Small Curvature Limit Research Articles

Curvature-induced drift and deformation of magnetic skyrmions: Comparison of the ferromagnetic and antiferromagnetic cases

The influence of the geometrical curvature of chiral magnetic films on the static and dynamic properties of hosted skyrmions is studied theoretically. We predict the effects of the curvature-induced drift of skyrmions under the action of the curvature gradients without any external stimuli. The strength of the curvature-induced driving force essentially depends on the skyrmion type, N\'eel or Bloch, while the trajectory of motion is determined by the type of magnetic ordering: ferromagnetic or antiferromagnetic. When moving on the surface, skyrmions undergo deformations that depend on the type of skyrmion. In the small-curvature limit, using the collective-variable approach we show that the driving force acting on a N\'eel skyrmion is linear in the gradient of the mean curvature. The driving acting on a Bloch skyrmion is much smaller: it is proportional to the product of the mean curvature and its gradient. In contrast to the fast N\'eel skyrmions, the dynamics of the slow Bloch skyrmions is essentially affected by the skyrmion profile deformation. For the sake of simplicity, we restrict ourselves to the case of zero Gaussian curvature and consider cylindrical surfaces of general type. Equations of motion for ferromagnetic and antiferromagnetic skyrmions in curved magnetic films are obtained in terms of collective variables. All analytical predictions are confirmed by numerical simulations.

Clockwork graviton contributions to muon g−2

The clockwork mechanism for gravity introduces a tower of massive graviton modes, "clockwork gravitons," with a very compressed mass spectrum, whose interaction strengths are much stronger than that of massless gravitons. In this work, we compute the lowest order contributions of the clockwork gravitons to the anomalous magnetic moment, $g-2$, of muon in the context of extra dimensional model with a five dimensional Planck mass, $M_5$. We find that the total contributions are rather insensitive to the detailed model parameters, and determined mostly by the value of $M_5$. In order to account for the current muon $g-2$ anomaly, $M_5$ should be around $0.2~{\rm TeV}$, and the size of the extra dimension has to be quite large, $l_5 \gtrsim 10^{-7}\,$m. For $M_5\gtrsim1~{\rm TeV}$, the clockwork graviton contributions are too small to explain the current muon $g-2$ anomaly. We also compare the clockwork graviton contributions with other extra dimension models such as Randall-Sundrum models or large extra dimension models. We find that the leading contributions in the small curvature limit are universal, but the cutoff-independent subleading contributions vary for different background geometries and the clockwork geometry gives the smallest subleading contributions.

Effect of Meniscus Curvature on Apparent Thermal Slip

We analytically consider the effect of meniscus curvature on heat transfer to laminar flow across structured surfaces. The surfaces considered are composed of ridges. Curvature of the menisci, which separates liquid in the Cassie state and gas trapped in cavities between the ridges, results from the pressure difference between the liquid and the gas. A boundary perturbation approach is used to develop expressions that account for the change in the temperature field in the limit of small curvature of a meniscus. The meniscus is considered adiabatic and a constant heat flux boundary condition is prescribed at the tips of the ridges in a semi-infinite and periodic domain. A solution for a constant temperature ridge is also presented using existing results from a mathematically equivalent hydrodynamic problem. We provide approximate expressions for the apparent thermal slip length as function of solid fraction over a range of small meniscus protrusion angles. Numerical results show good agreement with the perturbation results for protrusion angles up to ± 20 deg.

String theory in polar coordinates and the vanishing of the one-loop Rindler entropy

We analyze the string spectrum of flat space in polar coordinates, following the small curvature limit of the $SL(2,\mathbb{R})/U(1)$ cigar CFT. We first analyze the partition function of the cigar itself, making some clarifications of the structure of the spectrum that have escaped attention up to this point. The superstring spectrum (type 0 and type II) is shown to exhibit an involution symmetry, that survives the small curvature limit. We classify all marginal states in polar coordinates for type II superstrings, with emphasis on their links and their superconformal structure. This classification is confirmed by an explicit large $\tau_2$ analysis of the partition function. Next we compare three approaches towards the type II genus one entropy in Rindler space: using a sum-over-fields strategy, using a Melvin model approach and finally using a saddle point method on the cigar partition function. In each case we highlight possible obstructions and motivate that the correct procedures yield a vanishing result: $S=0$. We finally discuss how the QFT UV divergences of the fields in the spectrum disappear when computing the free energy and entropy using Euclidean techniques.

Static black holes and strictly static spacetimes in Einstein-Gauss-Bonnet gravity with gauge field

We examine strictly static asymptotically flat spacetimes in Einstein-Gauss-Bonnet gravity with U(1) gauge field, revealing that, up to small curvature corrections, confomally flat slices of the spacetime in question are of Minkowski origin. We consider uncharged and charged black hole solutions in the theory, showing that, up to the small curvature limit, they are diffeomorphic to Schwarzschild_Tangherlini or Reissner-Nordstrom solutions, respectively.

N-DBI gravity

n-DBI gravity is a gravitational theory introduced in arXiv:1109.1468 [hep-th], motivated by Dirac-Born-Infeld type conformal scalar theory and designed to yield non-eternal inflation spontaneously. It contains a foliation structure provided by an everywhere time-like vector field n, which couples to the gravitational sector of the theory, but decouples in the small curvature limit. We show that any solution of Einstein gravity with a particular curvature property is a solution of n-DBI gravity. Amongst them is a class of geometries isometric to Reissner-Nordstrom-(Anti) de Sitter black hole, which is obtained within the spherically symmetric solutions of n-DBI gravity minimally coupled to the Maxwell field. These solutions have, however, two distinct features from their Einstein gravity counterparts: 1) the cosmological constant appears as an integration constant and can be positive, negative or vanishing, making it a variable quantity of the theory; 2) there is a non-uniqueness of solutions with the same total mass, charge and effective cosmological constant. Such inequivalent solutions cannot be mapped to each other by a foliation preserving diffeomorphism. Physically they are distinguished by the expansion and shear of the congruence tangent to n, which define scalar invariants on each leave of the foliation.

Diocotron instability in non-neutral plasmas with a stationary point in the rotation frequency profile

A new analytical solution to the problem of the l=1 diocotron mode instability in a hollow density non-neutral plasma column with finite lenght is presented. The starting point of the analysis is the paper of Finn et al. [J. M. Finn, D. del-Castillo-Negrete, and D. C. Barnes, Phys. Plasmas 6, 3744 (1999)], where the instability mechanism involves compression of the plasma in the direction parallel to the magnetic field, with conservation of its line-integrated density. In the limit of small curvature of the plasma end-fronts, the method presented here provides both eigenvalue and eigenfunction for the unstable l=1 “extreme mode.”

Exact Bianchi identity in Regge gravity

In the continuum the Bianchi identity implies a relationship between different components of the curvature tensor, thus ensuring the internal consistency of the gravitational field equations. In this paper the exact form for the Bianchi identity in Regge's discrete formulation of gravity is derived, by considering appropriate products of rotation matrices constructed around null-homotopic paths. The discrete Bianchi identity implies an algebraic relationship between deficit angles belonging to neighbouring hinges. As in the continuum, the derived identity is valid for arbitrarily curved manifolds without a restriction to the weak field small curvature limit, but is in general not linear in the curvatures.

Flow in a rotating curved circular pipe.

The flow in a rotating curved pipe with circular cross section is investigated theoretically and numerically. A perturbation solution up to the second order is obtained. A numerical procedure is used to solve the full governing equations and the simplified governing equations in the small curvature limit. Comparisons are made between the numerical and perturbation results, elucidating the lost information due to simplification and the valid range of the perturbation solution. The flow characteristics, including the secondary flow, the axial flow, and the friction factor ratio, are examined in detail.

Stability of curved amphiphilic interfaces

A comprehensive description of interfaces containing amphiphiles has been developed through the use of a free energy density functional with squared-gradient and squared-Laplacian terms. This elemental model functional contains the basic ingredients for the problem, it is technically tractable and a range of results for curved interfaces, many in analytical form, have been obtained from it. These are: (i) average equilibrium properties, such as pressure tensor, interfacial tension and position of the Gibbs dividing surface, (ii) order parameter fluctuation modes and stability matrix, and, (iii) an effective interfacial potential that in the small curvature limit corresponds to the Helfrich free energy. Here we survey these results and make some technical remarks. Our exposition is meant to fill an existing gap, mostly conceptual, left by previous work.

Large Curvature Tunneling Effects Reveal Concerted Hydrogen Exchange Rates in Cyclic Hydrogen Fluoride Clusters Comparable to Carboxylic Acid Dimers

Reaction rate constants for the concerted proton transfer in cyclic hydrogen fluoride clusters obtained by using a variational transition state theory approach with high-level data at three stationary points and with interpolated corrections based on semiempirical Hamiltonians specially parametrized for these systemsMP2/6-311++G(3df,3pd)///PM3-SRPare reported. For the first time multidimensional tunneling is included in the large curvature limit. The corresponding small curvature limit is benchmarked against higher level calculations. The ridge of the reaction swath is defined in a general way and serves together with an estimate of the barrier width as a validation of the potential energy hypersurfaces. Recent experimental and theoretical results concerning carboxylic acids, whose hypersurfaces are found to be very similar to those of the HF clusters, underline the relevancy of the investigated concerted proton exchange motion. A reaction rate constant k(300 K) = 2.86 × 109 s-1 is found for (HF)5, which is similar to carboxylic acid dimers, whose experimental k(300 K) lie near 1010 s-1.

Competition between curvature and chemistry in a spherically expanding detonation

The methods of bifurcation theory and asymptotic analysis are used to study curvilinear perturbations of a plane detonation wave. An asymptotic model is derived for the small curvature limit. The nonlinear competition between curvature and chemistry is manifested by a highly degenerate critical point in the state space of the model equations. Computer simulations are presented showing agreement of this model with the reactive Euler equations in the small curvature limit. In particular, we find that the leading order correction to the wave speed due to the curvature of the detonation front depends on the order of the chemical reaction to leading order in curvature.

Effects of dislocations on the energy loss of channeled particles

A simple model to calculate the effects of dislocations on the energy loss of channeled particles is discussed. The curvature in the channel produced by the dislocation is approximated by an arc of constant radius which is determined by using the displacement equations for the dislocation. An analytical expression for the change in the energy loss of initially well channeled particles is obtained in the limit of small curvature i.e. for a channel not very near to the dislocation.