南京市 Nanjing City. 河海大学 -Hohai University. College of Civil Engineering in Hohai University. Basic facts of the College (largest in our university): Close to 200 staffs 4 departments (“civil engineering”, “survey & mapping”, “earth sciences & engineering”, “engineering mechanics”)
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Basic facts of the College (largest in our university):
Wen Chen （陈文）
Institute of Soft Matter Mechanics
Hohai University, Nanjing, China
3 September 2007
highly deformable, porous, thermal fluctuations play major role, highly unstable
Pierre-Gilles de Gennes proposed the term in his Nobel acceptance speech in 1991.
widely viewed as the beginning of the soft matter science.
_ P. G. De Gennes
a jammed colloid system, a pile of sand,
a polymer gel, or a folding protein.
conservation of mass, momentum and energy
stress, strain, energy and entropic elasticity
obeys a frequency-dependent power law
Courtesy of Prof. Thomas Szabo
Left: Brownian motion; Right: Levy flight
with the same number (7000) of steps.
A characteristic Levy walk
Cauchy distribution (=1)
Tsallis non-extensive entropy
A. Komnik, J. Harting, H.J. Herrmann
Multirelaxation models, nonlinear models; varied models for different media with quite a few parameters having no explicit physical significance. For instance, nonlinear power law fluids:
Master equation (phenomenological)
I. Podlubny, Fractional Differential equation, Academic Press, 1999
Positive fractional derivative：
Positivity requirments in modeling of dissipation
Samko et al. 1993. Fractional Integrals and Derivives: Theory and Applications
Journal of Acoustic Society of America, 115(4), 1424-1430, 2004
Courtesy of Prof. Thomas Szabo
Imaging (sonography) and ablating the objects inside human body for medical diagnosis and therapy.
Our fractional calculus models：
Thermoviscous wave equation (y=2):
Damped wave equation (y=0):
Phenomenological master equation
Fourier transform of probability density function of Lévy -stable distribution is the characteristic function of solution of “anomalous” diffusion equation：
1) In terms of Lévy statistics, the media having >2 power law attenuation are not statistically stable in nature;
2) =0 is simply an ideal approximation.
Special relativity transforms:
Fractional quantum relationships between energy and frequency, momentum and wavenumber（fractional Schrodinger equation）
Hausdorff derivative diffusion equation:
Nature, 409, 1017–1019, 2001
Oak Ridge National Laboratory
Power law decay of Levy distribution
Richardson diffusion consistent with Kolmogorov scaling
Three order of magnitude: turbulence vs. molecule viscousity
471,031 scattered data made by U.S. Geological Survey
200 millions DOFs matrix for 2D FEMengineering precision; 30000 full matrix & 13.5Gb storage for the standard BEM
SLangdon, Lecture notes on “Finite element methods for acoustic scattering”, July 11, 2005
S. Chandler-Wilde & S. Langdon, Lecture notes on “Boundary element methods for acoustics”, July 19, 2005