TY  - JOUR
A1  - Jeon, Jae-Hyung
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
JF  - Physical chemistry, chemical physics : PCCP
N2  - Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.
KW  - single-particle tracking
KW  - living cells
KW  - random-walks
KW  - subdiffusion
KW  - dynamics
KW  - nonergodicity
KW  - coefficients
KW  - transport
KW  - membrane
KW  - behavior
Y1  - 2014
U6  - https://doi.org/10.1039/C4CP02019G
VL  - 30
IS  - 16
SP  - 15811
EP  - 15817
PB  - The Royal Society of Chemistry
CY  - Cambridge
ER  - 
TY  - GEN
A1  - Jeon, Jae-Hyung
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
N2  - Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 180 
KW  - single-particle tracking
KW  - living cells
KW  - random-walks
KW  - subdiffusion
KW  - dynamics
KW  - nonergodicity
KW  - coefficients
KW  - transport
KW  - membrane
KW  - behavior
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-76302
SP  - 15811
EP  - 15817
ER  - 
TY  - JOUR
A1  - Cooper, Ryan C.
A1  - Bruno, Giovanni
A1  - Wheeler, M. R.
A1  - Pandey, A.
A1  - Watkins, T. R.
A1  - Shyarn, A.
T1  - Effect of microcracking on the uniaxial tensile response of beta-eucryptite ceramics
BT  - Experiments and constitutive model
JF  - Acta Materialia
N2  - A constitutive model for the nonlinear or "pseudoplastic" mechanical behavior in a linear-elastic solid with thermally induced microcracks is developed and applied to experimental results. The model is termed strain dependent microcrack density approximation (SDMDA) and is an extension of the modified differential scheme that describes the slope of the stress-strain curves of microcracked solids. SDMDA allows a continuous variation in the microcrack density with tensile loading. Experimental uniaxial tensile response of beta-eucryptite glass and ceramics with controlled levels of microcracking is reported. It is demonstrated that SDMDA can well describe the extent of non-linearity in the experimental uniaxial tensile response of beta-eucryptite with varying levels of microcracking. The advantages of the SDMDA are discussed in regard to tensile loading.
KW  - behavior
Y1  - 2017
U6  - https://doi.org/10.1016/j.actamat.2017.06.033
SN  - 1359-6454
SN  - 1873-2453
VL  - 135
SP  - 361
EP  - 371
PB  - Elsevier
CY  - Oxford
ER  -