Periodicities in data observed during the minimum and the rising phase of solar cycle 23; years 1996 - 1999

Three types of observations: the daily values of the solar radio flux at 7 frequencies, the daily international sunspot number and the daily Stanford mean solar magnetic field were processed in order to find all the periodicities hidden in the data. Using a new approach to the radio data, two time series were obtained for each frequency examined, one more sensitive to spot magnetic fields, the other to large magnetic structures not connected with sunspots. Power spectrum analysis of the data was carried out separately for the minimum (540 days from 1 March 1996 to 22 August 1997) and for the rising phase (708 days from 23 August 1997 to 31 July 1999) of the solar cycle 23. The Scargle periodograms obtained, normalized for the effect of autocorrelation, show the majority of known periods and reveal a clear difference between the periodicities found in the minimum and the rising phase. We determined the rotation rate of the `active longitudes' in the rising phase as equal to 444.4 $\pm$ 4 nHz (26\fd0 \pm 0\fd3). The results indicate that appropriate and careful analysis of daily radio data at several frequencies allows the investigation of solar periodicities generated in different layers of the solar atmosphere by various phenomena related to the periodic emergence of diverse magnetic structures.Comment: 15 pages, 8 figure

Exponential Mixing for a Stochastic PDE Driven by Degenerate Noise

We study stochastic partial differential equations of the reaction-diffusion type. We show that, even if the forcing is very degenerate (i.e. has not full rank), one has exponential convergence towards the invariant measure. The convergence takes place in the topology induced by a weighted variation norm and uses a kind of (uniform) Doeblin condition.Comment: 10 pages, 1 figur

Legal geographies of irregular migration : An outlook on immigration detention

In this article, I discuss legal geographies of irregular migration, drawing on a case study on immigration detention in Finland. Based on analysis of detention records, four different types of legal geographies are identified, relating to south–north movement of third‐country nationals inside Europe, criminalised Eastern European EU citizens, irregularity during the asylum process (in particular, related to the Dublin Regulation) and irregularly residing foreign nationals, including deportable long‐term residents. The analysis focuses on the relations between space, law and persons during detainees' irregular migration trajectories, paying attention to their varying entry routes, residence times, legal grounds for removal and detention and removal countries. I argue for the need for empirically contextualised analysis that addresses the complex relations between law and geography beyond a particular national context, in order to better understand the dynamics of irregular migration in all its variety.In this article, I discuss legal geographies of irregular migration, drawing on a case study on immigration detention in Finland. Based on analysis of detention records, four different types of legal geographies are identified, relating to south–north movement of third‐country nationals inside Europe, criminalised Eastern European EU citizens, irregularity during the asylum process (in particular, related to the Dublin Regulation) and irregularly residing foreign nationals, including deportable long‐term residents. The analysis focuses on the relations between space, law and persons during detainees' irregular migration trajectories, paying attention to their varying entry routes, residence times, legal grounds for removal and detention and removal countries. I argue for the need for empirically contextualised analysis that addresses the complex relations between law and geography beyond a particular national context, in order to better understand the dynamics of irregular migration in all its variety.Peer reviewe

Stochastic evolution equations driven by Liouville fractional Brownian motion

Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of L(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in the interval (0,1). For Hurst parameters in (0,1/2) we show that a function F:(0,T)\to L(H,E) is stochastically integrable with respect to an H-cylindrical Liouville fBm if and only if it is stochastically integrable with respect to an H-cylindrical fBm with the same Hurst parameter. As an application we show that second-order parabolic SPDEs on bounded domains in \mathbb{R}^d, driven by space-time noise which is white in space and Liouville fractional in time with Hurst parameter in (d/4,1) admit mild solution which are H\"older continuous both and space.Comment: To appear in Czech. Math.

Statistical properties of stochastic 2D Navier-Stokes equations from linear models

A new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence has been proposed and tested through numerical simulations. This is achieved by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. In this paper, we investigate this conjecture for the 2D Navier-Stokes equations driven by an additive noise. In order to check this conjecture, we analyze the coupled system Navier-Stokes/linear advection system in the unknowns $(u,w)$. We introduce a parameter $\lambda$ which gives a system $(u^\lambda,w^\lambda)$; this system is studied for any $\lambda$ proving its well posedness and the uniqueness of its invariant measure $\mu^\lambda$. The key point is that for any $\lambda \neq 0$ the fields $u^\lambda$ and $w^\lambda$ have the same scaling exponents, by assuming universality of the scaling exponents to the force. In order to prove the same for the original fields $u$ and $w$, we investigate the limit as $\lambda \to 0$, proving that $\mu^\lambda$ weakly converges to $\mu^0$, where $\mu^0$ is the only invariant measure for the joint system for $(u,w)$ when $\lambda=0$.Comment: 23 pages; improved versio

On a Unique Ergodicity of Some Markov Processes

It is proved that the sufficient condition for the uniqueness of an invariant measure for Markov processes with the strong asymptotic Feller property formulated by Hairer and Mattingly (Ann Math 164(3):993–1032, 2006) entails the existence of at most one invariant measure for e-processes as well. Some application to timehomogeneous Markov processes associated with a nonlinear heat equation driven by an impulsive noise is also given

Causes and evolution of winter polynyas north of Greenland

During the 42-year period (1979–2020) of satellite measurements, four major winter (December–March) polynyas have been observed north of Greenland: one in December 1986 and three in the last decade, i.e., February of 2011, 2017, and 2018. The 2018 polynya was unparalleled in its magnitude and duration compared to the three previous events. Given the apparent recent increase in the occurrence of these extreme events, this study aims to examine their evolution and causality, in terms of forced versus natural variability. The limited weather station and remotely sensed sea ice data are analyzed combining with output from the fully coupled Regional Arctic System Model (RASM), including one hindcast and two ensemble simulations. We found that neither the accompanying anomalous warm surface air intrusion nor the ocean below had an impact (i.e., no significant ice melting) on the evolution of the observed winter open-water episodes in the region. Instead, the extreme atmospheric wind forcing resulted in greater sea ice deformation and transport offshore, accounting for the majority of sea ice loss in all four polynyas. Our analysis suggests that strong southerly winds (i.e., northward wind with speeds greater than 10 m s−1) blowing persistently over the study region for at least 2 d or more were required over the study region to mechanically redistribute some of the thickest Arctic sea ice out of the region and thus to create open-water areas (i.e., a latent heat polynya). To assess the role of internal variability versus external forcing of such events, we carried out and examined results from the two RASM ensembles dynamically downscaled with output from the Community Earth System Model (CESM) Decadal Prediction Large Ensemble (DPLE) simulations. Out of 100 winters in each of the two ensembles (initialized 30 years apart: one in December 1985 and another in December 2015), 17 and 16 winter polynyas were produced north of Greenland, respectively. The frequency of polynya occurrence had no apparent sensitivity to the initial sea ice thickness in the study area pointing to internal variability of atmospheric forcing as a dominant cause of winter polynyas north of Greenland. We assert that dynamical downscaling using a high-resolution regional climate model offers a robust tool for process-level examination in space and time, synthesis with limited observations, and probabilistic forecasts of Arctic events, such as the ones being investigated here and elsewhere.</p

Controllability and Qualitative properties of the solutions to SPDEs driven by boundary L\'evy noise

Let $u$ be the solution to the following stochastic evolution equation (1) du(t,x)& = &A u(t,x) dt + B \sigma(u(t,x)) dL(t),\quad t>0; u(0,x) = x taking values in an Hilbert space \HH, where $L$ is a \RR valued L\'evy process, $A:H\to H$ an infinitesimal generator of a strongly continuous semigroup, \sigma:H\to \RR bounded from below and Lipschitz continuous, and B:\RR\to H a possible unbounded operator. A typical example of such an equation is a stochastic Partial differential equation with boundary L\'evy noise. Let \CP=(\CP_t)_{t\ge 0} %{\CP_t:0\le t<\infty}$the corresponding Markovian semigroup. We show that, if the system (2) du(t) = A u(t)\: dt + B v(t),\quad t>0 u(0) = x is approximate controllable in time$T>0$, then under some additional conditions on$B$and$A$, for any$x\in H$the probability measure$\CP_T^\star \delta_x$is positive on open sets of$H$. Secondly, as an application, we investigate under which condition on$\HH$and on the L\'evy process$L$and on the operator$A$and$B$ the solution of Equation [1] is asymptotically strong Feller, respective, has a unique invariant measure. We apply these results to the damped wave equation driven by L\'evy boundary noise

Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions

A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium. This system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes (obstacles or heterogeneities), together with random dynamical boundary conditions on the boundaries of these small holes. A homogenized macroscopic model for this microscopic heterogeneous stochastic system is derived. This homogenized effective model is a new stochastic partial differential equation defined on a unified domain without small holes, with static boundary condition only. In fact, the random dynamical boundary conditions are homogenized out, but the impact of random forces on the small holes' boundaries is quantified as an extra stochastic term in the homogenized stochastic partial differential equation. Moreover, the validity of the homogenized model is justified by showing that the solutions of the microscopic model converge to those of the effective macroscopic model in probability distribution, as the size of small holes diminishes to zero.Comment: Communications in Mathematical Physics, to appear, 200