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Constant Front Speed in Weakly Diffusive Non-Fickian Systems

David A. Edwards
1995 SIAM Journal on Applied Mathematics  
These fronts not only are sharper than in standard systems but also propagate at constant speed.  ...  Consequently, s u c h systems often exhibit concentration fronts unlike those seen in classical Fickian systems.  ...  H o wever, in so-called case II di usion in polymers, concentration fronts move with constant speed 6], 7]. These fronts are usually sharper than those of the Fickian di usion model.  ... 
doi:10.1137/s0036139993259039 fatcat:6qst65uc35esvhb6t5jcsr5auy

Page 1848 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
| (1-CAIT-AM; Pasadena, CA) Constant front speed in weakly diffusive non-Fickian systems. (English summary) SIAM J. Appl. Math. 55 (1995), no. 4, 1039-1058.  ...  These fronts are not only sharper than in standard systems but also propagate at constant speed.  ... 

Non-fickian diffusion in thin polymer films

D. A. Edwards
1996 Journal of Polymer Science Part B: Polymer Physics  
One type of non-Fickian behavior that results is so-called case I1 diffusion, where Fickian-like fronts initially move like fi with a transition to a non-Fickian concentration profile and front speed for  ...  An unusual result is derived In certain parameter ranges, the concentration profile can change concavity, reflecting Fickian behavior for short times and non-Fickian behavior for moderate times.  ...  We show in this paper that the system we are modeling is indeed a non-Fickian diffusion system.  ... 
doi:10.1002/(sici)1099-0488(19960415)34:5<981::aid-polb16>;2-7 fatcat:qoqh5nfpnna2hij6f6vlpgpkdq

Molecular dynamics simulation of solvent–polymer interdiffusion: Fickian diffusion

Mesfin Tsige, Gary S. Grest
2004 Journal of Chemical Physics  
The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self diffusion constant in the dilute solvent limit.  ...  The weight gain is found to scale as t^1/2, which is expected for Fickian type of diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity.  ...  a sharp concentration front that propagates at constant speed.  ... 
doi:10.1063/1.1640347 pmid:15268446 fatcat:p5iqjw3ex5hftawzunifa36hom

Effects of Soret Diffusion on Premixed Counterflow Flames

Wang Han, Zheng Chen
2015 Combustion Science and Technology  
Soret diffusion is a secondary mass diffusion and it affects laminar flames with very light or heavy species and large temperature gradients.  ...  Results show that Soret diffusion quantitatively affects the premixed counterflow flame and that the influence of Soret diffusion strongly depends on Lewis number and stretch rate.  ...  For fuel-lean case, fuel is completely consumed in a flame front and it appears only in the unburned zone.  ... 
doi:10.1080/00102202.2015.1019623 fatcat:ebjdo64o5fcf7auai7qijb5kjm

Coexistence of competitors mediated by nonlinear noise

Ivo Siekmann, Michael Bengfort, Horst Malchow
2017 The European Physical Journal Special Topics  
Instead, concentration accumulates in regions of low diffusivity and tends to lower levels for areas of high diffusivity.  ...  However, this segregation can be broken by nonlinear noise leading to coexistence of resident and invader across the whole spatial domain, an effect that would not be possible in the non-spatial version  ...  In summary, for Fokker-Planck diffusion and a noise term (8) in the weakly non-linear parameter regime, we observe that the strength of a competitor can be elevated by increasing the diffusivity or the  ... 
doi:10.1140/epjst/e2017-70038-6 fatcat:jb5odxgfy5b45kqz5nz6t2buwa

Preparation, structure and diffusional behavior of hydrogels in controlled release

Nikolaos A. Peppas, Atul R. Khare
1993 Advanced Drug Delivery Reviews  
For swelling-controlled systems, the coupling of diffusion and macromolecular relaxation control the mechanism of drug release, providing conditions of zero-order release.  ...  Application of such systems in various delivery situations is discussed with emphasis on the delivery rate and the stability of the releasing bioactive agents.  ...  , non-Fickian or Case II transport.  ... 
doi:10.1016/0169-409x(93)90025-y fatcat:lckffdebuzc5nnxjg2os5r4ds4

Viscous and gravitational fingering in multiphase compositional and compressible flow

Joachim Moortgat
2016 Advances in Water Resources  
This work presents a detailed study of fingering behavior in compositional multiphase flow in two and three dimensions and considers the effects of 1) Fickian diffusion, 2) mechanical dispersion, 3) flow  ...  These instabilities have been studied extensively in the past for 1) single-phase flow (e.g., contaminant transport in groundwater, first-contact-miscible displacement of oil by gas in hydrocarbon production  ...  With Gravity Effects of Mechanical and Fickian Dispersion Unlike in most reservoir simulators, Fickian diffusion coefficients are not assumed to be a constant diagonal matrix, but are computed from irreversible  ... 
doi:10.1016/j.advwatres.2016.01.002 fatcat:v6mhmwoy3zerppx3snlqmbp4dy

Gel Strength of Hydrophilic Matrix Tablets in Terms of In Vitro Robustness

Seyedreza Goldoozian, Valentyn Mohylyuk, Andriy Dashevskiy, Roland Bodmeier
2021 Pharmaceutical Research  
In this case, the drug was predominantly released via erosional mechanism and very susceptible to stirring speed.  ...  In this case, the release mechanism was predominantly diffusional and, therefore, not affected by stirring speed and mechanical stress.  ...  In cases where the relaxation time was approaching the diffusion time, the non-Fickian, or anomalous diffusion, was observed (11) (12) (13) (14) .  ... 
doi:10.1007/s11095-021-03068-y pmid:34152536 pmcid:PMC8292303 fatcat:wohfpjakmbar3hco32tll7bkk4

Sea urchin feeding fronts [article]

Edward R Abraham
2006 arXiv   pre-print
Sea urchin feeding fronts are a striking example of spatial pattern formation in an ecological system.  ...  Bounds on when stable fronts will form are obtained in terms of urchin density and grazing, and algal growth.  ...  Because Fickian diffusion will always lead to the density of a population decreasing (at least in the absence of any reproduction or migration) it is unable to generate sharp fronts.  ... 
arXiv:q-bio/0610004v1 fatcat:va3tawsmsbd2ldw2abw6bd2ymu

The Geometry and Motion of Sharp Fronts within Geochemical Transport Problems

P. Grindrod
1995 Proceedings of the Royal Society A  
We develop an asymptotic approach in which we solve equations for the evolv ing geometry of the front and indicate how the non-smooth perturbations, due to natural heterogeneity of the mineralogy on underlying  ...  We consider some reactive geochemical transport problems in groundwater sys tems. When incoming fluid is in disequilibrium with the mineralogy, sharp tran sition fronts may develop.  ...  The waves are curvature damped by the Fickian terms within the original system.  ... 
doi:10.1098/rspa.1995.0035 fatcat:fj7bfnwdjbbhxjjz7g6tz3vn6e

Pattern formation and localized structures in monoatomic layer deposition

M. G. Clerc, E. Tirapegui, M. Trejo
2007 The European Physical Journal Special Topics  
The transport properties of the model lead to non Fickian diffusion.  ...  The characteristic lengths are in the nanometer region in agreement with recent experiments.  ...  Our analysis is done in the frame of reaction diffusion systems with non Fickian diffusion which we have recently studied generically [13] .  ... 
doi:10.1140/epjst/e2007-00196-5 fatcat:ylvx46qmgfecznlthuyg4k4aoe

The Development of Direct Extrusion-Injection Moulded Zein Matrices as Novel Oral Controlled Drug Delivery Systems

Jacob Bouman, Peter Belton, Paul Venema, Erik van der Linden, Renko de Vries, Sheng Qi
2015 Pharmaceutical Research  
Release was found to be largely independent of drug loading but strongly dependent upon device dimensions, and predominately governed by a Fickian diffusion mechanism, while the hydration kinetics shows  ...  the features of Case II diffusion.  ...  Recently the sharp diffusion front was also explained by a 'change of state' theory, in which it assumes that when the freely diffused small solvent molecules reach the glassy polymer core (diffusion front  ... 
doi:10.1007/s11095-015-1663-9 pmid:25777612 fatcat:uubk7c73x5bgdgoczt4cgcswbu

Stability and accuracy of the weakly compressible SPH with particle regularization techniques [article]

Mojtaba Jandaghian, Herman Musumari Siaben, Ahmad Shakibaeinia
2021 arXiv   pre-print
We introduce a general form of the Dynamic pair-wise Particle Collision (DPC) regularization technique that we recently proposed in the context of the Moving Particle Semi-implicit (MPS) method in [1].  ...  The DPC coupled with the standard Particle Shifting (PS) technique has given rise to a hybrid approach that we propose to alleviate particle clustering issues in the free-surface and splashed regions.  ...  The non-dimensional constant, A, is suggested to be set between 1-6 [16] .  ... 
arXiv:2110.10076v1 fatcat:an7fsjzumzhyrlla5edaeek52y

Oscillatory instability in super-diffusive reaction – diffusion systems: Fractional amplitude and phase diffusion equations

Y. Nec, A. A. Nepomnyashchy, A. A. Golovin
2008 Europhysics letters  
Nonlinear evolution of a reaction--super-diffusion system near a Hopf bifurcation is studied.  ...  In this letter, weakly non-linear dynamics of a reaction-diffusion system characterized by Lévy flights near a long wave bifurcation point is investigated.  ...  In conclusion, we have derived fractional Ginzburg-Landau and Kuramoto-Sivashinsky equations that describe weakly non-linear dynamics of a super-diffusive reaction-diffusion system, characterized by Lévy  ... 
doi:10.1209/0295-5075/82/58003 fatcat:3cjfmacb7zghlakvrrpmfwku5u
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