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brownian
1
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
0
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
... equations ,” Comput. Phys. Commun. 108 ( 2 ), 147 – 158 ( 1998 ). 10.1016/S0010-4655(97)00115-X Cook , H. , “ Brownian motion in spinodal decomposition ,” Acta Metallurgica 18 ( 3 ), 297 – 306 ( 1970 ). 10.1016/0001-6160(70)90144-6 Damjanovic , D. , “ Ferroelectric...
Book Chapter
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477_002
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
... undergraduate courses in calculus and differential equations and their applications to problems in fluid dynamics. The authors analyze the relationship between LE and FP representations of particles moving in a fluid due to Brownian motion in the presence of external fields. Although each description offers...
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590_006
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
... , J. et al. , “ Applications of semi-implicit Fourier-spectral method to phase field equations ,” Comput. Phys. Commun. 108 ( 2 ), 147 – 158 ( 1998 ). 10.1016/S0010-4655(97)00115-X Cook , H. , “ Brownian motion in spinodal decomposition ,” Acta Metallurgica 18 ( 3 ), 297 – 306...
Book
Series: AIPP Books, Professional
Published: March 2023
10.1063/9780735425477
EISBN: 978-0-7354-2547-7
ISBN: 978-0-7354-2544-6
Book
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735425590
EISBN: 978-0-7354-2559-0
ISBN: 978-0-7354-2556-9
Book Chapter
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735424395_007
EISBN: 978-0-7354-2439-5
ISBN: 978-0-7354-2436-4
... Qm, the thermal Brownian motion ( Gabrielson, 1993 ; and Krause et al., 2012 ) of the spring-mass contributes ath to NEA, given by a t h = 4 π k B T ω m m Q m . Hence, the thermal noise can be reduced by increasing...
Book
Series: AIPP Books, Principles
Published: March 2023
10.1063/9780735424395
EISBN: 978-0-7354-2439-5
ISBN: 978-0-7354-2436-4
Images
in Colloidal Hard Spheres
> Recent Advances in RheologyTheory, Biorheology, Suspension and Interfacial Rheology
Published: July 2022
FIG. 6.4 Depiction of mean squared displacement of Brownian HS colloids under various concentrations. More about this image found in Depiction of mean squared displacement of Brownian HS colloids under variou...
Images
in Contact Force Effects on Rheology of Dense Suspensions
> Recent Advances in RheologyTheory, Biorheology, Suspension and Interfacial Rheology
Published: July 2022
FIG. 7.4 Relative viscosity for a suspension of frictionally interacting Brownian particles ( Pednekar et al., 2017 ). Here, ϕ = 0.5 with varying strength of pair attraction (cohesion) in units of kT/a, where k is Boltzmann’s constant, T is absolute temperature, and P e = 6 π η 0 γ ˙ a 3 / k T . The larger attraction strength obscures shear thickening. The slope of −1 indicates that the materials with strong cohesion exhibit yield stress. More about this image found in Relative viscosity for a suspension of frictionally interacting Brownian pa...
Book Chapter
Series: AIPP Books, Methods
Published: December 2022
10.1063/9780735425422_002
EISBN: 978-0-7354-2542-2
ISBN: 978-0-7354-2540-8
... dispersed in a liquid. The DLS technique relies on the Brownian motion carried out by particles in a dispersion. A well-defined correlation was observed between DLS output and transmission electron microscopy measurements. The correlation between the data is explained by the output of the DLS instrument...
Book Chapter
Series: AIPP Books, Principles
Published: December 2021
10.1063/9780735423718_006
EISBN: 978-0-7354-2371-8
ISBN: 978-0-7354-2368-8
...Brownian motion has two rather different connotations. On the one hand, there is the point of view of the scientist, which sees Brownian motion as the phenomenon observed when a small particle suspended in a fluid is seen to undergo irregular and incessant motion. This what we will call...
Book Chapter
Series: AIPP Books, Principles
Published: December 2021
10.1063/9780735423718_016
EISBN: 978-0-7354-2371-8
ISBN: 978-0-7354-2368-8
... to the total range of years being considered. This would lead to the replacement g → gε2H−1, which, when H < 1 2 diverges as ε → 0. This will be an issue when we consider the increments of fractional Brownian motion in Sec. 16.2.2 . This leading...
Book
Series: AIPP Books, Methods
Published: December 2022
10.1063/9780735425422
EISBN: 978-0-7354-2542-2
ISBN: 978-0-7354-2540-8
Images
in Colloidal Hard Spheres
> Recent Advances in RheologyTheory, Biorheology, Suspension and Interfacial Rheology
Published: July 2022
FIG. 6.6 Viscoelasticity of a colloidal suspension of silica particles in index matching solvent at a volume fraction of 37% ( Shikata and Pearson, 1994 ) where the purely viscous contribution to the viscosity ν ∞ ′ ω has been removed from the loss modulus to reveal the viscoelastic... More about this image found in Viscoelasticity of a colloidal suspension of silica particles in index matc...
Images
in Colloidal Hard Spheres
> Recent Advances in RheologyTheory, Biorheology, Suspension and Interfacial Rheology
Published: July 2022
FIG. 6.11 (a) Relative shear viscosity, (b) first and (c) second normal stress differences, and (d) osmotic pressure calculated from the two-body GSmE equation with full hydrodynamic interaction, plotted as the order ϕ 2 coefficient. Thick line (total), thin line (Brownian), and dashed line (hydrodynamic) contributions indicated. Data from Bergenholtz et al. (2002) . More about this image found in (a) Relative shear viscosity, (b) first and (c) second normal stress differ...
Book Chapter
Series: AIPP Books, Perspectives
Published: July 2022
10.1063/9780735424715_006
EISBN: 978-0-7354-2471-5
ISBN: 978-0-7354-2469-2
... experimentally determined the correct value of the intrinsic viscosity ( Einstein, 1911 ). This effort to study the properties of Brownian hard spheres was to validate the atomistic theory of matter, which may seem incredible to a modern reader only a little more than a hundred years later. This and related work...
Book Chapter
Series: AIPP Books, Perspectives
Published: July 2022
0
EISBN: 978-0-7354-2471-5
ISBN: 978-0-7354-2469-2
.... , “ The stress system in a suspension of force-free particles ,” J. Fluid Mech. 41 ( 3 ), 545 – 570 ( 1970 ). 10.1017/S0022112070000745 Batchelor , G. K. , “ Brownian diffusion of particles with hydrodynamic interactions ,” J. Fluid Mech. 74 , 1 – 29 ( 1976 ). 10.1017/S0022112076001663...
Book Chapter
Series: AIPP Books, Perspectives
Published: July 2022
10.1063/9780735424715_009
EISBN: 978-0-7354-2471-5
ISBN: 978-0-7354-2469-2
... and St denote the magnitudes of fluid and particle inertia relative to viscous forces, while Pe and Per characterize the competition between the shear-induced microstructural distortion, and its relaxation due to translational and rotational Brownian motion...
Book Chapter
Series: AIPP Books, Perspectives
Published: July 2022
0
EISBN: 978-0-7354-2471-5
ISBN: 978-0-7354-2469-2
... Batchelor , G. K. , “ The stress system in a suspension of force-free particles ,” J. Fluid Mech. 41 ( 3 ), 545 – 570 ( 1970 ). 10.1017/S0022112070000745 Batchelor , G. K. , “ Brownian diffusion of particles with hydrodynamic interaction ,” J. Fluid Mech. 74 ( 1 ), 1 – 29 ( 1976...
Book Chapter
Series: AIPP Books, Perspectives
Published: July 2022
0
EISBN: 978-0-7354-2471-5
ISBN: 978-0-7354-2469-2
... ( 2001 ). 10.1122/1.1349711 Sato , T. , Kwon , Y. , Matsumiya , Y. , and Watanabe , H. , “ A constitutive equation for Rouse model modified for variations of spring stiffness, bead friction, and Brownian force intensity under flow ,” Phys. Fluids 33 ( 6 ), 1 – 11 ( 2021...
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