Finite amplitude vibrations of a circular plate

The problem of finite-amplitude, axisymmetric free and forced vibration of a circular plate is examined with various boundary conditions. The non-linear boundary-value problem is converted into the corresponding eigenvalue problem by elimination of the time variable. Then by a Newton-Raphson iteration scheme, and the concept of analytical continuation, the solution to the non-linear eigenvalue problem for the vibrations is obtained in a discrete form. It is seen that the removal of radial restraint causes drastic changes in the plate responses and the patterns of membrane stresses. Comparison with solutions based on the Berger assumption reveals the unsuitability of the assumption when the plate is not radially restrained.     

板结构功率流的参数研究

板以及肋板结构在工程中有着广泛的应用，其振动嗓声问题一直受到理论和工程领域的关注。本文在板结构功率流理论的基础上￣［１］，对板的损耗因子和不同加肋形式对其功率流的影响进行了分析和测量。     

On the boundary value problem of elastostatics in terms of stresses

The boundary value problem of elastostatics in terms of six components of the stress consists of nine equations and three boundary conditions. In this paper, we distinguished between the possible cases and impossible cases, i.e., the problem is or is not equivalent to a boundary value problem of six equations and six boundary conditions.     

An atomistic-based continuum theory for carbon nanotubes: analysis of fracture nucleation

Carbon nanotubes (CNTs) display unique properties and have many potential applications. Prior theoretical studies on CNTs are based on atomistic models such as empirical potential molecular dynamics (MD), tight-binding methods, or first-principles calculations. Here we develop an atomistic-based continuum theory for CNTs. The interatomic potential is directly incorporated into the continuum analysis through constitutive models. Such an approach involves no additional parameter fitting beyond those introduced in the interatomic potential. The atomistic-based continuum theory is then applied to study fracture nucleation in CNTs by modelling it as a bifurcation problem. The results agree well with the MD simulations.     

Synthesis of 5-Mercaptoalkylthiopyrazolyl-and 3-Mercaptoalkylthioisoxazolyl)-1,2,4-triazoles by Ring Chain Transformation

Cyclic α-oxo-α-(1,2,4-triazolyl)ketene S,S-acetals 1a-e react with hydrazine affording the substituted pyrazolyl-1,2,4-triazoles 3a-e. With hydroxylamine hydrochloride under basic conditions the substituted isoxazolyl-1,2,4-triazoles 5a-c are obtained.     

Solitons and Soliton Molecules in two Nonlocal Alice-Bob Fifth-Order KdV Systems

International Journal of Theoretical Physics - Soliton molecules were first discovered in optical systems and they have recently received reinvigorating scientific interests in physics and beyond....     

Avoiding Self-Reversed D Lines in Laser-Induced Breakdown Spectroscopy of Trace-Level Sodium in Soil

Journal of Applied Spectroscopy - Self-reversed sodium D lines in laser-induced plasmas generated from soil samples with a sodium trace concentration of 42.3 ppm was examined using laser-induced...     

Exact Recovery of Stochastic Block Model by Ising Model

In this paper, we study the phase transition property of an Ising model defined on a special random graph—the stochastic block model (SBM). Based on the Ising model, we propose a stochastic estimator to achieve the exact recovery for the SBM. The stochastic algorithm can be transformed into an optimization problem, which includes the special case of maximum likelihood and maximum modularity. Additionally, we give an unbiased convergent estimator for the model parameters of the SBM, which can be computed in constant time. Finally, we use metropolis sampling to realize the stochastic estimator and verify the phase transition phenomenon thfough experiments.     

Consensus-Related Performance of Triplex MASs Based on Partial Complete Graph Structure

This article mainly studies first-order coherence related to the robustness of the triplex MASs consensus models with partial complete graph structures; the performance index is studied through algebraic graph theory. The topologies of the novel triplex networks are generated by graph operations and the approach of graph spectra is applied to calculate the first-order network coherence. The coherence asymptotic behaviours of the three cases of the partial complete structures are analysed and compared. We find that under the condition that the number of nodes in partial complete substructures n tends to infinity, the coherence asymptotic behaviour of the two sorts of non-isomorphic three-layered networks will be increased by r−12(r+1), which is irrelevant to the peripheral vertices number p; when p tends to infinity, adding star copies to the original triplex topologies will reverse the original size relationship of the coherence under consideration of the triplex networks. Finally, the coherence of the three-layered networks with the same sorts of parameters, but non-isomorphic graphs, are simulated to verify the results.