A simple stochastic model which describes microtubule dynamics and explicitly takes into account the relevant biochemical processes is presented. The model incorporates binding and unbinding of monomers and random phosphate release inside the polymer. It is shown that this theoretical approach provides a microscopic picture of the dynamic instability phenomena of microtubules. The cap size, the concentration dependence of the catastrophe times and the delay before observing catastrophes following a dilution can be quantitatively predicted by this approach in a direct and simple way. Furthermore, the model can be solved analytically to a large extend, thus offering a valuable starting point for more refined studies of microtubules dynamics.

Ranjith Padinhateeri Anatoly B. Kolomeisky David Lacoste

We consider the problem of minimizing a function, which is the sum of a linear function and a composition of a strongly convex function with a linear transformation, over a compact polyhedral set. Jaggi and Lacoste-Julien [14] showed that the conditional gradient method with away steps employed on the aforementioned problem without the additional linear term has linear rate of convergence, depending on the so-called pyramidal width of the feasible set. We revisit this result and provide a variant of the algorithm and an analysis that is based on simple duality arguments, as well as corresponding error bounds. This new analysis (a) enables the incorporation of the additional linear term, (b) does not require a linear-oracle that outputs an extreme point of the linear mapping of the feasible set and (c) depends on a new constant, termed "the vertex-facet distance constant", which is explicitly expressed in terms of the problem's parameters and the geometry of the feasible set. This constant replaces the pyramidal width, which is difficult to evaluate.

Amir Beck Shimrit Shtern

Experiments, numerical simulations and an analytic model were developed to elucidate the effects of noise in the synchronized state of a tunnel junction based spin torque nano oscillator (STNO). It is demonstrated that in the in plane magnetized structure, while the frequency is locked, much higher reference currents are needed to reduce the noise by phase locking. Our analysis shows that it is possible to control the phase noise by the reference microwave current (IRF) and that it can be further reduced by increasing the bias current (IDC) of the oscillator, keeping the reference current in feasible limits for applications.

M. Tortarolo B. Lacoste J. Hem C. Dieudonné M. -C. Cyrille J. A. Katine D. Mauri A. Zeltser L. D. Buda-Prejbeanu U. Ebels

We prove that the set of symplectic lattices in the Siegel space $\mathfrak{h}_g$ whose systoles generate a subspace of dimension at least 3 in $\mathbb{R}^{2g}$ does not contain any $\mathrm{Sp}(2g,\mathbb{Z})$-equivariant deformation retract of $\mathfrak{h}_g$.

Cyril Lacoste

We compare the behavior of the magnetothermoelectric power (MTEP)in metallic ferromagnetic thin films of Ni80Fe20 (Permalloy; Py), Co and CrO2 at temperatures in the range of 100 K to 400 K. In 25 nm thick Py films and 50 nm thick Co films both the anisotropic magnetoresistance (AMR) and MTEP show a relative change in resistance and thermoelectric power (TEP) of the order of 0.2% when the magnetic field is reversed, and in both cases there is no significant change in AMR or MTEP any more after the saturation field has been reached. Surprisingly, both Py and Co films have opposite MTEP behavior although both have the same sign for AMR and TEP. The data on 100 nm films of fully spin-polarized CrO2, grown both on TiO2 and on sapphire, show a different picture. The MTEP behavior at low fields shows peaks similar to the AMR in these films, with variations up to 1%. With increasing field both the MR and the MTEP variations keeps growing, with MTEP showing relative changes of 1.5% with the thermal gradient along the b-axis and even 20% with the gradient along the c-axis, with an intermediate value of 3% for the film on sapphire. It appears that the low-field effects are due to magnetic domain switching, while the high-field effects are intrinsic to the electronic structure of CrO2.

M. S. Anwar B. Lacoste J. Aarts

In this paper, a 3-terminal spin-transfer torque nano-oscillator (STNO) is studied using the concurrent spin injection of a spin-polarized tunneling current and a spin Hall current exciting the free layer into dynamic regimes beyond what is achieved by each individual mechanism. The pure spin injection is capable of inducing oscillations in the absence of charge currents effectively reducing the critical tunneling current to zero. This reduction of the critical charge currents can improve the endurance of both STNOs and non-volatile magnetic memories (MRAM) devices. It is shown that the system response can be described in terms of an injected spin current density $J_s$ which results from the contribution of both spin injection mechanisms, with the tunneling current polarization $p$ and the spin Hall angle $\theta$ acting as key parameters determining the efficiency of each injection mechanism. The experimental data exhibits an excellent agreement with this model which can be used to quantitatively predict the critical points ($J_s = -2.26\pm 0.09 \times 10^9 \hbar/e$ A/m$^2$) and the oscillation amplitude as a function of the input currents. In addition, the fitting of the data also allows an independent confirmation of the values estimated for the spin Hall angle and tunneling current polarization as well as the extraction of the damping $\alpha = 0.01$ and non-linear damping $Q = 3.8\pm 0.3$ parameters.

M. Tarequzzaman T. Böhnert M. Decker J. D. Costa J. Borme B. Lacoste E. Paz A. S. Jenkins S. Serrano-Guisan C. H. Back R. Ferreira P. P. Freitas

This article presents a derivation of the transport mean free path for magneto-transverse light diffusion, $\ell^*_\perp$, in an arbitrary random mixture of Faraday-active and non-Faraday active Mie scatterers. This derivation is based on the standard radiative transfer equation. The expression of the transport mean free path obtained previously from the Bethe-Salpether equation, for the case where only Faraday-active scatterers are present,is recovered. This simpler formulation can include the case of homogeneous mixtures of Faraday-active and non-Faraday active scatterers.

D. Lacoste

We formulate a framework for the depolarization of linearly polarized backscattered light based on the concept of geometric phase, {\it i.e} Berry's phase. The predictions of this theory are applied to the patterns formed by backscattered light between crossed or parallel polarizers. This theory should be particularly adapted to the situation in which polarized light is scattered many times but predominantly in the forward direction. We apply these ideas to the patterns which we obtained experimentally with backscattered polarized light from a colloidal suspension.

D. Lacoste V. Rossetto F. Jaillon H. Saint-Jalmes

We present measurements of the fluctuation spectrum of giant vesicles containing bacteriorhodopsin (BR) pumps using video-microscopy. When the pumps are activated, we observe a significant increase of the fluctuations in the low wavevector region, which we interpret as due to a lowering of the effective tension of the membrane.

M. D. El Alaoui Faris D. Lacoste J. Pecreaux J-F. Joanny J. Prost P. Bassereau

We study the thermal expansion of chains formed by self-assembly of magnetic colloidal particles in a magnetic field. Using video-microscopy, complete positional data of all the particles of the chains is obtained. By changing the ionic strength of the solution and the applied magnetic field, the interaction potential can be tuned. We analyze the thermal expansion of the chain using a simple model of a one dimensional anharmonic crystal of finite size.

D. Lacoste C. Brangbour J. Bibette J. Baudry