Fractional-order viscoelastic model of musculoskeletal tissues: correlation with fractals

2021 ◽  
Vol 477 (2249) ◽  
pp. 20200990
Author(s):  
Jianqiao Guo ◽  
Yajun Yin ◽  
Gang Peng
Keyword(s):  
Fractional Order ◽  
Cross Sections ◽  
Viscoelastic Model ◽  
Temporal Correlation ◽  
Human Cartilage ◽  
Functional Changes ◽  
Viscoelastic Models ◽  
Musculoskeletal Tissues ◽  
Relaxation Experiments ◽  
Spatio Temporal

Self-similar fractals are widely obtained from biomaterials within the human musculoskeletal system, and their viscoelastic behaviours can be described by fractional-order derivatives. However, existing viscoelastic models neglect the internal correlation between the fractal structure of biomaterials and their fractional-order temporal responses. We further expanded the fractal hyper-cell (FHC) viscoelasticity theory to investigate this spatio-temporal correlation. The FHC element was first compared with other material elements and spring–dashpot viscoelastic models, thereby highlighting its discrete and fractal nature. To demonstrate the utility of an FHC, tree-like, ladder-like and triangle-like FHCs were abstracted from human cartilage, tendons and muscle cross-sections, respectively. The duality and symmetry of the FHC element were further discussed, where operating the duality transformation generated new types of FHC elements, and the symmetry breaking of an FHC altered its fractional-order viscoelastic responses. Thus, the correlations between the staggering patterns of FHCs and their rheological power-law orders were established, and the viscoelastic behaviour of the multi-level FHC elements fitted well in stress relaxation experiments at both the macro- and nano-levels of the tendon hierarchy. The FHC element provides a theoretical basis for understanding the connections between structural degeneration of bio-tissues during ageing or disease and their functional changes.

A Comparison Between Fractional-Order and Integer-Order Differential Finite Deformation Viscoelastic Models: Effects of Filler Content and Loading Rate on Material Parameters

2018 ◽  
Vol 10 (09) ◽  
pp. 1850099 ◽  
Author(s):  
Hesam Khajehsaeid
Keyword(s):  
Fractional Order ◽  
Differential Operators ◽  
Filler Content ◽  
Viscoelastic Model ◽  
Constitutive Models ◽  
Viscoelastic Behavior ◽  
Fractional Model ◽  
Material Parameters ◽  
Integer Order ◽  
Viscoelastic Models

Elastomers or rubber-like materials exhibit nonlinear viscoelastic behavior such as creep and relaxation upon mechanical loading. Differential constitutive models and hereditary integrals are the main frameworks followed in the literature for modeling the viscoelastic behavior at finite deformations. Regular differential operators can be replaced by fractional-order derivatives in the standard models in order to make fractional viscoelastic models. In the present paper, the relaxation behavior of elastomers is formulated both in terms of ordinary (integer-order) and fractional differential viscoelastic models. The derived constitutive equations are fitted to several experimental data to compare their efficiency in modeling the stress relaxation phenomenon. Specifically, a fractional viscoelastic model with one fractional dashpot (FD) is compared with two ordinary models including respectively one and two ordinary dashpots (OD). The models are compared in fitting accuracy, number of required material parameters and also variation of parameters from one compound to another to clarify the effects of filler content and deformation rate. It is shown that, the results of the ordinary model with one OD is not good at all. The fractional model with one FD and the ordinary model with two ODs provide good fittings for all compounds whereas the former uses only three parameters and the latter uses five material parameters. For the fractional model, the order of the Maxwell element and the associated relaxation time approximately remain the same for different compounds of each material at certain loading rates, but it is not the case for the ordinary differential models.

Learning spatio-temporal correlation filter for visual tracking

2021 ◽  
Vol 436 ◽  
pp. 273-282
Author(s):  
Youmin Yan ◽  
Xixian Guo ◽  
Jin Tang ◽  
Chenglong Li ◽  
Xin Wang
Keyword(s):  
Visual Tracking ◽  
Temporal Correlation ◽  
Correlation Filter ◽  
Spatio Temporal

scholarly journals A Spatio-Temporal Local Association Query Algorithm for Multi-Source Remote Sensing Big Data

2021 ◽  
Vol 13 (12) ◽  
pp. 2333
Author(s):  
Lilu Zhu ◽  
Xiaolu Su ◽  
Yanfeng Hu ◽  
Xianqing Tai ◽  
Kun Fu
Keyword(s):  
Remote Sensing ◽  
Remote Sensing Data ◽  
Temporal Correlation ◽  
Local Association ◽  
Sensing Data ◽  
Multi Scale ◽  
Correlation Networks ◽  
Efficient Integration ◽  
Spatio Temporal ◽  
Query Algorithm

It is extremely important to extract valuable information and achieve efficient integration of remote sensing data. The multi-source and heterogeneous nature of remote sensing data leads to the increasing complexity of these relationships, and means that the processing mode based on data ontology cannot meet requirements any more. On the other hand, the multi-dimensional features of remote sensing data bring more difficulties in data query and analysis, especially for datasets with a lot of noise. Therefore, data quality has become the bottleneck of data value discovery, and a single batch query is not enough to support the optimal combination of global data resources. In this paper, we propose a spatio-temporal local association query algorithm for remote sensing data (STLAQ). Firstly, we design a spatio-temporal data model and a bottom-up spatio-temporal correlation network. Then, we use the method of partition-based clustering and the method of spectral clustering to measure the correlation between spatio-temporal correlation networks. Finally, we construct a spatio-temporal index to provide joint query capabilities. We carry out local association query efficiency experiments to verify the feasibility of STLAQ on multi-scale datasets. The results show that the STLAQ weakens the barriers between remote sensing data, and improves their application value effectively.

Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Uniaxial Compression ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Compression Data ◽  
Computationally Intensive ◽  
Nonlinear Viscoelastic Model ◽  
Flexible Polyurethane

Flexible polyethylene foam is used in many engineering applications. It exhibits nonlinear and viscoelastic behavior which makes it difficult to model. To date, several models have been developed to characterize the complex behavior of foams. These attempts include the computationally intensive microstructural models to continuum models that capture the macroscale behavior of the foam materials. In this research, a nonlinear viscoelastic model, which is an extension to previously developed models, is proposed and its ability to capture foam response in uniaxial compression is investigated. It is hypothesized that total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher-order polynomial, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at six different rates. The estimated model parameters for individual tests were used to develop a model with parameters that are a function of strain rates. The parameter estimation technique was modified to also develop a comprehensive model which captures the uniaxial behavior of all six tests. The performance of this model was compared to that of other nonlinear viscoelastic models.

Technology Research on the Fault Diagnosis of Wireless Sensor Network System

2013 ◽  
Vol 846-847 ◽  
pp. 442-445
Author(s):  
Chun Lin He
Keyword(s):  
Fault Diagnosis ◽  
Sensor Network ◽  
Simulation Experiment ◽  
Temporal Correlation ◽  
Sensor Nodes ◽  
Wireless Sensor ◽  
Network System ◽  
Technology Research ◽  
Spatio Temporal ◽  
Network Fault

The fault diagnosis technology have emerged and developed rapidly with the development of wireless sensor networks and requirements of applications improve. This paper describes two commonly used sensor network fault modeling. What is more, in order to solve this problem that sensor nodes are vulnerable and therefore produce wrong data, the paper proposes a distributed fault detecting algorithm based on spatio-temporal correlation among data of adjacent nodes. The simulation experiment shows that the algorithm can efficiently detect errors in the network and very few errors are introduced.

Invariant solutions of fractional-order spatio-temporal partial differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nkosingiphile Mnguni ◽  
Sameerah Jamal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Growth Models ◽  
Spatial Patterning ◽  
Partial Differential ◽  
Symmetry Approach ◽  
Time Component ◽  
Spatio Temporal ◽  
Lie Symmetry Approach

Abstract This paper considers two categories of fractional-order population growth models, where a time component is defined by Riemann–Liouville derivatives. These models are studied under the Lie symmetry approach, and we reduce the fractional partial differential equations to nonlinear ordinary differential equations. Subsequently, solutions of the latter are determined numerically or with the aid of Laplace transforms. Graphical representations for integral and trigonometric solutions are presented. A key feature of these models is the connection between spatial patterning of organisms versus competitive coexistence.

scholarly journals Energy Production Benefits by Wind and Wave Energies for the Autonomous System of Crete

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2741 ◽  
Author(s):  
George Lavidas ◽  
Vengatesan Venugopal
Keyword(s):  
Wind Turbine ◽  
Wave Energy ◽  
Energy Production ◽  
Large Scale ◽  
Capital Expenditure ◽  
Temporal Correlation ◽  
Clean Energy ◽  
Limiting Factor ◽  
Spatio Temporal ◽  
Visual Impacts

At autonomous electricity grids Renewable Energy (RE) contributes significantly to energy production. Offshore resources benefit from higher energy density, smaller visual impacts, and higher availability levels. Offshore locations at the West of Crete obtain wind availability ≈80%, combining this with the installation potential for large scale modern wind turbines (rated power) then expected annual benefits are immense. Temporal variability of production is a limiting factor for wider adaptation of large offshore farms. To this end multi-generation with wave energy can alleviate issues of non-generation for wind. Spatio-temporal correlation of wind and wave energy production exhibit that wind and wave hybrid stations can contribute significant amounts of clean energy, while at the same time reducing spatial constrains and public acceptance issues. Offshore technologies can be combined as co-located or not, altering contribution profiles of wave energy to non-operating wind turbine production. In this study a co-located option contributes up to 626 h per annum, while a non co-located solution is found to complement over 4000 h of a non-operative wind turbine. Findings indicate the opportunities associated not only in terms of capital expenditure reduction, but also in the ever important issue of renewable variability and grid stability.

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