Microscopic Theory of the Long-Time Diffusivity and Intermediate-Time Anomalous Transport of a Nanoparticle in Polymer Melts

2014 ◽  
Vol 48 (1) ◽  
pp. 152-163 ◽  
Author(s):  
Umi Yamamoto ◽  
Kenneth S. Schweizer
Keyword(s):  
Polymer Melts ◽  
Microscopic Theory ◽  
Anomalous Transport ◽  
Long Time ◽  
Intermediate Time

scholarly journals Lagrangian Velocity Correlations and Absolute Dispersion in the Midlatitude Troposphere

2005 ◽  
Vol 62 (10) ◽  
pp. 3831-3836 ◽  
Author(s):  
Jai Sukhatme
Keyword(s):  
Time Scales ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Velocity Correlation ◽  
Planetary Scale ◽  
Time Correlations ◽  
Lagrangian Velocity ◽  
Long Time ◽  
Intermediate Time ◽  
Velocity Correlation Functions

Abstract Employing daily wind data from the ECMWF, passive particle advection is performed to estimate the Lagrangian velocity correlation functions (LVCF) associated with the midlatitude tropospheric flow. In particular, the velocity field is decomposed into time mean and transient (or eddy) components to better understand the nature of the LVCFs. A closely related quantity, the absolute dispersion (AD), is also examined. Given the anisotropy of the flow, meridional and zonal characteristics are considered separately. The zonal LVCF is seen to be nonexponential. In fact, for intermediate time scales it can either be interpreted as a power law of the form τ−α with 0 < α < 1 or as the sum of exponentials with differing time scales—both interpretations being equivalent. More importantly the long time correlations in the zonal flow result in a superdiffusive zonal AD regime. On the other hand, the meridional LVCF decays rapidly to zero. Before approaching zero the meridional LVCF shows a region of negative correlation—a consequence of the presence of planetary-scale Rossby waves. As a result the meridional AD, apart from showing the classical asymptotic ballistic and diffusive regimes, displays transient subdiffusive behavior.

DYNAMICS ON MULTILAYERED HYPERBRANCHED FRACTALS THROUGH CONTINUOUS TIME RANDOM WALKS

2012 ◽  
Vol 26 (09) ◽  
pp. 1250055 ◽  
Author(s):  
ANTONIO VOLTA ◽  
MIRCEA GALICEANU ◽  
AUREL JURJIU ◽  
TOMMASO GALLO ◽  
LUCIANO GUALANDRI
Keyword(s):  
Nearest Neighbor ◽  
Linear Chain ◽  
Three Dimensional ◽  
Connectivity Matrix ◽  
Eigenvalue Spectrum ◽  
Large Structures ◽  
Long Time ◽  
Continuous Time Random Walks ◽  
Intermediate Time ◽  
Short Time

We introduce a new method to generate three-dimensional structures, with mixed topologies. We focus on Multilayered Regular Hyperbranched Fractals (MRHF), three-dimensional networks constructed as a set of identical generalized Vicsek fractals, known as Regular Hyperbranched Fractals (RHF), layered on top of each other. Every node of any layer is directly connected only to copies of itself from nearest-neighbor layers. We found out that also for MRHF the eigenvalue spectrum of the connectivity matrix is determined through a semi-analytical method, which gives the opportunity to analyze very large structures. This fact allows us to study in detail the crossover effects of two basic topologies: linear, corresponding to the way we connect the layers and fractal due to the layers' topology. From the wealth of applications which depends on the eigenvalue spectrum we choose the return-to-the-origin probability. The results show the expected short-time and long-time behaviors. In the intermediate time domain we obtained two different power-law exponents: the first one is given by the combination linear-RHF, while the second one is peculiar either of a single RHF or of a single linear chain.

Microscopic Theory for the Fast Flow of Polymer Melts

2000 ◽  
Vol 85 (21) ◽  
pp. 4550-4553 ◽  
Author(s):  
Alexei E. Likhtman ◽  
Scott T. Milner ◽  
Tom C. B. McLeish
Keyword(s):  
Polymer Melts ◽  
Microscopic Theory ◽  
Fast Flow

scholarly journals ADVECTION OF PASSIVE TRACERS IN THE ATMOSPHERE: BATCHELOR SCALING

2012 ◽  
Vol 22 (10) ◽  
pp. 1250241 ◽  
Author(s):  
TÍMEA HASZPRA ◽  
PÉTER KISS ◽  
TAMÁS TÉL ◽  
IMRE M. JÁNOSI
Keyword(s):  
Time Evolution ◽  
Center Of Mass ◽  
Time Interval ◽  
Wind Fields ◽  
Tracer Dispersion ◽  
Pair Separation ◽  
Long Time ◽  
Intermediate Time ◽  
Passive Tracers ◽  
One Year

Extensive numerical experiments are performed on tracer dispersion in global reanalysis wind fields. Particle trajectories are computed both along an isobaric (500 hPa) and an isentropic (315 K) surface in a time interval of one year. Besides mean quantities such as advection of the center of mass and growth of tracer clouds, special attention is paid to the evaluation of particle pair separation dynamics. The characteristic behavior for intermediate time scales is Batchelor's dispersion along both surfaces, where the zonal extent of the tracer cloud increases linearly in time. The long-time evolution after 70–80 days exhibits a slower, diffusive dispersion (Taylor regime), in agreement with expectations. Richardson–Obukhov scaling (superdiffusion with an exponent of 3/2) could not be identified in the numerical tests. The results confirm the classical prediction by Batchelor that the initial pair-separation determines subsequent time evolution of tracers. The quantitative dependence on the initial distance differs however from the prediction of the theory.

Long-Time Creep in a Pure-Gum Rubber Vulcanizate: Influence of Humidity and Atmospheric Oxygen

1975 ◽  
Vol 48 (2) ◽  
pp. 154-163 ◽  
Author(s):  
L. A. Wood ◽  
G. W. Bullman ◽  
F. L. Roth
Keyword(s):  
Experimental Data ◽  
Linear Relation ◽  
Degradation Products ◽  
Atmospheric Oxygen ◽  
Creep Equation ◽  
Dry Air ◽  
Long Time ◽  
Intermediate Time ◽  
Almost All ◽  
Range Of Values

Abstract The long-time creep of natural rubber cured with a conventional sulfur-accelerator recipe containing no filler can be conveniently shown near room temperature by a plot of ΔE/E1 with a double-abscissa scale, one marked in units of log t and the other in units of t. When experimental data from the present work and from previous studies reported in the literature are plotted in this manner it is noted that invariably the first scale yields a linear relation at short times and the second a linear relation at long times. The limiting linear relations just mentioned suggest the two-constant Equation (2), already proposed as a general creep equation for many materials. In the case of rubber the range of values of t investigated is from about 10 ms as studied by previous investigators to about 70 days in our work and other studies. Any significant deviations from the equation can be noted by inspection of the double-abscissa plot. We found that the equation furnished an excellent representation of almost all our experimental data up to the longest times. In one instance in our work and in a few other cases there was a prerupture increase of ΔE/E1 above the values given by the equation. This behavior can reduce somewhat the upper limit of validity of the general equation. The constants A and B can be evaluated from experimental observations of ΔE/E1 by solving two simultaneous equations obtained from the values at the longest time, at one minute, and at an intermediate time. In the present work, the constant A was essentially the same (about 2.4%/ (unit log t)) when the atmosphere surrounding the specimen was a vacuum, dry nitrogen, or dry air. The value was raised when the atmosphere was room air at 35% relative humidity and became about 4%/ (unit long t) when the air was saturated with water. The constant B was raised tenfold when the atmosphere was dry air instead of dry nitrogen. It was further increased by a factor of about 2, when the air was saturated. The value of B for the specimen in an atmosphere of stagnant room air was still greater than this by another factor of more than 2. It is possible that this atmosphere contained autocatalytic degradation products or other constituents which were removed when the air was bubbled through water or passed over CaCl2. The approximate boundaries of three different regions of time are determinable from the ratios A/B. In the first region, where t is less than 0.1(A/B), ΔE/E1 is approximately linear with log t. In the second region, where t is between 0.1(A/B) and 4.343 (A/B), ΔE/E1 is not linear with either log t or t. In the third region, where t is greater than 4.343 (A/B), ΔE/E1 is approximately linear with t. A fourth region of anomalous increase preceding rupture is sometimes found, especially when B is large.

Long-Time Diffusion in Polymer Melts Revealed by 1H NMR Relaxometry

2013 ◽  
Vol 2 (2) ◽  
pp. 96-99 ◽  
Author(s):  
R. Meier ◽  
A. Herrmann ◽  
B. Kresse ◽  
A. F. Privalov ◽  
D. Kruk ◽  
...  
Keyword(s):  
1H Nmr ◽  
Polymer Melts ◽  
Nmr Relaxometry ◽  
Long Time ◽  
1H Nmr Relaxometry

INTEGRO-DIFFERENTIAL EQUATIONS ASSOCIATED WITH CONTINUOUS-TIME RANDOM WALK

2013 ◽  
Vol 27 (12) ◽  
pp. 1330006 ◽  
Author(s):  
KWOK SAU FA ◽  
K. G. WANG
Keyword(s):  
Random Walk ◽  
Differential Equations ◽  
Continuous Time ◽  
Analytic Solutions ◽  
Continuous Time Random Walk ◽  
Kolmogorov Equation ◽  
Long Time ◽  
Intermediate Time ◽  
And Diffusion ◽  
Probability Density Function Pdf

The continuous-time random walk (CTRW) model is a useful tool for the description of diffusion in nonequilibrium systems, which is broadly applied in nature and life sciences, e.g., from biophysics to geosciences. In particular, the integro-differential equations for diffusion and diffusion-advection are derived asymptotically from the decoupled CTRW model and a generalized Chapmann–Kolmogorov equation, with generic waiting time probability density function (PDF) and external force. The advantage of the integro-differential equations is that they can be used to investigate the entire diffusion process i.e., covering initial-, intermediate- and long-time ranges of the process. Therefore, this method can distinguish the evolution detail for a system having the same behavior in the long-time limit but with different initial- and intermediate-time behaviors. An integro-differential equation for diffusion-advection is also presented for the description of the subdiffusive and superdiffusive regime. Moreover, the methods of solving the integro-differential equations are developed, and the analytic solutions for PDFs are obtained for the cases of force-free and linear force.

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