Dynamic Scaling Law Research Articles

Water saturation effect on the dynamic mechanical behaviour and scaling law effect on the dynamic strength of coral aggregate concrete

The variation in impact resistance of coral aggregate concrete (CAC) under different levels of water saturation was investigated. Results show that the free water improves not only the strain rate effect of the dynamic compressive strength of CAC but also the increasing amplitude of the dynamic elastic modulus with the strain rate. In general, the strain rate effect on the dynamic elastic modulus is less than that on the dynamic compressive strength. The higher the water saturation, the greater are the critical strain and toughness of CAC. The promoting effect of free water on crack propagation at a low strain rate and the increasing effect of free water on the damage degree at a high strain rate improve the deformation and energy absorption properties of CAC. The proposed scaling law effect model can be effectively applied to characterise the statistical distribution of the dynamic strength of CAC.

Experimental and Numerical Studies on Setback Buildings Considering the SSI Effect under Seismic Response

From the previous studies it is observed that due to the effect of the earthquake, several irregular buildings failed vulnerably. Further the effect of sub soil conditions where these buildings have been founded also play an important role on the seismic response of these buildings. In the past, experimental studies on the seismic response of different setback building configurations have not been carried out. Therefore, in the present study the seismic behaviour of setback buildings considering Soil Structure Interaction (SSI) has been evaluated by conducting experimental and numerical investigations. Buildings with various setback configurations were considered and are designed as pile foundation supported structures. The irregularity index of these building configurations have been determined as per the existing codal provisions. These piles supported buildings representing the prototype structure have been scaled down according to geometric, kinematic and dynamic scaling laws. The scaled building models are subjected to vibrations beyond resonant frequencies using shake table facility. A comparison of the results has been made between experimental and numerical investigations. Based on the study it has been observed that storey displacements of building with regular configurations are higher in comparison with the setback buildings. It is also found that asymmetrical and symmetrical setback buildings having different irregularity indices as per IS:1893-2016 indicate nearly the same displacements at resonant frequencies. Doi: 10.28991/cej-2021-03091664 Full Text: PDF

Critical magnetic behavior in [Ag8/Co0.5]x64, [Ag8/Co1]x32 and [Ag16/Co1]x32 epitaxial multilayers

We investigate the low temperature magnetic behavior of three epitaxial Co/Ag multilayers, grown onto MgO (001) substrates, with a nominal content per period of either half a monolayer or one monolayer of Co, and either 8 or 16 Ag monolayers. The samples were studied by X-ray reflectivity and diffraction, transmission electron microscopy, magnetometry and ac susceptometry. The results indicated a well defined stacking sequence in the growth direction, the number of periods and of Ag monolayers per period being coincident with the nominal values for each sample. The Co layers were found to be discontinuous and corresponded to a quasi-monodisperse in-plane distribution of Co nanoparticles embedded in a Ag(001) matrix. The zero-field cooled and field cooled temperature variations of the low field magnetization indicated the presence of irreversibilities at temperatures below 20 K. The ac field frequency (f) and temperature (T) dependencies of the real part of the susceptibility (χ′) corresponded to a Vogel–Fulcher behavior in the three samples, and indicated a frequency shift parameter (Γ) of the order of 4 x 10-2. For each sample, the experimental data corresponding to the variations of the imaginary part of the ac susceptibility (χ″) with f and T were found to collapse into a single curve according to the dynamic scaling law. Taken together, these results allow us to conclude that the three multilayers experience a phase transition of the paramagnetic to superspin glass type, driven by the dipolar interactions between the Co nanoparticles. Regarding the influence of the multilayer features, we found a clear dependence of the order parameter of the transition on the nominal number of Co monolayers per period.

Cluster glass characteristics of disordered La2CuMnO6 double perovskite oxides

The structural and magnetic properties of disordered La2CuMnO6 double perovskite oxide are reported. Temperature variation of dc magnetization in zero field cooled and field cooled protocols manifest the cluster glass feature of the compound. The cooperative glassy magnetic state is explored by the memory effect in thermal variation as well as relaxation dynamics. The frequency dependent shift of the ac susceptibility peak satisfies dynamical scaling law with Tc ~ 26.4 K and dynamic exponent zν ~ 3.26 proposing a cluster-glass like state. The anti-site disorder and competing exchange interactions of two different transition metal have been argued for the observed cluster glass state in this B-site disordered La2CuMnO6 double perovskite.

Verification of Rotordynamic Design Using 1/5 Scaled Model Rotor of 270 MW-Class Gas Turbine Center-Tied Rotor

Gas turbine power generation is relatively minor in terms of pollutant emissions, such as nitrogen oxides or sulfur oxides, as compared to thermal power generation using coal or petroleum. This is because of the use of liquefied natural gas, known as an eco-friendly power generation solution. Large gas turbines used for power generation are suitable for the power load demanded by modern society, which fluctuates very much with respect to power consumption because it takes only about 10–20 min to reach the entire output from the start-up. A large gas turbine used for power generation is a rotating machine that features a high degree of difficulty in mechanical design due to its fast start-up characteristics, structural complexity, and high operating temperature, while also emphasizing stability. Customers are demanding operational reliability as a prerequisite before evaluating the performance of a gas turbine. It is very important to design and verify the rotor dynamics sufficiently and accurately from the design stage prior to fabrication in light of that it is very difficult to change the rotor dynamics characteristics once the design is completed and finished. Many researchers are trying to improve the design completeness, but the researches that actually design and verify the power generation gas turbine are limited only to a few manufacturers with the original technology, so there is little verification of actual gas turbine. In this paper, rotor dynamics analysis and verification of a 270 MW class DGT-300H gas turbine rotor newly developed by DHI. To verify the center tie-rod type rotor design of a large gas turbine for power generation, which was conceptually designed using in-house design tools, a 1/5 scaled model was designed by applying the dynamic scaling law. In order to verify the suitability of the applied tie-rod design, the characteristics of the variation of the natural frequency with the variation of the pre-tightening force were tested in order to confirm the dynamic proper pre-tightening force. The design of the scaled model rotor was created, the model was designed and fabricated, and the natural frequencies were analyzed and tested to confirm the validity of the design method and the suitability of the analysis results. After the design of the large gas turbine rotor for 270 MW class power generation, the natural frequencies of the rotor before the blade installation were analyzed and the suitability of the design was verified by implementing a vibration test of the rotor before blade installation.

Mechanism underlying dynamic scaling properties observed in the contour of spreading epithelial monolayer.

We found evidence of dynamic scaling in the spreading of Madin-Darby canine kidney (MDCK) cell monolayer, which can be characterized by the Hurst exponent α=0.86 and the growth exponent β=0.73, and theoretically and experimentally clarified the mechanism that governs the contour shape dynamics. Dynamic scaling refers to the roughness of the surface scales, both spatially and temporally. During the spreading of the monolayer, it is known that so-called leader cells generate the driving force and lead the other cells. Our time-lapse observations of cell behavior showed that these leader cells appeared at the early stage of the spreading and formed the monolayer protrusion. Informed by these observations, we developed a simple mathematical model that included differences in cell motility, cell-cell adhesion, and random cell movement. The model reproduced the quantitative characteristics obtained from the experiment, such as the spreading speed, the distribution of the increment, and the dynamic scaling law. Analysis of the model equation shows that the model can reproduce different scaling laws from (α=0.5,β=0.25) to (α=0.9,β=0.75), where the exponents α and β are determined by two dimensionless quantities determined by the microscopic cell behavior. From the analytical result, parameter estimation from the experimental results was achieved. The monolayer on the collagen-coated dishes showed a different scaling law, α=0.74,β=0.68, suggesting that cell motility increased ninefold. This result was consistent with the assay of the single-cell motility. Our study demonstrated that the dynamics of the contour of the monolayer were explained by the simple model, and we propose a mechanism that exhibits the dynamic scaling property.

Understanding the relationship between the local crystal structure and the ferrimagnetic ordering of CoxMn3-xO4 (x = 0–0.5) solid solutions

The local crystal structure alterations in the tetrahedral positions of the hausmannite Mn3O4 structure by Co2+ ions and its consequence on the magnetic ordering are studied in detail. The cation composition, bond distance and bond angle of the CoxMn3-xO4 series (x = 0.0. 0.1, 0.3 and 0.5) is determined by XRD Rietveld refinement. The charge state of the elements Co, Mn and O are investigated using XPS measurements, which confirm the bivalent cobalt ion occupation in the tetrahedral lattice. Considerable reduction in tetrahedral and axial octahedral bonds with the introduction of Co2+ ions dramatically increased the Curie temperature (TC) from 43 K (Mn3O4) to 62 K (Co0.5Mn2.5O4). The Lotgering-Srinivasan-Seehra model is employed to study the canted spin arrangement and the exchange interactions of Co0.5Mn2.5O4. The presence of cluster glass transition at TP = 42 K in Co0.3Mn2.7O4 is well-established through the AC susceptibility measurements and it is further substantiated by Vogel-Fulcher law and dynamic scaling power law. The origin of the cluster glass state is confirmed by the calculated strong geometric frustration factor (f = 19.5), due to the inhomogeneous distribution of cobalt ions in the intermediate concentrations. Field cooled isothermal magnetic measurements corroborated the exchange bias phenomenon in the Co0.3Mn2.7O4 sample, because of the interaction between ferrimagnetic-cluster glass phases occurring below the spin freezing temperature TP.

Control Verifications of Space Manipulators Using Ground Platforms

The article discusses dynamic requirements for designing ground manipulator platforms that can be utilized to verify the performance of controllers developed for space manipulators. Dimensional analysis is used to formalize the dynamic equivalence conditions and control scaling laws between a given space manipulator and the ground manipulator to be designed, such that the space manipulator and the designed ground manipulator are dynamically equivalent. Given that, unlike its space counterpart, the ground manipulator may not have the complete six degrees of freedom for its base and it must function under the gravity effects, as well as manufacturing imprecisions in building the ground manipulator, the sensitivity of dynamic equivalence conditions to the abovementioned factors is analyzed. Furthermore, an error compensation scheme based on the feedback linearization technique is developed to make the closed-loop ground manipulator have similar joint movements to those of the space manipulator under its controller. As a result, ground-based verification experiments can be performed for the controllers that will operate on the space manipulator. The design of a ground manipulator with the error compensation scheme for a specific space manipulator is illustrated through simulations, and it is shown how the performance of a PID controller for the space manipulator can be verified using the designed ground manipulator.

New scaling laws of passive scalar with a constant mean gradient in decaying isotropic turbulence

We use the Lie symmetry theory to derive new scaling laws for passive scalar dynamics under the influence of a constant mean gradient of the scalar in decaying homogeneous isotropic turbulence. For this purpose, we apply symmetry analysis to the equations for two-point correlation of the scalar and velocity fluctuations. It is shown that, in contrast to the classical self-similarity approach, the general invariant solutions, respectively scaling laws, of the two-point functions are constructed using the symmetry approach, without requiring an a priori set of similarity scales to carry on the analysis. In the context of the current analysis also, scaling laws for one-point quantities of the scalar variance , the transverse scalar flux and the variance of the turbulent velocity fluctuations are established, which are essentially related to the scaling symmetries. A key step to derive the scaling laws is the symmetry breaking induced by the constant mean scalar gradient. We use the results of a highly resolved direct numerical simulation of Gauding et al. (Comput. Fluids, vol. 180, 2019, pp. 206–217) to verify the scaling laws and the self-similarity of the two-point correlation functions. It is shown that the general symmetry solutions obtained from symmetry results provide a very good similarity to these functions.

Spin glass transition of single-crystalline TmFe2O4−δ

TmFe2O4 is one kind of multiferroic material in which equivalent amounts of Fe2+ and Fe3+ occupy a two-dimensional triangular lattice, leading to charge and spin frustrations. The spin frustration is expected to be increased as the fraction of Fe2+ (Fe3+) becomes larger than that of Fe3+ (Fe2+). We have grown single-crystalline TmFe2O4−δ with oxygen vacancies by using floating zone melting method and examined its magnetic properties. On cooling the compound, a long-range magnetic ordering develops around ∼240 K. With further cooling, a maximum of zero-field-cooled (ZFC) magnetization is observed at 186.2 K. The ac magnetic susceptibility obtained by ZFC process also manifests a maximum in its temperature dependence, and the variation of spin-freezing temperature with frequency of ac magnetic field is explainable in terms of the dynamic scaling law with the critical component of 8.68(8). This value suggests that the spin glass transition occurs at 186.2 K. The effect of external dc magnetic field on the irreversible transition temperature is coincident with the de Almeida–Thouless (AT) line. Aging-memory and rejuvenation effect is also observed below the spin-freezing temperature. These facts support the idea that TmFe2O4−δ undergoes spin glass transition below the ferrimagnetic transition temperature. In other words, TmFe2O4−δ can be regarded as a reentrance spin glass. It is thought that the oxygen vacancies bring about unequal number of Fe2+ and Fe3+ ions and thereby strengthen the magnetic frustration among the iron ions coupled with antiferromagnetic interactions, leading to the spin glass behavior.

Annihilation dynamics of reverse tilt domains in nematic liquid crystals

Reverse tilt domains are induced in a nematic liquid crystal confined in cells with near-zero pretilt angle homogeneous alignment. The domains emerge in the shape of “closed loops” and will annihilate over a time scale of seconds to minutes. The annihilation dynamics of single isolated domains as well as the coarsening dynamics of a number of domains are investigated in detail. The system maps onto the uniform Ising model and is characterized by a single length scale L(t). The dynamical scaling laws previously proposed for coarsening dynamics of topological defects in symmetry breaking phase transitions are verified also for the electric field induced reverse tilt domains while varying external parameters, including electric field amplitude, frequency, temperature and cell gap.

Scale-invariant topology and bursty branching of evolutionary trees emerge from niche construction

Phylogenetic trees describe both the evolutionary process and community diversity. Recent work has established that they exhibit scale-invariant topology, which quantifies the fact that their branching lies in between the two extreme cases of balanced binary trees and maximally unbalanced ones. In addition, the backbones of phylogenetic trees exhibit bursts of diversification on all timescales. Here, we present a simple, coarse-grained statistical model of niche construction coupled to speciation. Finite-size scaling analysis of the dynamics shows that the resultant phylogenetic tree topology is scale-invariant due to a singularity arising from large niche construction fluctuations that follow extinction events. The same model recapitulates the bursty pattern of diversification in time. These results show how dynamical scaling laws of phylogenetic trees on long timescales can reflect the indelible imprint of the interplay between ecological and evolutionary processes.

Cluster glass behavior of the frustrated birnessites AxMnO2·yH2O(A=Na,K)

We report on the synthesis and magnetic properties of frustrated Na0.22MnO2*0.39H2O and K0.6MnO2*0.48H2O with the birnessite structure. The structure, static and dynamic magnetic properties of the compounds are investigated in detail. A combination of DC and AC magnetic susceptibility measurements and magnetization decay measurements reveal cluster glass behavior below the freezing temperature of 4 K for Na-birnessite and 6 K for K-birnessite. The frequency dependence of the freezing temperature is analyzed on the basis of dynamic scaling laws including the critical slowing down formula and the Vogel-Fulcher law, which further confirm cluster glass formation in both compounds.

Dynamical scaling laws of out-of-time-ordered correlators

The out-of-time-ordered correlator (OTOC) is central to the understanding of information scrambling in quantum many-body systems. In this work, we show that the OTOC in a quantum many-body system close to its critical point obeys dynamical scaling laws which are specified by a few universal critical exponents of the quantum critical point. Such scaling laws of the OTOC imply a universal form for the butterfly velocity of a chaotic system in the quantum critical region and allow one to locate the quantum critical point and extract all universal critical exponents of the quantum phase transitions. We numerically confirm the universality of the butterfly velocity in a chaotic model, namely the transverse axial next-nearest-neighbor Ising model, and show the feasibility of extracting the critical properties of quantum phase transitions from OTOC using the Lipkin-Meshkov-Glick (LMG) model.

Determination method of scaling laws based on least square method and applied to rectangular thin plates and rotor-bearing systems

In this study, we investigate the dynamic scaling laws of geometrically similitude models and systems for predicting their vibration characteristics accurately. A determination method of scaling laws based on least square method for calculating weighted powers of scaling factors is proposed for the first time. Taking geometric parameters as input (design) parameters and vibration characteristics parameters as output parameters, the weighted powers of scaling factors are calculated by least squares similitude method (LSSM) with several design models, and then scaling factors of the output parameters are obtained by combining weighted powers and corresponding scaling factors. Applicability of the LSSM is verified in the following two cases with rectangular plate and rotor-bearing system that the stiffness of supports is taken into account. The vibration characteristics are calculated by using finite element method in MATLAB and compared with simulation analysis software ANSYS. As a result, stable weighted powers and good predictions are obtained for two cases.

High-pressure synthesis of A-site ordered perovskite CaMn3(Fe3Mn)O12 and sequential long-range antiferromagnetic ordering and spin glass transition

An AA’3B4O12-type perovskite oxide CaMn3(Fe3Mn)O12 was synthesized at 8 GPa and 1473 K. X-ray diffraction shows a cubic crystal structure with space group Im-3. The charge states are verified by soft x-ray absorption spectroscopy to be CaMn3+3(Fe3+3Mn4+)O12, where the Ca2+ and Mn3+ are 1:3 ordered respectively at A and A′ sites, while the Mn4+ and Fe3+ are disorderly distributed at B site. The spin interaction of A′-site Mn3+ ions causes a long-range antiferromagnetic phase transition at about 39 K. Subsequently, a spin glass transition is found to occur around 14 K due to the randomly distributed Fe3+ and Mn4+ at B site. Moreover, the spin glass behavior follows a dynamic scaling power law. The temperature dependent resistivity can be well fitted by a 3D Mott variable-range hopping model, indicating the insulating nature of CaMn3(Fe3Mn)O12 due to the strong electron correlation effects.

Martensitic ferromagnetism and spin glass behaviour in Ni47Mn36Cr4Sn13 ribbons

Ni47Mn36Cr4Sn13 ribbons were prepared by melt-spinning of the as synthesised bulk alloy. The room temperature structure of the ribbon is dominantly cubic L21 with small admixture of the martensitic orthorhombic phase. The dominance of odd superlattice peak (111) over (200) peak suggests noticeable presence of chemical disorder and hence antisite defects. The temperature dependent resistivity and magnetization measurements unravel the martensitic phase (MP) around ∼360 K in the high temperature austenite phase (AP), while the AP-MP transition occurs at 307 K during cooling and the reverse appears at 328 K in warming cycle. The low field magnetoresistance is rather small and exhibits nonlinear temperature dependence in the low field region. A robust re-entrant ferromagnetic transition whose magnetic moment is almost thrice that of the austenite phase occurs in the martensitic phase. At further lower temperatures, the ferromagnetic transition is succeeded by a re-entrant spin glass (RSG). The analysis of the frequency dispersion of the spin freezing temperature within the Vogel-Fulcher law yields a high value of activation energy (Ea ≈ 50.8 meV) and smaller time constant (τ = 3.28 × 10−12 s) as compared to usual SG behaviour generally observed in Heusler ribbons. However, alternative analysis in terms of the dynamic scaling law validates the canonical nature of the spin glass and hence appears to be better option for analysing the spin glass states associated with the re-entrant ferromagnetism.

Differences in the scaling laws of canonical and microcanonical coarsening dynamics for long-range interacting systems

We investigate the effects of Hamiltonian and Langevin microscopic dynamics on the growth laws of domains in coarsening. Using a one-dimensional class of generalized models with power-law decaying interactions, we show that the two dynamics exhibit scaling regimes characterized by different scaling laws for the coarsening dynamics. For Langevin dynamics, they concur with the exponents of defect dynamics, while Hamiltonian dynamics reveals new scaling laws with distinct early-time and late-time regimes. This new behaviour can be understood as an effect of energy conservation, which induces a coupling between the dynamics of the local temperature field and of the order parameter.

Disordered and Frustrated Magnetization in Coated MnFe<sub>2</sub>O<sub>4</sub> Nanoparticles Prepared by Microwave Plasma Synthesis

Disordered and frustrated magnetization of different surface coated (Cr2O3, Co3O4, ZrO2, and SiO2) MnFe2O4nanoparticles have been studied using SQUID-magnetometry. Magnetic measurements, such as ZFC/FC and ac-susceptibility evidence surface spin-glass behavior. ZFC/FC curves were also compared with numerical simulation to get information about effective anisotropy constants. Frequency dependent ac susceptibility results were analyzed by using Arrhenius, Vogel Fulcher and dynamic scaling laws to further confirm the spin-glass behavior. It is observed that the strength of surface spins disorder and frustration strongly depends upon the type of the coating material. All these analyses signify that disordered and frustrated surface magnetization in MnFe2O4nanoparticles greatly depend on the type of the surface coating materials and are useful for controlling the nanoparticle’s magnetism for different practical applications.

Prediction of vibration characteristics of blisks using similitude models

This study investigates the determination approach of distorted scaling laws for predicting the dynamic characteristic of an aero engine’s blisk. Based on the dynamic scaling laws of typical thin-walled structures, an assumption of geometrically complete scaling laws is firstly proposed and numerically validated. For distorted models of disk thickness, in order to simplify the design procedure, a simplification condition is proposed and applied to the first 10 orders’ distorted scaling laws (blade-dominated vibrations) by combining sensitivity analysis. Next, the 11th–14th orders’ distorted scaling laws are determined for disk-dominated vibrations. Numerical validation demonstrates that distorted scaling laws possess a good accuracy. Finally, the applicability of these new scaling laws is validated by the experimental data. The results indicate that, by using the new scaling laws, the simple models can predict vibration characteristics of blisk by employing similitude models.