Planet formation models: the interplay with the planetesimal disc

Context. According to the sequential accretion model (or core-nucleated accretion model), giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. The most critical part of the model is the formation time of the core: to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. Aims: We calculate planetary formation models including a detailed description of the dynamics of the planetesimal disc, taking into account both gas drag and excitation of forming planets. Methods: We computed the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. Here we introduce a more realistic treatment for the evolution of planetesimals' relative velocities, which directly impact on the formation timescale. For this, we computed the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. Results: We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate-mass planets that have not yet started their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have masses either below 10 M⊕ or above several Jupiter masses. Conclusions: To form giant planets before the dissipation of the disc, small planetesimals (~0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate-mass planets. Other processes must therefore be at work to explain the population of extrasolar planets that are presently known.

A Lagrangian Analysis of the Northern Hemisphere Subtropical Jet

This study presents a 5-yr climatology of 7-day back trajectories started from the Northern Hemisphere subtropical jet. These trajectories provide insight into the seasonally and regionally varying angular momentum and potential vorticity characteristics of the air parcels that end up in the subtropical jet. The trajectories reveal preferred pathways of the air parcels that reach the subtropical jet from the tropics and the extratropics and allow estimation of the tropical and extratropical forcing of the subtropical jet. The back trajectories were calculated 7 days back in time and started every 6 h from December 2005 to November 2010 using the Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) dataset as a basis. The trajectories were started from the 345-K isentrope in areas where the wind speed exceeded a seasonally varying threshold and where the wind shear was confined to upper levels. During winter, the South American continent, the Indian Ocean, and the Maritime Continent are preferred areas of ascent into the upper troposphere. From these areas, air parcels follow an anticyclonic pathway into the subtropical jet. During summer, the majority of air parcels ascend over the Himalayas and Southeast Asia. Angular momentum is overall well conserved for trajectories that reach the subtropical jet from the deep tropics. In winter and spring, the hemispheric-mean angular momentum loss amounts to approximately 6%; in summer, it amounts to approximately 18%; and in fall, it amounts to approximately 13%. This seasonal variability is confirmed using an independent potential vorticity–based method to estimate tropical and extratropical forcing of the subtropical jet.

Review of lattice results concerning low-energy particle physics

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle-physics community. More specifically, we report on the determination of the lightquark masses, the form factor f+(0), arising in semileptonic K → π transition at zero momentum transfer, as well as the decay-constant ratio fK / fπ of decay constants and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)L × SU(2)R and SU(3)L×SU(3)R Chiral Perturbation Theory and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, we focus here on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant αs.

Dispersive analysis of the pion transition form factor

We analyze the pion transition form factor using dispersion theory. We calculate the singly-virtual form factor in the time-like region based on data for the e+e−→3π cross section, generalizing previous studies on ω,ϕ→3π decays and γπ→ππ scattering, and verify our result by comparing to e+e−→π0γ data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below 1GeV, and extract the slope of the form factor at vanishing momentum transfer aπ=(30.7±0.6)×10−3. We derive the dispersive formalism necessary for the extension of these results to the doubly-virtual case, as required for the pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

Measurement of the total cross section from elastic scattering in pp collisions at √s=7TeV with the ATLAS detector

A measurement of the total pp cross section at the LHC at √s = 7 TeV is presented. In a special run with high-β* beam optics, an integrated luminosity of 80 μb−1 was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable t . The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the |t | range from 0.01 GeV2 to 0.1 GeV2 to extrapolate to |t | →0, the total cross section, σtot(pp→X), is measured via the optical theorem to be: σtot(pp→X) = 95.35± 0.38 (stat.)± 1.25 (exp.)± 0.37 (extr.) mb, where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to |t | → 0. In addition, the slope of the elastic cross section at small |t | is determined to be B = 19.73 ±0.14 (stat.) ±0.26 (syst.) GeV−2.

Measurement of the Inclusive Electron Neutrino Charged Current Cross Section on Carbon with the T2K Near Detector

The T2K off-axis near detector ND280 is used to make the first differential cross-section measurements of electron neutrino charged current interactions at energies ∼1  GeV as a function of electron momentum, electron scattering angle, and four-momentum transfer of the interaction. The total flux-averaged νe charged current cross section on carbon is measured to be ⟨σ⟩ϕ=1.11±0.10(stat)±0.18(syst)×10−38  cm2/nucleon. The differential and total cross-section measurements agree with the predictions of two leading neutrino interaction generators, NEUT and GENIE. The NEUT prediction is 1.23×10−38  cm2/nucleon and the GENIE prediction is 1.08×10−38  cm2/nucleon. The total νe charged current cross-section result is also in agreement with data from the Gargamelle experiment.

Introduction to Soft-Collinear Effective Theory

Among resummation techniques for perturbative QCD in the context of collider and flavor physics, soft-collinear effective theory (SCET) has emerged as both a powerful and versatile tool, having been applied to a large variety of processes, from B-meson decays to jet production at the LHC. This book provides a concise, pedagogical introduction to this technique. It discusses the expansion of Feynman diagrams around the high-energy limit, followed by the explicit construction of the effective Lagrangian - first for a scalar theory, then for QCD. The underlying concepts are illustrated with the quark vector form factor at large momentum transfer, and the formalism is applied to compute soft-gluon resummation and to perform transverse-momentum resummation for the Drell-Yan process utilizing renormalization group evolution in SCET. Finally, the infrared structure of n-point gauge-theory amplitudes is analyzed by relating them to effective-theory operators. This text is suitable for graduate students and non-specialist researchers alike as it requires only basic knowledge of perturbative QCD.

Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

Space debris attitude simulation - ιOTA (In-Orbit Tumbling Analysis)

Today, there is little knowledge on the attitude state of decommissioned intact objects in Earth orbit. Observational means have advanced in the past years, but are still limited with respect to an accurate estimate of motion vector orientations and magnitude. Especially for the preparation of Active Debris Removal (ADR) missions as planned by ESA’s Clean Space initiative or contingency scenarios for ESA spacecraft like ENVISAT, such knowledge is needed. ESA's “Debris Attitude Motion Measurements and Modelling” project (ESA Contract No. 40000112447), led by the Astronomical Institute of the University of Bern (AIUB), addresses this problem. The goal of the project is to achieve a good understanding of the attitude evolution and the considerable internal and external effects which occur. To characterize the attitude state of selected targets in LEO and GTO, multiple observation methods are combined. Optical observations are carried out by AIUB, Satellite Laser Ranging (SLR) is performed by the Space Research Institute of the Austrian Academy of Sciences (IWF) and radar measurements and signal level determination are provided by the Fraunhofer Institute for High Frequency Physics and Radar Techniques (FHR). The In-Orbit Tumbling Analysis tool (ιOTA) is a prototype software, currently in development by Hyperschall Technologie Göttingen GmbH (HTG) within the framework of the project. ιOTA will be a highly modular software tool to perform short-(days), medium-(months) and long-term (years) propagation of the orbit and attitude motion (six degrees-of-freedom) of spacecraft in Earth orbit. The simulation takes into account all relevant acting forces and torques, including aerodynamic drag, solar radiation pressure, gravitational influences of Earth, Sun and Moon, eddy current damping, impulse and momentum transfer from space debris or micro meteoroid impact, as well as the optional definition of particular spacecraft specific influences like tank sloshing, reaction wheel behaviour, magnetic torquer activity and thruster firing. The purpose of ιOTA is to provide high accuracy short-term simulations to support observers and potential ADR missions, as well as medium-and long-term simulations to study the significance of the particular internal and external influences on the attitude, especially damping factors and momentum transfer. The simulation will also enable the investigation of the altitude dependency of the particular external influences. ιOTA's post-processing modules will generate synthetic measurements for observers and for software validation. The validation of the software will be done by cross-calibration with observations and measurements acquired by the project partners.

Finite volume effects in chiral perturbation theory with twisted boundary conditions

We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We apply Chiral Perturbation Theory in the p-regime and introduce the twist by means of a constant vector field. The corrections of masses, decay constants, pseudoscalar coupling constants and form factors are calculated at next-to-leading order. We detail the derivations and compare with results available in the literature. In some case there is disagreement due to a different treatment of new extra terms generated from the breaking of the cubic invariance. We advocate to treat such terms as renormalization terms of the twisting angles and reabsorb them in the on-shell conditions. We confirm that the corrections of masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. Furthermore, we show that the matrix elements of the scalar (resp. vector) form factor satisfies the Feynman–Hellman Theorem (resp. the Ward–Takahashi identity). To show the Ward–Takahashi identity we construct an effective field theory for charged pions which is invariant under electromagnetic gauge transformations and which reproduces the results obtained with Chiral Perturbation Theory at a vanishing momentum transfer. This generalizes considerations previously published for periodic boundary conditions to twisted boundary conditions. Another method to estimate the corrections in finite volume are asymptotic formulae. Asymptotic formulae were introduced by Lüscher and relate the corrections of a given physical quantity to an integral of a specific amplitude, evaluated in infinite volume. Here, we revise the original derivation of Lüscher and generalize it to finite volume with twisted boundary conditions. In some cases, the derivation involves complications due to extra terms generated from the breaking of the cubic invariance. We isolate such terms and treat them as renormalization terms just as done before. In that way, we derive asymptotic formulae for masses, decay constants, pseudoscalar coupling constants and scalar form factors. At the same time, we derive also asymptotic formulae for renormalization terms. We apply all these formulae in combination with Chiral Perturbation Theory and estimate the corrections beyond next-to-leading order. We show that asymptotic formulae for masses, decay constants, pseudoscalar coupling constants are related by means of chiral Ward identities. A similar relation connects in an independent way asymptotic formulae for renormalization terms. We check these relations for charged pions through a direct calculation. To conclude, a numerical analysis quantifies the importance of finite volume corrections at next-to-leading order and beyond. We perform a generic Analysis and illustrate two possible applications to real simulations.

The Hydrogen Atom: The Bohr Model in Detail

The Bohr Model for the Hydrogen Atom's electron is discussed in detail, with a recapitulation of angular momentum and a detailed discussion of relevant units (out of the cgs system).

The Runge0Lenz Vector (continued)

We continue our discussion of the Runge-Lenz vector in a quantum mechanical context. The traditional form of the Runge-Lenz vector is obtained, and the commutation relations between the Runge-Lenz vector, the Hamiltonian, and the Angular Momentum are obtained using Maple.

Comment on "From geodesics of the multipole solutions to the perturbed Kepler problem"

In this Comment we explain the discrepancies mentioned by the authors between their results and ours about the in?uence of the gravitational quadrupole moment in the perturbative calculation of corrections to the precession of the periastron of quasielliptical Keplerian equatorial orbits around a point mass. The discrepancy appears to be a consequence of two different calculations of the angular momentum of the orbits.

Evolution and breakup of viscous rotating drops

We study the evolution of a viscous fluid drop rotating about a fixed axis at constant angular velocity $Omega$ or constant angular momentum L surrounded by another viscous fluid. The problem is considered in the limit of large Ekman number and small Reynolds number. The analysis is carried out by combining asymptotic analysis and full numerical simulation by means of the boundary element method. We pay special attention to the stability/instability of equilibrium shapes and the possible formation of singularities representing a change in the topology of the fluid domain. When the evolution is at constant $Omega$, depending on its value, drops can take the form of a flat film whose thickness goes to zero in finite time or an elongated filament that extends indefinitely. When evolution takes place at constant L and axial symmetry is imposed, thin films surrounded by a toroidal rim can develop, but the film thickness does not vanish in finite time. When axial symmetry is not imposed and L is sufficiently large, drops break axial symmetry and, depending on the value of L, reach an equilibrium configuration with a 2-fold symmetry or break up into several drops with a 2- or 3-fold symmetry. The mechanism of breakup is also described

Electromagnetic Instability Studies in Fusion Plasmas Edge

Este trabajo esta dedicado al estudio de las estructuras macroscópicas conocidas en la literatura como filamentos o blobs que han sido observadas de manera universal en el borde de todo tipo de dispositivos de fusión por confinamiento magnético. Estos filamentos, celdas convectivas elongadas a lo largo de las líneas de campo que surgen en el plasma fuertemente turbulento que existe en este tipo de dispositivos, parecen dominar el transporte radial de partículas y energía en la región conocida como Scrape-off Layer, en la que las líneas de campo dejan de estar cerradas y el plasma es dirigido hacia la pared sólida que forma la cámara de vacío. Aunque el comportamiento y las leyes de escala de estas estructuras son relativamente bien conocidos, no existe aún una teoría generalmente aceptada acerca del mecanismo físico responsable de su formación, que constituye una de las principales incógnitas de la teoría de transporte del borde en plasmas de fusión y una cuestión de gran importancia práctica en el desarrollo de la siguiente generación de reactores de fusión (incluyendo dispositivos como ITER y DEMO), puesto que la eficiencia del confinamiento y la cantidad de energía depositadas en la pared dependen directamente de las características del transporte en el borde. El trabajo ha sido realizado desde una perspectiva eminentemente experimental, incluyendo la observación y el análisis de este tipo de estructuras en el stellarator tipo heliotrón LHD (un dispositivo de gran tamaño, capaz de generar plasmas de características cercanas a las necesarias en un reactor de fusión) y en el stellarator tipo heliac TJ-II (un dispositivo de medio tamaño, capaz de generar plasmas relativamente más fríos pero con una accesibilidad y disponibilidad de diagnósticos mayor). En particular, en LHD se observó la generación de filamentos durante las descargas realizadas en configuración de alta _ (alta presión cinética frente a magnética) mediante una cámara visible ultrarrápida, se caracterizó su comportamiento y se investigó, mediante el análisis estadístico y la comparación con modelos teóricos, el posible papel de la Criticalidad Autoorganizada en la formación de este tipo de estructuras. En TJ-II se diseñó y construyó una cabeza de sonda capaz de medir simultáneamente las fluctuaciones electrostáticas y electromagnéticas del plasma. Gracias a este nuevo diagnóstico se pudieron realizar experimentos con el fin de determinar la presencia de corriente paralela a través de los filamentos (un parámetro de gran importancia en su modelización) y relacionar los dos tipos de fluctuaciones por primera vez en un stellarator. Así mismo, también por primera vez en este tipo de dispositivo, fue posible realizar mediciones simultáneas de los tensores viscoso y magnético (Reynolds y Maxwell) de transporte de cantidad de movimiento. ABSTRACT This work has been devoted to the study of the macroscopic structures known in the literature as filaments or blobs, which have been observed universally in the edge of all kind of magnetic confinement fusion devices. These filaments, convective cells stretching along the magnetic field lines, arise from the highly turbulent plasma present in this kind of machines and seem to dominate radial transport of particles and energy in the region known as Scrapeoff Layer, in which field lines become open and plasma is directed towards the solid wall of the vacuum vessel. Although the behavior and scale laws of these structures are relatively well known, there is no generally accepted theory about the physical mechanism involved in their formation yet, which remains one of the main unsolved questions in the fusion plasmas edge transport theory and a matter of great practical importance for the development of the next generation of fusion reactors (including ITER and DEMO), since efficiency of confinement and the energy deposition levels on the wall are directly dependent of the characteristics of edge transport. This work has been realized mainly from an experimental perspective, including the observation and analysis of this kind of structures in the heliotron stellarator LHD (a large device capable of generating reactor-relevant plasma conditions) and in the heliac stellarator TJ-II (a medium-sized device, capable of relatively colder plasmas, but with greater ease of access and diagnostics availability). In particular, in LHD, the generation of filaments during high _ discharges (with high kinetic to magnetic pressure ratio) was observed by means of an ultrafast visible camera, and the behavior of this structures was characterized. Finally, the potential role of Self-Organized Criticality in the generation of filaments was investigated. In TJ-II, a probe head capable of measuring simultaneously electrostatic and electromagnetic fluctuations in the plasma was designed and built. Thanks to this new diagnostic, experiments were carried out in order to determine the presence of parallel current through filaments (one of the most important parameters in their modelization) and to related electromagnetic (EM) and electrostatic (ES) fluctuations for the first time in an stellarator. As well, also for the first time in this kind of device, measurements of the viscous and magnetic momentum transfer tensors (Reynolds and Maxwell) were performed.