A general substructure synthesis method for the dynamic simulation of complex structures

In this paper a general substructure synthesis method is developed for the dynamic analysis of complex flexible structures. The motion of each substructure is represented by a given number of substructure admissible functions. Substructure admissible functions are often low-order polynomials, and hence computationally easy to work with. The otherwise disjoint substructures are connected together to form a whole structure by imposing approximate geometric compatibility conditions by means of the method of weighted residuals. The behavior of the estimated eigenvalues obtained by the substructures synthesis method can be ascertained by means of a bracketing theorem. The estimated eigenvalues do converge to the actual eigenvalues of the original structure, although it is necessary to consider two limiting processes, one in which the number of substructure admissible functions is increased and the other in which the number of internal boundary weighting functions is increased.     

The dynamic synthesis of general non-conservative structures from separately identified substructure models

The idea of synthesizing a number of directly identified substructure models is developed. Each substructure is tested separately and a substructure model is determined from time domain test data. Structural modeling concepts significantly affect the substructure identification and substructure coupling. The effects are examined in detail.     

A simplified nonlinear dynamic model for the analysis of pipe structures with bolted flange joints

Bolted flange joints are widely used in engineering structures; however, the dynamic behavior of this connection is complex in nature. In this paper, a simplified nonlinear dynamic model with bi-linear springs is proposed and validated for pipe structures with bolted flange joints. First, static mechanical properties of the bolted flange joint are investigated. The analytical solution reveals that the axial stiffness of the bolted flange joint is different in tension and compression. Then, nonlinear springs with different stiffness in tension and compression are employed to represent the bolted flange joint. A special type of dynamic behavior, coupling vibration in the transverse and longitudinal directions, is observed in analytical derivation. Finally, relevant physical experiments and numerical simulations are performed. The physical experiments confirm the existence of the coupling vibration behavior. The relationship of longitudinal and transverse vibration frequencies is discussed. The numerical solutions reveal that the simplified nonlinear dynamic model better fits the physical response than conventional reduced linear beam model.     

Nonlinear nonautonomous discrete dynamical systems from a general discrete isomonodromy problem

Nonlinear nonautonomous discrete dynamical systems (DDS) whose continuum limits are the well-known Painlevé equations, have recently arisen in models of quantum gravity. The Painlevé equations are believed integrable because each is the isomonodromy condition for an associated linear differential equation. However, not every DDS with an integrable continuum limit is necessarily integrable. Which of the many discrete versions of the Painlevé equations inherit their integrability is not known. How to derive all their integrable discrete versions is also not known. We provide a systematic method of attacking these questions by giving a general discrete isomonodromy problem. Discrete versions of the first and second Painlevé equations are deduced from this general problem.     

QCD resummation for jet substructures

We provide a novel development in jet physics by predicting the energy profiles of light-quark and gluon jets in the framework of perturbative QCD. Resumming large logarithmic contributions to all orders in the coupling constant, our predictions are shown to agree well with Tevatron CDF and Large Hadron Collider CMS data. We also extend our resummation formalism to the invariant mass distributions of light-quark and gluon jets produced in hadron collisions. The predicted peak positions and heights in jet mass distributions are consistent with CDF data within uncertainties induced by parton distribution functions.     

A new eigensolution of structures via dynamic condensation

Dynamic condensation (or model reduction) is a commonly used algorithm to fast estimate some low eigenvalues and corresponding eigenvectors of structures by reducing the order of the original structural model to a smaller one. This paper proposes a new eigensolution technique via iterated dynamic condensation. The technique retains all the inertia terms associated with the removed degrees of freedom in an iterated form, which generates the reduced mass matrix similar to that obtained in the Guyan reduction method with a frequency-dependent perturbed term. The corresponding eigenvalues and eigenvectors of interest are obtained as those of the Guyan reduction method with perturbations by using an eigensensitivity-based iterative method. The effectiveness and accuracy of the proposed technique are numerically verified by using a steel frame and the GARTEUR structure.     

Properties of dynamic windows in discrete maps

The problem of appearance and disappearance of dynamic windows in discrete maps is important and interesting in both fundamental and applied aspects. The appearance of dynamic windows and their structural (parametric) stability were analytically and numerically studied. By the example of the cubic map model, it was shown that the transitions to the window and out of it depend on variations in the control parameter, initial conditions, and calculation scheme details. In practical problems, the initial data accuracy is always limited; therefore, the calculation accuracy should be adequate to problem objectives. It was shown that data processing with higher accuracy within the model is not only inexpedient, but can lead to artifacts.     

A simplified method for treating the dynamic response of embedded structures to SH-waves

A simplified method is proposed to treat the dynamic response of rigid embedded structures subjected to plane SH-waves. The soil-structure interface is discretized into a finite number of strips, resulting in an analysis which involves only plane surfaces and plane waves. The interaction force on any strip is determined easily and the contributions from all the strips are superposed to obtain the total force on the structure. The equation of motion then yields the steady state response of the structure. The Green function for the structure is obtained by Fourier synthesis. The transient response of the structure to any other excitation is then obtained by using the Green function and the Duhamel integral. Numerical examples are presented both to validate and illustrate the method.     

Non-linear vibrations of general structures

Based on the finite element and perturbation procedures, an analytical-numerical approach to non-linear vibrations is developed. In particular, the overall solution employs the finite element method to handle spatial dependencies while the constrained version of the perturbation procedure is used to treat the temporal behavior. Due to the generality of the method developed, any combination of structure and boundary restraints can be treated as well as the possibility of conservative and non-conservative situations wherein the system can have any number of frequency branches. Furthermore, the procedure is not restricted to excitations in the neighborhood of specific frequencies, but rather applies to the full range. To demonstrate the capabilities of the solution approach, the results of several numerical studies are included along with experimental verification.     

Canonical quantization of general relativity in discrete space-times

It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.     

Investigating halo substructures with annual modulation signature

Galaxy hierarchical formation theories, numerical simulations, the discovery of the Sagittarius Dwarf Elliptical Galaxy (SagDEG) in 1994 and more recent investigations suggest that the dark halo of the Milky Way can have a rich phenomenology containing non-thermalized substructures. In the present preliminary study, we investigate the case of the SagDEG (the best known satellite galaxy in the Milky Way crossing the solar neighborhood) analyzing the consequences of its dark matter stream contribution to the galactic halo on the basis of the DAMA/NaI annual modulation data. The present analysis is restricted to some WIMP candidates and to some of the astrophysical, nuclear and particle physics scenarios. Other candidates such as e.g. the light bosonic ones we discussed elsewhere, and other non-thermalized substructures are not yet addressed here. PACS 95.35.+d     

A variational determination of few-nucleon substructures in nuclei

We present a method for a variational and self-consistent determination of the substructures in nuclei described as two interacting subsystems outside a core. Results for pairs and quartets in ²⁰Ne and ²⁴Mg are given.     

Dynamic behavior of discrete-time multiagent systems with general communication structures

In this paper, we discuss the dynamic behavior of networks of dynamic agents with general communication topologies. We first analyze the basic case: systems with communication topologies that have spanning trees, i.e., the systems that solve consensus problems. We establish an algebraic condition to characterize each agent's contributions to the final state. And we also study the influence of time-delays on each agent's contributions. Then, we investigate the general case: systems with weakly connected topologies. By using matrix theory, we prove that the states of internal agents will converge to a convex combination of boundary agents in the absence or presence of communication time-delays, and we also show that the coefficients of the convex combination are independent of time-delays even if the delays are time-varying. These results have broad applications in other areas, e.g., study of swarm behavior, formation control of vehicles, etc.     

Self-similarities of periodic structures for a discrete model of a two-gene system

We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps.     

Efficient and environmentally sustainable domino protocol for the synthesis of diversified spiroheterocycles with privileged heterocyclic substructures using bio-organic catalyst in aqueous medium

Molecular Diversity - An efficient and environmentally sustainable synthetic protocol has been presented to synthesize structurally diverse spiroxindoles spiroannulated with...     

用子结构模态综合法求解光学反射镜组件结构动响应

在航天光学成像仪器中光学反射镜组件结构复杂,相应的有限元分析模型大,因此分析效率较低。针对此问题,引入子结构模态综合法作为光学反射镜组件结构动响应的求解方法。具体讨论了子结构模态综合法求解结构动响应的基本原理,说明了该法在工程上的实现方法。以某反射镜组件为例进行了计算,结果表明,子结构模态综合法与经典的整体FE分析法比较,求解的前10个固有频率误差小于7%,计算时间前者为后者的2/3;加速度响应曲线符合良好,计算时间前者为后者的2/5,子结构模态综合法的计算效率明显提高,工程适用性良好。     

Lorentzian framed structures in general relativity

We study a class of four-dimensional real Lorentzian manifolds generated by a global operator (satisfying a cubic equation). We characterize empty, Einstein, conformally flat spaces and construct mathematical models of two physical space-times. Locally, the solutions presented have been identified with known solutions. Kruskal space-time is generated by using the warped product technique [11].