Complex Linear Structures Research Articles

Dynamic response of asymmetric suspended structure subjected to random wind excitation

SummarySuspended structures, regarded as the expression of structural beauty, have attracted the focus of many architects and engineers. With the complexity of dynamic responses of the asymmetric suspended structures subjected to the random alongside wind excitation, an innovative method was proposed through combining the finite element method (FEM), the complex mode method (CMM), the pseudo excitation method (PEM), and the quadratic decomposition method (QDM) of frequency response function. The method could obtain unified closed‐form solutions of spectral moment and variance of node displacement and velocity and acceleration of asymmetric structures and its correctness was verified by existing numerical approaches. The proposed method is applicable to the random wind‐induced vibration response analysis of diverse linear complex structures. Notably, its efficacy lies in its circumvention of numerical integration, endowing it with high computational efficiency and accuracy. Extended comparative studies and discussion were also performed on effect of suspended span and comparisons of normal framed structure and symmetry structure. The results showed that the suspended span presented positive relation to horizontal displacement and inverse tendency to horizontal acceleration of the whole structure and vertical and horizontal acceleration of the columns near to suspended part should also be considered in engineering design.

Application of Management Information Systems in Road Infrastructure Management

In the field of spatial management, especially from the point of view of spatial economics, many decisions have long-term effects on the environment. Therefore, it is essential that the boundary conditions of the decision-making process are not only transparent, but also aligned with the sustainable development goals. At the same time, road infrastructure represents one of the most complex linear structures in the area, and its comprehensive management should respond to various types of problems, from structured to unstructured, which occur at all levels of decision-making. To solve such problems, management information systems (UIS) can help decision-makers to apply appropriate models and methods during the decision-making process. This paper provides an overview of the different types of UIS that can be used in road infrastructure management. The method of selecting an appropriate UIS and the method of interaction between data and models in such a management system are also discussed.

Entanglement dualities in supersymmetry

We derive a general relation between the bosonic and fermionic entanglement in the ground states of supersymmetric quadratic Hamiltonians. For this, we construct canonical identifications between bosonic and fermionic subsystems. Our derivation relies on a unified framework to describe both, bosonic and fermionic Gaussian states in terms of so-called linear complex structures $J$. The resulting dualities apply to the full entanglement spectrum between the bosonic and the fermionic systems, such that the von Neumann entropy and arbitrary Renyi entropies can be related. We illustrate our findings in one and two-dimensional systems, including the paradigmatic Kitaev honeycomb model. While typically SUSY preserves features like area law scaling of the entanglement entropies on either side, we find a peculiar phenomenon, namely, an amplified scaling of the entanglement entropy ("super area law") in bosonic subsystems when the dual fermionic subsystems develop almost maximally entangled modes.

Local optimization on pure Gaussian state manifolds

We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily convert from and to other parametrization of Gaussian states, such as wave functions for pure Gaussian states, quasiprobability distributions and Bogoliubov transformations. We review applications ranging from approximating ground states to computing circuit complexity and the entanglement of purification that have both been employed in the context of holography. Finally, we use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.

A non-unital generalized trace and linear complex structures

A non-unital generalized trace and linear complex structures

Time‐Resolved AU‐Scale Jets Traced by Masers in the IRAS 4A/B Regions of NGC 1333

We present results of VLBI observations of the water masers associated with IRAS 4A and IRAS 4B in the NGC 1333 star-forming region taken in four epochs over a two month period. Both objects have been classified as extremely young sources, and each source is known to be a multiple system. Using the Very Long Baseline Array, we detected 35 masers in epoch I, 40 masers in epoch II, 35 in epoch III, and 24 in epoch IV. Only one identified source in each system is associated with these masers. These data are used to calculate proper motions for the masers and trace the jet outflows within 100 AU of IRAS 4A2 and IRAS 4BW. In IRAS 4A2 there are two groups of masers, one near the systemic cloud velocity and one redshifted. They expand linearly away from each other at velocities of 53 km s−1. In IRAS 4BW, masers are observed in two groups that are blueshifted and redshifted relative to the cloud velocity. They form complex linear structures with a thickness of 3 mas (1 AU at a distance of 320 pc) that expand linearly away from each other at velocities of 78 km s−1. Neither of the jet outflows traced by the maser groups align with the larger scale outflows. We suggest the presence of unresolved companions to both IRAS 4A2 and 4BW.

The Vibration of Stepped Beams and Rectangular Plates By an Elemental Dynamic Flexibility Method

A new method for the concise and efficient solution of the free and forced vibration of a class of complex linear structures is proposed. The structures, having discontinuous properties, are divided into elemental substructures, and the displacement field for each is obtained in terms of its dynamic Green's function. The characteristic equation of the system is derived from interelement compatibility conditions, from which the system eigenvalues are found. The system eigenfunctions and the orthogonality relation for the eigenfunctions are derived, leading to an analytical solution for the forced response of the system.

Mutual Residual Energy Method for Parameter Estimation in Structures

In this work we describe an approach to parameter estimation of complex linear structures that we call the mutual residual energy approach. We have endeavored to develop a unified approach to the discrete inverse problems describing static equilibrium and free, undamped vibration, with a particular view toward evolving methods that are amenable to large-scale computation. The mutual residual energy method is based on the assumption that the topology and geometry of the structure are known, and that the system matrices can be linearly parameterized in terms of kernel matrices that have a solid physical basis and are easy to assemble. Measured motions of the structure are used (in conjunction with measured loads for the static case) to make estimates of the constitutive parameters. The method is based on a particular statement of the principle of virtual work and yields equations for estimating stiffness and mass parameters of linear structures. A condensation procedure is presented to deal with the case of incompletely measured systems. The quantity and quality of response measurements required, the consequences of noisy data, and the choice of load form are among the issues important to the success of our parameter estimation scheme. A numerical simulation is presented to demonstrate the features of the method.

A Convolution Approach for the Transient Analysis of Locally Nonlinear Rotor Systems

A computationally efficient convolution method, based on discretized impulse response and transition matrix integral formulations, is developed for the transient analysis of complex linear structures interacting through strong local nonlinearities. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a generic rotor-housing model representing a turbopump of a space shuttle main engine (SSME). In that model, the local nonlinearity is due to clearances between the rotor bearing outer races and the carrier attached to the housing. As compared to the fourth-order Runge-Kutta numerical integration methods, the convolution approach proved more efficient and robust for the same accuracy requirement. This is due to the closed-form formulation of the convolution approach which allows for the use of relatively larger time increments and for a reduction in the roundoff errors.