Multiparton scattering at the LHC

The large parton flux at high energy gives rise to events where different pairs of partons interact contemporarily with large momentum exchange. A main effect of multiple parton interactions is to generate events with many jets at relatively large transverse momenta. The large value of the heavy quarks production cross section may however give also rise a sizable rate of events with several $b$-quarks produced. We summarize the main features of multiparton interactions and make some estimate of the inclusive cross section to produce two $b{\bar b}$ pairs within the acceptance of the ALICE detector.Comment: 10 pages, 4 figures, contribution to ALICE PP

Local and nonlocal parallel heat transport in general magnetic fields

A novel approach that enables the study of parallel transport in magnetized plasmas is presented. The method applies to general magnetic fields with local or nonlocal parallel closures. Temperature flattening in magnetic islands is accurately computed. For a wave number $k$, the fattening time scales as $\chi_{\parallel} \tau \sim k^{-\alpha}$ where $\chi$ is the parallel diffusivity, and $\alpha=1$ ($\alpha=2$) for non-local (local) transport. The fractal structure of the devil staircase temperature radial profile in weakly chaotic fields is resolved. In fully chaotic fields, the temperature exhibits self-similar evolution of the form $T=(\chi_{\parallel} t)^{-\gamma/2} L \left[ (\chi_{\parallel} t)^{-\gamma/2} \delta \psi \right]$, where $\delta \psi$ is a radial coordinate. In the local case, $f$ is Gaussian and the scaling is sub-diffusive, $\gamma=1/2$. In the non-local case, $f$ decays algebraically, $L (\eta) \sim \eta^{-3}$, and the scaling is diffusive, $\gamma=1$

Boolean versus continuous dynamics on simple two-gene modules

We investigate the dynamical behavior of simple modules composed of two genes with two or three regulating connections. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method, we study within a single framework different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations. These conditions concern the time scales, the degree of cooperativity of the regulating interactions, and the signs of the interactions. Not all models that show oscillations under Boolean dynamics can have oscillations under continuous dynamics, and vice versa.Comment: 8 pages, 10 figure

The first nontrivial eigenvalue for a system of p−p-Laplacians with Neumann and Dirichlet boundary conditions

We deal with the first eigenvalue for a system of two $p-$Laplacians with Dirichlet and Neumann boundary conditions. If \Delta_{p}w=\mbox{div}(|\nabla w|^{p-2}w) stands for the $p-$Laplacian and $\frac{\alpha}{p}+\frac{\beta}{q}=1,$ we consider $$\begin{cases} -\Delta_pu= \lambda \alpha |u|^{\alpha-2} u|v|^{\beta} &\text{ in }\Omega,\\ -\Delta_q v= \lambda \beta |u|^{\alpha}|v|^{\beta-2}v &\text{ in }\Omega,\\ \end{cases}$$ with mixed boundary conditions $$u=0, \qquad |\nabla v|^{q-2}\dfrac{\partial v}{\partial \nu }=0, \qquad \text{on }\partial \Omega.$$ We show that there is a first non trivial eigenvalue that can be characterized by the variational minimization problem $$\lambda_{p,q}^{\alpha,\beta} = \min \left\{\dfrac{\displaystyle\int_{\Omega}\dfrac{|\nabla u|^p}{p}\, dx +\int_{\Omega}\dfrac{|\nabla v|^q}{q}\, dx} {\displaystyle\int_{\Omega} |u|^\alpha|v|^{\beta}\, dx} \colon (u,v)\in \mathcal{A}_{p,q}^{\alpha,\beta}\right\},$$ where $$\mathcal{A}_{p,q}^{\alpha,\beta}=\left\{(u,v)\in W^{1,p}_0(\Omega)\times W^{1,q}(\Omega)\colon uv\not\equiv0\text{ and }\int_{\Omega}|u|^{\alpha}|v|^{\beta-2}v \, dx=0\right\}.$$ We also study the limit of $\lambda_{p,q}^{\alpha,\beta}$ as $p,q\to \infty$ assuming that $\frac{\alpha}{p} \to \Gamma \in (0,1)$, and $\frac{q}{p} \to Q \in (0,\infty)$ as $p,q\to \infty.$ We find that this limit problem interpolates between the pure Dirichlet and Neumann cases for a single equation when we take $Q=1$ and the limits $\Gamma \to 1$ and $\Gamma \to 0$.Comment: 21 pages, 1 figur

Evaluation of Monilinia fructicola on apricot fruits

Monilinia fructicola has been a quarantine pathogen in Europe until 2014; however, the disease risk remains large for Prunus species, because of the continuing spreading around Europe. In order to assess the impact of this fungus on apricot fruits, differences in variety susceptibility need to be evaluated

Optimal generation of entanglement under local control

We study the optimal generation of entanglement between two qubits subject to local unitary control. With the only assumptions of linear control and unitary dynamics, by means of a numerical protocol based on the variational approach (Pontryagin's Minimum Principle), we evaluate the optimal control strategy leading to the maximal achievable entanglement in an arbitrary interaction time, taking into account the energy cost associated to the controls. In our model we can arbitrarily choose the relative weight between a large entanglement and a small energy cost.Comment: 4 page