Non-normal tracer diffusion from stirring by swimming microorganisms.

The experimentally observed non-Gaussian form of passive tracer distributions in media stirred by active swimmers (Leptos et al., Phys. Rev. Lett. 103, 198103 (2009)) are analyzed in terms of continuous time random walks. The walks are characterized by a trapping time distribution ψ(τ) with long time behaviour ψ(τ) is proportional to τ (-1-α) and a step size distribution p(Δx) is proportional to (Δx)(-2-ß). The experimentally observed behaviour that 〈x (2)〉is proportional to t is obtained for a one-parameter family of exponents with ß = 2α. However, the distribution function for this case is non-Gaussian and shows exponential tails. The shape of the distributions agrees rather well with the experimental observations from Leptos et al. and allows for the determination of the exponents.

Primary tumour expression of the cysteine cathepsin inhibitor Stefin A inhibits distant metastasis in breast cancer.

Using the clinically relevant 4T1-derived syngeneic murine model of spontaneous mammary metastasis to bone, we have identified the cysteine cathepsin inhibitor Stefin A as a gene differentially expressed in primary and metastatic mammary tumours. In primary tumours, Stefin A expression correlated inversely with metastatic potential in 4T1-derived lines and was not detected in tumour cells in culture, indicating induction only within the tumour microenvironment. Enforced expression of Stefin A in the highly metastatic 4T1.2 cell line significantly reduced spontaneous bone metastasis following orthotopic injection into the mammary gland. Consistent with the mouse data, Stefin A expression correlated with disease-free survival (absence of distant metastasis) in a cohort of 142 primary tumours from breast cancer patients. This was most significant for patients with invasive ductal carcinoma expressing Stefin A, who were less likely to develop distant metastases (log rank test, p = 0.0075). In a multivariate disease-free survival analysis (Cox proportional hazards model), Stefin A expression remained a significant independent prognostic factor in patients with invasive ductal carcinoma (p = 0.0014), along with grade and progesterone receptor (PR) status. In human lung and bone metastases, we detected irregular Stefin A staining patterns, with expression often localizing to micrometastases (<0.2 mm) in direct contact with the stroma. We propose that Stefin A, as a cysteine cathepsin inhibitor, may be a marker of increased cathepsin activity in metastases. Using immunohistology, the cathepsin inhibitor was detected co-expressed with cathepsin B in lung and bone metastases in both the murine model and human tissues. We conclude that Stefin A expression reduces distant metastasis in breast cancer and propose that this may be due to the inhibition of cysteine cathepsins, such as cathepsin B.

The "dark cerebellar sign".

We present and discuss the "dark cerebellar sign" in contrast to the well known "white cerebellar sign". The "white cerebellar sign" relates to a normal cerebellum which appears hyperdense in contrast to a pathological hypodense cerebrum on computer tomography (CT). We present a child with a "dark cerebellar sign" characterized by an ischemic or edematous cerebellum which appears hypodense in contrast to a normal relatively dense cerebrum. Isolated infarction of the cerebellum is a rare finding in premature neonates. Even rarer, cerebellar infarction may be observed in children and young adults due to an overdose of tricyclic antidepressants (TCA). The reason for the selective cerebellar infarction with TCA intoxication is still unknown. Our case shows that TCA intoxication should be included in the differential diagnosis of children with a "dark cerebellar sign".

Onset of fast magnetic reconnection.

We demonstrate the existence of a new steady-state magnetic reconnection configuration which lies at the boundary of the basins of attraction between the Sweet-Parker and Hall reconnection configurations. The solution is linearly unstable to small perturbations and its identification required a novel iterative numerical technique. The eigenmodes of the unstable solution are localized near the X line, suggesting that the onset of fast reconnection in a weakly collisional plasma is initiated locally at the X line as opposed to remotely at the boundaries.

Abnormal mixing of passive scalars in chaotic flows.

We study the relaxation of a passive scalar towards the uniform equilibrium distribution in an advection-diffusion problem where the phase space for the pure advection problem is a mixture of chaotic domains and elliptic islands. Since the advection-diffusion problem is linear, the relaxation can be characterized by the eigenvalues and eigenmodes of the evolution operator. Almost degenerate eigenvalues then give rise to deviations from simple exponential decay behavior. We show by example that the corresponding eigenmodes can be supported by islands or weakly connected chaotic domains. These theoretical considerations are related to some experimental observations in two-dimensional flows.

Metallothionein-III inhibits initial neurite formation in developing neurons as well as postinjury, regenerative neurite sprouting.

Human metallothionein-III (MT-III) is an inhibitory factor deficient in the Alzheimer's disease (AD) brain. MT-III has been identified as an inhibitor of neurite sprouting, and its deficiency has been proposed to be involved in the formation of neurofibrillary tangles (NFT) in the neuropathology of AD. However, there has been limited investigation of the proposed neurite growth inhibitory properties of MT-III. We have applied recombinant human MT-III to both single cell embryonic cortical neurons (to investigate initial neurite formation), as well as mature (21 days postplating) clusters of cortical neurons (to investigate the regenerative sprouting response following injury). We report that MT-III inhibited the initial formation of neurites by rat embryonic (E18) cortical neurons. This was based on both the percentage of neurite positive neurons and the number of neurites per neuron (45 and 30% inhibition, respectively). Neurite inhibition was only observed in the presence of adult rat brain extract, and was also reversible following replacement of MT-III-containing medium. MT-III inhibited the formation and growth of both axons and dendrites. Of more physiological significance, MT-III also inhibited the regenerative neurite sprouting response following axonal transection. The morphology of sprouting neurites was also altered, with the distal tip often ending in bulb-like structures. Based on these results, we propose that MT-III, in the presence of brain extract, is a potent inhibitor of neurite sprouting, and may be involved in abnormal sprouting potentially underlying both AD and epilepsy.

Vortex pairs in viscoelastic Couette-Taylor flow.

In experiments on dilute polymers between rotating cylinders Groisman and Steinberg [Phys. Rev. Lett. 78, 1460 (1997)] observed the formation of vortices that were not equidistantly spaced but rather paired up in what they called "diwhirls." We calculate these states within an Oldroyd-B model with parameters adapted to the experiment and find good agreement with the observed characteristics of the diwhirls.

Turbulence and passive scalar transport in a free-slip surface.

We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible nor incompressible but strongly influenced by the 3D flow underneath the surface. The velocity correlation functions in the 2D surface and in the 3D volume scale with the same exponents. In the viscous subrange the amplitudes are the same, but in the inertial subrange the 2D one is reduced to 2/3 of the 3D amplitude. The surface flow is more strongly intermittent than the 3D volume flow. Geometric scaling theory is used to derive a relation between the scaling of the velocity field and the density fluctuations of a passive scalar advected on the surface.

Turbulence in a free surface.

We report an experimental and numerical study of turbulent fluid motion in a free surface. The flow is realized experimentally on the surface of a tank filled with water stirred by a vertically oscillating grid positioned well below the surface. The effect of surface waves appears to be negligible so that the flow can numerically be realized with a flat surface and stress-free boundary conditions. The surface flow is unconventional in that it is not incompressible and neither energy nor enstrophy are conserved. Nevertheless, according to both experiment and numerical simulation, the second order structure function S2(R) scales essentially as for a three-dimensional system. However, the surface flow seems to be more intermittent.

Evolution of turbulent spots in a parallel shear flow.

The evolution of turbulent spots in a parallel shear flow is studied by means of full three-dimensional numerical simulations. The flow is bounded by free surfaces and driven by a volume force. Three regions in the spanwise spot cross section can be identified: a turbulent interior, an interface layer with prominent streamwise streaks and vortices, and a laminar exterior region with a large scale flow induced by the presence of the spot. The lift-up of streamwise streaks that is caused by non-normal amplification is clearly detected in the region adjacent to the spot interface. The spot can be characterized by an exponentially decaying front that moves with a speed different from that of the cross-stream outflow or the spanwise phase velocity of the streamwise roll pattern. Growth of the spots seems to be intimately connected to the large scale outside flow, for a turbulent ribbon extending across the box in the downstream direction does not show the large scale flow and does not grow. Quantitatively, the large scale flow induces a linear instability in the neighborhood of the spot, but the associated front velocity is too small to explain the spot spreading.

Phase-space structure of a thermoreceptor.

We analyze the phase-space structure of a model for thermoreceptors in fish and mammals. As a function of the temperature we identify a period doubling scenario at low temperatures, a regime where an unstable stationary fixed point collides with the attractor and blocks the thermoreceptor, and a transition from period n+1 to period n as the temperature is further increased. The period reduction phenomenon is due to an autoresonance between fast and slow ion channels and shows the features typical for mode locking.

Transition from the Couette-Taylor system to the plane Couette system.

We discuss the flow between concentric rotating cylinders in the limit of large radii where the system approaches plane Couette flow. We discuss how in this limit the linear instability that leads to the formation of Taylor vortices is lost and how the character of the transition approaches that of planar shear flows. In particular, a parameter regime is identified where fractal distributions of lifetimes and spatiotemporal intermittency occur. Experiments in this regime should allow us to study the characteristics of shear flow turbulence in a closed flow geometry.

Semiclassical cross section correlations

We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.

Phase space localization and matrix element distributions in systems with mixed classical phase space.

We consider distributions of diagonal matrix elements for smooth observables in systems whose classical phase space has a mixture of chaotic and nearly integrable regions. The quantum distributions agree very well with distributions obtained from classical trajectory segments whose length is the Heisenberg time. Non-Gaussian wings in the distributions can be linked to classical trapping in certain parts of phase space, sometimes connected to islands, but also to regions separated by other barriers to transport. Thus classical deviations from ergodicity are quantitatively reflected in quantum matrix elements. The relation to scars is discussed.

Transition to turbulence in a shear flow.

We analyze the properties of a 19-dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large Re additional stationary flows occur; they are all unstable. The lifetimes of finite amplitude perturbations shows a fractal dependence on amplitude and Reynolds number. These findings are in accord with observations on plane Couette flow and suggest a universality of this transition scenario in shear flows.

Structure function of passive scalars in two-dimensional turbulence.

The structure function of a scalar theta(x,t), passively advected in a two-dimensional turbulent flow u(x,t), is discussed by means of the fractal dimension delta1g of the passive-scalar graph. A relation between delta1g, the scaling exponent zeta(theta)(1) of the scalar structure function D1(theta)r, and the structure function D2(r) of the underlying flow field is derived. Different from the three-dimensional (3D) case, the 2D structure function also depends on an additional parameter, characteristic of the driving of the passive scalar. In the enstrophy inertial subrange a mean-field approximation for the velocity structure function gives a scaling of the passive scalar graph with delta1g<2 for intermediate and large values of the Prandtl number Pr. In the energy inertial subrange a model for the energy spectrum and thus D2(r) gives a passive-scalar graph scaling with exponent delta1g=5/3. Finally, we discuss an application to recent observations of scalar dispersion in nonuniversal 2D flows.