scholarly journals A hierarchical cellular structural model to unravel the universal power-law rheological behavior of living cells

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jiu-Tao Hang ◽  
Yu Kang ◽  
Guang-Kui Xu ◽  
Huajian Gao
Keyword(s):  
Power Law ◽  
Rheological Behavior ◽  
Structural Model ◽  
Complex Modulus ◽  
Structural Characteristics ◽  
Living Cells ◽  
Mechanical Responses ◽  
Universal Power Law ◽  
Power Law Exponent ◽  
Self Similar

AbstractLiving cells are a complex soft material with fascinating mechanical properties. A striking feature is that, regardless of their types or states, cells exhibit a universal power-law rheological behavior which to this date still has not been captured by a single theoretical model. Here, we propose a cellular structural model that accounts for the essential mechanical responses of cell membrane, cytoplasm and cytoskeleton. We demonstrate that this model can naturally reproduce the universal power-law characteristics of cell rheology, as well as how its power-law exponent is related to cellular stiffness. More importantly, the power-law exponent can be quantitatively tuned in the range of 0.1 ~ 0.5, as found in most types of cells, by varying the stiffness or architecture of the cytoskeleton. Based on the structural characteristics, we further develop a self-similar hierarchical model that can spontaneously capture the power-law characteristics of creep compliance over time and complex modulus over frequency. The present model suggests that mechanical responses of cells may depend primarily on their generic architectural mechanism, rather than specific molecular properties.

Dynamic Mechanical Properties of Agarose Gels Modeled by a Fractional Derivative Model

2004 ◽  
Vol 126 (5) ◽  
pp. 666-671 ◽  
Author(s):  
Qingshan Chen ◽  
Bela Suki ◽  
Kai-Nan An
Keyword(s):  
Fractional Derivative ◽  
Power Law ◽  
Complex Modulus ◽  
Dynamic Mechanical Properties ◽  
Model Parameters ◽  
Culture Studies ◽  
Agarose Gels ◽  
Dynamic Mechanical ◽  
Fractional Derivative Model ◽  
Power Law Exponent

The complex modulus E* and elastic modulus E′ of agarose gels (2% to 4%) are measured with a dynamic mechanical analyzer in frequency sweep shear sandwich mode between 0.1 and 20 Hz. The data showed that E* and E′ increase with frequency according to a power law which can be described by a fractional derivative model to characterize the dynamic viscoelasticity of the gel. The functions between the model parameters including storage modulus coefficient H and the power law exponent (β) and the agarose concentration are established. A molecular basis for the application of the fractional derivative model to gel polymers is also discussed. Such an approach can be useful in tissue culture studies employing dynamic pressurization or for validation of magnetic resonance elastography.

THE SCALE-FREE AND SMALL-WORLD PROPERTIES OF COMPLEX NETWORKS ON SIERPINSKI-TYPE HEXAGON

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050054
Author(s):  
KUN CHENG ◽  
DIRONG CHEN ◽  
YUMEI XUE ◽  
QIAN ZHANG
Keyword(s):  
Power Law ◽  
Path Length ◽  
Small World ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Scale Free ◽  
Power Law Exponent ◽  
Self Similar ◽  
Encoding Method

In this paper, a network is generated from a Sierpinski-type hexagon by applying the encoding method in fractal. The criterion of neighbor is established to quantify the relationships among the nodes in the network. Based on the self-similar structures, we verify the scale-free and small-world effects. The power-law exponent on degree distribution is derived to be [Formula: see text] and the average clustering coefficients are shown to be larger than [Formula: see text]. Moreover, we give the bounds of the average path length of our proposed network from the renewal theorem and self-similarity.

Effect of H2SO4 Treated TiO2 Nano Fillers on the AC Conductivity of Hexanoyl Chitosan-Polystyrene-LiCF3SO3 Polymer Electrolytes

2013 ◽  
Vol 832 ◽  
pp. 228-232
Author(s):  
Tan Winie ◽  
Nur Syuhada Mohd Shahril ◽  
Nur Shazlinda Muhammad Hanif ◽  
Ri Hanum Yahaya Subban ◽  
Chin Han Chan
Keyword(s):  
Power Law ◽  
Polymer Electrolytes ◽  
Ac Conductivity ◽  
Theoretical Models ◽  
Angular Frequency ◽  
Casting Technique ◽  
Hexanoyl Chitosan ◽  
Universal Power Law ◽  
Power Law Exponent ◽  
Solution Casting Technique

Hexanoyl chitosan exhibited solubility in tetrahydrofuran (THF) was prepared by acyl modification of chitosan. Polystyrene with molecular weight 280,000 g mol-1 was chosen to blend with hexanoyl chitosan. LiCF3SO3 was employed as the doping salt. Untreated and H2SO4 treated TiO2 was added as the filler. Films of hexanoyl chitosan-polystyrene-LiCF3SO3-TiO2 polymer electrolyte were obtained by solution casting technique. The ac conductivity of the sample was calculated from the relation σac = εoεiω, where εo is the permittivity of the free space, the angular frequency, ω=2πf, and εi is the dielectric loss. The ac conductivity dispersion observed is analyzed using the Jonshers universal power law, σ (ω) = σdc + Aωn where A is a pre-exponential constant and n is the power law exponent with value in the range 0 < n < 1. The temperature dependence of exponent n will then be interpreted using the existing theoretical models.

scholarly journals Maximal modularity and the optimal size of parliaments

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Luca Gamberi ◽  
Yanik-Pascal Förster ◽  
Evan Tzanis ◽  
Alessia Annibale ◽  
Pierpaolo Vivo
Keyword(s):  
Power Law ◽  
Real World ◽  
Empirical Data ◽  
Random Network ◽  
Functional Relation ◽  
Optimal Size ◽  
Real World Data ◽  
Universal Power Law ◽  
The Empirical Analysis ◽  
Democratic Country

AbstractAn important question in representative democracies is how to determine the optimal parliament size of a given country. According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with an exponent equal to 1/3, between the size of an elected parliament and the country’s population. Empirical data in modern European countries support such universality but are consistent with a larger exponent. In this work, we analyse this intriguing regularity using tools from complex networks theory. We model the population of a democratic country as a random network, drawn from a growth model, where each node is assigned a constituency membership sampled from an available set of size D. We calculate analytically the modularity of the population and find that its functional relation with the number of constituencies is strongly non-monotonic, exhibiting a maximum that depends on the population size. The criterion of maximal modularity allows us to predict that the number of representatives should scale as a power-law in the size of the population, a finding that is qualitatively confirmed by the empirical analysis of real-world data.

Effect of Adsorbed Water and Temperature on the Universal Power Law Behavior of Lepidocrocite-Type Alkali Titanate Ceramics

2021 ◽  
Author(s):  
Saichon Sriphan ◽  
Phieraya Pulphol ◽  
Thitirat Charoonsuk ◽  
Tosapol Maluangnont ◽  
Naratip Vittayakorn
Keyword(s):  
Power Law ◽  
Adsorbed Water ◽  
Universal Power Law ◽  
Titanate Ceramics

Regional variation of recession flow power-law exponent

2018 ◽  
Vol 32 (7) ◽  
pp. 866-872 ◽  
Author(s):  
Swagat Patnaik ◽  
Basudev Biswal ◽  
Dasika Nagesh Kumar ◽  
Bellie Sivakumar
Keyword(s):  
Power Law ◽  
Regional Variation ◽  
Power Law Exponent ◽  
Flow Power

scholarly journals Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers

2005 ◽  
Vol 73 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Timothy T. Clark ◽  
Ye Zhou
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Mixing Layer ◽  
Power Laws ◽  
Mixing Layers ◽  
Spatial Gradients ◽  
Power Law Exponent ◽  
Virtual Time ◽  
Time Origin ◽  
Density Ratios

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

scholarly journals Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Prakash ◽  
S. Gouse Mohiddin ◽  
S. Vijaya Kumar Varma
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Mass Flux ◽  
Numerical Study ◽  
Convection Boundary Layer ◽  
Vertical Cone ◽  
Local Skin ◽  
Surface Mass ◽  
Flow Past ◽  
Power Law Exponent

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

A universal power law and proportionate change process characterize the evolution of metabolic networks

2007 ◽  
Vol 57 (1) ◽  
pp. 75-80 ◽  
Author(s):  
S. Singh ◽  
A. Samal ◽  
V. Giri ◽  
S. Krishna ◽  
N. Raghuram ◽  
...  
Keyword(s):  
Power Law ◽  
Change Process ◽  
Metabolic Networks ◽  
Universal Power Law ◽  
Proportionate Change

scholarly journals Breakdown coefficients and scaling properties of rain fields

1998 ◽  
Vol 5 (2) ◽  
pp. 93-104 ◽  
Author(s):  
D. Harris ◽  
M. Menabde ◽  
A. Seed ◽  
G. Austin
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Power Law ◽  
Scale Parameter ◽  
Probability Distributions ◽  
Scaling Analysis ◽  
Scaling Properties ◽  
Power Law Exponent ◽  
Scale Similarity ◽  
Parameter Estimation Techniques

Abstract. The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf) of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter  estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width), σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.

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