradual control of the disease.

Simulation of the ozone pretreatment of wheat straw

Wheat straw is a potential feedstock in biorefinery for sugar production. However, the cellulose, which is the major source of sugar, is protected by lignin. Ozonolysis deconstructs the lignin and makes cellulose accessible to enzymatic digestion. In this study, the change in lignin concentration with different ozonolysis times (0, 1, 2, 3, 5, 7, 10, 15, 20, 30, 60min) was fit to two different kinetic models: one using the model developed by Garcia-Cubero et al. (2012) and another including an outer mass transfer barrier or “cuticle” region where ozone mass transport is reduced in proportion to the mass of unreacted insoluble lignin in the cuticle. The kinetic parameters of two mathematical models for predicting the soluble and insoluble lignin at different pretreatment time were determined. The results showed that parameters derived from the cuticle-based model provided a better fit to experimental results compared to a model without a cuticle layer.

Nonlinear energy channeling in the two-dimensional, locally resonant, unit-cell model. I. High energy pulsations and routes to energy localization.

Present paper is the first one in the series devoted to the analytical investigation of energy channeling phenomena emerging in the locally resonant unit-cell model comprising an outer mass incorporating internal rotator and subject to the 2D, nonlinear local potential. In the current study, we mainly focus on the analysis of the mechanisms of formation and bifurcations of the special type of non-stationary regimes, characterized by the massive, bidirectional energy transport between the axial and the lateral vibrations of the outer element controlled by the internal, rotational device as well as the regimes of the unidirectional energy localization. The devised analytical procedure is based on a singular multi-scale analysis constructed for the special asymptotic limit corresponding to the high energy excitations. The basic question of possible coexistence of various stationary and non-stationary system regimes as well as their local and global bifurcations is addressed via the reduction of the global flow on the slow invariant manifold in the vicinity of the fundamental resonance. Numerical simulations fully confirm the analytical predictions concerning the structure of the response regimes and their bifurcations.

Nonlinear energy channeling in the two-dimensional, locally resonant, unit-cell model. II. Low energy excitations and unidirectional energy transport.

This paper completes a series of two publications devoted to the analytical investigation of energy channeling phenomena, emerging in a locally resonant unit-cell model. The system under consideration comprises an outer mass with internal rotator and subject to the 2D nonlinear local potential. In the present study, we focus on the analysis of the regimes of two-dimensional, nonlinear energy transport forming in the special asymptotic limit of low energy excitations. Unlike the previously considered case, this limit can also be characterized by the absence of resonant interactions between the internal rotator and the motion of an outer element. In the considered limit, we report the emergence of all new, highly nonlinear, transient regimes of unidirectional energy channeling. This phenomenon is manifested by partial and complete targeted energy flow from axial to lateral vibrations, controlled by an internal device. Here, we also show that regimes corresponding to the bidirectional energy channeling as well as the spontaneous energy locking reported in the first paper of the series-persist in the low energy limit as well. In this study, we use a regular multi-scale asymptotic procedure and completely unveil the intrinsic mechanisms governing bi- and unidirectional energy channeling. Numerical simulations are found to be in a fairly good agreement with the predictions of analytic model.

Outer and inner mass distributions of the irregular galaxies UGC 4284 and UGC 11861: constraining the baryonic content through stellar population synthesis studies

In this article we investigate the outer and inner mass distributions of the irregular galaxies UGC 4284 and UGC 11861, taking advantage of published HI and H{\alpha} high resolution rotation curves and constraining the stellar disk of both galaxies throughout stellar population synthesis studies. In addition we take into account the gas content of both galaxies deriving the HI+He rotation curve. The deduced baryonic rotation curves (star+gas) are inadequate to account for the total mass of UGC 4284 and UGC 11861, for that reason we examine the possibility of dark matter to explain the incongruity between the observed HI and H{\alpha} rotation curves of UGC 4284 and UGC 11861 and the derived baryonic rotation curves. We consider NFW, Burkert, DiCintio, Einasto, and the Stadel dark matter halos, to analyse the dark matter content of UGC 4284 and UGC 11861. The principal results of this work are that cored dark matter models better reproduce the dark matter H{\alpha} and HI rotation curves of UGC 11861 and the dark matter HI rotation curve of UGC 4284, while, the H{\alpha} rotation curve of UGC 4284 is better reproduced by a cuspy DiCintio DM model. In general, cored exponential two-parameters models Einasto and Stadel, give better fits than Burkert. This trend, as well as to confirm past results, presents for the first time a comparison between two different exponential dark matter models, Einasto and Stadel, in an attempt to better constrain the range of possible exponential dark matter models applied to real galaxies.

A multi-objective design optimization strategy for vertical ground heat exchangers

A multi-objective design optimization strategy for vertical U-tube ground heat exchangers (GHEs) is presented to minimize the system upfront cost and entropy generation number simultaneously. Five design variables of vertical U-tube GHEs, including borehole number, borehole depth, borehole radius, U-tube outer radius and fluid mass flow rate, are first selected via a global sensitivity analysis method, and then optimized by a genetic algorithm (GA) optimizer implemented in MATLAB. Based on the Pareto frontier obtained from the GA optimization, a decision-making strategy is then used to determine a final solution. Two case studies are presented to validate the effectiveness of the proposed strategy. The results based on a small scale GSHP system in Australia show that, compared to the original design, the use of this proposed strategy can decrease the total system cost (i.e. the upfront cost and 20 years’ operating cost) by 9.5%. Compared to a single-objective design optimization strategy, 6.2% more energy can be saved by using this multi-objective design optimization strategy. The result from a relatively large scale GSHP system implemented in China shows that a 5.2% decrease in the total system cost can be achieved by using this proposed strategy, compared with using the original design.

INTEGRATED MULTIPLE TUNED MASS DAMPERS FOR TALL BUILDINGS

As tall buildings become taller and more slender, wind-induced vibration is a serious design issue. Installing auxiliary damping devices, such as tuned mass dampers (TMD), is a very reliable solution. TMDs are usually large and located near the top of tall buildings for their effective performance. As a result, very valuable occupiable space near the top of tall buildings is sacrificed to contain large TMDs, and installing TMD systems results in adding additional masses to tall buildings. In order to address these issues, more integrated TMD systems for tall buildings are studied. First, distributing multiple small TMDs to multiple upper floors of tall buildings is investigated. The study results suggest this can be done without substantial loss of the effectiveness of the system. Second, designing existing masses in tall buildings to provide damping mechanism is studied. An emphasis is placed on studying the potential of double skin façades (DSF) as an integrated damping system. For this, the connectors between the inner and outer skins of the DSF system are designed to have very low axial stiffness, and the outer skin masses of the DSF system is utilized as damping mass. Wind-induced vibration of tall building structure can be substantially reduced through this design. Finally, TMD/DSF interaction system is studied to synergistically enhance the performance of the TMD and DSF damping systems.