An Immersed Boundary method with divergence-free velocity interpolation and force spreading

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.Comment: 49 pages, 13 figure

The geometry of thermodynamic control

A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold, and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory

Verbal Learning and Memory After Cochlear Implantation in Postlingually Deaf Adults: Some New Findings with the CVLT-II

OBJECTIVES: Despite the importance of verbal learning and memory in speech and language processing, this domain of cognitive functioning has been virtually ignored in clinical studies of hearing loss and cochlear implants in both adults and children. In this article, we report the results of two studies that used a newly developed visually based version of the California Verbal Learning Test-Second Edition (CVLT-II), a well-known normed neuropsychological measure of verbal learning and memory. DESIGN: The first study established the validity and feasibility of a computer-controlled visual version of the CVLT-II, which eliminates the effects of audibility of spoken stimuli, in groups of young normal-hearing and older normal-hearing (ONH) adults. A second study was then carried out using the visual CVLT-II format with a group of older postlingually deaf experienced cochlear implant (ECI) users (N = 25) and a group of ONH controls (N = 25) who were matched to ECI users for age, socioeconomic status, and nonverbal IQ. In addition to the visual CVLT-II, subjects provided data on demographics, hearing history, nonverbal IQ, reading fluency, vocabulary, and short-term memory span for visually presented digits. ECI participants were also tested for speech recognition in quiet. RESULTS: The ECI and ONH groups did not differ on most measures of verbal learning and memory obtained with the visual CVLT-II, but deficits were identified in ECI participants that were related to recency recall, the buildup of proactive interference, and retrieval-induced forgetting. Within the ECI group, nonverbal fluid IQ, reading fluency, and resistance to the buildup of proactive interference from the CVLT-II consistently predicted better speech recognition outcomes. CONCLUSIONS: Results from this study suggest that several underlying foundational neurocognitive abilities are related to core speech perception outcomes after implantation in older adults. Implications of these findings for explaining individual differences and variability and predicting speech recognition outcomes after implantation are discussed

The Gounkoto Au deposit, West Africa: Constraints on ore genesis and volatile sources from petrological, fluid inclusion and stable isotope data

The Loulo–Gounkoto complex in the Kédougou–Kéniéba Inlier hosts three multi-million ounce orogenic gold deposits, situated along the Senegal–Mali Shear Zone. This west Malian gold belt represents the largest West African orogenic gold district outside Ghana. The Gounkoto deposit is hosted to the south of the Gara and Yalea gold mines in the Kofi Series metasedimentary rocks. The ore body is structurally controlled and is characterised by sodic and phyllic alteration, As- and Fe-rich ore assemblages, with abundant magnetite, and overall enrichment in Fe–As–Cu–Au–Ag–W–Ni–Co–REE + minor Te–Pb–Se–Cd. Fluid inclusion analysis indicates that the deposit formed at P–T conditions of approximately 1.4 kbar and 340 °C and that two end member fluids were involved in mineralisation: (1) a moderate temperature (315–340 °C), low salinity (< 10 wt.% NaCl equiv.), low density (≤ 1 g·cm− 3), H2O–CO2–NaCl–H2S ± N2–CH4 fluid; (2) a high temperature (up to 445 °C), hypersaline (~ 40 wt.% NaCl equiv.), high density (~ 1.3 g·cm− 3), H2O–CO2–NaCl ± FeCl2 fluid. Partial mixing of these fluids within the Jog Zone at Gounkoto enhanced phase separation in the aqueo-carbonic fluid and acted as a precipitation mechanism for Au. These findings demonstrate the widespread, if heterogeneously distributed, nature of fluid mixing as an ore forming process in the Loulo–Gounkoto complex, operating over at least a 30 km strike length of the shear zone. Stable isotope analyses of ore components at Gounkoto indicate a dominant metamorphic source for H2O, H2S and CO2, and by extension Au. It thus can be reasoned that both the aqueo-carbonic and the hypersaline fluid at Gounkoto are of metamorphic origin and that the high levels of salinity in the brine are likely derived from evaporite dissolution

The Fundamental Plane of QSOs and the Relationship Between Host and Nucleus

We present results from an archival study of 70 medium-redshift QSOs observed with the Wide Field Planetary Camera 2 on board the Hubble Space Telescope. The QSOs have magnitudes M_V <= -23 (total nuclear plus host light) and redshifts $0.06 <= z <= 0.46$. The aim of the present study is to investigate the connections between the nuclear and host properties of QSOs, using high-resolution images and removing the central point source to reveal the host structure. We confirm that more luminous QSO nuclei are found in more luminous host galaxies. Using central black hole masses from the literature, we find that nuclear luminosity also generally increases with black hole mass, but it is not tightly correlated. Nuclear luminosities range from 2.3% to 200% of the Eddington limit. Those in elliptical hosts cover the range fairly evenly, while those in spirals are clustered near the Eddington limit. Using a principal components analysis, we find a kind of fundamental plane relating the nuclear luminosity to the size and effective surface magnitude of the bulge. Using optical nuclear luminosity, this relationship explains 96.1% of the variance in the overall sample, while another version of the relationship uses x-ray nuclear luminosity and explains 95.2% of the variance. The form of this QSO fundamental plane shows similarities to the well-studied fundamental plane of elliptical galaxies, and we examine the possible relationship between them as well as the difficulties involved in establishing this connection.Comment: 49 pages, 6 figures. Accepted by Ap

The host galaxies of luminous quasars

We present results of a deep HST/WFPC2 imaging study of 17 quasars at z~0.4, designed to determine the properties of their host galaxies. The sample consists of quasars with absolute magnitudes in the range -24>M_V>-28, allowing us to investigate host galaxy properties across a decade in quasar luminosity, but at a single redshift. We find that the hosts of all the RLQs, and all the RQQs with nuclear luminosities M_V<-24, are massive bulge-dominated galaxies, confirming and extending the trends deduced from our previous studies. From the best-fitting model host galaxies we have estimated spheroid and black-hole masses, and the efficiency (with respect to Eddington luminosity) with which each quasar is radiating. The largest inferred black-hole mass in our sample is \~3.10^9 M_sun, comparable to those at the centres of M87 and Cygnus A. We find no evidence for super-Eddington accretion in even the most luminous objects. We investigate the role of scatter in the black-hole:spheroid mass relation in determining the ratio of quasar to host-galaxy luminosity, by generating simulated populations of quasars lying in hosts with a Schechter mass function. Within the subsample of the highest luminosity quasars, the observed variation in nuclear-host luminosity ratio is consistent with being the result of the scatter in the black-hole:spheroid relation. Quasars with high nuclear-host ratios can be explained by sub-Eddington accretion onto black holes in the high-mass tail of the black-hole:spheroid relation. Our results imply that, owing to the Schechter cutoff, host mass should not continue to increase linearly with quasar luminosity, at the very highest luminosities. Any quasars more luminous than M_V=-27 should be found in massive elliptical hosts which at the present day would have M_V ~ -24.5.Comment: Accepted for publication in MNRAS. 18 pages; 7 figures and 17 greyscale images are reproduced here at low quality due to space limitations. High-resolution figures are available from ftp://ftp.roe.ac.uk/pub/djef/preprints/floyd2004

American Black Bear Population Fragmentation Determined Through Pedigrees in the Trans-Border Canada-United States Region

Fragmentation of species with large numbers of individuals in adjacent areas can be challenging to detect using genetic tools as there often is no differentiation because genetic drift occurs very slowly. We used a genetic-based pedigree analysis to detect fragmentation in the American black bear (Ursus americanus) across 2 highways with large adjacent populations. We used 20 locus microsatellite genotypes to detect parent-offspring and full sibling pairs within a sample of 388 black bears. We used the spatial patterns of capture locations of these first order relatives relative to US Highway 2 in northwest Montana and Highway 3 in southeast British Columbia to estimate the number of close relatives sampled across the highways (migrants/km of highway length) as an index of fragmentation. We compared these values to an expected migrant/km rate derived from the mean values of simulated fractures in the Highway 2 and Highway 3 region. We found evidence that these highway corridors were fragmenting black bear populations, but not completely. The observed migrant/km rate for Highway 2 was 0.05, while the expected rate was 0.21 migrants/km. Highway 3 had an observed migrant/km rate of 0.09 compared to the expected rate of 0.26. None of the 16 bears carrying GPS radio collars for 1 year crossed Highway 2, yet 6 of 18 crossed Highway 3. Pedigree and telemetry results were more closely aligned in the Highway 2 system evidencing more intense fragmentation than we found along Highway 3. Our results demonstrate that pedigree analysis may be a useful tool for investigating population fragmentation in situations where genetic signals of differentiation are too weak to determine migration rates using individual-based methods, such as population assignment

Simulating Cardiac Fluid Dynamics in the Human Heart

Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin, flexible valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid-structure interactions. However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the cardiac valves are limited in their abilities to predict valve performance, resolve fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac fluid dynamics in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart's microstructure. Further, it is the first fluid-structure interaction model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure-volume loops that automatically capture isovolumetric contraction and relaxation, and predicts fine-scale flow features. None of these outputs are prescribed; instead, they emerge from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical devices or clinical interventions. They also can serve as platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients