Perturbation Of Symmetry Research Articles

First-principles calculations of phonons and Raman and infrared spectra in Cd-IV-N2 compounds

A first-principles study of the phonons at the zone center in Cd-IV-N2 compounds is presented with IV = Si, Ge, Sn. The calculations are performed for the most likely Pbn21 crystal structure, after showing that it is indeed lower in total energy compared to the closely related Pmc21 structure. The normal mode frequencies are calculated using density functional perturbation theory and symmetry labeled. The longitudinal optical-transverse optical splittings are determined using the Born effective charges which are also reported. These are used to simulate polarized Raman spectra for different scattering configurations as well as the infrared absorption and reflection spectra. The mode frequencies are found to decrease from Si to Ge to Sn as group-IV cation. The spectra show a wide variety of number of prominent peaks and relative intensities in spite of the great similarities of these three materials. Phonon densities of states and their analysis in atom by atom contributions are also reported.

Experimental investigation of the Kelvin–Helmholtz instabilities of cylindrical gas columns in viscous fluids

This paper derives analytical solutions for the critical Kelvin–Helmholtz (KH) instability conditions at the interface between a cylindrical gas column and a pool of viscous immiscible fluid confined in a chamber of finite size. The analysis focuses on conditions of negligible heat and mass transfer. The derivations are based on the established approaches reported in the literature with different boundary conditions. The most unstable instability conditions have also been calculated numerically. Experiments designed to measure the actual air column break-up conditions in water have been carried out to validate the analytical models. Comparisons show that the most unstable conditions predicted by the Viscous Corrections of the Viscous Potential Flow KH model are the best match to the experimentally measured break-up conditions. Parametric investigation of the instability theories shows that the vapour column size has a noticeable effect on the critical conditions, but has a negligible effect on the most unstable conditions when the column radius is greater than 1.2 mm. Furthermore, the critical instability conditions are sensitive to the chamber size and the perturbation symmetry, while the most unstable conditions are insensitive to these parameters.

Cycloidal meandering of a mesoscale anticyclonic eddy

By applying a theoretical approach, we propose a hypothetical scenario that might explain some features of the movement of a long-lived mesoscale anticyclone observed during 1990 in the Bay of Biscay [R. D. Pingree and B. Le Cann, “Three anticyclonic slope water oceanic eddies (SWODDIES) in the southern Bay of Biscay in 1990,” Deep-Sea Res., Part A 39, 1147 (1992)]. In the remote-sensing infrared images, at the initial stage of observations, the anticyclone was accompanied by two cyclonic eddies, so the entire structure appeared as a tripole. However, at later stages, only the anticyclone was seen in the images, traveling generally west. Unusual for an individual eddy were the high speed of its motion (relative to the expected planetary beta-drift) and the presence of almost cycloidal meanders in its trajectory. Although surface satellites seem to have quickly disappeared, we hypothesize that subsurface satellites continued to exist, and the coherence of the three vortices persisted for a long time. A significant perturbation of the central symmetry in the mutual arrangement of three eddies constituting a tripole can make reasonably fast cycloidal drift possible. This hypothesis is tested with two-layer contour-dynamics f-plane simulations and with finite-difference beta-plane simulations. In the latter case, the interplay of the planetary beta-effect and that due to the sloping bottom is considered.

Nanocross: A Highly Tunable Plasmonic System

With the help of electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) and boundary element method (BEM) simulations, we have shown that silver nanocross can be used to tune the plasmon modes and especially the higher order modes in a very controlled manner. Morphing a nanorod to a nanocross by growing another arm along the perpendicular bisector of a nanorod can lead to a spectacular evolution of various order modes in the EEL spectra. One can keep a mode fixed in energy while bringing the next higher order mode close to it, or even make it cross. This allows one to control the relative separation of energy of the plasmon modes. Hybridization of individual nanocross plasmon modes have also been studied by bringing two nanocrosses close together along one of their arms. An analytical approach based on first order perturbation theory and symmetry arguments based on group theory aptly fits the experimental observations.

Cracks and fingers: Dynamics of ductile fracture in an aqueous foam

Fracture of a quasi-two-dimensional aqueous foam by injection of air can occur via two distinct mechanisms, termed brittle and ductile, which are analogous to crack modes observed for crystalline atomic solids such as metals. In the present work we focus on the dynamics and morphology of the ductile process, in which no films between bubbles are broken. A network modeling approach allows detailed analysis of the foam morphology from individual bubbles to the shape of the propagating crack. This crack develops similarly to fingering instabilities in Hele–Shaw cells filled with homogeneous fluids. We show that the observed width and shape of the crack are compatible this interpretation, and that the discreteness of the bubble structure provides symmetry perturbations and limiting scales characteristic of anomalous fingering. The model thus bridges the gap between fracture of the solid foam lattice and instability growth of interfaces in a fluid system.

Two-component generalizations of the Camassa–Holm equation

A classification of integrable two-component systems of non-evolutionary partial differential equations that are analogous to the Camassa–Holm equation is carried out via the perturbative symmetry approach. Independently, a classification of compatible pairs of Hamiltonian operators of specific forms is carried out, in order to obtain bi-Hamiltonian structures for the same systems of equations. Using reciprocal transformations, some exact solutions and Lax pairs are also constructed for the systems considered.

Abrupt onset of tongue deformation and phase space response of ions in magnetically-confined plasmas.

An abrupt onset of the new tongue-shaped deformation of magnetic surface in magnetized plasmas, which was conjectured in since the 1960s but has not been observed, is experimentally identified just before an abrupt onset of a large-scale collapse event. Two novel properties of the event are identified. First, the transition of symmetry of perturbation (rather than a growth of linearly unstable MHD modes) was found to be a key for the onset of abrupt collapse, i.e., the transition of symmetry gives a new route to the collapse from stable state. Second, as a phase-space response of ions, the distortion from Maxwell-Boltzmann distribution of epithermal ions was observed for the first time.

Optimizing high-level nuclear waste disposal within a deep geologic repository

Many countries produce significant quantities of nuclear waste which will have to be permanently and safely placed in a repository. We develop a mixed integer program that determines where to place each waste package of a specific waste type in a given time period with the goal of minimizing heat load concentration within a repository. Operational constraints include: (1) heat load limitations, (2) location and time at which waste packages can be placed, and (3) the number of waste packages that must be placed based on type and time period. Although applicable to other settings, we use the Yucca Mountain repository in Nevada as a case study. Each of the three objectives used for minimizing heat load concentration improves upon existing greedy and sequential filling methods. Existing filling methods give at least a 17 % to an 873 % higher, i.e., worse, heat load concentration in the repository with respect to these objectives than do optimal methods. Enhancements, i.e., symmetry reduction constraints, perturbations, and heuristics, increase the size of solvable problem instances. This research can be applied to any deep geologic repository planned for operation around the world with slight modifications to incorporate site-specific objectives and constraints.

Subleading effects and the field range in axion inflation

An attractive candidate for the inflaton is an axion slowly rolling down a flat potential protected by a perturbative shift symmetry. Realisations of this idea within large field, natural and monomial inflation have been disfavoured by observations and are difficult to embed in string theory. We show that subleading, but significant non-perturbative corrections can superimpose sharp cliffs and gentle plateaus into the potential, whose overall effect is to enhance the number of e-folds of inflation. Sufficient e-folds are therefore achieved for smaller field ranges compared to the potential without such corrections. Thus, both single-field natural and monomial inflation in UV complete theories like string theory, can be restored into the favour of current observations, with distinctive signatures. Tensor modes result un-observably small, but there is a large negative running of the spectral index. Remarkably, natural inflation can be achieved with a single field whose axion decay constant is sub-Planckian.

Inverse amplitude method for the perturbative electroweak symmetry breaking sector: The singlet Higgs portal as a study case

We explore the use of the Inverse Amplitude Method for unitarization of scattering amplitudes to derive the existence and properties of possible new heavy states associated with perturbative extensions of the electroweak breaking sector of the Standard Model starting from the low energy effective theory. We use a toy effective theory generated by integrating out a heavy singlet scalar and compare the pole mass and width of the unitarized amplitudes with those of the original model. Our results show that the Inverse Amplitude Method reproduces correctly the singlet mass up to factors of O(1-3), but its width is overestimated.

FAST MAGNETOACOUSTIC WAVE TRAINS OF SAUSAGE SYMMETRY IN CYLINDRICAL WAVEGUIDES OF THE SOLAR CORONA

Fast magnetoacoustic waves guided along the magnetic field by plasma non-uniformities, in particular coronal loops, fibrils and plumes, are known to be highly dispersive, which leads to the formation of quasi-periodic wave trains excited by a broadband impulsive driver, e.g. a solar flare. We investigated effects of cylindrical geometry on the fast sausage wave train formation. We performed magnetohydrodynamic numerical simulations of fast magnetoacoustic perturbations of a sausage symmetry, propagating from a localised impulsive source along a field-aligned plasma cylinder with a smooth radial profile of the fast speed. The wave trains are found to have pronounced period modulation, with the longer instant period seen in the beginning of the wave train. The wave trains have also a pronounced amplitude modulation. Wavelet spectra of the wave trains have characteristic tadpole features, with the broadband large-amplitude heads preceding low-amplitude quasi-monochromatic tails. The mean period of the wave train is about the transverse fast magnetoacoustic transit time across the cylinder. The mean parallel wavelength is about the diameter of the waveguiding plasma cylinder. Instant periods are longer than the sausage wave cutoff period. The wave train characteristics depend on the fast magnetoacoustic speed in both the internal and external media, and the smoothness of the transverse profile of the equilibrium quantities, and also the spatial size of the initial perturbation. If the initial perturbation is localised at the axis of the cylinder, the wave trains contain higher radial harmonics that have shorter periods.

Perturbative conformal symmetry and dilaton

Spontaneous symmetry breaking with necessity leads to the presence of Goldstone field(s). In the case of scale or conformal symmetries the corresponding Goldstone mode is called the dilaton. Consistently coupling a system to the dilaton poses certain difficulties, for the trace of the energy momentum tensor may not necessary be zero, which in turn leads to the dilaton acquiring a mass. In this paper we present the approach allowing perturbatively to keep the dilaton massless, i.e. to preserve conformal symmetry, at any fixed order in perturbation theory.

Optical second-harmonic generation in few-layer MoSe2

We show that optical second-harmonic generation (SHG) from few-layer MoSe2 can sensitively probe external symmetry perturbations such as chemical doping. The SHGs from few-layer MoSe2 are enhanced after AuCl3 chemical doping, especially more so for the thicker MoSe2 samples. This enhancement is due to an electric-field-induced SHG contribution originating from the charge transfer between the adsorbed chemical dopants and the MoSe2. By using this sensitivity, we demonstrate an in-situ monitoring of the thermal desorption of adsorbed chemical dopants. Moreover, we find that the SHG generated from monolayer MoSe2 is counter-circularly polarized for a circularlypolarized fundamental beam due to the three-fold rotational symmetry of MoSe2. Our work shows that SHG can probe not only the symmetry properties of atomically-thin 2D semiconductors, but also the external symmetry perturbations on them.

New families of symmetric periodic solutions of the spatial anisotropic Manev problem

Applying perturbation theory and symmetry conditions, we prove the existence of new families of periodic orbits for the 3-dimensional anisotropic Manev problem, which depends on three parameters.

Exact invariants and adiabatic invariants for nonholonomic systems in non-Chetaev's type based on El-Nabulsi dynamical models

In this paper, the problem of exact invariants and adiabatic invariants for nonholonomic system in non-Chetaev's type based on the El-Nabulsi dynamical model is studied. First, the El-Nabulsi-d'Alembert-Lagrange principle is deduced and the differential equations of motion of the system are established. Then, the relation between the Noether symmetry and the exact invariant that is led directly by the symmetry for undisturbed nonholonomic system in non-Chetaev's type is given. Furthermore, by introducing the concept of high-order adiabatic invariant of a mechanical system, the conditions that the perturbation of symmetry leads to the adiabatic invariant and its formulation are studied for the nonholonomic system in non-Chetaev's type under the action of small disturbance. As a special case, the problem of the exact invariants and the adiabatic invariants for the nonholonomic system in Chetaev's type in El-Nabulsi model is discussed. At the end of the paper, two examples for the nonholonomic systems in non-Chetaev's type constraints and also the Chetaev's type constraints are given respectively to show the application of the methods and the results of this paper.

Effectively enhancing blue excitation of red phosphor Mg2TiO4:Mn4+ by Bi3+ sensitization

The red phosphors Mg2TiO4:Mn4+, Bi3+, Li+ with strong absorption at blue region were synthesized. Through the excitation and emission spectra, diffuse reflection spectra and Raman spectra, it is proved that Bi3+ ion plays a role of sensitizer to the enhancement of optical property, especially the increased excitation intensity of blue light. It is the first time to report about asynchronous increases of different excitation bands with Bi3+ as a sensitizer, primarily resulting from the perturbation of symmetry and lattice vibration along with crystal defect in the host lattice with larger Bi3+ occupied at a small octahedral site of Mg2+. The sensitization of Bi3+ works not only in the case of powder phosphors but also even better in ceramic phosphors. For powder phosphor, the intensity of the blue excitation band of Mg2−2xTi0.999O4:0.1%Mn4+, xBi3+, xLi+ grows to at least 1.5 times than that of Mg2Ti0.999O4:0.1%Mn4+ when x = 0.5%, following with a uplift at about 410nm. Meanwhile, Mg2TiO4:Mn4+, Bi3+, Li+-based luminescent ceramic manifests with a more than 2.5 times increase as x = 0.8%. The red phosphors with a broad emission band in the pure red light region show a promising application in blue LEDs as a red component.

Lorentz Invariant Berry Phase for a Perturbed Relativistic Four Dimensional Harmonic Oscillator

We show the existence of Lorentz invariant Berry phases generated, in the Stueckleberg-Horwitz-Piron manifestly covariant quantum theory (SHP), by a perturbed four dimensional harmonic oscillator. These phases are associated with a fractional perturbation of the azimuthal symmetry of the oscillator. They are computed numerically by using time independent perturbation theory and the definition of the Berry phase generalized to the framework of SHP relativistic quantum theory.

Electronic properties of silicene superlattices: roles of degenerate perturbation and inversion symmetry breaking

Using both the first-principles method and the tight-binding method, we have carried out detailed studies on the electronic properties of silicene superlattices. According to the band-folding picture, in the hexagonal silicene superlattice (M,N) when both M and N are integer multiples of 3, the simultaneous folding of K and K′ points to the Γ point results in the fourfold degeneracy. In the orthogonal one [P,Q], the fourfold degeneracy occurs if Q = 3q (q is an integer) is satisfied. By introducing degenerate perturbation to remove the fourfold degeneracy, the bandgap could be opened no matter whether the inversion symmetry remains or not. For the other cases, the bandgaps could be kept closed by the inversion symmetry preservation. Besides, the studied transport properties confirm the bandgap tuning by applying degenerate perturbation to the silicene superlattice. The new bandgap opening mechanism with degenerate perturbation could benefit further experimental studies of the silicene-based nanostructures for applications in nanoelectronics.

Sausage oscillations of coronal plasma slabs

Context. Sausage oscillations are observed in plasma non-uniformities of the solar corona as axisymmetric perturbations of the non-uniformity. Often, these non-uniformities can be modelled as field-aligned slabs of the density enhancement. Aims. We perform parametric studies of sausage oscillations of plasma slabs, aiming to determine the dependence of the oscillation period on its parameters, and the onset of leaky and trapped regimes of the oscillations. Methods. Slabs with smooth transverse profiles of the density of a zero-beta plasma are perturbed by an impulsive localised perturbation of the sausage symmetry. In particular, the slab can contain an infinitely thin current sheet in its centre. The initial value problem is then solved numerically. The numerical results are subject to spectral analysis. The results are compared with analytical solutions for a slab with a step-function profile and also with sausage oscillations of a plasma cylinder. Results. We established that sausage oscillations in slabs generally have the same properties as in plasma cylinders. In the trapped regime, the sausage oscillation period increases with the increase in the longitudinal wavelength. In the leaky regime, the dependence of the period on the wavelength experiences saturation, and the period becomes independent of the wavelength in the long-wavelength limit. In the leaky regime the period is always longer than in the trapped regime. The sausage oscillation period in a slab is always longer than in a cylinder with the same transverse profile. In slabs with steeper transverse profiles, sausage oscillations have longer periods. The leaky regime occurs at shorter wavelengths in slabs with smoother profiles.

Quantum vacuum instability of “eternal” de Sitter space

The Euclidean or Bunch-Davies O(4,1) invariant 'vacuum' state of quantum fields in global de Sitter space is shown to be unstable to small perturbations, even for a massive free field with no self-interactions. There are perturbations of this state with arbitrarily small energy density at early times that is exponentially blueshifted in the contracting phase of 'eternal' de Sitter space, and becomes large enough to disturb the classical geometry through the semiclassical Einstein eqs. at later times. In the closely analogous case of a constant, uniform electric field, a time symmetric state equivalent to the de Sitter invariant one is constructed, which is also not a stable vacuum state under perturbations. The role of a quantum anomaly in the growth of perturbations and symmetry breaking is emphasized in both cases. In de Sitter space, the same results are obtained either directly from the renormalized stress tensor of a massive scalar field, or for massless conformal fields of any spin, more directly from the effective action and stress tensor associated with the conformal trace anomaly. The anomaly stress tensor shows that states invariant under the O(4) subgroup of the de Sitter group are also unstable to perturbations of lower spatial symmetry, implying that both the O(4,1) isometry group and its O(4) subgroup are broken by quantum fluctuations. Consequences of this result for cosmology and the problem of vacuum energy are discussed.