Advection of vector fields by chaotic flows

We have introduced a new transfer operator for chaotic flows whose leading eigenvalue yields the dynamo rate of the fast kinematic dynamo and applied cycle expansion of the Fredholm determinant of the new operator to evaluation of its spectrum. The theory hs been tested on a normal form model of the vector advecting dynamical flow. If the model is a simple map with constant time between two iterations, the dynamo rate is the same as the escape rate of scalar quantties. However, a spread in Poincar\'e section return times lifts the degeneracy of the vector and scalar advection rates, and leads to dynamo rates that dominate over the scalar advection rates. For sufficiently large time spreads we have even found repellers for which the magnetic field grows exponentially, even though the scalar densities are decaying exponentially.Comment: 12 pages, Latex. Ask for figures from [email protected]

modCHIMERA: A novel murine closed-head model of moderate traumatic brain injury

AbstractTraumatic brain injury is a major source of global disability and mortality. Preclinical TBI models are a crucial component of therapeutic investigation. We report a tunable, monitored model of murine non-surgical, diffuse closed-head injury—modCHIMERA—characterized by impact as well as linear and rotational acceleration. modCHIMERA is based on the Closed-Head Impact Model of Engineered Rotational Acceleration (CHIMERA) platform. We tested this model at 2 energy levels: 1.7 and 2.1 Joules—substantially higher than previously reported for this system. Kinematic analysis demonstrated linear acceleration exceeding injury thresholds in humans, although outcome metrics tracked impact energy more closely than kinematic parameters. Acute severity metrics were consistent with a complicated-mild or moderate TBI, a clinical population characterized by high morbidity but potentially reversible pathology. Axonal injury was multifocal and bilateral, neuronal death was detected in the hippocampus, and microglial neuroinflammation was prominent. Acute functional analysis revealed prolonged post-injury unconsciousness, and decreased spontaneous behavior and stimulated neurological scores. Neurobehavioral deficits were demonstrated in spatial learning/memory and socialization at 1-month. The overall injury profile of modCHIMERA corresponds with the range responsible for a substantial portion of TBI-related disability in humans. modCHIMERA should provide a reliable platform for efficient analysis of TBI pathophysiology and testing of treatment modalities.</jats:p

Transient Shear Wave Propagation in a Viscoelastic Gel Cylinder: Comparison of Theory to MRI-Based Measurements

ABSTRACT Shear strain patterns in a cylindrical gelatin sample under transient angular acceleration were measured by tagged magnetic resonance imaging (MRI). Measured strain fields were compared to theoretical strain fields obtained by finite element (FE) simulation. Agreement between theory and experiment is very good. The current results support the utility of the experimental approach for tasks such as measurement of shear waves in brain tissue during angular acceleration of the skull. The results also show that a simple viscoelastic model is suitable to describe rapid shear deformation of a gel biomaterial

Density probability distribution in one-dimensional polytropic gas dynamics

We discuss the generation and statistics of the density fluctuations in highly compressible polytropic turbulence, based on a simple model and one-dimensional numerical simulations. Observing that density structures tend to form in a hierarchical manner, we assume that density fluctuations follow a random multiplicative process. When the polytropic exponent $\gamma$ is equal to unity, the local Mach number is independent of the density, and our assumption leads us to expect that the probability density function (PDF) of the density field is a lognormal. This isothermal case is found to be singular, with a dispersion $\sigma_s^2$ which scales like the square turbulent Mach number $\tilde M^2$, where $s\equiv \ln \rho$ and $\rho$ is the fluid density. This leads to much higher fluctuations than those due to shock jump relations. Extrapolating the model to the case $\gamma \not =1$, we find that, as the Mach number becomes large, the density PDF is expected to asymptotically approach a power-law regime, at high densities when $\gamma<1$, and at low densities when $\gamma>1$. This effect can be traced back to the fact that the pressure term in the momentum equation varies exponentially with $s$, thus opposing the growth of fluctuations on one side of the PDF, while being negligible on the other side. This also causes the dispersion $\sigma_s^2$ to grow more slowly than $\tilde M^2$ when $\gamma\not=1$. In view of these results, we suggest that Burgers flow is a singular case not approached by the high-$\tilde M$ limit, with a PDF that develops power laws on both sides.Comment: 9 pages + 12 postscript figures. Submitted to Phys. Rev.

The Wicked Machinery of Government: Malta and the Problems of Continuity under the New Model Administration

This is a study focused on the early years of British rule in Malta (1800-1813). It explores the application to the island of the “new model” of colonial government, one based on direct rule from London mediated by the continuation of existing laws and institutions. Systemic deficiencies are identified. These tended to undermine the effectiveness of direct British rule. This study also reveals, in the context of legal and constitutional continuity, unresolved tensions between modernity and tradition. The political stability of the island was damaged and the possibility of continued British possession was threatened

Effects of radial immersion and cutting direction on chatter instability

ABSTRACT Low radial immersion end-milling involves intermittent cutting. If the tool is flexible, its motion in both the x-and ydirections affects the chip load and cutting forces, leading to chatter instability under certain conditions. Interrupted cutting complicates stability analysis by imposing sharp periodic variations in the dynamic model. Stability predictions for the 2-DOF model differ significantly from prior 1-DOF models of interrupted cutting. In this paper stability boundaries of the 2-DOF milling process are determined by three techniques and compared: (1) a frequency-domain technique developed b

Size-Dependent Transition to High-Dimensional Chaotic Dynamics in a Two-Dimensional Excitable Medium

The spatiotemporal dynamics of an excitable medium with multiple spiral defects is shown to vary smoothly with system size from short-lived transients for small systems to extensive chaos for large systems. A comparison of the Lyapunov dimension density with the average spiral defect density suggests an average dimension per spiral defect varying between three and seven. We discuss some implications of these results for experimental studies of excitable media.Comment: 5 pages, Latex, 4 figure

The regulatory subunit of PKA-I remains partially structured and undergoes β-aggregation upon thermal denaturation

Background: The regulatory subunit (R) of cAMP-dependent protein kinase (PKA) is a modular flexible protein that responds with large conformational changes to the binding of the effector cAMP. Considering its highly dynamic nature, the protein is rather stable. We studied the thermal denaturation of full-length RIα and a truncated RIα(92-381) that contains the tandem cyclic nucleotide binding (CNB) domains A and B. Methodology/Principal Findings: As revealed by circular dichroism (CD) and differential scanning calorimetry, both RIα proteins contain significant residual structure in the heat-denatured state. As evidenced by CD, the predominantly α-helical spectrum at 25°C with double negative peaks at 209 and 222 nm changes to a spectrum with a single negative peak at 212-216 nm, characteristic of β-structure. A similar α→β transition occurs at higher temperature in the presence of cAMP. Thioflavin T fluorescence and atomic force microscopy studies support the notion that the structural transition is associated with cross-β-intermolecular aggregation and formation of non-fibrillar oligomers. Conclusions/Significance: Thermal denaturation of RIα leads to partial loss of native packing with exposure of aggregation-prone motifs, such as the B' helices in the phosphate-binding cassettes of both CNB domains. The topology of the β-sandwiches in these domains favors inter-molecular β-aggregation, which is suppressed in the ligand-bound states of RIα under physiological conditions. Moreover, our results reveal that the CNB domains persist as structural cores through heat-denaturation. © 2011 Dao et al