Lp Fourier multipliers on compact Lie groups

In this paper we prove Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give applications to a-priori estimates for non-hypoelliptic operators. Already in the case of tori we get an interesting refinement of the classical multiplier theorem.Comment: 22 pages; minor correction

The effectiveness of therapeutic interventions on psychological distress in refugee children : A systematic review

Objective To systematically review existing research exploring the effectiveness of psychological interventions in reducing symptoms of distress amongst refugee and asylum-seeker children. Method Six databases were searched to identify English studies presenting original empirical quantitative data (published before September 2022) testing the efficacy of psychological interventions for children from refugee and asylum-seeking backgrounds. Quality of studies were assessed through the Appraisal Tool for Cross-Sectional Studies as well as the Cochrane Risk of Bias Tool. Relevant data were extracted to facilitate a narrative synthesis. Results Seventy-one eligible articles were identified (n > 10,000). A number of cognitive-behavioral, psychosocial, and trauma-focused interventions that catered specifically to children and their families were identified. A synthesis of these results suggest that interventions may assist in the reduction of various psychopathologies, although the effects were mixed across intervention types. Conclusions While the review yielded promising findings, most findings were derived from small pilot and empirical studies, leading to difficulties with drawing conclusions. There remains a need for studies using more rigorous research methodologies to expand and ratify this valuable knowledge base. Clinical significance: Forced displacement is at an all-time high. Many children are being forced to seek asylum and refuge, and they become vulnerable to the development of poor mental health, with limited understanding surrounding how to appropriately intervene. This review aims to equip clinicians with increased knowledge and confidence in working therapeutically alongside clients from refugee or asylum-seeking background, with the goal of fostering positive mental health and wellbeing

Growth rate degeneracies in kinematic dynamos

We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also called pseudovacuum) or tangent (perfect electrical conductor) to the boundaries of the domain. These boundary conditions correspond to well-defined physical limits often used in numerical models and relevant to laboratory experiments. The only constraint is for the velocity field u to be reversible, meaning there exists a transformation changing u into −u. We illustrate this surprising property using S2T2 type of flows in spherical geometry inspired by [Dudley and James, Proc. R. Soc. London A 425, 407 (1989)]. Using both types of boundary conditions, it is shown that the growth rates of the dynamos are identical, although the corresponding magnetic eigenmodes are drastically different

Thirty years of change in the fynbos vegetation of the Cape of Good Hope Nature Reserve, South Africa

This study used permanently marked 50 m: sites, surveyed at a 30 year interval, to provide a descriptive account of the temporal change in the fynbos vegetation of the Cape of Good Hope Nature Reserve. South Africa. Management records were used to examine the role of post-fire age. fire frequency and intensity, as well as biotic interactions (competition from overstorey proteoids and alien plants) in influencing vegetation composition over this time period. The mean similarity in species composition of sites between surveys was 62%, indicating an average of nearly 40% turnover in species over the 30 year period. The main causes of this change included differences resulting from different stages in the post-fire succession as well as the impact of differential fire regimes (especially frequency effects). Competition from serotinous Proteaceae. which proved highly mobile after fire, as well as invasive Australian acacias also impacted on the composition of the vegetation over time. The study demonstrated that fynbos communities are temporally dynamic and that the changes over time in species composition are caused by a variety of processes. The study also provided evidence for the role of temporal diversity in contributing to the high species diversity in fynbos systems

Bounds on the Magnetic Fields in the Radiative Zone of the Sun

We discuss bounds on the strength of the magnetic fields that could be buried in the radiative zone of the Sun. The field profiles and decay times are computed for all axisymmetric toroidal Ohmic decay eigenmodes with lifetimes exceeding the age of the Sun. The measurements of the solar oblateness yield a bound <~ 7 MG on the strength of the field. A comparable bound is expected to come from the analysis of the splitting of the solar oscillation frequencies. The theoretical analysis of the double diffusive instability also yields a similar bound. The oblateness measurements at their present level of sensitivity are therefore not expected to measure a toroidal field contribution.Comment: 15 pages, 6 figure

Ullemar's formula for the Jacobian of the complex moment mapping

The complex moment sequence m(P) is assigned to a univalent polynomial P by the Cauchy transform of the P(D), where D is the unit disk. We establish the representation of the Jacobian det dm(P) in terms of roots of the derivative P'. Combining this result with the special decomposition for the Hurwitz determinants, we prove a formula for the Jacobian which was previously conjectured by C. Ullemar. As a consequence, we show that the boundary of the class of all locally univalent polynomials in $U$ is contained in the union of three irreducible algebraic surfaces.Comment: 14 pages, submitted for "Complex Variables. Theory and Application

Thermodynamics of MHD flows with axial symmetry

We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation

A Critique of Current Magnetic-Accretion Models for Classical T-Tauri Stars

Current magnetic-accretion models for classical T-Tauri stars rely on a strong, dipolar magnetic field of stellar origin to funnel the disk material onto the star, and assume a steady-state. In this paper, I critically examine the physical basis of these models in light of the observational evidence and our knowledge of magnetic fields in low-mass stars, and find it lacking. I also argue that magnetic accretion onto these stars is inherently a time-dependent problem, and that a steady-state is not warranted. Finally, directions for future work towards fully-consistent models are pointed out.Comment: 2 figure

Dust-driven Dynamos in Accretion Disks

Magnetically driven astrophysical jets are related to accretion and involve toroidal magnetic field pressure inflating poloidal magnetic field flux surfaces. Examination of particle motion in combined gravitational and magnetic fields shows that these astrophysical jet toroidal and poloidal magnetic fields can be powered by the gravitational energy liberated by accreting dust grains that have become positively charged by emitting photo-electrons. Because a dust grain experiences magnetic forces after becoming charged, but not before, charging can cause irreversible trapping of the grain so dust accretion is a consequence of charging. Furthermore, charging causes canonical angular momentum to replace mechanical angular momentum as the relevant constant of the motion. The resulting effective potential has three distinct classes of accreting particles distinguished by canonical angular momentum, namely (i) "cyclotron-orbit", (ii) "Speiser-orbit", and (iii) "zero canonical angular momentum" particles. Electrons and ions are of class (i) but depending on mass and initial orbit inclination, dust grains can be of any class. Light-weight dust grains develop class (i) orbits such that the grains are confined to nested poloidal flux surfaces, whereas grains with a critical weight such that they experience comparable gravitational and magnetic forces can develop class (ii) or class (iii) orbits, respectively producing poloidal and toroidal field dynamos.Comment: 70 pages, 16 figure

Effects of Large-Scale Convection on p-mode Frequencies

We describe an approach for finding the eigenfrequencies of solar acoustic modes (p modes) in a convective envelope in the WKB limit. This approximation restricts us to examining the effects of fluid motions which are large compared to the mode wavelength, but allows us to treat the three-dimensional mode as a localized ray. The method of adiabatic switching is then used to investigate the frequency shifts resulting from simple perturbations to a polytropic model of the convection zone as well as from two basic models of a convective cell. We find that although solely depth-dependent perturbations can give frequency shifts which are first order in the strength of the perturbation, models of convective cells generate downward frequency shifts which are second order in the perturbation strength. These results may have implications for resolving the differences between eigenfrequencies derived from solar models and those found from helioseismic observations.Comment: 27 pages + 6 figures; accepted for publication in Ap