Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs

The short time evolution of three dimensional small perturbations is studied. Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to host intensive hydrodynamical activity in the shape of non modal growth of initial small perturbations. Two mechanisms that lead to such behavior are identified and studied, namely, non-resonant excitation of vertically confined sound waves by stable planar inertia-coriolis modes that results in linear growth with time, as well as resonant coupling of those two modes that leads to a quadratic growth of the initial perturbations. It is further speculated that the non modal growth can give rise to secondary strato-rotational instabilities and thus lead to a new route to turbulence generation in thin discs

A weakly nonlinear analysis of the magnetorotational instability in a model channel flow

We show by means of a perturbative weakly nonlinear analysis that the axisymmetric magnetorotational instability (MRI) of a viscous, resistive, incompressible rotating shear flow in a thin channel gives rise to a real Ginzburg-Landau equation for the disturbance amplitude. For small magnetic Prandtl number (${\cal P}_{\rm m}$), the saturation amplitude is $\propto \sqrt{{\cal P}_{\rm m}}$ and the resulting momentum transport scales as ${\cal R}^{-1}$, where $\cal R$ is the {\em hydrodynamic} Reynolds number. Simplifying assumptions, such as linear shear base flow, mathematically expedient boundary conditions and continuous spectrum of the vertical linear modes, are used to facilitate this analysis. The asymptotic results are shown to comply with numerical calculations using a spectral code. They suggest that the transport due to the nonlinearly developed MRI may be very small in experimental setups with ${\cal P}_{\rm m} \ll 1$.Comment: Accepted to Physical Review Letters - Nov. 30, 2006. In final for

Effects of dissipation in an adiabatic quantum search algorithm

We consider the effect of two different environments on the performance of the quantum adiabatic search algorithm, a thermal bath at finite temperature, and a structured environment similar to the one encountered in systems coupled to the electromagnetic field that exists within a photonic crystal. While for all the parameter regimes explored here, the algorithm performance is worsened by the contact with a thermal environment, the picture appears to be different when considering a structured environment. In this case we show that, by tuning the environment parameters to certain regimes, the algorithm performance can actually be improved with respect to the closed system case. Additionally, the relevance of considering the dissipation rates as complex quantities is discussed in both cases. More particularly, we find that the imaginary part of the rates can not be neglected with the usual argument that it simply amounts to an energy shift, and in fact influences crucially the system dynamics.Comment: 18 pages, 9 figure

A Process Calculus for Molecular Interaction Maps

We present the MIM calculus, a modeling formalism with a strong biological basis, which provides biologically-meaningful operators for representing the interaction capabilities of molecular species. The operators of the calculus are inspired by the reaction symbols used in Molecular Interaction Maps (MIMs), a diagrammatic notation used by biologists. Models of the calculus can be easily derived from MIM diagrams, for which an unambiguous and executable interpretation is thus obtained. We give a formal definition of the syntax and semantics of the MIM calculus, and we study properties of the formalism. A case study is also presented to show the use of the calculus for modeling biomolecular networks.Comment: 15 pages; 8 figures; To be published on EPTCS, proceedings of MeCBIC 200

Hydrodynamic response of rotationally supported flows in the Small Shearing Box model

The hydrodynamic response of the inviscid small shearing box model of a midplane section of a rotationally supported astrophysical disk is examined. An energy functional ${\cal E}$ is formulated for the general nonlinear problem. It is found that the fate of disturbances is related to the conservation of this quantity which, in turn, depends on the boundary conditions utilized: ${\cal E}$ is conserved for channel boundary conditions while it is not conserved in general for shearing box conditions. Linearized disturbances subject to channel boundary conditions have normal-modes described by Bessel Functions and are qualitatively governed by a quantity $\Sigma$ which is a measure of the ratio between the azimuthal and vertical wavelengths. Inertial oscillations ensue if $\Sigma >1$ - otherwise disturbances must in general be treated as an initial value problem. We reflect upon these results and offer a speculation.Comment: 6 pages, resubmitted to Astronomy and Astrophysics, shortened with references adde

How much measurement independence is needed in order to demonstrate nonlocality?

If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the hypothetical local variables. We study the case where this assumption is weakened, so that measurement settings and local variables are at least partially correlated. As we show, there is a connection between this type of model and models which reproduce nonlocal correlations by allowing classical communication between the distant parties, and a connection with models that exploit the detection loophole. We show that even if Bob's choices are completely independent, all correlations obtained from projective measurements on a singlet can be reproduced, with the correlation (measured by mutual information) between Alice's choice and local variables less than or equal to a single bit.Comment: 5 pages, 1 figure. v2 Various improvements in presentation. Results unchange

The Determination of induction and differentiation in grape vines

The induction and differentiation of 8-year-old Alphonse Lavallee and Sultana grape vines were studied.Defoliation methods enabled us to determine the induction time in grape vines as in other fruit species.Induction and differentiation in the tested varieties were not connected with temporary growth cessation; on the contrary, process took place during the most intensive growth.A correlation was found between the number of leaves and induction period. 18-21 leaves above the examined buds were needed in bot-h varieties to complete the induction.The leaf area needed for induction in a bud of Sultana was lYe times larger than that needed for Alphonse. The efficiency of the leaves of Alphonse to induce differentiation was thus greater.The primordia ,development from induction to detection under the microscope (differentiation) was connected with a constant vegetative development. The time needed for this development was determined by the growth rate of the variety (18 days in Sultana, 14 days in Alphonse).The translocation of materials inducing differentiation from the base of the shoot upwar,ds has not been proved in our work.In Alphonse a lag period of two days was found for the differentiation of each bud along the cane

The Hall instability of thin weakly-ionized stratified Keplerian disks

The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio. The leading order of the asymptotic expansions in the aspect ratio is applied to both equilibrium as well as the perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial, and unstable to vertical short-wave perturbations. The marginal stability surface is found in the space of the local Hall and inverse plasma beta parameters, as well as the free parameter of the model which is related to the total current through the disk. To estimate the minimal values of the equilibrium magnetic field that leads to instability, the latter is constructed as a sum of a current free magnetic field and the simplest approximation for magnetic field created by a distributed electric current.Comment: 13 pages, 7 figure