Chaos in Shear Flows

Almost 25 years ago Lorenz published his seminal study on the existence of a strange attractor in the phase space of a severely truncated model system arising from the hydrodynamical equations describing two-dimensional convection. Nearly a century ago Poincare published his famous treatise Les Methodes Noovelles de la Mecaniaue Celeste (1892) in which the possible complexity of behavior in nonintegrable, conservative systems was first envisioned. Both these works address an age old puzzle: How do apparently stochastic outputs arise from an entirely deterministic system subject to non-stochastic inputs

Measuring Topological Chaos

The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a chaotic flow, the braid generated by the motion of three or more fluid particles is computed. A ``braiding exponent'' is then defined to characterize the complexity of the braid. This exponent is proportional to the usual Lyapunov exponent of the flow, associated with separation of nearby trajectories. Measuring chaos in this manner has several advantages, especially from the experimental viewpoint, since neither nearby trajectories nor derivatives of the velocity field are needed.Comment: 4 pages, 6 figures. RevTeX 4 with PSFrag macro

Assessment of regional bone tissue perfusion in rats using fluorescent microspheres

Disturbances in bone blood flow have been shown to have deleterious effects on bone properties yet there remain many unanswered questions about skeletal perfusion in health and disease, partially due to the complexity of measurement methodologies. The goal of this study was use fluorescent microspheres in rats to assess regional bone perfusion by adapting mouse-specific fluorescent microsphere protocol. Ten fifteen-week old Sprague Dawley rats were injected with fluorescent microspheres either via cardiac injection (n = 5) or via tail vein injection (n = 5). Femora and tibiae were harvested and processed to determine tissue fluorescence density (TFD) which is proportional to the number of spheres trapped in the tissue capillaries. Right and left total femoral TFD (2.77 ± 0.38 and 2.70 ± 0.24, respectively) and right and left tibial TFD (1.11 ± 0.26 and 1.08 ± 0.34, respectively) displayed bilateral symmetry in flow when assessed in cardiac injected animals. Partitioning of the bone perfusion into three segments along the length of the bone showed the distal femur and proximal tibia received the greatest amount of perfusion within their respective bones. Tail vein injection resulted in unacceptably low TFD levels in the tibia from 4 of the 5 animals. In conclusion this report demonstrates the viability of cardiac injection of fluorescent microspheres to assess bone tissue perfusion in rats

Rain, power laws, and advection

Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws are generated by treating rain as a passive tracer undergoing advection in a velocity field generated by a two-dimensional system of point vortices.Comment: 7 pages, 4 figure

Zoledronate treatment has different effects in mouse strains with contrasting baseline bone mechanical phenotypes

Aref, M. W., McNerny, E. M. B., Brown, D., Jepsen, K. J., & Allen, M. R. (2016). Zoledronate treatment has different effects in mouse strains with contrasting baseline bone mechanical phenotypes. Osteoporosis International : A Journal Established as Result of Cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA, 27(12), 3637–3643. https://doi.org/10.1007/s00198-016-3701-

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

Raloxifene neutralizes bone brittleness induced by anti-remodeling treatment and increases fatigue life through non-cell mediated mechanisms

Pre-clinical data have shown that tissue level effects stemming from bisphosphonateinduced suppression of bone remodeling can result in bone that is stronger yet more brittle. Raloxifene has been shown to reduce bone brittleness through non-cellular mechanisms. The goal of this work was to test the hypothesis that raloxifene can reverse the bone brittleness resulting from bisphosphonate treatment. Dog and mouse bone from multiple bisphosphonate dosing experiments were soaked in raloxifene and then assessed for mechanical properties. Mice treated with zoledronate in vivo had lower post-yield mechanical properties compared to controls. Raloxifene soaking had significant positive effects on select mechanical properties of bones from both vehicle and zoledronate treated mice. Although the effects were blunted in zoledronate bones relative to vehicle, the soaking was sufficient to normalize properties to control levels. Additional studies showed that raloxifene-soaked bones had a significant positive effect on cycles to failure (+114%) compared to control-soaked mouse bone. Finally, raloxifene soaking significantly improved select properties of ribs from dogs treated for 3 years with alendronate. These data show that ex vivo soaking in raloxifene can act through non-cellular mechanisms to enhance mechanical properties of bone previously treated with bisphosphonate. We also document that the positive effects of raloxifene soaking extend to enhancing fatigue properties of bone

Implementation of the LANS-alpha turbulence model in a primitive equation ocean model

This paper presents the first numerical implementation and tests of the Lagrangian-averaged Navier-Stokes-alpha (LANS-alpha) turbulence model in a primitive equation ocean model. The ocean model in which we work is the Los Alamos Parallel Ocean Program (POP); we refer to POP and our implementation of LANS-alpha as POP-alpha. Two versions of POP-alpha are presented: the full POP-alpha algorithm is derived from the LANS-alpha primitive equations, but requires a nested iteration that makes it too slow for practical simulations; a reduced POP-alpha algorithm is proposed, which lacks the nested iteration and is two to three times faster than the full algorithm. The reduced algorithm does not follow from a formal derivation of the LANS-alpha model equations. Despite this, simulations of the reduced algorithm are nearly identical to the full algorithm, as judged by globally averaged temperature and kinetic energy, and snapshots of temperature and velocity fields. Both POP-alpha algorithms can run stably with longer timesteps than standard POP. Comparison of implementations of full and reduced POP-alpha algorithms are made within an idealized test problem that captures some aspects of the Antarctic Circumpolar Current, a problem in which baroclinic instability is prominent. Both POP-alpha algorithms produce statistics that resemble higher-resolution simulations of standard POP. A linear stability analysis shows that both the full and reduced POP-alpha algorithms benefit from the way the LANS-alpha equations take into account the effects of the small scales on the large. Both algorithms (1) are stable; (2) make the Rossby Radius effectively larger; and (3) slow down Rossby and gravity waves.Comment: Submitted to J. Computational Physics March 21, 200