Spherical Background Research Articles

A combinatorial curvature flow in spherical background geometry

In [12], the existence of ideal circle patterns in Euclidean or hyperbolic background geometry under combinatorial conditions was proved using flow approaches. It remains as an open problem for the spherical case. In this paper, we introduce a combinatorial geodesic curvature flow in spherical background geometry, which is analogous to the combinatorial Ricci flow of Chow and Luo in [4]. We characterize the sufficient and necessary condition for the convergence of the flow. That is, the prescribed geodesic curvature satisfies certain geometric and combinatorial condition if and only if for any initial data the flow converges exponentially fast to a circle pattern with given total geodesic curvature on each circle. Our result could be regarded as a resolution of the problem in the spherical case. As far as we know, this is the first combinatorial curvature flow in spherical background geometry with fine properties, and it provides an algorithm to find the desired ideal circle pattern.

Faster photoswitching and amplified NBE emission from mg doped sol-gel derived ZnO thin films

ABSTRACT Photoconductivity and photoluminescence of highly transparent predominantly c-axis oriented hexagonal wurtzite nanocrystalline Mg doped zinc oxide thin films are reported here. These films prepared by sol-gel spin coating are useful for switching and UV detector applications. The increase in dopant concentration tunes the optical band-gap from 3.15 to 3.41 eV. Amplified NBE emission with low defect emission is obtained in appropriately doped sample along with high suitability for switching applications since the photocurrent sharply falls to a very low value as the illumination is put off and the rise and decay pattern is reproducible for several consecutive cycles. The films have crystallite size less than 16 nm and rod-like structures of diameter 50 to 100 nm are seen to grow out of spherical granular background. Doping reduces the size of grains and rods as well as the surface roughness.

Evolution of eccentric stellar discs around supermassive black holes: the complex disc disruption dynamics and the milliparsec stars

ABSTRACT We study the 10 Myr evolution of parsec-scale stellar discs with initial masses of Mdisc = 1.0–$7.5 \times 10^4\, \mathrm{M}_\odot$ and eccentricities einit = 0.1–0.9 around supermassive black holes (SMBHs). Our disc models are embedded in a spherical background potential and have top-heavy single and binary star initial mass functions (IMF) with slopes of 0.25–1.7. The systems are evolved with the N-body code BIFROST, including post-Newtonian (PN) equations of motion and simplified stellar evolution. All discs are unstable and evolve on Myr time-scales towards similar eccentricity distributions peaking at e⋆ ∼ 0.3–0.4. Models with high einit also develop a very eccentric (e⋆ ≳ 0.9) stellar population. For higher disc masses Mdisc ≳ 3 × 104 M⊙, the disc disruption dynamics is more complex than the standard secular eccentric disc instability with opposite precession directions at different disc radii – a precession direction instability. We present an analytical model describing this behaviour. A milliparsec population of N ∼ 10–100 stars forms around the SMBH in all models. For low einit, stars migrate inward while for einit ≳ 0.6 stars are captured by the Hills mechanism. Without PN, after 6 Myr, the captured stars have a sub-thermal eccentricity distribution. We show that including PN effects prevents this thermalization by suppressing resonant relaxation effects and cannot be ignored. The number of tidally disrupted stars is similar or larger than the number of milliparsec stars. None of the simulated models can simultaneously reproduce the kinematic and stellar population properties of the Milky Way centre clockwise disc and the S-cluster.

EDGE: the puzzling ellipticity of Eridanus II’s star cluster and its implications for dark matter at the heart of an ultra-faint dwarf

ABSTRACT The Eridanus II (EriII) ‘ultra-faint’ dwarf has a large (15 pc) and low-mass (4.3 × 103 M⊙) star cluster (SC) offset from its centre by 23 ± 3 pc in projection. Its size and offset are naturally explained if EriII has a central dark matter core, but such a core may be challenging to explain in a ΛCDM cosmology. In this paper, we revisit the survival and evolution of EriII’s SC, focusing for the first time on its puzzlingly large ellipticity ($0.31^{+0.05}_{-0.06}$). We perform a suite of 960 direct N-body simulations of SCs, orbiting within a range of spherical background potentials fit to ultra-faint dwarf (UFD) galaxy simulations. We find only two scenarios that come close to explaining EriII’s SC. In the first scenario, EriII has a low-density dark matter core (of size ${\sim}70\, \text{pc}$ and density $\lesssim 2\times 10^8\, \text{M}_{\odot }\, \text{kpc}^{-3}$). In this model, the high ellipticity of EriII’s SC is set at birth, with the lack of tidal forces in the core allowing its ellipticity to remain frozen for long times. In the second scenario, EriII’s SC orbits in a partial core, with its high ellipticity owing to its imminent tidal destruction. However, this latter model struggles to reproduce the large size of EriII’s SC, and it predicts substantial tidal tails around EriII’s SC that should have already been seen in the data. This leads us to favour the cored model. We discuss potential caveats to these findings, and the implications of the cored model for galaxy formation and the nature of dark matter.

The shadow and observation appearance of black hole surrounded by the dust field in Rastall theory

In the context of Rastall gravity, the shadow and observation intensity casted by the new Kiselev-like black hole with dust field have been numerically investigated. In this system, the Rastall parameter and surrounding dust field structure parameter have considerable consequences on the geometric structure of spacetime. Considering the photon trajectories near the black hole, we investigate the variation of the radii of photon sphere, event horizon and black hole shadow under the different related parameters. Furthermore, taking into account two different spherically symmetric accretion models as the only background light source, we also studied the observed luminosity and intensity of black holes. For the both spherical accretions background, the results show that the decrease or increase of the observed luminosity depends on the value range of relevant parameters, and the promotion effect is far less obvious than the attenuation effect on the observed intensity. One can find that the inner shadow region and outer bright region of the black hole wrapped by infalling accretion are significantly darker than those of the static model, which is closely related to the Doppler effect. In addition, the size of the shadow and the position of the photon sphere are always the same in the two accretion models, which means that the black hole shadow depend only on the geometry of spacetime, while the observation luminosity is affected by the form of accretion material and the related spacetime structure.

The F-theorem in the melonic limit

The F-theorem states that in three dimensions the sphere free energy of a field theory must decrease between ultraviolet and infrared fixed points of the renormalization group flow, and it has been proven for unitary conformal field theories (CFTs).We consider here the long-range bosonic O(N)3 model on a spherical background, at next-to-next-to-leading order of the 1/N expansion. The model displays four large-N fixed points and we test and confirm the F-theorem holds in this case. This is non-trivial as one of the couplings is imaginary, and therefore the model is non-unitary at finite N. Despite this, several tests indicating that the large-N CFTs are in fact unitary have been performed: for instance all the OPE coefficients computed so far in the large-N limit are real, and the spectrum of bilinear operators is real and above unitarity bounds. Our result, namely that the F theorem holds at large N, can be viewed as further indication that such theories are unitary.As an added bonus, we show how conformal partial waves expansions in conformal field theory can be used to resum infinite classes of vacuum diagrams. Non-perturbatively, the jump in the value of the free energy has the interpretation of the inclusion at the ultraviolet fixed point of an extra non-normalizable contribution in the conformal partial wave expansion. This can be seen in perturbation theory as the reversal of the sign of an infinite class of diagrams due to the flow of a coupling constant.

Realization of C-60 whiskers incorporated chalcopyrite CuInxGa1-xSe2 in Cu2Se/C-60/In3Se2/C-60/Ga2Se3 multilayer structures

The current article is focused on developing a new class of chalcogenide absorber layer. A multiple stacking of metal selenides with C-60 as an intermatrix layer is fabricated on a glass substrate. Post-annealing of sequential temperatures from 150 °C to 350 °C is applied to the multilayer thin film structure. X-ray diffraction revealed a dominant CIGS chalcopyrite structure with a preferential (112) plane orientation upon maximal annealing temperature. Morphological analysis has displayed fullerene whiskers imposed in spherical grains background surface. Films have displayed an appreciable absorption coefficient (≥105 cm−1). Tauc plots revealed a near-optimal single direct band gap transition at 1.64 eV for annealed (350 °C) film.

Constructing spherically symmetric Einstein\u2013Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions

In this paper we present a detailed calculation of an Ansatz that allows to obtain spherically symmetric Einstein–Dirac configurations in d-dimensions. We show that this is possible by combining 2^{lfloor frac{d-2}{2} rfloor } Dirac fields, making use of the properties of the angular dependence of the spinors in a spherical background. By applying this Ansatz, we investigate some simple analytical solutions. One of them is a regular wormhole supported by the Dirac fields. Other solutions include a pathological black hole and a naked singularity. We analyze the domain of existence and properties of all these solutions.

Statistical Mechanics of Thin Spherical Shells

We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes, and the local out-of-plane undulations leads to novel phenomena. In spherical shells, thermal fluctuations produce a radius-dependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated “pressure.” Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows nonlinearly with increasing outward pressure, with the same universal power-law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.Received 20 June 2016DOI:https://doi.org/10.1103/PhysRevX.7.011002Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCell mechanicsClassical statistical mechanicsContinuum mechanicsEquilibrium fluctuationsMembranesTechniquesRenormalization groupStatistical PhysicsPolymers & Soft MatterBiological PhysicsInterdisciplinary PhysicsCondensed Matter, Materials & Applied Physics

A generalization of the Zerilli master variable for a dynamical spherical spacetime

The evolution of polar perturbations on a spherical background spacetime is analyzed. The matter content is assumed to be a massless scalar field. This provides a nontrivial dynamics to the background and the linearized equations of motion become much more involved than in the vacuum case. The analysis is performed in a Hamiltonian framework, which makes explicit the dynamical role of each of the variables. After performing a number of canonical transformations, it is possible to completely decouple the different perturbative degrees of freedom into constrained, pure-gauge and gauge-invariant variables. In particular, two master variables are obtained: one corresponding to the polar mode of the gravitational wave, whereas the other encodes the complete physical information about the perturbative matter degree of freedom. The evolution equations for these master variables are obtained and simplified.

Summation by parts methods for spherical harmonic decompositions of the wave equation in any dimensions

We investigate numerical methods for wave equations in n + 2 spacetime dimensions, written in spherical coordinates, decomposed in spherical harmonics on Sn, and finite-differenced in the remaining coordinates r and t. Such an approach is useful when the full physical problem has spherical symmetry, for perturbation theory about a spherical background, or in the presence of boundaries with spherical topology. The key numerical difficulty arises from lower order 1/r terms at the origin r = 0. As a toy model for this, we consider the flat space linear wave equation in the form , , where p = 2l + n and l is the leading spherical harmonic index. We propose a class of summation by parts (SBP) finite-differencing methods that conserve a discrete energy up to boundary terms, thus guaranteeing stability and convergence in the energy norm. We explicitly construct SBP schemes that are second- and fourth-order accurate at interior points and the symmetry boundary r = 0, and first- and second-order accurate at the outer boundary r = R.

Galileon radiation from binary systems

We calculate the power emitted in scalar modes for a binary system, including binary pulsars, with a conformal coupling to the most general Galileon effective field theory by considering perturbations around a static, spherical background. While this method is effective for calculating the power in the cubic Galileon case, here we find that if the quartic or quintic Galileon dominate, for realistic pulsar systems the classical perturbative expansion about spherically symmetric backgrounds breaks down (although the quantum effective theory is well defined). The basic reason is that the equations of motion for the fluctuations are then effectively one dimensional. This leads to many multipoles radiating with equal strength, as opposed to the normal Minkowski spacetime and cubic Galileon cases, where increasing multipoles are suppressed by increasing powers of the orbital velocity. We consider the following two cases where perturbation theory gives trustworthy results: (1) when there is a large hierarchy between the masses of two orbiting objects and (2) when we choose scales such that the quartic Galileon only begins to dominate at distances smaller than the inverse pulsar frequency. Implications for future calculations with the full Galileon that account for the Vainshtein mechanism are considered.

Two-dimensional isotropic harmonic oscillator on a time-dependent sphere

In this paper, we investigate a two-dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a fluctuating background, transition probabilities per unit time are obtained. Transitions are possible if the energy eigenvalues of the oscillator Ei and frequencies of the fluctuating background ωn satisfy the following two simple relations: Ej ≃ Ei − ℏωn (stimulated emission) and Ej ≃ Ei + ℏωn (absorption). This indicates that a background fluctuating at a frequency of ωn interacts with the oscillator as a quantum field of the same frequency. We believe this result is also applicable for an arbitrary quantum system defined on a fluctuating maximally symmetric background.

NUMERICAL STUDY OF THE VISHNIAC INSTABILITY IN SUPERNOVA REMNANTS

The Vishniac instability is thought to explain the complex structure of radiative supernova remnants in their Pressure-Driven Thin Shell (PDTS) phase after a blast wave (BW) has propagated from a central explosion. In this paper, the propagation of the BW and the evolution of the PDTS stage are studied numerically with the two-dimensional (2D) code HYDRO-MUSCL for a finite-thickness shell expanding in the interstellar medium (ISM). Special attention is paid to the adiabatic index, γ, and three distinct values are taken for the cavity (γ1), the shell (γ2), and the ISM (γ3) with the condition γ2 < γ1, γ3. This low value of γ2 accounts for the high density in the shell achieved by a strong radiative cooling. Once the spherical background flow is obtained, the evolution of a 2D-axisymmetric perturbation is computed from the linear to the nonlinear regime. The overstable mechanism, previously demonstrated theoretically by E. T. Vishniac in 1983, is recovered numerically in the linear stage and is expected to produce and enhance anisotropies and clumps on the shock front, leading to the disruption of the shell in the nonlinear phase. The period of the increasing oscillations and the growth rate of the instability are derived from several points of view (the position of the perturbed shock front, mass fluxes along the shell, and density maps), and the most unstable mode differing from the value given by Vishniac is computed. In addition, the influence of several parameters (the Mach number, amplitude and wavelength of the perturbation, and adiabatic index) is examined and for wavelengths that are large enough compared to the shell thickness, the same conclusion arises: in the late stage of the evolution of the radiative supernova remnant, the instability is dampened and the angular initial deformation of the shock front is smoothed while the mass density becomes uniform with the angle. As a result, our model shows that the supernova remnant returns to a stable evolution and the Vishniac instability does not lead to the fragmentation of the shock as predicted by the theory.

High-order perturbations of a spherical collapsing star

In Ref. [1, 2] a formalism to deal with high-order perturbations of a general spherical background was developed. In this article, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density and velocity. In general, these expressions are not linear and have sources depending on lower order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular the surface separating the perfect fluid interior from the exterior vacuum.

Extremal rotating solutions in Hořava gravity

Recently a new four-dimensional nonrelativistic renormalizable theory of gravity was proposed by Ho\ifmmode \check{r}\else \v{r}\fi{}ava. In this paper we have found different near horizon geometries in Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity. We find the rotating solutions in a special range of parameters of the theory. This range allows us to include up to six derivative terms in the equations of motion. We have found our solutions as perturbed solutions over spherical symmetric background with small rotating parameter.

Automatic Graph Cut Segmentation of Lesions in CT Using Mean Shift Superpixels.

This paper presents a new, automatic method of accurately extracting lesions from CT data. It first determines, at each voxel, a five-dimensional (5D) feature vector that contains intensity, shape index, and 3D spatial location. Then, nonparametric mean shift clustering forms superpixels from these 5D features, resulting in an oversegmentation of the image. Finally, a graph cut algorithm groups the superpixels using a novel energy formulation that incorporates shape, intensity, and spatial features. The mean shift superpixels increase the robustness of the result while reducing the computation time. We assume that the lesion is part spherical, resulting in high shape index values in a part of the lesion. From these spherical subregions, foreground and background seeds for the graph cut segmentation can be automatically obtained. The proposed method has been evaluated on a clinical CT dataset. Visual inspection on different types of lesions (lung nodules and colonic polyps), as well as a quantitative evaluation on 101 solid and 80 GGO nodules, both demonstrate the potential of the proposed method. The joint spatial-intensity-shape features provide a powerful cue for successful segmentation of lesions adjacent to structures of similar intensity but different shape, as well as lesions exhibiting partial volume effect.

Phase-Field Modeling and Simulations of Lipid Membranes Coupling Composition with Membrane Mechanical Properties

The plasma membrane, a lipid bilayer membrane surrounding all mammalian cells, is not homogeneous, but rather contains domains termed ‘rafts,’ defined as regions enriched with cholesterol and saturated lipids. Understanding how and why these rafts form is of great importance to cell biologists and immunologists, since they are involved in many important cell functions and processes including endocytosis, cell adhesion, signaling, protein organization, lipid regulation, and infection by pathogens. These raft structures also show great potential for technological applications, especially in connection with biosensors and drug delivery systems. We examine the formation and evolution of lipid raft-like domains in multicomponent lipid membrane vesicles using a continuum-level simulation method. Our objective is to investigate how various physical parameters input into the model, such as spontaneous curvature, bending rigidity, and phase fraction, affect the dynamics and equilibrium morphological phases formed in two-phase lipid membrane systems. This model is applied to membranes with spherical background geometries, simulating the compositional and shape evolution of lipid vesicles, coupled using a modified Helfrich free energy. The compositional evolution is modeled using a phase-field method and is described by a Cahn-Hilliard-type equation, while the shape changes are described by relaxation dynamics in which the vesicle surface area is conserved. We find that the compositional and morphological evolution are significantly altered when the mechanical coupling is present by comparing the results with those of systems where this coupling is absent. More specifically, we find that the evolution is significantly slowed when the phases have equal and opposite spontaneous curvatures and are present in roughly equal amounts. We also investigate equilibrium shapes formed by completely phase-separated vesicles as a function of spontaneous curvature, bending rigidity, and phase fraction.

Simulations of the Morphological Evolution of Lipid Bilayer Membranes Using a Phase-Field Method

We present a continuum-level simulation method for modeling phase separation and morphological evolution of multicomponent lipid bilayer membranes. Our objective is to investigate how various physical parameters input into the model, such as spontaneous curvature, phase fraction, and interleaflet coupling strength, affect the dynamics and equilibrium morphological phases formed in two-phase lipid bilayer membrane systems. The model applies to membranes with planar and spherical background geometries, simulating a nearly planar portion of membrane or entire vesicle, respectively. The compositions and shape of the membrane are coupled through a modified Helfrich free energy. The planar model treats the composition of each leaflet, and thus includes a term coupling these compositions across the bilayer. The compositional evolution is modeled using a phase-field method and is described by a Cahn-Hilliard-type equation, while shape changes are described by relaxation dynamics. For nearly planar bilayer systems with each leaflet having the same phase fraction, we find that domains in both leaflets align to reduce the interaction energy, as expected. When the coupling effect is stronger, this alignment occurs more quickly and more precisely, showing that the coupling affects the dynamics. This leaflet coupling is found to heavily influence morphological evolution; in some cases the equilibrium morphological phase observed is very different from what was observed with our simpler monolayer model using similar conditions. We construct a phase diagram of equilibrium morphological phases in the composition space for a few values of the strength of the leaflet coupling. This model has been able to reproduce results found in lipid bilayer experiments probing interleaflet interactions, including the effect of domain registration across leaflets. For the vesicle model, we investigate how an ellipsoidal geometry imposed in the initial conditions affects the phase and morphological evolution.

Hamiltonian theory for the axial perturbations of a dynamical spherical background

We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial gravitational wave in a Hamiltonian pair of variables. Then, switching to a more geometrical description of the system, we construct the only scalar combination of them. We obtain the well-known Gerlach and Sengupta scalar for axial perturbations, with no known equivalent for polar perturbations. The strategy, suggested and tested here, will be applied to the polar case in a separate article.