3D gravity in a box

The quantization of pure 3D gravity with Dirichlet boundary conditions on a finite boundary is of interest both as a model of quantum gravity in which one can compute quantities which are ``more local" than S-matrices or asymptotic boundary correlators, and for its proposed holographic duality to T\overline{T}TT¯-deformed CFTs. In this work we apply covariant phase space methods to deduce the Poisson bracket algebra of boundary observables. The result is a one-parameter nonlinear deformation of the usual Virasoro algebra of asymptotically AdS_33 gravity. This algebra should be obeyed by the stress tensor in any T\overline{T}TT¯-deformed holographic CFT. We next initiate quantization of this system within the general framework of coadjoint orbits, obtaining — in perturbation theory — a deformed version of the Alekseev-Shatashvili symplectic form and its associated geometric action. The resulting energy spectrum is consistent with the expected spectrum of T\overline{T}TT¯-deformed theories, although we only carry out the explicit comparison to \mathcal{O}(1/\sqrt{c})𝒪(1/c) in the 1/c1/c expansion.

Comparative Analysis of The Correction Effect of Different Environmental Loading Products On Global GNSS Coordinate Time Series

The global navigation satellite system (GNSS) coordinate time series is affected by the environmental loading (including atmospheric loading (ATML), hydrological loading (HYDL), non-tidal oceanic loading (NTOL), etc.) and many organizations now provide grid products of these loadings. The temporal and spatial resolutions of these products, the loading models and data sources used are not the same, so the effect of correcting the nonlinear deformation of the GNSS coordinate time series is obviously different. This study mainly selects the three agencies, namely, School and Observatory of Earth Sciences (EOST) in France, German Research Center for Geosciences (GFZ) in Germany, and International Mass Loading Service (IMLS) in the United States, including 6 types of ATML models, 7 types of HYDL models and 5 NTOL models. The classification of these 18 environmental loading models was discussed, and the root mean square (RMS) reduction rate of the GNSS coordinate time series after environmental loading corrections (ELCs) was used to evaluate the performance differences of various models. Our results show that both the different models provided by the same organization and the same model provided by different organizations have different correction effects. Regardless of the models, it has a significant impact on the vertical coordinate time series. In order to correct the nonlinear deformation of the GNSS stations to the greatest extent, based on the above analysis, this study selects the optimal model combination of three environmental loadings as ECMWF_IB+MERRA2+ECCO1, and then explores its influence on the periodic signals in the GNSS coordinate time series. Research suggests that environmental loadings have a significant impact on the amplitude and phase of GNSS time series. Especially in the vertical direction, the largest RMS value can reach 8.42 mm. Before and after ELCs, the maximal difference of the annual amplitude and the half-annual amplitude at global 631 stations can reach 8.96 mm and 1.51 mm, respectively. Among them, 84.60% of the stations were corrected by the optimal environmental loading combination model, thus the nonlinear deformation was weakened.

Nonlinear Elastic Deformation of Mindlin Torus

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.

NONLINEAR DEFORMATION-FORCE MODEL OF A CONCRETE BAR WITH NON-METALLIC COMPOSITE REINFORCEMENT IN THE GENERAL CASE OF A STRESSED STATE

The article discusses a nonlinear deformation-force model of a concrete bar structure with a non-metallic composite reinforcement (NKA-FRP) in the general case of a stressed state, when all four internal force factors from an external load (namely, bending and twisting moments, transverse and longitudinal forces). A sufficiently deep and meaningful analysis of well-known studies on the selected topic is given. It has been established that the proposed nonlinear deformation-force model of a bar structure with FRP in the general case of a stressed state can be practically useful due to the possibility of its application in the design or reinforcement of beams, girders, columns and elements of rosette trusses of rectangular cross-section, which are operated under aggressive environmental conditions. This model can also be used to check the bearing capacity of existing FRP concrete bar structures, which operate not only under the influence of an aggressive environment, but also under conditions of a complex stress-strain state. In the course of the research, an algorithm was developed for determining the bearing capacity of the design section of a concrete rod with FRP under its complex stress state. General physical relations for the design section are given in the form of a stiffness matrix. The algorithm for calculating a concrete bar with FRP consists of a block for inputting the initial data, the main part, auxiliary subroutines for checking the conditions for increasing the load vector and depletion of the bearing capacity, as well as a block for printing the calculation results. At each stage of a simple static stepwise increasing load, the calculation is carried out by performing a certain number of iterations until the accuracy of determining all components of the deformation vector satisfies a certain predetermined value. The features and patterns of changes in normal and tangential stresses, generalized linear and angular deformations, as well as the equations of equilibrium of a concrete bar with FRP, which operates under the influence of an aggressive environment under conditions of a complex stress state, are also considered.