On coupling between the Poincaré equation and the heat equation

1994 ◽  
Vol 268 ◽  
pp. 211-229 ◽  
Author(s):  
Keke Zhang
Keyword(s):  
Quantitative Agreement ◽  
Equatorial Region ◽  
Inertial Oscillation ◽  
Leading Order ◽  
Rotating Fluid ◽  
Fluid Systems ◽  
Oscillation Modes ◽  
Prandtl Numbers ◽  
Spherical Fluid ◽  
First Time

It has been suggested that in a rapidly rotating fluid sphere, convection would be in the form of slowly drifting columnar rolls with small azimuthal scale (Roberts 1968; Busse 1970). The results in this paper show that there are two alternative convection modes which are preferred at small Prandtl numbers. The two new convection modes are, at leading order, essentially those inertial oscillation modes of the Poincaré equation with the simplest structure along the axis of rotation and equatorial symmetry: one propagates in the eastward direction and the other propagates in the westward direction; both are trapped in the equatorial region. Buoyancy forces appear at next order to drive the oscillation against the weak effects of viscous damping. On the basis of the perturbation of solutions of the Poincaré equation, and taking into account the effects of the Ekman boundary layer, complete analytical convection solutions are obtained for the first time in rotating spherical fluid systems. The condition of an inner sphere exerts an insignificant influence on equatorially trapped convection. Full numerical analysis of the problem demonstrates a quantitative agreement between the analytical and numerical analyses.

scholarly journals Complete leading-order standard model corrections to quantum leptogenesis

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Paul Frederik Depta ◽  
Andreas Halsch ◽  
Janine Hütig ◽  
Sebastian Mendizabal ◽  
Owe Philipsen
Keyword(s):  
Standard Model ◽  
Gauge Coupling ◽  
Thermal Bath ◽  
Leading Order ◽  
Boltzmann Equations ◽  
The Standard Model ◽  
Majorana Neutrinos ◽  
Infinite Loop ◽  
First Time ◽  
The Universe

Abstract Thermal leptogenesis, in the framework of the standard model with three additional heavy Majorana neutrinos, provides an attractive scenario to explain the observed baryon asymmetry in the universe. It is based on the out-of-equilibrium decay of Majorana neutrinos in a thermal bath of standard model particles, which in a fully quantum field theoretical formalism is obtained by solving Kadanoff-Baym equations. So far, the leading two-loop contributions from leptons and Higgs particles are included, but not yet gauge corrections. These enter at three-loop level but, in certain kinematical regimes, require a resummation to infinite loop order for a result to leading order in the gauge coupling. In this work, we apply such a resummation to the calculation of the lepton number density. The full result for the simplest “vanilla leptogenesis” scenario is by $$ \mathcal{O} $$ O (1) increased compared to that of quantum Boltzmann equations, and for the first time permits an estimate of all theoretical uncertainties. This step completes the quantum theory of leptogenesis and forms the basis for quantitative evaluations, as well as extensions to other scenarios.

scholarly journals Coriolis effects on the elliptical instability in cylindrical and spherical rotating containers

2007 ◽  
Vol 585 ◽  
pp. 323-342 ◽  
Author(s):  
M. LE BARS ◽  
S. LE DIZÈS ◽  
P. LE GAL
Keyword(s):  
Growth Rates ◽  
Close Agreement ◽  
Unstable Mode ◽  
Quantitative Agreement ◽  
Fixed Rate ◽  
Elliptical Instability ◽  
Normal Mode Theory ◽  
Set Up ◽  
First Time ◽  
Selection Of

The effects of the Coriolis force on the elliptical instability are studied experimentally in cylindrical and spherical rotating containers placed on a table rotating at a fixed rate $\tilde{\Omega}^G$. For a given set-up, changing the ratio ΩG of global rotation $\tilde{\Omega}^G$ to flow rotation $\tilde{\Omega}^F$ leads to the selection of various unstable modes due to the presence of resonance bands, in close agreement with the normal-mode theory. No instability occurs when ΩG varies between −3/2 and −1/2 typically. On decreasing ΩG toward −1/2, resonance bands are first discretized for ΩG<0 and progressively overlap for −1/2 ≪ ΩG < 0. Simultaneously, the growth rates and wavenumbers of the prevalent stationary unstable mode significantly increase, in quantitative agreement with the viscous short-wavelength analysis. New complex resonances have been observed for the first time for the sphere, in addition to the standard spin-over. We argue that these results have significant implications in geo- and astrophysical contexts.

Convection in a rotating spherical fluid shell with an inhomogeneous temperature boundary condition at infinite Prandtl number

1993 ◽  
Vol 250 ◽  
pp. 209-232 ◽  
Author(s):  
Keke Zhang ◽  
David Gubbins
Keyword(s):  
Numerical Solutions ◽  
Unstable Mode ◽  
Mode Analysis ◽  
Mathematical Framework ◽  
Fluid Systems ◽  
Critical Wavelength ◽  
Resonance Solution ◽  
Inhomogeneous Temperature ◽  
Spherical Fluid ◽  
The Stability

We examine thermal convection in a rotating spherical shell with a spatially non-uniformly heated outer surface, concentrating on three distinct heating modes: first, with wavelength and symmetry corresponding to the most unstable mode of the uniformly heated problem; secondly, with the critical wavelength but opposite equatorial symmetry; and thirdly, with wavelength much larger than that of the most unstable mode. Analysis is focused on boundary-locked convection, the associated spatial resonance phenomena, the stability properties of the resonance solution, and time-dependent secondary convection. A number of new forms of instability and convection are found: the most interesting is perhaps the saddle-node bifurcation, which is the first to be found for realistic fluid systems governed by partial differential equations. An analogous Landau amplitude equation is also analysed, providing an important mathematical framework for understanding the complicated numerical solutions.

scholarly journals Constraining the dense matter equation-of-state with radio pulsars

2020 ◽  
Vol 497 (3) ◽  
pp. 3118-3130 ◽  
Author(s):  
Huanchen Hu ◽  
Michael Kramer ◽  
Norbert Wex ◽  
David J Champion ◽  
Marcel S Kehl
Keyword(s):  
Equations Of State ◽  
Dense Matter ◽  
Leading Order ◽  
Radio Pulsars ◽  
Mass Measurements ◽  
Pulsar Timing ◽  
Orbital Periods ◽  
To Come ◽  
The Moment ◽  
First Time

ABSTRACT Radio pulsars provide some of the most important constraints for our understanding of matter at supranuclear densities. So far, these constraints are mostly given by precision mass measurements of neutron stars (NS). By combining single measurements of the two most massive pulsars, J0348+0432 and J0740+6620, the resulting lower limit of 1.98 M⊙ (99 per cent confidence) of the maximum NS mass, excludes a large number of equations of state (EOSs). Further EOS constraints, complementary to other methods, are likely to come from the measurement of the moment of inertia (MOI) of binary pulsars in relativistic orbits. The Double Pulsar, PSR J0737−3039A/B, is the most promising system for the first measurement of the MOI via pulsar timing. Reviewing this method, based in particular on the first MeerKAT observations of the Double Pulsar, we provide well-founded projections into the future by simulating timing observations with MeerKAT and the SKA. For the first time, we account for the spin-down mass-loss in the analysis. Our results suggest that an MOI measurement with 11 per cent accuracy (68 per cent confidence) is possible by 2030. If by 2030 the EOS is sufficiently well known, however, we find that the Double Pulsar will allow for a 7 per cent test of Lense–Thirring precession, or alternatively provide a ∼3σ-measurement of the next-to-leading order gravitational wave damping in GR. Finally, we demonstrate that potential new discoveries of double NS systems with orbital periods shorter than that of the Double Pulsar promise significant improvements in these measurements and the constraints on NS matter.

Granular ripples under rotating flow: a new experimental technique for studying ripples in non-rotating, geophysical applications?

2005 ◽  
Vol 363 (1832) ◽  
pp. 1663-1676 ◽  
Author(s):  
P.J Thomas ◽  
F Zoueshtiagh
Keyword(s):  
Scaling Law ◽  
Research Community ◽  
New Technique ◽  
Rotating Flow ◽  
Rotating Fluid ◽  
Geophysical Research ◽  
Rotating Systems ◽  
Experimental Parameters ◽  
First Time ◽  
Ripple Pattern

A review of our research investigating a new pattern formation process in granular material underlying a rotating fluid is given. The purpose of this summary is to introduce the phenomenon to the geophysical research community and to draw attention to the potential practical benefits of our new experimental method. To this end, the applied and scientific advantages of the technique over traditional studies employing, for instance, water channels, are discussed for the first time. It is shown here that the system rotation in our new technique does not appear to affect the scaling law expressing the dependence of the ripple-pattern wavelength on the governing independent experimental parameters. This suggests that it may become possible to extrapolate appropriate results from rotating to non-rotating systems and, hence, to geophysical environments. Consequently, our new technique may find applications in the context of geophysical research on the formation of sedimentary granular ripple structures.

N3LO Chiral Predictions for Spin Observables in Nucleon-Deuteron Elastic Scattering at Low Energies

2016 ◽  
Vol 40 ◽  
pp. 1660069
Author(s):  
R. Skibiński ◽  
J. Golak ◽  
K. Topolnicki ◽  
H. Witała
Keyword(s):  
Leading Order ◽  
Nuclear Forces ◽  
Nucleon Force ◽  
Deuteron Scattering ◽  
Nucleon Potential ◽  
Spin Observables ◽  
Low Energies ◽  
Short Range Part ◽  
Range Part ◽  
First Time

The chiral next-to-next-to-next-to leading order nuclear forces1−3 are used to obtain predictions for spin observables in elastic nucleon-deuteron scattering at E=13 MeV. The three-nucleon force is taken into account with all its complexity, including the short-range part and relativistic corrections. Presented examples of the polarization observables for elastic nucleon-deuteron scattering show visible contributions from these new structures in the three-nucleon potential which emerge for the first time at the next-to-next-to-next-to leading order. However, our results suggest that some modifications of the currently used model of the nuclear forces are necessary.

NLO EVOLUTION OF STRUCTURE FUNCTIONS AT SMALL x

2011 ◽  
Vol 04 ◽  
pp. 46-55
Author(s):  
GIOVANNI ANTONIO CHIRILLI
Keyword(s):  
Impact Factor ◽  
Energy Operator ◽  
High Energy ◽  
Structure Functions ◽  
Coordinate Space ◽  
Operator Product ◽  
Leading Order ◽  
Small X ◽  
Evolution Of Structure ◽  
First Time

Using the high-energy Operator Product Expansion of the T-product of two electromagnetic currents, we calculate the Photon Impact Factor for Deep Inelastic Scattering at small value of the Bjorken variable x B at the next-to-leading order (NLO) accuracy in αs. We provide for the first time an analytic expression in coordinate space and in Mellin space of the NLO impact factor for the forward unpolarized structure functions.

The effect of shear and stratification on the stability of a rotating fluid layer

1973 ◽  
Vol 59 (2) ◽  
pp. 369-390 ◽  
Author(s):  
A. R. Brunsvold ◽  
C. M. Vest
Keyword(s):  
Stratified Flow ◽  
Reynolds Numbers ◽  
Travelling Wave ◽  
Taylor Number ◽  
Critical Parameters ◽  
Rotating Fluid ◽  
Critical Mode ◽  
Shear Rates ◽  
Prandtl Numbers ◽  
The Stability

The stability of a layer of Newtonian fluid confined between two horizontal disks which rotate with different angular velocities is studied. Both isothermal and adversely stratified fluids are considered for small shear rates at low to moderate Taylor numbers. The linearized formulation of the stability problem is given a finite-difference representation, and the resulting algebraic eigenvalue problem is solved using efficient numerical techniques. The critical parameters and disturbance orientations are determined as a function of the Taylor number for the isothermal flow, and for the stratified flow for Prandtl numbers of 0·025, 1·0 and 6·0.At high Taylor numbers, the unstratified fluid flows in Ekman-like layers near the disks, and two modes of instability are noted: the viscous-type ‘class A’ travelling wave, whose existence depends on Coriolis forces, and the inflexional ‘class B’ mode, which is nearly stationary with respect to the nearer bounding disk. As the Taylor number is decreased, the Ekman layers coalesce to form a fully developed flow. In this regime there is a Taylor number below which the class A waves are always damped. The critical Reynolds number for the class B waves increases rapidly as the Taylor number approaches zero.For Prandtl numbers of 1·0 and 6·0, the adversely stratified flow exhibits two distinct types of instability: convective and dynamical. At low Reynolds numbers, a stationary mode associated with Bénard convection in a rotating fluid is critical. It is stabilized and given orientation by the shear. At higher Reynolds numbers, the critical mode is a travelling wave of the nature of either the class A or class B waves, depending upon the Taylor number. For a Prandtl number of 0·025, the critical mode resembles oscillatory convection at small Reynolds numbers and a class A wave at larger shear rates.

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