Trapping dust particles in the outer regions of protoplanetary disks

Aims. We attempt to explain grain growth to mm sized particles and their retention in the outer regions of protoplanetary disks, as observed at sub-mm and mm wavelengths, by investigating whether strong inhomogeneities in the gas density profiles can decelerate excessive radial drift and help the dust particles to grow. Methods. We use coagulation/fragmentation and disk-structure models, to simulate the evolution of dust in a bumpy surface density profile, which we mimic with a sinusoidal disturbance. For different values of the amplitude and length scale of the bumps, we investigate the ability of this model to produce and retain large particles on million-year timescales. In addition, we compare the pressure inhomogeneities considered in this work with the pressure profiles that come from magnetorotational instability. Using the Common Astronomy Software Applications ALMA simulator, we study whether there are observational signatures of these pressure inhomogeneities that can be seen with ALMA. Results. We present the conditions required to trap dust particles and the corresponding calculations predicting the spectral slope in the mm-wavelength range, to compare with current observations. Finally, we present simulated images using different antenna configurations of ALMA at different frequencies, to show that the ring structures will be detectable at the distances of either the Taurus Auriga or Ophiucus star-forming regions

Entrando en cintura: implicaciones de política económica sobre la sostenibilidad de la deuda pública en la zona euro.

En este artículo se muestra el marco teórico implícito en la restricción presupuestaria intertemporal del gobierno. A partir de este, se realizan una serie de simulaciones sobre el problema de sostenibilidad de la deuda pública, y los sacrificios fiscales necesarios para juzgar el actual nivel de endeudamiento sostenible en algunos países de la zona Euro. En particular, Grecia, Portugal, Italia y España deben generar un superávit primario de 44.1%, 10.5%, 6.8% y 4.5% del PIB, respectivamente para mantener sus actuales niveles de endeudamiento. La situación de Reino unido, Alemania y Francia es diferente, puesto que pueden presentar déficits debido a la relación entre crecimiento esperado y tasa de interés

Weighted norm inequalities for the geometric maximal operator

We consider two closely related but distinct operators,This extends the work of X. Shi; H. Wei, S. Xianliang and S. Qiyu; X. Yin and B. Muckenhoupt; and C. Sbordone and I. Wik. F I W e give sufficient conditions for the two operators to be equal and show that these conditions are sharp. We also prove two-weight, weighted norm inequalities for both operators using our earlier results about weighted norm inequalities for the minimal operator: \ text{\mgran{m}} f(x) = \inf_{I \ni x} \frac{1}{ \ align M_0f(x)&= \sup_{I\ni x}\exp\left(\frac{1}{\ ,dy\right) \quad\text{and}\\M_0^*f(x) &= \lim_{r\rightarrow0} \sup_{I\ni x}\left(\frac{1}{ \ ,dy. ^ r\,dy\right)^{1/r}.\endalign } \int_I\log } \int_

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

Mass fluctuation kinetics: analysis and computation of equilibria and local dynamics

The mass fluctuation kinetics (MFK) model is a set of coupled ordinary differential equations approximating the time evolution of means and covariances of species concentrations in chemical reaction networks. It generalises classical mass action kinetics (MAK), in which fluctuations around the mean are ignored. MFK may be used to approximate stochasticity in system trajectories when stochastic simulation methods are prohibitively expensive computationally. This study presents a set of tools to aid in the analysis of systems within the MFK framework. A closed-form expression for the MFK Jacobian matrix is derived. This expression facilitates the computation of MFK equilibria and the characterisation of the dynamics of small deviations from the equilibria (i.e. local dynamics). Software developed in MATLAB to analyse systems within the MFK framework is also presented. The authors outline a homotopy continuation method that employs the Jacobian for bifurcation analysis, that is, to generate a locus of steady-state Jacobian eigenvalues corresponding to changing a chosen MFK parameter such as system volume or a rate constant. This method is applied to study the effect of small-volume stochasticity on local dynamics at equilibria in a pair of example systems, namely the formation and dissociation of an enzyme-substrate complex and a genetic oscillator. For both systems, this study reveals volume regimes where MFK provides a quantitatively and/or qualitatively correct description of system behaviour, and regimes where the MFK approximation is inaccurate. Moreover, our analysis provides evidence that decreasing volume from the MAK regime (infinite volume) has a destabilising effect on system dynamics