MPolSys Modeler, a tool for computational modeling of linear polymer systems

The computational study of intermolecular relationships of a given material can be used as a route for predicting quantities impossible or difficult to be determined experimentally. Furthermore properties of new materials can also be predicted by techniques of this type, when they are still in the modeling phase. This technique reproduces the classical dynamic relationships between the constituent elements of the material, atoms or unicorpuscular approximations of molecules, from interaction potential models called force fields. This work aims to develop a tool that performs the composition of linear polymeric chain systems through a self-avoided walk. For this, the concept of self-experimentation of long walks (SAWLC) was used, together with the Python language to develop MpolSys Modeler. This tool is a non-overlapping polymer chain generator, which in turn generates outputs that can be used as input to Moltemplate. To validate the tool's results, experiments were carried out in which the numbers and polymerization chains of the simulated polymer were varied, observing the overlap or not of the molecules that make up the simulation. At the end of the simulations, there were positive results that indicate a promising usage of the tool for the creation of polymers with a high number of chains and degrees of polymerization.

Vibrational energy flow cancelling by loading a reverse excitation: Visualization and analysis

Vibration control is a permanent and significant issue in all forms of structural dynamic analysis with the consistent objective being to minimize vibration levels. Considering that the propagation of vibration waves is essentially the transmission of vibrational energy flow (VEF), the fundamental requirement, therefore, is to minimize the VEF transmitted from sources to sinks and then to control and block the flow of vibration energy. Structural intensity (SI) method, combining forces with velocities to assess the magnitude and directions of VEF, is alternative to classical dynamic assessment methods offering insight into the transmission of VEF and studying additional phenomena which cannot be obtained by conventional dynamic analysis. In the field of noise, active noise control has been widely used in vehicles and headphones, which has achieved remarkable results by introducing a cancelling ‘anti-noise’ wave through an appropriate array of secondary sources. Analogically, it is considered whether the vibration of the structure can be attenuated by introducing a secondary reverse excitation (SRE) to offset the VEF transmitted in the structure. Therefore, this article combines the SI method and SRE to carry out related research on this issue. The rectangular plate with the circular hole subjected to the transient sinusoidal force, being widely used and found in various engineering branches, is taken as the research object. The developed simulation system consisting of the finite element tool and the in-house program is used to assess and visualize the instantaneous SI fields. The effects of the SRE acting on this structure on the transmission behaviours of VEF and the vibration suppression have been investigated in detail. Moreover, the transmission, conversion and balance relationships of the VEF have been derived from the general equation of motion and analysed as well. This study sheds new light on the vibration attenuation by introducing the secondary source from the perspective of VEF.

DMGA: A Distributed Shortest Path Algorithm for Multistage Graph

The multistage graph problem is a special kind of single-source single-sink shortest path problem. It is difficult even impossible to solve the large-scale multistage graphs using a single machine with sequential algorithms. There are many distributed graph computing systems that can solve this problem, but they are often designed for general large-scale graphs, which do not consider the special characteristics of multistage graphs. This paper proposes DMGA (Distributed Multistage Graph Algorithm) to solve the shortest path problem according to the structural characteristics of multistage graphs. The algorithm first allocates the graph to a set of computing nodes to store the vertices of the same stage to the same computing node. Next, DMGA calculates the shortest paths between any pair of starting and ending vertices within a partition by the classical dynamic programming algorithm. Finally, the global shortest path is calculated by subresults exchanging between computing nodes in an iterative method. Our experiments show that the proposed algorithm can effectively reduce the time to solve the shortest path of multistage graphs.

Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems

We apply the semi-classical limit of the generalized SO(3) map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on T*S2. Using the asymptotic form of the star-product, we manage to “quantize” one of the classical dynamic variables and introduce a discretized version of the Truncated Wigner Approximation (TWA). Two emblematic examples of quantum dynamics (rotor in an external field and two coupled spins) are analyzed, and the results of exact, continuous, and discretized versions of TWA are compared.

Variable-Order Fractional Dynamic Behavior of Viscoelastic Damping Material

Viscoelastic damping material has been widely used in engineering machinery to absorb vibration and noise. In engineering, the dynamic behavior of the viscoelastic material is mainly affected by temperature and frequency. Classical dynamic behavior equations of the viscoelastic damping material have complex structures with multiple and ambiguous parameters. So a novel variable-order fractional constitutive model (VOFC) is established based on the variable-order fractional operator. Then the viscoelastic dynamic equations are derived by the Laplace transform of the VOFC model. The DMA test by the three-point bending mode is carried out at variable temperatures and frequencies and the frequency spectrum of the dynamic behaviors, i.e., the loss modulus, the storage modulus and the loss factor are obtained. Against the test data ,the VOFC model is compared with classical models such as the integer-order Maxwell model (IOM), the constant fractional-order Kelvin-Voigt model (CFK), the constant fractional-order Maxwell model (CFM) and the constant fractional-order standard linear solid model (CFS). Through the comparison , it can be found that the VOFC model can describe dynamic behaviors of the viscoelastic damping material at different temperatures and frequencies more accurately. Furthermore, the VOFC model has simpler structure and only two parameters with clearly-physical meanings.

A Dynamic Oligopoly with Price Stickiness and Risk-Averse Agents

In this paper we present a dynamic discrete-time model that allows to investigate the impact of risk-aversion in an oligopoly characterized by a homogeneous non-storable good, sticky prices and uncertainty. The continuous-time limit of our formulation nests the classical dynamic oligopoly model with sticky prices by Fershtman and Kamien (Econometrica 55:1151–1164, 1987) and extends it by accommodating uncertainty and risk-aversion. We show that in the continuous-time limit of our infinite horizon formulation the optimal production strategy and the consequent equilibrium price are, respectively, directly and inversely related to the degrees of uncertainty and risk-aversion. However, the effect of uncertainty and risk-aversion crucially depends on price stickiness since, when prices can adjust instantaneously, the steady state equilibrium in our model with uncertainty and risk-aversion collapses to Fershtman and Kamien’s analogue.

Critical remarks on Rayleigh damping model considering the explicit scheme for the dynamic response analysis of high rise buildings

This paper numerically investigates the validity of Rayleigh damping model considering explicit operator to assess the dynamic response of high rise buildings under seismic loads. Considering transverse and longitudinal seismic waves, the bending moment, shear force, axial force, and and inter story drift are evaluated for a Core wall and a frame system of 46 story each. It is found that considering the explicit scheme, the dynamic responses are amplified significantly especially for axial forces. The reported amplification can be attributed to the ignorance of stiffness proportional Rayleigh damping coefficient which is associated with the stability issue of the implemented explicit operator. The paper indicates that Rayleigh damping model does not provide the required/expected damping for the higher modes of higher frequencies hence, it is not appropriate to be used along with the explicit operator especially for buildings of wide range of frequencies. It is worth pointing out that for classical dynamic analysis which follows the implicit scheme, Rayleigh damping seems to well consider the higher modes of high frequencies with higher damping ratio in comparison to the initial mode shapes. Consequently, the literature explicit scheme should be revised to accurately consider a proper damping for the higher modes which is crucial to assess the total response of structures of long periods and wide range of frequencies such as high rise buildings among others.

Detection of different type events in hybrid dynamical systems

Hybrid dynamical or simply hybrid systems (HS) are a modern apparatus for modeling discrete-continuous processes in different applications such as power engineering, aeronautics, manufacturing, economics, transport dispatching, etc. The key difference of HSs from classical dynamic systems is the presence of continuous mode switching events. Event times are defined by the zeroes of continuous event functions. If it is impossible to symbolically compute an event time. To do it one uses an event detection algorithm working together with a differential equation integration algorithm. Events in HSs are traditionally divided into state events and time events. Only explicit time events with event functions in the form of linear polynomials in time are usually considered in the literature. This paper addresses the class of implicit time events and lists their possible sources. Moreover, the traditional classification of events into unilateral, bilateral and accuracy critical events is expanded by adding difficult-to-detect events. These events are characterized by event functions crossing zero several times within one integration step. Not all algorithms can guarantee detecting events of this type. Heterogeneous HSs including processes of different physical nature are in general characterized by significantly stiff and high-dimensional modes usually defined in a form of differential-algebraic systems of equations with events of different types. The last feature limits the application of classical event detection algorithms oriented to a single event type. That is why the paper proposes the methodology of complex event detection consisting in using separate event detection algorithm for each event type. The joint work of several algorithms can ensure correct detection of events of different types and also may improve the efficiency. A complex event detection algorithm guaranteeing detection of all events is constructed for a particular HS. The complex algorithm demonstrates an average speed up of 17%.

Application of Improved Dynamic Substructure Finite Element Model-Based State-Space Techniques in Mistuned Blisks

Aeroengine is a complex mechanical equipment, and it works at high temperature, pressure, rotational-speed, and severe loads. One of the core problems is that the vibration and mistuning of bladed disk lead to failure and affect the safety and reliability of aeroengine. Previously, one sector taken as the research object is not suitable; the integrally mistuned bladed disk (blisk) is taken as the research object is very necessary; however, the computational efficiency of mistuned blisk is very low. Therefore, a reduced-order model approach, i.e., an improved dynamic substructure finite element model-based state-space technique (IDSFEM-SST), is proposed to investigate the mistuned blisk. Firstly, the reduced-order substructure finite element model is established by this method, and then, the modal frequencies and modal strain energy amplitudes are investigated. Secondly, the maximum displacement responses are analyzed. Finally, the computational efficiency and accuracy of mistuned blisk via IDSFEM-SST is compared with that of the classical dynamic substructure finite element model and the high-fidelity finite element model to verify the effectiveness of this approach. This study has significance to the dynamic research and engineering practices for complex mechanical structures.