Breaking Of Axial Symmetry Research Articles

Odd viscous flow past a sphere at low but non-zero Reynolds numbers

The measurement of lift on symmetrically shaped obstacles immersed in low Reynolds number flow is the quintessential way to signal odd viscosity. For flow past cylinders, such a lift force does not arise if incompressibility and no-slip boundary conditions are fulfilled, whereas for spheres, a lift force has been found in Stokes flow, which is valid for cases where the Reynolds numbers are negligible and convection can be ignored. When considering the role of convection at low but non-zero Reynolds numbers, two hurdles arise, the Whitehead paradox and the breaking of axial symmetry, which are overcome by the method of matched asymptotic expansions and the Lorentz reciprocal theorem, respectively. We also consider the case where axial symmetry is preserved because the translation of the sphere is aligned with the axis of chirality of odd viscosity. We find that while lift vanishes, the interplay between odd viscosity and convection gives rise to a stream-induced torque.

Role of partial stable stratification on fluid flow and heat transfer in rotating thermal convection

The liquid iron core of the Earth undergoes vigorous convection driven by thermal and compositional buoyancy. The dynamics of convective fluid motions and heat transfer in such conditions are determined by background rotation, geometrical symmetry, and thermal interactions across the boundaries. In this study, rotating thermal convection in a horizontal fluid layer is considered to understand the fluid flow characteristics in the Earth's outer core focusing on the regions close to the rotational axis. The effects of a partial stable stratification on fluid flow and heat transfer are investigated to ascertain the physical significance of thermal core–mantle interaction on geomagnetic field generation driven by core fluid motion. It is found that even with non-linear evolution, convective instabilities retain the fundamental characteristics of linear onset modes. Mildly supercritical regimes lead to near laminar flows with the transition to turbulent convection occurring for strongly driven convection around 50–100 times enhanced buoyancy. Axial symmetry breaking and preferential damping of small-scale vortical structures are the hallmark of penetrative convection. Rapid rotation sustains small-scale helical flows in stable regions, a necessary ingredient for the sustenance of Earthlike dipolar magnetic fields. Coherent flow structures for strongly turbulent convection are obtained using reduced-order modeling. The overall total heat transfer is suppressed (up to 25%) due to the stable stratification although convective efficiency is enhanced (up to 30%) in the unstable regions favored by rapid rotation. Flow suppression is overcome under strong buoyancy forces, a relevant dynamical regime for deep-seated dynamo action in the Earth's core.

Interaction of Two Charged Dielectric Spheres with a Point Charge

We consider the problem of interaction of three charged particles, the size of one of which can be disregarded. The equations for the expansion coefficients of the electric field potential are derived using the method of expansion in spherical harmonics. Expressions are obtained for the Cartesian components of the interaction force and the torque due to this force. It is shown that in spite of the axial symmetry breaking after the addition of the third particle, if the free charge is distributed uniformly over the surface of a spherical particle, all vector components of the torque acting on this particle are equal to zero. By separating the contributions from image charges in explicit form, we have derived the expressions for the surface charge density and the force of interaction of the particles. The conditions for the emergence of attraction between similarly charged spherical particles depending on the position of the point particle are investigated.

Two-point Correlation Function Studies for the Milky Way: Discovery of Spatial Clustering from Disk Excitations and Substructure

We introduce a two-particle correlation function (2PCF) for the Milky Way, constructed to probe spatial correlations in the orthogonal directions of the stellar disk in the Galactic cylindrical coordinates of R, ϕ, and z. We use this new tool to probe the structure and dynamics of the Galaxy using the carefully selected set of solar neighborhood stars (d ≲ 3 kpc) from Gaia Data Release 2 that we previously employed for studies of axial symmetry breaking in stellar number counts. We make additional, extensive tests, comparing to reference numerical simulations, to ensure our control over possibly confounding systematic effects. Supposing either axial or north–south symmetry, we divide this data set into two nominally symmetric sectors and construct the 2PCF, in the manner of the Landy–Szalay estimator, from the Gaia data. In so doing, working well away from the midplane region in which the spiral arms appear, we have discovered distinct symmetry-breaking patterns in the 2PCF in its orthogonal directions, thus establishing the existence of correlations in stellar number counts alone at subkiloparsec length scales for the very first time. In particular, we observe extensive wavelike structures of amplitude greatly in excess of what we would estimate if the system were in a steady state. We study the variations in these patterns across the Galactic disk, and with increasing ∣z∣, and we show how our results complement other observations of non-steady-state effects near the Sun, such as vertical asymmetries in stellar number counts and the Gaia snail.

Broken axial symmetry as essential feature for a consistent modelling of various observables in heavy nuclei

Although most nuclear spectroscopy as well as atomic hyperfine structure data do not deliver accurate information on nuclear axiality the ad-hoc assumption of symmetry about one axis found widespread use in nuclear model calculations. In the theoretical interpretation of nuclear properties as well as in the analysis of experimental data triaxiality was considered – if at all – only for some, often exotic, nuclides. A breaking of axial symmetry combined to a spin-independent moment of inertia results in a surprisingly simple heuristic triaxial parametrization of the yrast sequence in all heavy nuclei, including well deformed ones. No additional fit parameters are needed in detailed studies of the mass and charge dependence of the electric dipole strength in the range of and outside of giant dipole resonances. Allowing triaxiality also avoids the introduction of an arbitrary level density parameter ã to fit the accurate values observed in n-capture experiments and ã can be taken from nuclear matter studies. A combination of this value to the yrast energies no longer based on axiality and the related I(I+1) rule results in agreement to data independent of spin. And predictions for radiative neutron capture as derived on the basis of non-axiality are improved as well. The experimentally favoured broken axial symmetry is in accord to HFB and MC-shell model calculations already for nuclei in the valley of stability.

Efficiency improvement of an E × B Penning discharge source by enhanced cross-field transport of electrons

Precise control of the particle motion in externally applied electric and magnetic fields is of great significance in the development of the E × B source to generate high-density plasma and deliver a stable ion beam current. Especially, in the E × B Penning discharge source, the heating and energy relaxation of the beam electrons is concentrated in the plasma column along the magnetic field line. Plasma researchers have thus far focused on the relevant physical phenomena of the partially magnetized plasma that arises from the gradient of the plasma properties in the E × B Penning source. Here, we point out that current methods of radially centered electron confinement do not guarantee efficient ion beam extraction, and newly introduce the improvement of the efficiency of a cylindrical E × B Penning source targeting radial extraction of ion beam. We concentrate on the method to enhance the cross-field transport of electrons toward the extraction region. The generation of a spatially asymmetric sheath structure allows the beam and energetic electrons to be transported to the extraction region via the E × B drift of the electrons. The transported electrons contribute to expansion of the electron heating and ionization regions to the extraction region by breaking of axial symmetry of the sheath, thereby increasing the temperature and density of the electrons in the extraction region as the magnetic field strength increases. The enhanced discharge efficiency defined as the ratio of the electron density to the discharge current is noticeable, recording approximately twice the improved efficiency compared to the conventional mode with symmetric sheath structure.

Energy dependent ratios of level-density parameters in superheavy nuclei

The nuclear level densities and level-density parameters in fissioning nuclei at their saddle points of fission barriers, ${a}_{f}$, as well as those for neutron, ${a}_{n}$, proton, ${a}_{p}$, and $\ensuremath{\alpha}$-particle, ${a}_{\ensuremath{\alpha}}$, emission residues at the ground states are calculated for isotopic chains of superheavy nuclei with $Z$ = 112--120. The calculations are performed with the superfluid formalism using the single-particle energies obtained from the diagonalization of the deformed Woods-Saxon potential. Spectra were generated at global minima of the adiabatic potential energy surfaces, found by the multidimensional minimization method, and at the proper saddle points, found by the ``immersion water flow'' technique on multidimensional energy grids, with allowed reflection and axial symmetry breaking. The influence of shell effects on the energy dependence of the ratios of level-density parameters corresponding to residues of the considered decay modes to those of neutron emission is studied. As shown, in contrast to the ${a}_{f}/{a}_{n}$ ratio, the ${a}_{p}/{a}_{n}$ and ${a}_{\ensuremath{\alpha}}/{a}_{n}$ ratios do not show characteristic maxima depending on the excitation energy of the compound nucleus being formed. In the case of $\ensuremath{\alpha}$ decay, we identified the collective enhancement caused by cluster degrees of freedom as playing quite an important role. The energetic course of the variability of the level-density parameters before reaching the asymptotic value, not taken into account so far, is of great importance for the estimation of the probabilities of de-excitation cascades via light particles emission in competition with fission and, thus, for the determination of the survival probabilities and finally for the total production cross sections of superheavy nuclei.

Fine structure in the odd-odd proton emitter Tm144

Axial symmetry breaking in $^{144}\mathrm{Tm}$ is probed by examining its proton emission fine structure. The ground-state spin and parity in $^{144}\mathrm{Tm}$ and daughter $^{143}\mathrm{Er}$ are assigned unambiguously based on the corroboration of our calculations with the present data. We establish the first microscopic description of fine structure in odd-odd proton emitters, which is capable of resolving ambiguities present in the assignments of transitions in such nuclei.

Axial Asymmetry Studies in Gaia Data Release 2 Yield the Pattern Speed of the Galactic Bar

Abstract Our recent studies of axial-symmetry breaking in the nearby (d < 3 kpc) star counts are sensitive to the distortions of stellar orbits perpendicular and parallel to the orientation of the bar just within and beyond the outer Lindblad resonance (OLR) radius. Using the location of the sign flip in the left–right asymmetry in stars counts about the anticenter line to determine the OLR radius R OLR, and treating the bar as if it were a weakly nonaxisymmetric effect, we use R OLR and recent measurements of the Galactic rotation curve and the Sun–Galactic-center distance R 0 to determine the pattern speed Ωp of the Galactic bar, as well as the Galactic corotation radius R CR. After removing the effect of the Large and Small Magellanic Clouds from our asymmetry measurement, we find that R OLR = (0.96 ± 0.03)R 0 = 7.85 ± 0.25 kpc, Ωp = 49.3 ± 2.2 km s−1 kpc−1, R CR = (0.58 ± 0.04)R 0 = 4.76 ± 0.27 kpc, revealing, as we shall show, that the Milky Way’s bar is likely both weak and fast, though we also note possible evidence for non-steady-state effects in the bar region.

Topological susceptibility, divergent chiral density, and phase diagram of chirally imbalanced QCD medium at finite temperature

We show that the nonlocal two-flavor Nambu--Jona-Lasinio model predicts the enhancement of both chiral and axial symmetry breaking as the chiral imbalance of hot QCD matter, regulated by a chiral chemical potential $\mu_5$, increases. The two crossovers are reasonably close to each other in the range of $\mu_5$ examined here and the pseudocritical temperatures rise with $\mu_5$. The curvatures of the chiral and axial crossovers for the chiral quark chemical potential approximately coincide and give $\kappa_5 \simeq - 0.011$. We point out that the presence of $\mu_5$ in thermodynamic equilibrium is inconsistent with the fact that the chiral charge is not a Noether-conserved quantity for massive fermions. The chiral chemical potential should not, therefore, be considered as a true chemical potential that sets a thermodynamically stable environment in the massive theory, but rather than as a new coupling that may require a renormalization in the ultraviolet domain. The divergence of an unrenormalized chiral density, \corr{coming from zero-point fermionic fluctuations,} is a consequence of this property. We propose a solution to this problem via a renormalization procedure.

Exact solutions to steady radial flow in a porous medium with variable permeability

A wide class of exact solutions to equations of steady flow of ideal gas in a porous medium is obtained in a planar annular domain comprising sectors of distinct permeabilities. The formulation involves an unconventional Sturm–Liouville problem. The class also admits solutions to configurations with respective distinct generation rates. The solutions are expected to be applicable to landfill gas or natural gas extraction. The breaking of axial symmetry enables realistic modeling of the radius of influence for both horizontal and vertical wells. The analysis proves that the well’s reach would have an azimuthal dependence in any problem with a heterogeneous medium. Therefore, it is suggested that the concept of radius of influence as perceived today be revised.

Hyperon polarization in relativistic heavy ion collisions and axial U(1) symmetry breaking at high temperature

Experiments at the Relativistic Heavy Ion Collider (RHIC) have measured the net polarization of $\Lambda$ and $\bar{\Lambda}$ hyperons and attributed it to a coupling between their spin and the vorticity of the fluid created in heavy ion collisions, but how the spin comes to equilibrium with vorticity is an open problem. Recently we found that vorticity fluctuations and helicity flip of strange quarks in quark-gluon plasma through perturbative QCD processes resulted in equilibration times far too long to be relevant. Here we consider the Nambu--Jona-Lasinio model with the inclusion of the six-quark Kobayashi--Maskawa--'t Hooft interaction which breaks axial U(1). Using instanton inspired models for the temperature dependence of the axial symmetry breaking, we find that constituent strange quarks can reach spin equilibrium at temperatures below about 170 MeV, just before they hadronize to form hyperons.

The spontaneous breaking of axisymmetry in shallow rotating flows

We show that the axial symmetry of a shallow rotating flow is spontaneously broken in the absence of an externally forced velocity gradient. It is caused by an instability excited by the gradients that arise from the axisymmetric counter-rotating vortices. The experimental setup consists of an electrolyte poured into a cylindrical container with radius R and height h and subject to electromagnetic forcing caused by an axial magnetic field and a radial current (J) leading to an azimuthal rotation Vθ. The flow motion is considered to be two-dimensional at large aspect ratio (R/h) and low Reynolds number, Re = Vθh/ν, where ν is the kinematic viscosity. At a moderate aspect ratio, we record the existence of an axisymmetric vortex at the edge caused by the no-slip boundary condition at the walls. When Re is increased by changing h or J, the flow becomes unstable at the radial position where gradients exist due to the edge vortices at a critical Reynolds number of about 220. The most unstable mode of this nonaxisymmetric instability is found to be m = 1 followed by m = 2 and other higher mode numbers. Using perturbation theory, we found that two counter-rotating vortices that are in azimuthal motion are unstable when subject to nonaxisymmetric perturbations with the onset of low azimuthal mode numbers in agreement with the experiment. We conclude that the axial symmetry breaking in shallow rotating flows occurs at relatively low Reynolds numbers caused by the gradients generated by the vortices in the height-radial plane.

A 3D model of a human epiblast reveals BMP4-driven symmetry breaking.

Breaking the anterior-posterior symmetry in mammals occurs at gastrulation. Much of the signalling network underlying this process has been elucidated in the mouse; however, there is no direct molecular evidence of events driving axis formation in humans. Here, we use human embryonic stem cells to generate an in vitro three-dimensional model of a human epiblast whose size, cell polarity and gene expression are similar to a day 10 human epiblast. A defined dose of BMP4 spontaneously breaks axial symmetry, and induces markers of the primitive streak and epithelial-to-mesenchymal transition. We show that WNT signalling and its inhibitor DKK1 play key roles in this process downstream of BMP4. Our work demonstrates that a model human epiblast can break axial symmetry despite the absence of asymmetry in the initial signal and of extra-embryonic tissues or maternal cues. Our three-dimensional model is an assay for the molecular events underlying human axial symmetry breaking.

“Stiff” deformed nuclei, configuration dependent pairing and the $\beta$β and $\gamma$γ degrees of freedom

We review the current experimental data on collective structures within the pairing gap of even-even deformed nuclei, with emphasis on nuclei near mass number $A \sim 150$. The essential physics that determines the characteristics of the first excited 0+ (02+) state in these nuclei has been in dispute for several decades. Interpretation of these states in terms of surface $\beta$ quadrupole vibrations has often been challenged. We examine the role that configuration dependent pairing can play in these levels particularly at the onset of deformation as major shells fill. In all deformed nuclei rotational bands are found experimentally, starting at a state with spin 2+ with excitation energies near the middle of the pairing gap. These rotational bands, with quantum number $K^{\pi} = 2^{+}$, are usually referred to as $\gamma$ bands and have been identified with quadrupole surface vibrations in the plane perpendicular to the major axis of deformation. However $K^{\pi} = 2^{+}$ bands can also arise due to the breaking of axial symmetry of the quadrupole shape. We discuss data that can help with these different interpretations.

Consequences of broken axial symmetry in heavy nuclei—an overview of the situation in the valley of stability

An overview on the various effects of axial symmetry breaking is presented for medium heavy and heavy nuclei covering the mass number range 70 < A < 240. The discussion includes various observations for nuclei: level densities, spectroscopic features as energies and transition rates, ground state masses and finally the splitting of giant dipole resonances. Quadrupole moments and rates can be derived from models of triaxial rigid rotation or cranking for a given triaxiality parameters γ, but microscopic considerations are needed to predict these for each nucleus investigated. Respective predictions were adopted from recently made Hartree–Fock–Bogolyubov (HFB) calculations extended to arbitrary triaxiality by a generator coordinate method. In accord to these, various observations as reported in this overview demonstrate the importance of allowing a breaking of axial symmetry for heavy nuclei already in the valley of stability. Considering this breaking as indicated from the HFB approach surprisingly many experimental data are well described globally without the need for local fit parameters. In addition to these comparisons it will be shown that it is advantageous to consider cγ = cos(3γ) an indicator of axiality for heavy nuclei independent of their quadrupole moment.

Fluctuation and dissipation of axial charge from massive quarks

In quantum chromodynamics (QCD), axial charge is known to be non-conserved due to chiral anomaly and non-vanishing quark mass. In this paper, we explore the role of quark mass in axial charge fluctuation and dissipation. We present two separate calculations of axial charge correlator, which describe dynamics of axial charge. The first is free quarks at finite temperature. We find that axial charge can be generated through effective quantum fluctuations in free theory. However the fluctuation does not follow a random walk behavior. Due to the presence of axial symmetry breaking mass term, the axial charge also does not settle asymptotically to the thermodynamic limit given by susceptibility. The second calculation is in weakly coupled quark gluon plasma (QGP). We find in the hard thermal loop (HTL) approximation, the quark-gluon interaction leads to random walk growth of axial charge, but dissipation is not visible. We estimate relaxation time scale for axial charge, finding it lies beyond the HTL regime.

Experimental Signals for Broken Axial Symmetry in Excited Heavy Nuclei from the Valley of Stability

An increasing number of experimental data indicates the breaking of axial symmetry in many heavy nuclei already in the valley of stability: Multiple Coulomb excitation analysed in a rotation invariant way, gamma transition rates and energies in odd nuclei, mass predictions, the splitting of Giant Resonances (GR), the collective enhancement of nuclear level densities and Maxwellian averaged neutron capture cross sections. For the interpretation of these experimental observations the axial symmetry breaking shows up in nearly all heavy nuclei as predicted by Hartree-Fock-Bogoliubov (HFB) calculations [1] ; this indicates a nuclear Jahn-Teller effect. We show that nearly no parameters remain free to be adjusted by separate fitting to level density or giant resonance data, if advance information on nuclear deformations, radii etc. are taken from such calculations with the force parameters already fixed. The data analysis and interpretation have to include the quantum mechanical requirement of zero point oscillations and the distinction between static vs. dynamic symmetry breaking has to be regarded.

Breaking of axial symmetry in excited heavy nuclei as identified in giant dipole resonance data

A recent theoretical prediction of a breaking of axial symmetry in quasi all heavy nuclei is confronted to a new critical analysis of photon strength functions of nuclei in the valley of stability. For the photon strength in the isovector giant dipole resonance (IVGDR) regime a parameterization of GDR shapes by the sum of three Lorentzians (TLO) is extrapolated to energies below and above the IVGDR. The impact of non-GDR modes adding to the low energy slope of photon strength is discussed including recent data on photon scattering and other radiative processes. These are shown to be concentrated in energy regions where various model calculations predict intermediate collective strength; thus they are obviously separate from the IVGDR tail. The triple Lorentzian (TLO) ansatz for giant dipole resonances is normalized in accordance to the dipole sum rule. The nuclear droplet model with surface dissipation accounts well for positions and widths without local, nuclide specific, parameters. Very few and only global parameters are needed when a breaking of axial symmetry already in the valley of stability is admitted and hence a reliable prediction for electric dipole strength functions also outside of it is expected.

Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking

The Greek aperitif Ouzo is not only famous for its specific anise-flavoured taste, but also for its ability to turn from a transparent miscible liquid to a milky-white coloured emulsion when water is added. Recently, it has been shown that this so-called Ouzo effect, i.e. the spontaneous emulsification of oil microdroplets, can also be triggered by the preferential evaporation of ethanol in an evaporating sessile Ouzo drop, leading to an amazingly rich drying process with multiple phase transitions (Tan et al., Proc. Natl Acad. Sci. USA, vol. 113 (31), 2016, pp. 8642–8647). Due to the enhanced evaporation near the contact line, the nucleation of oil droplets starts at the rim which results in an oil ring encircling the drop. Furthermore, the oil droplets are advected through the Ouzo drop by a fast solutal Marangoni flow. In this article, we investigate the evaporation of mixture droplets in more detail, by successively increasing the mixture complexity from pure water over a binary water–ethanol mixture to the ternary Ouzo mixture (water, ethanol and anise oil). In particular, axisymmetric and full three-dimensional finite element method simulations have been performed on these droplets to discuss thermal effects and the complicated flow in the droplet driven by an interplay of preferential evaporation, evaporative cooling and solutal and thermal Marangoni flow. By using image analysis techniques and micro-particle-image-velocimetry measurements, we are able to compare the numerically predicted volume evolutions and velocity fields with experimental data. The Ouzo droplet is furthermore investigated by confocal microscopy. It is shown that the oil ring predominantly emerges due to coalescence.