scholarly journals A TLM Formulation Based on Fractional Derivatives for Dispersive Cole-Cole Media

2021 ◽  
Author(s):  
Mohammed Kanjaa ◽  
Otman El Mrabet ◽  
Mohsine Khalladi
Keyword(s):  
Dispersion Model ◽  
Time Discretization ◽  
Biological Tissues ◽  
Reflection Coefficients ◽  
Polarization Current ◽  
Linear Behavior ◽  
Transmission Line Method ◽  
Air Muscle ◽  
Definition Of ◽  
Fractional Derivation

An auxiliary differential equation (ADE) transmission line method (TLM) is proposed for broadband modeling of electromagnetic (EM) wave propagation in biological tissues with the Cole-Cole dispersion Model. The fractional derivative problem is surmounted by assuming a linear behavior of the polarization current when the time discretization is short enough. The polarization current density is approached using Lagrange extrapolation polynomial and the fractional derivation is obtained according to Riemann definition of a fractional α -order derivative. Reflection coefficients at an air/muscle and air/fat tissues interfaces simulated in a 1-D domain are found to be in good agreement with those obtained from the analytic model over a broad frequency range, demonstrating the validity of the proposed approach.

Optimal Charging Management of Microgrid-Integrated Electric Vehicles

2022 ◽  
pp. 133-155
Author(s):  
Giulio Ferro ◽  
Riccardo Minciardi ◽  
Luca Parodi ◽  
Michela Robba
Keyword(s):  
Electric Vehicles ◽  
Discrete Event ◽  
Time Discretization ◽  
Small Time ◽  
Storage Element ◽  
Charging Station ◽  
Decision Variables ◽  
Discretization Step ◽  
Definition Of ◽  
The Cost

The relevance of electric vehicles (EVs) is increasing along with the relative issues. The definition of smart policies for scheduling the EVs charging process represents one of the most important problems. A discrete-event approach is proposed for the optimal scheduling of EVs in microgrids. This choice is due to the necessity of limiting the number of the decision variables, which rapidly grows when a small-time discretization step is chosen. The considered optimization problem regards the charging of a series of vehicles in a microgrid characterized by renewable energy source, a storage element, the connection to the main grid, and a charging station. The objective function to be minimized results from the weighted sum of the cost for purchasing energy from the external grid, the weighted tardiness of the services provided, and a cost related to the occupancy of the socket. The approach is tested on a real case study.

scholarly journals AN ADE-TLM MODELING OF BIOLOGICAL TISSUES WITH COLE-COLE DISPERSION MODEL

2020 ◽  
Vol 89 ◽  
pp. 161-169
Author(s):  
Mohammed Kanjaa ◽  
Khalid Mounirh ◽  
Soufiane El Adraoui ◽  
Otman El Mrabet ◽  
Mohsine Khalladi
Keyword(s):  
Dispersion Model ◽  
Biological Tissues

scholarly journals A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues

2018 ◽  
Vol 15 (138) ◽  
pp. 20170766 ◽  
Author(s):  
Kewei Li ◽  
Ray W. Ogden ◽  
Gerhard A. Holzapfel
Keyword(s):  
Strain Energy ◽  
Dispersion Model ◽  
Substantial Reduction ◽  
Uniaxial Extension ◽  
Biological Tissues ◽  
Fibre Direction ◽  
Fibre Density ◽  
Integration Schemes ◽  
Simple Tension ◽  
Elementary Area

Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension–compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost.

Finite Element Analysis of the non Linear Behavior of a Multilayer Piezoelectric Actuator

2005 ◽  
Vol 881 ◽  
Author(s):  
M. Elhadrouz ◽  
T. Ben Zineb ◽  
E. Patoor
Keyword(s):  
Degrees Of Freedom ◽  
Constitutive Law ◽  
Element Analysis ◽  
Linear Behavior ◽  
Time Element ◽  
Non Linear ◽  
Multilayer Actuator ◽  
Element Type ◽  
Definition Of ◽  
The Right

AbstractA constitutive law for ferroelectric and ferroelastic piezoceramics is implemented in ABAQUS Standard using the subroutine user element. A linear solid element is defined: it is an eight-node hexahedron having the mechanical displacement components and the electric potential as degrees of freedom for each node. The element is formulated for static analysis and it needs the definition of the contribution of this element to the Jacobian (stiffness) and the definition of an array containing the contributions of this element to the right-hand-side vectors of the overall system of equations The subroutine is called for each element that is of a user-defined element type each time element calculations are required. As an example, the element is used for the simulation of a multilayer actuator made of piezoceramics. In this case, the piezoelectric equations are not valid since the electric loading induces non linear phenomena, which are captured through the constitutive law implemented in the user element.

A Micromechanical Model for Fibrous Biological Membranes at Finite Strain

2009 ◽  
Vol 3 ◽  
pp. 1-23 ◽  
Author(s):  
Mauro Borri-Brunetto ◽  
Bernardino Chiaia ◽  
Marco Deambrosi
Keyword(s):  
Mechanical Response ◽  
Micromechanical Model ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Two Dimensions ◽  
Arterial Walls ◽  
Proposed Model ◽  
Circular Holes ◽  
Definition Of ◽  
Validation Tests

The mechanical model of a number of biological tissues is a membrane, i.e., a sheetlike structure with small thickness, where deformation and stress can be described locally in two dimensions. Many bio-membranes, particularly if subjected to large mechanical loads, present a fibrous structure, with stiff fibers, sometimes with preferential orientations, embedded in a more compliant matrix. Among this tissues are, e.g., the arterial walls, the amniotic membrane, and the skin. The stiff fibers, typically made of collagen, are initially wrinkled and they follow the deformation of the embedding matrix without contributing to the mechanical response until they are fully distended. In this paper, the response of a fibrous membrane is described in the framework of hyperelasticity, with aim to the implementation in an existing finite element code. A micro-mechanical recruitment model, based on the statistical distribution of the activation stretch of the collagen fibers is introduced, leading to the definition of a simple form of the strain-energy function, depending on physically well-defined parameters. After some validation tests performed in homogeneous strain conditions, an application to the study of the stress field around circular holes in large deformation is presented, showing the capabilities of the proposed model.

scholarly journals INFLUENCE OF MODELLING CHOICES ON THE RESULTS OF LANDFILL ODOUR DISPERSION

Detritus ◽  
2020 ◽  
pp. 92-99
Author(s):  
Francesca Tagliaferri ◽  
Marzio Invernizzi ◽  
Selena Sironi ◽  
Laura Capelli
Keyword(s):  
Source Term ◽  
Dispersion Model ◽  
Dispersion Modelling ◽  
Dispersion Models ◽  
Large Area ◽  
Chemical Mechanisms ◽  
Modelling Studies ◽  
Odour Dispersion ◽  
Definition Of ◽  
Dynamic Olfactometry

Landfills are an important source of odour pollution, potentially causing nuisance to adjacent populations. The most commonly used odour impact assessment for this type of plants usually involves a combination of dynamic olfactometry with dispersion modelling. Despite the advantages associated with the use of dispersion models, there are still some important issues related to their uncertainty. The dispersion model requires the Odour Emission Rate (OER) as input, expressed as units of odour emitted per unit time. Source term characterization and the estimation of the OER are typically the most important steps in the model’s implementation, accounting for the highest contribution to the overall uncertainty. Another important element of uncertainty when modelling emissions from landfill surfaces is the geometrical implementation of the emission source in the dispersion model. This entails the definition of the initial dimensions of the emission, which is critical in the case of large area sources. This paper discusses issues related to uncertainty in the use of dispersion models for the evaluation of landfill odour impacts, particularly focusing on the estimation of the OER and the emission’s initial vertical dimension. This study shows that modelling choices may lead to a variance in the resulting modelled odour concentrations at receptors differing by up to a factor 3. This variability should not cause distrust in the method, but rather indicates the importance of having odour dispersion modelling studies carried out by experts with deep knowledge of the physical-chemical mechanisms underlying atmospheric emissions.

Time delay in quantum coherence and tunneling

1990 ◽  
Vol 68 (12) ◽  
pp. 1382-1388 ◽  
Author(s):  
M. Razavy ◽  
Ashok Pimpale
Keyword(s):  
Time Delay ◽  
Quantum Coherence ◽  
One Dimension ◽  
Reflection Coefficients ◽  
Classical Concept ◽  
Problem Of Time ◽  
Transmission And Reflection Coefficients ◽  
Definition Of ◽  
Derivatives Of ◽  
Transmission And Reflection

The problem of time delay in quantum mechanics and its relation to the classical concept of traversal time is studied. For a monochromatic wave, in one dimension, it is shown that the time delay is proportional to a linear combination of the derivatives of the phases of the transmission and reflection coefficients with respect to the frequency. In particular it is shown that the definition of time delay for quantum coherence given in terms of the periods of oscillations of a wave packet between the two wells, in the proper limit, agrees with the corresponding definition in tunneling.

scholarly journals An exponential constitutive model excluding fibres under compression: Application to extension–inflation of a residually stressed carotid artery

2017 ◽  
Vol 23 (8) ◽  
pp. 1206-1224 ◽  
Author(s):  
Kewei Li ◽  
Ray W Ogden ◽  
Gerhard A Holzapfel
Keyword(s):  
Finite Element ◽  
Carotid Artery ◽  
Constitutive Model ◽  
Dispersion Model ◽  
Three Dimensional ◽  
Uniaxial Extension ◽  
Collagen Fibre ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Finite Element Program

Detailed information on the three-dimensional dispersion of collagen fibres within layers of healthy and diseased soft biological tissues has been reported recently. Previously we have proposed a constitutive model for soft fibrous solids based on the angular integration approach which allows the exclusion of any compressed collagen fibre within the dispersion. In addition, a computational implementation of that model in a general purpose finite element program has been investigated and verified with the standard fibre-reinforcing model for fibre contributions. In this study, we develop the proposed fibre dispersion model further using an exponential form of the strain-energy function for the fibre contributions. The finite element implementation of this model with a rotationally symmetrical dispersion of fibres is also presented. This includes explicit expressions for the stress and elasticity tensors. The performance and implementation of the new model are demonstrated by means of a uniaxial extension test, a simple shear test, and an extension–inflation simulation of a residually stressed carotid artery segment. In each example we have obtained good agreement between the finite element solution and the analytical or experimental results.

Optimal Constitutive Parameters and Subject Specific Variability: An Application to the Aortic Sinuses

2013 ◽  
Author(s):  
Vittoria Flamini ◽  
Boyce E. Griffith
Keyword(s):  
Constitutive Models ◽  
Biological Tissues ◽  
Mechanical Tests ◽  
Tissue Samples ◽  
Subject Specific ◽  
Mechanical Models ◽  
Outlier Tests ◽  
Definition Of ◽  
Computational Analyses ◽  
Constitutive Parameters

Advanced analyses of soft biological tissues have shown substantial subject-specific variability in mechanical properties [1]. Such variability is also easily observed at a geometrical or morphological level, and has been reported also in mechanical tests on biological tissue samples [1, 2]. While there is wide interest in reproducing accurate geometries for subject-specific modeling, constitutive parameters for mechanical models often use averaged data from mechanical tests [3]. Outliers are typically neglected, and only the ‘mean’ tissue behavior is considered. However, due to an increased interest in using multi-scale and finite element (FE) models for medical device testing and surgical planning [4], understanding of the variability of the outlier tests becomes increasingly important. In particular, by using detailed mechanistic constitutive models, it might be possible to classify the different mechanical behaviors observed on the basis of the changes in the constitutive parameters. This process could lead to the definition of a library of different ‘healthy’ or ‘diseased’ constitutive parameters to be used in computational analyses.

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