The dynamic relaxation form finding method aided with advanced recurrent neural network

How to establish a self‐equilibrium configuration is vital for further kinematics and dynamics analyses of tensegrity mechanism.In this study,for investigating tensegrity form‐finding problems,a concise and efficient dynamic relaxation‐noise tolerant zeroing neural network(DR‐NTZNN)form‐finding algorithm is established through analysing the physical properties of tensegrity structures.In addition,the non‐linear constrained opti-misation problem which transformed from the form‐finding problem is solved by a sequential quadratic programming algorithm.Moreover,the noise may produce in the form‐finding process that includes the round‐off errors which are brought by the approximate matrix and restart point calculating course,disturbance caused by external force and manufacturing error when constructing a tensegrity structure.Hence,for the purpose of suppressing the noise,a noise tolerant zeroing neural network is presented to solve the search direction,which can endow the anti‐noise capability to the form‐finding model and enhance the calculation capability.Besides,the dynamic relaxation method is contributed to seek the nodal coordinates rapidly when the search direction is acquired.The numerical results show the form‐finding model has a huge capability for high‐dimensional free form cable‐strut mechanisms with complicated topology.Eventually,comparing with other existing form‐finding methods,the contrast simulations reveal the excellent anti‐noise performance and calculation capacity of DR‐NTZNN form‐finding algorithm.

Effective loading algorithm associated with explicit dynamic relaxation method for simulating static problems

Based on the fact that a static problem has an equivalent wave speed of infinity and a dynamic problem has a wave speed of finite value, an effective loading algorithm associated with the explicit dynamic relaxation method was presented to produce meaningful numerical solutions for static problems. The central part of the explicit dynamic relaxation method is to turn a time-independent static problem into an artificial time-dependent dynamic problem. The related numerical testing results demonstrate that: (1) the proposed effective loading algorithm is capable of enabling an applied load in a static problem to be propagated throughout the whole system within a given loading increment, so that the time-independent solution of the static problem can be obtained; (2) the proposed effective loading algorithm can be straightforwardly applied to the particle simulation method for solving a wide range of static problems.

A method to simulate multilayer welding process： Node dynamic relaxation method

A new method called node dynamic relaxation is proposed to simulate multilayer welding. A two dimensional plane strain model for multilayer welding is simulated and the results show that mesh distortion can be decreased, and it is also found that the node dynamic relaxation is a kind of method to calculate welding deformation accurately by comparing experiment results with simulation results.

Node dynamic relaxation method： principle and application

Two main methods, inactive eiement method and quiet element method, to simulate the process of multilayer ：and multipass welding：were reviewed, and the shortcomings of both methods were diScussed as well Based on these analyses, a method called node dynamic relaxation method was put into forward to simulate the multilayer and multipass welding process, and the principle and application of this method were discussed in detail. The simulating results show that using the node dynamic relaxation method can decrease mesh distortion, improve calculation efficiency, and obtain good simulation results. This method can also be used in the field of simulation addition or removing materials in finite element analysis.

Nonlinear analysis of cable structures using the dynamic relaxation method

The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers.Because they have highly nonlinear behavior,it is difficult to find solutions to these problems.Thus far,different assumptions and methods have been proposed to solve such structures.The dynamic relaxation method(DRM)is an explicit procedure for analyzing these types of structures.To utilize this scheme,investigators have suggested various stiffness matrices for a cable element.In this study,the efficiency and suitability of six well-known proposed matrices are assessed using the DRM.To achieve this goal,16 numerical examples and two criteria,namely,the number of iterations and the analysis time,are employed.Based on a comprehensive comparison,the methods are ranked according to the two criteria.The numerical findings clearly reveal the best techniques.Moreover,a variety of benchmark problems are suggested by the authors for future studies of cable structures.

Relaxation Dynamics in Condensation on Weighted Scale-Free Networks

Most of the realistic networks are weighted scale-free networks. How this structure influences the condensation on it is a challenging problem. Recently, we make a first step to discuss its condensation [Phys. Rev. E 74 （2006） 036101] and here we focus on its evolutionary process of phase transition. In order to show how the weighted transport influences the dynamical properties, we study the relaxation dynamics in a zero range process on weighted scale-free networks. We find that there is a hierarchical relaxation dynamics in the evolution and there is a scaling relation between the relaxation time and the jumping exponent. The relaxation dynamics can be illustrated by a mean-field equation. The theoretical predictions are confirmed by our numerical simulations.

Dielectric Analysis of Dynamic Fouling Behavior on Surface of Polyethersulfone Composite Ultrafiltration Membrane

A dielectric analysis model for the fouling layer on the polyethersulfone composite ultrafiltration （UF） membrane and solution system, which consists of the solution, concentration polarization layer （CPL）, and cake layer, was established by virtue of the interfacial polarization and the electrostatic field theory. The effect of some important parameters, such as the depth, conductivity of CPL, and cake layer, on the dielectric spectroscopy （or dielectric relaxation properties） of the UF system was discussed by the parameter sensitivity analysis and the dielectric measurement. The simulations indicate that the CPL can be created rapidly and the cake layer formation is the dynamic balance process of growth and erosion in the process of UF. The key factor affecting on the dielectric spectrum of UF system is the electrical properties of the CPL and the cake layer. In comparison to the results of dielectric measurement, the simulations indicate that the model proposed in this work is valid and reliable to some degree for describing and explaining the dielectric relaxation phenomenon in UF system. It is very important to further understand the fouling behavior of membrane surface and optimize the controlling techniques of membrane fouling in the process of UF.

Kagome Project:Physical and Numerical Modeling Comparison for a Post-formed Elastic Gridshell

An elastic gridshell is an efficient constructive typology for crossing large spans with little material.A flat elastic grid is built before buckling the structure into shape,in active and post-formed bending.The design and structural analysis of such a structure requires a stage of form finding that can mainly be done:(1)With a physical model:either by a suspended net method,or an active bending model;(2)With a numerical model performed by dynamic relaxation.All these solutions have various biases and assumptions that make them reflect more or less the reality.These three methods have been applied by Happold and Liddell[1]during the design of the Frei Otto’s Mannheim Gridshell which has allowed us to compare the results,and to highlight the significant differences between digital and physical models.Based on our own algorithm called ELASTICA[2],our study focuses on:(1)Comparing the results of the ELASTICA’s numerical models to load tests on physical models;(2)The identification of the various factors that can influence the results and explain the observed differences,some of which are then studied;(3)Applying the results to build a full-scale interlaced lattice elastic gridshell based on the Japanese Kagome pattern.

Simulations of the flipping images and microparameters of molecular orientations in liquids according to the molecule string model

The relaxation dynamics of liquids is one of the fundamental problems in liquid physics, and it is also one of the key issues to understand the glass transition mechanism. It will undoubtedly provide enlightenment on understanding and calculating the relaxation dynamics if the molecular orientation flipping images and relevant microparameters of liquids are studied. In this paper, we first give five microparameters to describe the individual molecular string （MS） relaxation based on the dynamical Hamiltonian of the MS model, and then simulate the images of individual MS ensemble, and at the same time calculate the parameters of the equilibrium state. The results show that the main molecular orientation flipping image in liquids （including supercooled liquid） is similar to the random walk. In addition, two pairs of the parameters are equal, and one can be ignored compared with the other. This conclusion will effectively reduce the difficulties in calculating the individual MS relaxation based on the single-molecule orientation flipping rate of the general Glauber type, and the computer simulation time of interaction MS relaxation. Moreover, the conclusion is of reference significance for solving and simulating the multi-state MS model.

Fast Optical Switching Using Oriented Cyanine Dye-Doped Nematic Liquid Crystal

A cyanine dye, 2-[7-（1,3-dihydro-1,3,3-trimethyl-2H-indol-2-ylidene）-1,3,5-heptatrienyl]-1,3,3-trimethyl-3H-indolium iodide （NK-125）, is doped in 4-cyano-4＇-pentylbiphenyl （5 CB）, and the mixture is sandwiched between two pieces of rubbed glass plates. The third-order nonlinear optical properties of the oriented NK-125-SCB layers are measured by the resonant femtosecond degenerate four-wave mixing （DFWM） technique at 760 nm. The third-order nonlinear optical susceptibility of one of the present samples is 5.5×10^-8 esu. The slow DFWM response of the NK-125-SCB layers due to a population grating is accelerated by the increasing laser power because of amplified spontaneous emission （ASE）. On the other hand, we do not observe a similar phenomenon for NK-125- polyethylene glycol （PEG-400）. Oriented NK-125 molecules in nematic liquid crystals must have very high ASE efficiency. Hence the population grating in a DFWM signal disappears within about 4 ps. It is expected that NK-125-SCB can be used as a material for very fast all-optical switching.

Dramatic Impact of Auxiliary Ligands on the Dynamic Magnetic Relaxation in Tetranuclear Dy^(III)_(2)Zn^(II)_(2) Single Molecule Magnets

Better understanding the determining factors of dynamic magnetic relaxation in polynuclear lanthanide based single-molecule magnets(SMMs)remains a challenge due to the complexity of such architectures involving interactions between the magnetic centers.To address this issue,two structurally related heterometal Dy^(III)_(2)Zn^(II)_(2) SMMs,[Zn_(2)Dy_(2)(L)_(4)(Ac)_(2)(DMF)(CH_(3)OH)]·CH_(3)OH·2H_(2)O(1)and[Zn_(2)Dy_(2)(L)_(4)(Ac)_(2)(DMF)_(2)]·4CH_(3)CN(2)(H_(2)L=(E)-2-((2-hydroxy-3-methoxybenzylidene)amino)-4-methyphenol,DMF=N,N-dimethylformamide),are introduced and investigated.Through modifying the auxiliary ligands on one Dy^(III) site while retaining that on the other Dy^(III),the intramolecular magnetic interactions and relaxation dynamics in these two heterometallic-Dy^(III)_(2)Zn^(II)_(2) SMMs can be tuned,demonstrating a dramatic change in the magnet relaxation behavior with energy barrier changing from a negligible value for 1 to 305 K for 2.Ab initio calculations reveal that changing the coordination geometries on the Dy^(III) sites can significantly affect the magnetic interactions as well as single-ion anisotropy.

Hydrogen-bonded Intramolecular Charge Transfer Excited State of Dimethylaminobenzophenone using Time Dependent Density Functional Theory

Density functional theory and time-dependent density-functional theory have been used to investigate the photophysical properties and relaxation dynamics of dimethylaminobenzophe- none （DMABP） and its hydrogen-bonded DMABP-MeOH dimer. It is found that, in non- polar aprotic solvent, the transitions from So to S1 and S2 states of DMABP have both n→π and π→π＊ characters, with the locally excited feature mainly located on the C=O group and the partial CT one characterized by electron transfer mainly from the dimethylaminophenyl group to the C=O group. But when the intermolecular hydrogen bond C=O…H-O is formed, the highly polar intramolecular charge transfer character switches over to the first excited state of DMABP-MeOH dimer and the energy difference between the two low- lying electronically excited states increases. To gain insight into the relaxation dynamics of DMABP and DMABP-MeOH dimer in the excited state, the potential energy curves for con- formational relaxation are calculated. The formation of twisted intramolecular charge trans- fer state via diffusive twisting motion of the dimethylamino/dimethylaminophenyl groups is found to be the major relaxation process. In addition, the decay of the Si state of DMABP-MeOH dimer to the ground state, through nonradiative intermolecular hydrogen bond stretching vibrations, is facilitated by the formation of the hydrogen bond between DMABP and alcohols.

Singlet relaxation dynamics and long triplet lifetimes of thiophene-coupled perylene diimides dyads:New insights for high efficiency organic solar cells

In the active layer of organic solar cells(OSCs),the lifetime of triplet excitons is one of the decisive factors in the diffusion length and therefore has important impact on the power conversion efficiency of the devices.Herein,we have investigated singlet excited state relaxation dynamics and their triplet exciton lifetimes of two thiophene-coupled perylene diimides(PDI)dyads(2 PDI-Th and fused-2 PDI-Th),in order to provide a unique explanation in depth on their different performances in OSC devices.From the transient absorption(TA)spectra,the singlet excitons of 2 PDI-Th form excimers in the time scale of 1.5 ps.Then the excimers go into the triplet state via intersystem crossing(ISC).In fused-2 PDI-Th,triplet excitons are generated directly from the singlet excited excitons via the efficient ISC.Density functional theory(DFT)calculations further support the formation of excimers.DFT results indicate that 2 PDI-Th exhibits an H-typed molecular configuration which is beneficial to form the excimers,while fused-2 PDITh gives a twisted X-shaped configuration in the optimized ground and excited state.In steady-state emission spectra,2 PDI-Th shows abroad and featureless spectral characteristics of the excimers with a decay time of 840 ps,which is much shorter than those of PDI(5.5 ns)and fused-2 PDI-Th(3.3 ns).The triplet lifetime(67 ms)of fused-2 PDI-Th is factor of 3 longer than that of 2 PDI-Th(22 ms).These results demonstrate that ring-fused structure is an efficient strategy to eliminate excimer formation and prolong the lifetime of triplet excitons,which provides a new insight for design of optoelectronic molecules for high efficiency organic solar cells.

Dual-comb soliton rains based on polarization multiplexing in a single-walled carbon nanotube mode-locked Er-doped fiber laser

We experimentally demonstrate tunable dual-comb soliton rains in a polarization multiplexing fiber laser based on a singlewalled carbon nanotube.The repetition frequency difference of dual-comb pulses is about 39 Hz,with a maximum extinction ratio of 29 dB.With suitable polarization states,one of the dual-comb pulses switches into soliton rain sequence with chirped isolating soliton trains.The signal-to-noise ratio reaches 61 dB,which is 11 dB higher than that of the normal dual-comb pulses.The intervals between chirped isolating solitons are distributed progressively,and the number of isolating solitons can be flexibly tuned from 2 to 11 by adjusting polarization state or pump power.Our work will provide support for further understanding of interaction dynamics of solitons and give a new route to the application of precision measurement.

Correlation of cooperatively localized rearrangement on the "fluidized domain" in glass substances (or polymers) to their fragility Ⅲ:Theory of dynamic fragility at isochoric state

A set of universal equations on the reduced stress relaxation modulus with K-W-W stretched exponential function has been derived from the dynamics of α and β structural relaxation processes. In the present work, the K-W-W decay function is used to define the three types of relaxations (single α, single β relaxation and α-β co-relaxation), then their average times of relaxation are theoretically calculated from the reduced shear stress relaxation modulus and the relaxation time spectrum function H(τ). When the average time of co-relaxation, the reference temperatures (ficitive Tf and glass transition Tg) and the isostructural parameter achieved from the conditions of isostructural glass state are introduced into the reduced shear stress relaxation modulus (GT) under the equilibrium state, a set of correlations between isochoric fragility index (mvα, mvβ and mvαβ) and the coupling strength (α and β) under the reference temperatures are derived from the exact definition of isochoric fragility. So the theory of dynamic fragility for glass substances at isochoric state is developed. The theory can predict the following main features of structural relaxations and behavior of isochoric fragility: the temperature dependence of peak relaxation frequency exhibits a bifurcation with a pair of single α and single β relaxations; the temperature dependence of Stickel equation on 1/T exhibits two crossovers with VFTH(1) and VFTH(2) at the temperatures of Tf and Tg regime; there are two linear correlations between isochoric fragility index (mvα and mvβ) and the coupling strength. Fine agreements between the theoretical calculation and experimental results are obtained.

Structural relaxation and glass transition behavior of binary hard-ellipse mixtures

Structural relaxation and glass transition in binary hard-spherical particle mixtures have been reported to exhibit unusual features depending on the size disparity and composition. However, the mechanism by which the mixing effects lead to these features and whether these features are universal for particles with anisotropic geometries remains unclear. Here, we employ event-driven molecular dynamics simulation to investigate the dynamical and structural properties of binary two-dimensional hard-ellipse mixtures. We find that the relaxation dynamics for translational degrees of freedom exhibit equivalent trends as those observed in binary hard-spherical mixtures. However, the glass transition densities for translational and rotational degrees of freedom present different dependencies on size disparity and composition. Furthermore,we propose a mechanism based on structural properties that explain the observed mixing effects and decoupling behavior between translational and rotational motions in binary hard-ellipse systems.

Simulation of construction shape-forming process of cable domes

A cable dome has no stiffness or load carrying capacity unless it has been prestressed.Analyses of cable domes are based on successful prestressing designs,making force finding analysis very important.A new force finding method named the imbal-ance force iterative method is proposed,which can overcome some limitations of the integrity feasible prestressing method.For instance,even if groups are assigned by mistake,the pretension distribution that satisfies the known geometry form can also be found.This method possess good stability and calculation efficiency,and a case study indicates that it is applicable to the force finding of large and complicated cable domes.On the other hand,form finding analysis of cable domes is also a key engineering problem.However,rigid displacement occurs in this process,which makes the analysis more complex.In this pa-per,the dynamic relaxation method was selected,and the problem of rigid displacement was therefore effectively solved.The method includes two steps:first,the stretching cables are released,and secondly,an axial force is imposed on the two ends of each released cable.This method is convenient in its calculation and clear in its conception.A case study indicates that the method is suitable for the simulation of the construction process of various cable domes and cable-strut tension structures.Moreover,a form finding experiment was conducted on a model of a cable dome with a diameter of 4.8 m by tensing diagonal cables.The behavior of the model in the form finding process was investigated.The experimental results indicate that the ini-tial lengths of members and prestress loss are key issues in cable domes design.The results also prove that the methods of form finding and force finding proposed in this paper are reliable and effective.

Computation of Two-Phase Biomembranes with Phase Dependent Material Parameters Using Surface Finite Elements

The shapes of vesicles formed by lipid bilayers with phase separation are governed by a bending energy with phase dependent material parameters together with a line energy associatedwith the phase interfaces.We present a numericalmethod to approximate solutions to the Euler-Lagrange equations featuring triangulated surfaces,isoparametric quadratic surface finite elements and the phase field approach for the phase separation.Furthermore,the method involves an iterative solution scheme that is based on a relaxation dynamics coupling a geometric evolution equation for the membrane surface with a surface Allen-Cahn equation.Remeshing and grid adaptivity are discussed,and in various simulations the influence of several physical parameters is investigated.

Probing the formation of ultrastable metallic glass from structural heterogeneity

Ultrastable metallic glasses(SMGs)exhibit enhanced stability comparable to those of conventional glasses aged for thousands of years.The ability to understand why certain alloy compositions and processing conditions generate an SMG is an emerging challenge.Herein,amplitude-modulation dynamic atomic force microscopy was utilized for tracking the structure of Zr_(50)Cu_(50),Zr_(50)Cu_(44.5)Al_(5.5)and Zr_(50)Cu_(41.5)Al_(5.5)Mo_(3) thin film metallic glasses(TFMGs)that were produced by direct current magnetron sputtering at room temperature with the rate of deposition being the only variable.The transition in stability from bulkto SMG-like behavior resides in the change of relaxation mechanism as the deposition rate is decreased.The formation of SMGs is directly linked with the degree of structural heterogeneity,whereby MGs with greater heterogeneity have a higher potential to form SMGs with more significant enhancement in stability.Slower deposition rates,however,are required to yield the more homogenous structure and lower energy state underlying the ultrastability.Ultrastability is closely linked with the geometric shape and distribution of loosely packed phases,whereby SMGs containing more slender loosely packed phases with a more skewed distribution achieve more significant improvements in stability.This work not only provides direct evidence of the structure of SMGs,but also opens new horizons for the design of SMGs.