Model for the Dynamics of the Cytoskeleton.

Particle tracking of microbeads attached to the cytoskeleton (CSK) reveals an intermittent dynamic. The mean squared displacement (MSD) is subdiffusive for small Δt and superdiffusive for large Δt, which are associated with periods of traps and periods of jumps respectively. The analysis of the displacements has shown a non-Gaussian behavior, what is indicative of an active motion, classifying the cells as a far from equilibrium material. Using Langevin dynamics, we reconstruct the dynamic of the CSK. The model is based on the bundles of actin filaments that link themself with the bead RGD coating, trapping it in an harmonic potential. We consider a one- dimensional motion of a particle, neglecting inertial effects (over-damped Langevin dynamics). The resultant force is decomposed in friction force, elastic force and random force, which is used as white noise representing the effect due to molecular agitation. These description until now shows a static situation where the bead performed a random walk in an elastic potential. In order to modeling the active remodeling of the CSK, we vary the equilibrium position of the potential. Inserting a motion in the well center, we change the equilibrium position linearly with time with constant velocity. The result found exhibits a MSD versus time ’tau’ with three regimes. The first regime is when ‘tau’ < ‘tau IND 0’, where ‘tau IND 0’ is the relaxation time, representing the thermal motion. At this regime the particle can diffuse freely. The second regime is a plateau, ‘tau IND 0’ < ‘tau’ < ‘tau IND 1’, representing the particle caged in the potential. Here, ‘tau IND 1’ is a characteristic time that limit the confinement period. And the third regime, ‘tau’ > ‘tau IND 1’, is when the particles are in the superdiffusive behavior. This is where most of the experiments are performed, under 20 frames per second (FPS), thus there is no experimental evidence that support the first regime. We are currently performing experiments with high frequency, up to 100 FPS, attempting to visualize this diffusive behavior. Beside the first regime, our simple model can reproduce MSD curves similar to what has been found experimentally, which can be helpful to understanding CSK structure and properties.

Decadal Variabilities and Trends in the Southwest Atlantic in a model forced with NCEP Reanalysis from 1960 to 2012

Analysis of the NCAR/NCEP Reanalysis show changes in the atmospheric circulation in the Southern hemisphere, with a strengthening and poleward displacement of the westerlies. Because the wind is one of the main sources of the ocean's kinetic energy, a numerical experiment with the Hybrid Coordinate Ocean Model (HYCOM) was forced with monthly means of the NCAR/NCEP Reanalysis products to investigate the effects of the changes in the wind on the ocean circulation in a geographical domain defined by 98W – 114E; 65S – 60N. The results show good agreement with other models and with available satellite data. In the western sector of the South Atlantic there are several indications of changes such as a poleward displacement of the Brazil-Malvinas Confluence and positive trends in temperature and salinity of the southwestern region of the subtropical gyre.

A Skyrme-like model with an exact BPS bound

We propose a new Skyrme-like model with fields taking values on the sphere S3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire three- dimensional space R3. We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S3, using toroidal like coordinates.