scholarly journals Dynamics of a Polymer Network Modeled by a Fractal Cactus

Polymers ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 787 ◽  
Author(s):  
Aurel Jurjiu ◽  
Mircea Galiceanu
Keyword(s):  
Power Law ◽  
Hydrodynamic Interaction ◽  
Strong Dependence ◽  
Polymer Network ◽  
Real Space ◽  
Hydrodynamic Interactions ◽  
Connectivity Matrix ◽  
Relaxation Dynamics ◽  
Intermediate Domain ◽  
Fractal Network

In this paper, we focus on the relaxation dynamics of a polymer network modeled by a fractal cactus. We perform our study in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. By performing real-space renormalization transformations, we determine analytically the whole eigenvalue spectrum of the connectivity matrix, thereby rendering possible the analysis of the Rouse-dynamics at very large generations of the structure. The evaluation of the structural and dynamical properties of the fractal network in the Rouse type-approach reveals that they obey scaling and the dynamics is governed by the value of spectral dimension. In the Zimm-type approach, the relaxation quantities show a strong dependence on the strength of the hydrodynamic interaction. For low and medium hydrodynamic interactions, the relaxation quantities do not obey power law behavior, while for slightly larger interactions they do. Under strong hydrodynamic interactions, the storage modulus does not follow power law behavior and the average displacement of the monomer is very low. Remarkably, the theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results from the literature.

Relaxation Dynamics of Non-Power-Law Fluids

2013 ◽  
Vol 34 (12) ◽  
pp. 2276-2285 ◽  
Author(s):  
Qi Min ◽  
Yuan-Yuan Duan ◽  
Xiao-Dong Wang ◽  
Zhan-Peng Liang ◽  
Duu-Jong Lee
Keyword(s):  
Power Law ◽  
Relaxation Dynamics ◽  
Power Law Fluids

scholarly journals MULTIFRACTALITY IN THE GENERALIZED AUBRY–ANDRÉ QUASIPERIODIC LOCALIZATION MODEL WITH POWER-LAW HOPPINGS OR POWER-LAW FOURIER COEFFICIENTS

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950007 ◽  
Author(s):  
CÉCILE MONTHUS
Keyword(s):  
Power Law ◽  
Fourier Coefficients ◽  
Nearest Neighbor ◽  
Real Space ◽  
Equivalent Model ◽  
Translation Invariant ◽  
Fourier Basis ◽  
Quasiperiodic Potential ◽  
Linear Spectrum ◽  
Localization Model

The nearest-neighbor Aubry–André quasiperiodic localization model is generalized to include power-law translation-invariant hoppings [Formula: see text] or power-law Fourier coefficients [Formula: see text] in the quasiperiodic potential. The Aubry–André duality between [Formula: see text] and [Formula: see text] manifests when the Hamiltonian is written in the real-space basis and in the Fourier basis on a finite ring. The perturbative analysis in the amplitude [Formula: see text] of the hoppings yields that the eigenstates remain power-law localized in real space for [Formula: see text] and are critical for [Formula: see text] where they follow the strong multifractality linear spectrum, as in the equivalent model with random disorder. The perturbative analysis in the amplitude [Formula: see text] of the quasiperiodic potential yields that the eigenstates remain delocalized in real space (power-law localized in Fourier space) for [Formula: see text] and are critical for [Formula: see text] where they follow the weak multifractality Gaussian spectrum in real space (or strong multifractality linear spectrum in the Fourier basis). This critical case [Formula: see text] for the Fourier coefficients [Formula: see text] corresponds to a periodic function with discontinuities, instead of the cosinus function of the standard self-dual Aubry–André model.

A volume integral approach for the modelling and design of HTS coils

2019 ◽  
Vol 38 (4) ◽  
pp. 1133-1140 ◽  
Author(s):  
Yazid Statra ◽  
Hocine Menana ◽  
Lamia Belguerras ◽  
Bruno Douine
Keyword(s):  
Power Law ◽  
Strong Dependence ◽  
Superconducting Devices ◽  
Electromagnetic Properties ◽  
Integral Approach ◽  
Volume Integral ◽  
Content Type ◽  
High Level ◽  
Modelling Approach

Purpose The purpose of this paper is to develop a rapid and realistic modelling approach for the design and characterization of high temperature superconducting (HTS) coils and windings carrying DC currents. Indeed, the strong dependence of the electromagnetic properties of such materials on the magnetic field makes the design and characterization of HTS systems a delicate operation where local quantities have to be evaluated. Design/methodology/approach A volume integral modelling approach has been developed taking into account the electric nonlinearity of the HTS material which is represented by power law. The variations of the characteristic quantities of the HTS (critical current density and power law exponent) with the magnetic flux density are also taken into account by using Kim’s law. The volume integral modelling allows to model only the active parts of the system and thus to overcome the difficulties linked to the multiscale dimensions. Findings The model has been tested in a case study in which simulation results were compared to measurements and to finite element analysis. A good agreement was found which validates the model as a rapid and efficient tool for HTS coils and windings design and modelling. Practical implications HTS coils are important elements of emerging superconducting devices which require a high level of reliability, such as generators or motors. The proposed approach is interesting to speed up the design and optimization procedures of such systems. Originality/value Advanced structures of the basic elements have been used in the volume integral modelling, which results in a considerable gain in computation time and in memory-space saving while keeping a high level of precision and realism of the modelling, which has been verified experimentally.

A cluster approach to the structure of imperfect materials and their relaxation spectroscopy

1983 ◽  
Vol 390 (1798) ◽  
pp. 131-180 ◽  
Keyword(s):  
Steady State ◽  
Power Law ◽  
Structural Organization ◽  
Configurational Entropy ◽  
Binding Energies ◽  
Coarse Grained ◽  
Dielectric Relaxation Spectroscopy ◽  
Relaxation Dynamics ◽  
Steady State Distribution ◽  
State Distribution

A new theory is proposed for the explanation of observed relaxation phenomena, which differs significantly from theories suggested by the authors before. The theory is based on a model of structural organization of macroscopically sized samples of imperfectly structured materials, both solids and liquids, and is intermediate in character. In terms of the model, a microscopic structure is maintained over a cluster containing a number of microscopic units, with an array of clusters described by a steady-state distribution completing the macroscopic picture. The structural regularity of each level of morphological organization is precisely defined by a coarse-grained index, which is given a thermodynamic interpretation in terms of binding energies and configurational entropy. The limiting cases of an ideal liquid and a perfect crystal are recovered as asymptotic extremes in terms of this definition. The consequences of this model for the relaxation dynamics of the structure are examined and it is shown that prepared fluctuations decay in a time-power law manner as coupled zero-point motions evolve either within clusters or between clusters, with a power determined by the relevant regularity index. As a result, the origin of power law noise in materials is explained in terms of configurational entropy, and its relation with gaussian and white noise, which appear as asymptotic limits, outlined. The shape of the steady-state distribution of the array of clusters is also determined without any a priori assumptions, and it is shown to range from an unbounded form to a δ function as the regularity of the array superstructure increases. Experimental examples of dielectric relaxation spectroscopy have been used to illustrate these structural concepts and outline the way in which this technique can be used to deduce the structural organization of the sample. Finally, a short description is given of some commonly observed forms of response and their structural interpretation.

Threshold speed for two-dimensional confinement of charged particles in certain axisymmetric magnetic fields

2018 ◽  
Vol 96 (5) ◽  
pp. 519-523 ◽  
Author(s):  
K. Kabin ◽  
G. Kalugin ◽  
E. Spanswick ◽  
E. Donovan
Keyword(s):  
Magnetic Field ◽  
Power Law ◽  
Critical Speed ◽  
Longitudinal Magnetic Field ◽  
Strong Dependence ◽  
Charged Particles ◽  
Transcendental Equation ◽  
Power Exponent ◽  
Magnetic Field Magnitude ◽  
The Magnetic Field

In this paper we discuss conditions under which charged particles are confined by an axisymmetric longitudinal magnetic field with power law dependence on the radius. We derive a transcendental equation for the critical speed corresponding to the threshold between bounded and unbounded trajectories of the particles. This threshold speed shows strong dependence on the direction, and this dependence becomes more prominent as the exponent of the power law increases. The equation for threshold speed can be solved exactly for several specific values of the power exponent, but in general it requires a numerical treatment. Remarkably, if the magnetic field magnitude decreases more slowly than the inverse of the radius, charged particles remain confined no matter how large their energies may be.

Effects of Temperature-Dependent Viscosity Variations and Boundary Conditions on Fully Developed Laminar Forced Convection in a Semicircular Duct

1998 ◽  
Vol 120 (3) ◽  
pp. 600-605 ◽  
Author(s):  
T. M. Harms ◽  
M. A. Jog ◽  
R. M. Manglik
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Numerical Solutions ◽  
Strong Dependence ◽  
Laminar Flows ◽  
Temperature Fields ◽  
Traditional Values ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

Fully developed laminar flows in a semicircular duct with temperature-dependent viscosity variations in the flow cross section are analyzed, where the viscosity-temperature behavior is described by the Arrhenius model. Both the T and H1 boundary conditions are considered, as they represent the most fundamental heating/cooling conditions encountered in practical compact heat exchanger applications. Numerical solutions for the flow velocity and the temperature fields have been obtained by finite difference technique. The friction factor and Nusselt number results display a strong dependence on the viscosity ratio (μw/μb), and this is correlated using the classical power-law relationship. However, results indicate that the power-law exponents are significantly different from traditional values for circular tube. They are found to be functions of the flow geometry, boundary condition, and direction of heat transfer (heating or cooling).

scholarly journals Financial Diversity and the Development Process: Case study of Rural Communes of Eastern Poland in 2009–2018

2020 ◽  
Vol 12 (16) ◽  
pp. 6446
Author(s):  
Paweł Dziekański ◽  
Piotr Prus
Keyword(s):  
Strong Dependence ◽  
Secondary Data ◽  
Data Bank ◽  
Real Space ◽  
The State ◽  
Local Economy ◽  
Local Data ◽  
State Budget ◽  
Financial Situation ◽  
The Impact

In the modern state, the role and importance of communes is growing. They can carry out their tasks when equipped with stable and efficient sources of income. Financial resources are the basis for the operation and implementation of current and development tasks. Their analysis makes it possible to assess the budget structure and provides information on the state of the local economy or endogenous growth potentials. The aim of the article is to assess the diversity of the financial situation of rural communes using a synthetic measure. In addition, using the econometric models, the impact of socio-economic factors on the diversity of the measure of synthetic financial situation was examined. In order to build synthetic measures, the Technique for Order Preference by Similarity to an Ideal Solution method and based on distance in real space with Euclidean metrics were used. The aggregated value of the synthetic variable facilitates the comparison of objects in multidimensional spaces, but also makes it possible to order them due to the examined phenomenon. Empirical data were collected in spatial terms of 484 rural communes in the Eastern Poland region. In the case of municipalities, the choice of variables was largely determined by the availability of secondary data collected in a municipal system at the Local Data Bank of the Central Statistical Office for 2009–2018. The analysis showed that the rural communes of eastern Poland are characterized by significant disproportions in terms of financial standing. Rural communes with the best financial condition were characterized by a higher share of own revenues in total revenues, a higher level of income from local taxes and obtained from the share in the tax on natural and legal persons. It seems that the main reason for the relatively small impact of financial conditions on economic and social development is their strong dependence on transfer revenues transferred from the state budget and the amount of current expenditure. The above circumstances stiffen and stabilize the financial economy, making it relatively less susceptible to the influence of other factors. The obtained results may constitute for the local authorities an important source of information on the disproportions occurring between units on setting out potential directions for optimizing the structure of local finances.

scholarly journals Meta-ecosystem dynamics and functioning on finite spatial networks

2014 ◽  
Vol 281 (1777) ◽  
pp. 20132094 ◽  
Author(s):  
Justin N. Marleau ◽  
Frédéric Guichard ◽  
Michel Loreau
Keyword(s):  
Spatial Structure ◽  
Strong Dependence ◽  
Spatial Models ◽  
Finite Size ◽  
Ecosystem Dynamics ◽  
Ecosystem Functions ◽  
Connectivity Matrix ◽  
Ecological Concepts ◽  
Local Ecosystem ◽  
Spatial Flows

The addition of spatial structure to ecological concepts and theories has spurred integration between sub-disciplines within ecology, including community and ecosystem ecology. However, the complexity of spatial models limits their implementation to idealized, regular landscapes. We present a model meta-ecosystem with finite and irregular spatial structure consisting of local nutrient–autotrophs–herbivores ecosystems connected through spatial flows of materials and organisms. We study the effect of spatial flows on stability and ecosystem functions, and provide simple metrics of connectivity that can predict these effects. Our results show that high rates of nutrient and herbivore movement can destabilize local ecosystem dynamics, leading to spatially heterogeneous equilibria or oscillations across the meta-ecosystem, with generally increased meta-ecosystem primary and secondary production. However, the onset and the spatial scale of these emergent dynamics depend heavily on the spatial structure of the meta-ecosystem and on the relative movement rate of the autotrophs. We show how this strong dependence on finite spatial structure eludes commonly used metrics of connectivity, but can be predicted by the eigenvalues and eigenvectors of the connectivity matrix that describe the spatial structure and scale. Our study indicates the need to consider finite-size ecosystems in meta-ecosystem theory.

Power law relaxation in an interpenetrating polymer network

1989 ◽  
Vol 267 (11) ◽  
pp. 1002-1006 ◽  
Author(s):  
Suresh Mani ◽  
H. H. Winter ◽  
M. Silverstein ◽  
M. Narkis
Keyword(s):  
Power Law ◽  
Polymer Network ◽  
Interpenetrating Polymer Network

Dynamics and Transport of Molecules in Polymer and Colloidal-Rod Networks

2007 ◽  
Vol 1060 ◽  
Author(s):  
Kyongok Kang
Keyword(s):  
Electric Field ◽  
Electrostatic Interactions ◽  
Polymer Network ◽  
Mesh Size ◽  
Limited Range ◽  
Correlation Spectroscopy ◽  
Relaxation Dynamics ◽  
Screening Length ◽  
Cholesteric Phase ◽  
Hydrodynamic Screening

ABSTRACTRe-orientational dynamics of liquid crystal molecules in a polymer network subjected to an electric field is studied by means of light diffraction [1]. When the optical pitch of the electric-field induced cholesteric phase is small compared to the optical wavelength of light, dynamic light scattering (DLS) can be performed to extract the relaxation dynamics of the chiral nematic molecules in the presence of the polymer network. Intriguingly, the reactive mesogenic type of polymer network exhibits a confinement effect, which can be probed within the limited range of scattering angles that comply with the structural correlation length in the system [2].Diffusive mass transport of molecules through a rod network can be studied via fluorescence correlation spectroscopy (FCS) and DLS. Long time self-diffusion of tracer spheres (silica and proteins) in isotropic and nematic colloidal-rod networks (fd-viruses) is systematically studied for various tracer-sphere sizes as compared to the mesh size of the network [3]. In addition, by varying the salt concentration, the relative contribution of electrostatic interactions can be varied. A theory is developed where the diffusion coefficient is expressed in terms of the hydrodynamic screening length of the highly entangled rod-network. The hydrodynamic screening length of rod networks is extracted from diffusion data as a function of the rod concentration both for isotropic and nematic networks [4-5].

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