Curvature Limit Research Articles

Superconformal inflationary α-attractors

Recently a broad class of superconformal inflationary models was found leading to a universal observational prediction $n_s=1-2/N$ and $r=12/N^2$. Here we generalize this class of models by introducing a parameter $\alpha$ inversely proportional to the curvature of the inflaton Kahler manifold. In the small curvature (large $\alpha$) limit, the observational predictions of this class of models coincide with the predictions of generic chaotic inflation models. However, for sufficiently large curvature (small $\alpha$), the predictions converge to the universal attractor regime with $n_s=1-2/N$ and $r=12\alpha/N^2$, which corresponds to the part of the $n_s-r$ plane favored by the Planck data.

Core‐annular two‐phase flow in a gently curved circular channel

The velocity field of a core‐annular two‐phase flow through a curved channel is investigated. The case of fully developed flow with a concentric, circular fluid–fluid interface is considered. In the limit of a gentle axial curvature of the curved channel, an analytical solution is obtained in the form of a regular asymptotic expansion to first order. The condition on the physical parameters for the core to be concentric and circular is derived by accounting for the normal stresses at the interface. Two key features of the flow, the secondary circulations and the redistribution of the axial velocity, are described in detail. The viscous coupling of the two fluids at the interface leads to a variety of circulation patterns and axial velocity profiles, depending on the system parameters. The parameter space is divided into different regions using analytical conditions at the transition between flow regimes. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4871–4886, 2013

Fluid/gravity correspondence for general non-rotating black holes

In this paper, we investigate the fluid/gravity correspondence in spacetime with general non-rotating weakly isolated horizon. With the help of a Petrov-like boundary condition and large mean curvature limit, we show that the dual hydrodynamical system is described by a generalized forced incompressible Navier–Stokes equation. Specially, for stationary black holes or those spacetime with some asymptotically stationary conditions, such a system reduces to a standard forced Navier–Stokes system.

Contractions of AdS brane algebra and superGalileon Lagrangians

We examine AdS Galileon Lagrangians using the method of nonlinear realization. By contractions (1) flat curvature limit, (2) non-relativistic brane algebra limit, and (3) (1) + (2) limits we obtain DBI, Newton-Hoock, and Galilean Galileons, respectively. We make clear how these Lagrangians appear as invariant 4-forms and/or pseudo-invariant Wess-Zumino (WZ) terms using Maurer-Cartan (MC) equations on the coset G/SO(3, 1). We show the equations of motion are written in terms of the MC forms only and explain why the inverse Higgs condition is obtained as the equation of motion for all cases. The supersymmetric extension is also examined using a supercoset SU(2, 2|1)/(SO(3, 1) × U(1)) and five WZ forms are constructed. They are reduced to the corresponding five Galileon WZ forms in the bosonic limit and are candidates for supersymmetric Galileon action.

Driver Assistance System for Passive Multi-Trailer Vehicles with Haptic Steering Limitations on the Leading Unit

Driving vehicles with one or more passive trailers has difficulties in both forward and backward motion due to inter-unit collisions, jackknife, and lack of visibility. Consequently, advanced driver assistance systems (ADAS) for multi-trailer combinations can be beneficial to accident avoidance as well as to driver comfort. The ADAS proposed in this paper aims to prevent unsafe steering commands by means of a haptic handwheel. Furthermore, when driving in reverse, the steering-wheel and pedals can be used as if the vehicle was driven from the back of the last trailer with visual aid from a rear-view camera. This solution, which can be implemented in drive-by-wire vehicles with hitch angle sensors, profits from two methods previously developed by the authors: safe steering by applying a curvature limitation to the leading unit, and a virtual tractor concept for backward motion that includes the complex case of set-point propagation through on-axle hitches. The paper addresses system requirements and provides implementation details to tele-operate two different off- and on-axle combinations of a tracked mobile robot pulling and pushing two dissimilar trailers.

曲率限制的红外焦平面告警系统目标搜索算法

曲率限制的红外焦平面告警系统目标搜索算法

THE γ-RAY SPECTRUM OF GEMINGA AND THE INVERSE COMPTON MODEL OF PULSAR HIGH-ENERGY EMISSION

We reanalyze the Fermi spectra of the Geminga and Vela pulsars. We find that the spectrum of Geminga above the break is exceptionally well approximated by a simple power law without the exponential cut-off, making Geminga's spectrum similar to that of Crab. Vela's broadband gamma-ray spectrum is equally well fit with both the exponential cut-off and the double power law shapes. In the broadband double power-law fits, for a typical Fermi spectrum of a bright \gamma-ray pulsar, most of the errors accumulate due to the arbitrary parametrization of the spectral roll-off. In addition, a power law with an exponential cut-off gives an acceptable fit for the underlying double power-law spectrum for a very broad range of parameters, making such fitting procedures insensitive to the underlying Fermi photon spectrum. Our results have important implications for the mechanism of pulsar high energy emission. A number of observed properties of \gamma-ray pulsars, i.e., the broken power law spectra without exponential cut-offs and stretching in case of Crab beyond the maximal curvature limit, spectral breaks close to or exceeding the maximal breaks due to curvature emission, a Crab patterns of relative intensities of the leading and trailing pulses repeated in the X-ray and \gamma-ray regions, all point to the inverse Compton origin of the high energy emission from majority of pulsars.

Gauge-fixed Wannier wave functions for fractional topological insulators

We propose an improved scheme to construct many-body trial wave functions for fractional Chern insulators (FCI), using one-dimensional localized Wannier basis. The procedure borrows from the original scheme on a continuum cylinder, but is adapted to finite-size lattice systems with periodic boundaries. It fixes several issues of the continuum description that made the overlap with the exact ground states insignificant. The constructed lattice states are translationally invariant, and have the correct degeneracy as well as the correct relative and total momenta. Our prescription preserves the (possible) inversion symmetry of the lattice model, and is isotropic in the limit of flat Berry curvature. By relaxing the maximally localized hybrid Wannier orbital prescription, we can form an orthonormal basis of states which, upon gauge fixing, can be used in lieu of the Landau orbitals. We find that the exact ground states of several known FCI models at $\ensuremath{\nu}=1/3$ filling are well captured by the lattice states constructed from the Laughlin wave function. The overlap is higher than $0.99$ in some models when the Hilbert space dimension is as large as $3\ifmmode\times\else\texttimes\fi{}{10}^{4}$ in each total momentum sector.

Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices

The Ising model is studied on a series of hyperbolic two-dimensional lattices which are formed by tessellation of triangles on negatively curved surfaces. In order to treat the hyperbolic lattices, we propose a generalization of the corner transfer matrix renormalization group method using a recursive construction of asymmetric transfer matrices. Studying the phase transition, the mean-field universality is captured by means of a precise analysis of thermodynamic functions. The correlation functions and the density-matrix spectra always decay exponentially even at the transition point, whereas power-law behavior characterizes criticality on the Euclidean flat geometry. We confirm the absence of a finite correlation length in the limit of infinite negative Gaussian curvature.

The curvature index and synchronization of dynamical systems

We develop a quantity, named the curvature index, for dynamical systems. This index is defined as the limit of the average curvature of the trajectory during evolution, which measures the bending of the curve on an attractor. The curvature index has the ability to differentiate the topological change of an attractor, as its alterations exhibit the structural changes of a dynamical system. Thus, the curvature index may indicate thresholds of some synchronization regimes. The Rössler system and a time-delay system are simulated to demonstrate the effectiveness of the index, respectively.

Geometry and friction of helically wrapped wires in a cable subjected to tension and bending

Helically wrapped wire cables were first introduced to overcome the difficulties in transporting and installing straight wires. Presently, helically wrapped wire cables are used as the important load-carrying elements in many structures such as suspension bridges, cable-stayed bridges, tall guyed towers, power transmission lines, and flexible electrical conductors. In design and analysis, cables are traditionally assumed to carry axial load only; thus, studies on the bending behavior of the cables have been limited. Although the small curvature assumption of the cable may be valid for most part, the possible development of a large curvature at the bearings and anchorage cannot be ignored nor avoided. In this study, an analytical model was developed for the helically wrapped wires in a cable subjected to tension and small bending, with full consideration of the helically wrapped wire geometry. Using the developed model, an approximate upper limit of the cable curvature -for which the conventional Bernoulli-Euler-Navier kinematic beam assumption can be adapted to evaluate the stress in the wires-was obtained.

Covariant quantization of “massive” spin- $\frac{3}{2}$ fields in the de sitter space

We present a covariant quantization of the free “massive” spin-\(\frac{3}{2}\) fields in four-dimensional de Sitter space-time based on analyticity in the complexified pseudo-Riemannian manifold. The field equation is obtained as an eigenvalue equation of the Casimir operator of the de Sitter group. The solutions are calculated in terms of coordinate-independent de Sitter plane-waves in tube domains and the null curvature limit is discussed. We give the group theoretical content of the field equation. The Wightman two-point function \(S^{i \bar{j}}_{\alpha\alpha'}(x,x')\) is calculated. We introduce the spinor-vector field operator Ψ α (f) and the Hilbert space structure. A coordinate-independent formula for the field operator Ψ α (x) is also presented.

Dynamics of the detonation-wave front in solid explosives

The important role of the shape of the front during detonation wave propagation in gas mixtures was substantiated by K. I. Shchelkin during construction of the theory of spinning detonation. Subsequently, a unique relationship between the curvature of the front and detonation wave parameters has been repeatedly confirmed in experiments, including for condensed high explosives (HEs). The existence of this relationship formed the basis of the theory of the dynamics of the detonation front which had been developed by the end of the 20th century. This paper presents the results of a study of detonation front propagation in cylindrical samples of a low-sensitivity HE of different diameters with one-point and plane-wave initiation. A unique relationship between the detonation velocity and the curvature of the detonation wave front has been found. Ordinary differential equations describing two-dimensional steady-state detonation front profiles for HE charges in the form of a plate, a cylinder, and a ring were derived assuming that the detonation velocity depends on the curvature of the front. It was taken into account that the boundary angle between the normal to the front and the HE edge is unique for each combination of HE and liner material. It was found that the same detonation front profile corresponds to several combinations of liner material and the determining size of the charge (plate thickness, radius of the cylinder or the inner radius of the ring). A comparison of experimental front profiles near the edges of HE charges for these combinations provides data on the dependence of detonation velocity on the curvature of the front at low velocities corresponding to shock-induced detonation regimes. Analysis of previously obtained data for detonating ring charges of low-sensitivity HEs shows that as the detonation velocity decreases, the total front curvature tends to a limit of about 0.05 mm−1, i.e., of the order of the inverse critical diameter. The limit of the front curvature allows predicting the critical detonation diameter.

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.

Bending of Layered Silicates on the Nanometer Scale: Mechanism, Stored Energy, and Curvature Limits

Bending and failure of aluminosilicate layers are common in polymer matrices although mechanical properties of curved layers and curvature limits are hardly known. We examined the mechanism of bending, the stored energy, and failure of several clay minerals. We employed molecular dynamics simulation, AFM data, and transmission electron microscopy (TEM) of montmorillonite embedded in epoxy and silk elastin polymer matrices with different weight percentage and different processing conditions. The bending energy per layer area as a function of bending radius can be converted into force constants for a given layer geometry and is similar for minerals of different cation exchange capacity (pyrophyllite, montmorillonite, mica). The bending energy increases from zero for a flat single layer to ∼10 mJ/m2 at a bending radius of 20 nm and exceeds 100 mJ/m2 at a bending radius of 6 nm. The smallest observed curvature of a bent layer is 3 nm. Failure proceeds through kink and split into two straight layers of shorter length. The mechanically stored energy per unit mass in highly bent aluminosilicate layers is close to the electrical energy stored in batteries. Molecular contributions to the bending energy include bond stretching and bending of bond angles in the mineral as well as rearrangements of alkali ions on the surface of the layers. When embedded in polymers, average radii of curvature of aluminosilicates exceed hundreds of nanometers. The small fraction of highly bent layers (<20 nm radius) can be increased by extrusion, especially in stacked layers, and by an increase in weight percentage of layered silicates above 5%. Extrusion also promotes failure and shortening of isolated layers.

Response of high-energy protons of the inner radiation belt to large magnetic storms

[1] The responses of the high-energy protons (35–70 MeV, 70–140 MeV and 140–500 MeV) below L = 3 to the large geomagnetic magnetic storms (|Dst| > 200 nT) during 1998 to 2005 have been investigated with the measurements by three NOAA POES satellites (NOAA-15, 16 and 17). The losses of protons in the outer region of the inner radiation belt are found during the large storms. Similar loss events were also measured by the HEO-3 satellite for lower energy protons (8.5–35 MeV, 16–40 MeV and 27–45 MeV). However, the response of higher energy protons to the storms observed by NOAA satellites is different from that of the lower energy protons. It is shown that some aspects of the loss event and energy dependence during large storms can be accounted for by the trapping limit of the field line curvature scattering mechanism. The maximal L shells of the observed trapped protons are consistent with the critical L shells of the field line curvature scattering. The modeling results based on the storm-time geomagnetic field model (TS04c) and the radiation belt model (AP8) show the inward motion of the outer boundary of trapped protons is caused by the distortion of geomagnetic field during the magnetic storms and depends on proton energy. The additional proton loss in the lower energy channel (35–70 MeV) could be attributed to the storm-caused weakening of geomagnetic field combined with L dependent lifetimes induced by curvature scattering during magnetic storms.

Valoración del análisis de la pieza operatoria en el cáncer gástrico por el cirujano

Concordance between the surgical piece observation by the surgeon and fi nal pathological report for gastric cancer Background: The systematic dissection of the surgical piece, performed by the surgeon during surgical treatment of gastric cancer, gives information about borders and lymph node involvement. Aim: To deter- mine the concordance between the fi ndings of the surgeon during initial dissection and the fi nal pathological report. Material and Methods: Prospective study of 48 patients aged 64 ± 10 years (74% males) subjected to curative surgery for gastric cancer. Patients were staged according to 2010 TNM classifi cation. Stomach size from the lesser curvature, oral and caudal limits, macroscopic aspect, tumor diameter and lymph node involvement were determined by the surgeon observing the surgical piece. The concordance of this observa- tion with the fi nal pathological report was assessed. Results: Fifty nine percent of patients were subjected to a total gastrectomy and there was a mean of 30 lymph nodes excised. There was a good concordance between surgeon observation and fi nal pathological report for tumor depth (Kappa = 0.64), macroscopic aspect (Ka- ppa = 0.69) and tumor size (Lin = 0.84). There was a bad concordance for lymph node involvement (Kappa = 0.21). The percentage of retraction of lesser curvature length was 24%, 30% for oral and 22% for caudal limits. Conclusions: There is a good concordance between surgeon observation and pathological report for macroscopic aspect, tumor size and depth but the concordance for lymph node involvement is bad.

Thermal diffusivity of nonflat plates using the flash method

The flash method is the standard technique to measure the thermal diffusivity of solid samples. It consists of heating the front surface of an opaque sample by a brief light pulse and detecting the temperature evolution at its rear surface. The thermal diffusivity is obtained by measuring the time corresponding to the half maximum of the temperature rise, which only depends on the sample thickness and thermal diffusivity through a simple formula. Up to now, the flash method has been restricted to flat samples. In this work, we extend the flash method to measure the thermal diffusivity of nonflat samples. In particular, we focus on plates with cylindrical and spherical shapes. The theoretical model indicates that the same expression for flat samples can also be applied to cylindrical and spherical plates, except for extremely curved samples. Accordingly, a curvature limit for the application of the expression for flat samples is established. Flash measurements on lead foils of cylindrical shape confirm the validity of the model.

Multispacecraft observations of interplanetary shock shapes on the scales of the Earth's magnetosphere

We are presenting a study of interplanetary shock shapes as observed by multiple spacecraft in the solar wind. The analysis of the 1 May 1998 shock observed by six spacecraft is presented in detail as an example to demonstrate possible complex shock shapes with small‐ and large‐scale curvatures of the shock surface. To systematically estimate the shock front deviation from planarity on different scales, we are presenting an analysis of 62 shocks observed by Wind and at least one other spacecraft. Our results show the presence of local (on scales up to ∼30 RE) shock curvatures with radii of less than ∼50 to ∼200 RE for the majority of analyzed shocks. On larger scales, the shock curvature decreases and reaches the limit of the strongest possible curvature with radius of ∼400 RE on scales greater than ∼100 RE for all analyzed shocks.

Controlling surface plasmon polaritons in transformed coordinates

Transformational optics allows for a markedly enhanced control of the electromagnetic wave trajectories within metamaterials, with interesting applications ranging from perfect lenses to invisibility cloaks, carpets, concentrators and rotators. Here we present a review of curved anisotropic heterogeneous meta-surfaces designed using the tool of transformational plasmonics, in order to achieve a similar control for surface plasmon polaritons in cylindrical and conical carpets (for the latter we provide some analytical insight), as well as cylindrical cloaks, concentrators and rotators of a non-convex cross-section. Finally, we provide an asymptotic form of the geometric potential for surface plasmon polaritons on such surfaces in the limit of a small curvature.