Error bounds for the nonlinear filtering of signals with small diffusion coefficients

1988 ◽  
Vol 34 (4) ◽  
pp. 710-721 ◽  
Author(s):  
B.-Z. Bobrovsky ◽  
M.M. Zakai ◽  
O. Zeitouni
Keyword(s):  
Error Bounds ◽  
Diffusion Coefficients ◽  
Nonlinear Filtering ◽  
Small Diffusion

scholarly journals Liquid-liquid phase separation and viscosity within secondary organic aerosol generated from diesel fuel vapors

2019 ◽  
Author(s):  
Mijung Song ◽  
Adrian M. Maclean ◽  
Yuanzhou Huang ◽  
Natalie R. Smith ◽  
Sandra L. Blair ◽  
...  
Keyword(s):  
Phase Separation ◽  
Liquid Phase ◽  
Diesel Fuel ◽  
Diffusion Coefficients ◽  
Secondary Organic Aerosol ◽  
Organic Aerosol ◽  
Liquid Phase Separation ◽  
Small Diffusion ◽  
Wide Range ◽  
Liquid Liquid Phase Separation

Abstract. Information on liquid-liquid phase separation (LLPS) and viscosity (or diffusion) within secondary organic aerosol (SOA) is needed to improve predictions of particle size, mass, reactivity, and cloud nucleating properties in the atmosphere. Here we report on LLPS and viscosities within SOA generated by the photooxidation of diesel fuel vapors. Diesel fuel contains a wide range of volatile organic compounds, and SOA generated by the photooxidation of diesel fuel vapors may be a good proxy for SOA from anthropogenic emissions. In our experiments, LLPS occurred over the relative humidity (RH) range of ~ 70 % to ~ 100 %, resulting in an organic-rich outer phase and a water-rich inner phase. These results may have implications for predicting the cloud nucleating properties of anthropogenic SOA since the organic-rich outer phase can lower the kinetic barrier for activation to a cloud droplet. At ≤ 10 % RH, the viscosity was in the range of ≥ 1 × 108 Pa s, which corresponds to roughly the viscosity of tar pitch. At 38–50 % RH the viscosity was in the range of 1 × 108–3 × 105 Pa s. These measured viscosities are consistent with predictions based on oxygen to carbon elemental ratio (O : C) and molar mass as well as predictions based on the number of carbon, hydrogen, and oxygen atoms. Based on the measured viscosities and the Stokes–Einstein relation, at ≤ 10 % RH diffusion coefficients of organics within diesel fuel SOA is ≤ 5.4 × 10−17cm2 s−1 and the mixing time of organics within 200 nm diesel fuel SOA particles (τmixing) is ≳ 50 h. These small diffusion coefficients and large mixing times may be important in laboratory experiments, where SOA is often generated and studied using low RH conditions and on time scales of minutes to hours. At 38–50 % RH, the calculated organic diffusion coefficients are in the range of 5.4 × 10−17 to 1.8 × 10−13 cm2 s−1 and calculated τmixing values are in the range of ~ 0.01 h to ~ 50 h. These values provide important constraints for the physicochemical properties of anthropogenic SOA.

scholarly journals Liquid–liquid phase separation and viscosity within secondary organic aerosol generated from diesel fuel vapors

2019 ◽  
Vol 19 (19) ◽  
pp. 12515-12529 ◽  
Author(s):  
Mijung Song ◽  
Adrian M. Maclean ◽  
Yuanzhou Huang ◽  
Natalie R. Smith ◽  
Sandra L. Blair ◽  
...  
Keyword(s):  
Phase Separation ◽  
Liquid Phase ◽  
Diesel Fuel ◽  
Diffusion Coefficients ◽  
Secondary Organic Aerosol ◽  
Organic Aerosol ◽  
Liquid Phase Separation ◽  
Small Diffusion ◽  
Wide Range ◽  
Liquid Liquid Phase Separation

Abstract. Information on liquid–liquid phase separation (LLPS) and viscosity (or diffusion) within secondary organic aerosol (SOA) is needed to improve predictions of particle size, mass, reactivity, and cloud nucleating properties in the atmosphere. Here we report on LLPS and viscosities within SOA generated by the photooxidation of diesel fuel vapors. Diesel fuel contains a wide range of volatile organic compounds, and SOA generated by the photooxidation of diesel fuel vapors may be a good proxy for SOA from anthropogenic emissions. In our experiments, LLPS occurred over the relative humidity (RH) range of ∼70 % to ∼100 %, resulting in an organic-rich outer phase and a water-rich inner phase. These results may have implications for predicting the cloud nucleating properties of anthropogenic SOA since the presence of an organic-rich outer phase at high-RH values can lower the supersaturation with respect to water required for cloud droplet formation. At ≤10 % RH, the viscosity was ≥1×108 Pa s, which corresponds to roughly the viscosity of tar pitch. At 38 %–50 % RH, the viscosity was in the range of 1×108 to 3×105 Pa s. These measured viscosities are consistent with predictions based on oxygen to carbon elemental ratio (O:C) and molar mass as well as predictions based on the number of carbon, hydrogen, and oxygen atoms. Based on the measured viscosities and the Stokes–Einstein relation, at ≤10 % RH diffusion coefficients of organics within diesel fuel SOA is ≤5.4×10-17 cm2 s−1 and the mixing time of organics within 200 nm diesel fuel SOA particles (τmixing) is 50 h. These small diffusion coefficients and large mixing times may be important in laboratory experiments, where SOA is often generated and studied using low-RH conditions and on timescales of minutes to hours. At 38 %–50 % RH, the calculated organic diffusion coefficients are in the range of 5.4×10-17 to 1.8×10-13 cm2 s−1 and calculated τmixing values are in the range of ∼0.01 h to ∼50 h. These values provide important constraints for the physicochemical properties of anthropogenic SOA.

scholarly journals Convergence in competition models with small diffusion coefficients

2005 ◽  
Vol 211 (1) ◽  
pp. 135-161 ◽  
Author(s):  
V. Hutson ◽  
Y. Lou ◽  
K. Mischaikow
Keyword(s):  
Diffusion Coefficients ◽  
Small Diffusion ◽  
Competition Models

A complex corona between olivine and plagioclase from the Jotun Nappe, Norway, and the diffusion modelling of multimineralic layers

1992 ◽  
Vol 56 (385) ◽  
pp. 511-525 ◽  
Author(s):  
J. R. Ashworth ◽  
J. J. Birdi ◽  
T. F. Emmett
Keyword(s):  
Electron Microscopy ◽  
Diffusion Coefficients ◽  
Local Equilibrium ◽  
Mineral Layer ◽  
Small Diffusion ◽  
Phase Rule ◽  
Transmission Electron ◽  
Diffusion Controlled ◽  
State Diffusion

AbstractCoronas containing Ca-amphibole with aluminous minerals have been characterised optically and by scanning electron microscopy, analytical transmission electron microscopy and electron-probe microanalysis. The layers nearest to plagioclase are amphibole + epidote + kyanite, followed by amphibole + epidote + staurolite + spinel. These assemblages are consistent with waterundersaturated conditions, possibly at lower metamorphic grade than the commoner assemblage amphibole + spinel. Observed mineral proportions and compositions were used in a seven-layer model of steady-state, diffusion-controlled growth with local equilibrium. This model is not fully realistic, because the observed amphibole is strongly zoned from tschermakitic to actinolitic away from plagioclase, suggesting disequilibrium. However, the four-mineral layer has been successfully modelled assuming local equilibrium, with diffusion coefficients Lii larger for i = FeO and MgO than for SiO2, AlO3/2, CaO and FeO3/2. Retarded grain-boundary diffusion of the latter components is explicable by crystal-chemical effects. The number of minerals per layer is constrained by a modified form of the metasomatic phase rule of Korzhinskii, with the role of 'inert' components played by relatively immobile ones (having relatively small fluxes and relatively small diffusion coefficients).

Solutions with Singular Initial Data for a Model of Electrophoretic Separation

1990 ◽  
Vol 33 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Joel D. Avrin
Keyword(s):  
Initial Data ◽  
Diffusion Coefficients ◽  
Existence Result ◽  
Strong Solutions ◽  
Approximate Solutions ◽  
Electrophoretic Separation ◽  
Small Diffusion ◽  
Singular Initial Data ◽  
Global Strong Solutions ◽  
Global Existence Result

AbstractUnique global strong solutions of a Cauchy problem arising in electrophoretic separation are constructed with arbitrary initial data in L1, thus generalizing an earlier global existence result. For small diffusion coefficients, the solutions can be viewed as approximate solutions for the corresponding zero-diffusion Riemann problem.

Dopant Diffusion in TiSi2

1986 ◽  
Vol 77 ◽  
Author(s):  
F. M. d'Heurle ◽  
A. E. Michel ◽  
F. K. LeGoues ◽  
G. Scilla ◽  
J. T. Wetzel ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Diffusion Process ◽  
Diffusion Coefficients ◽  
Boundary Diffusion ◽  
Radioactive Tracer ◽  
Lattice Diffusion ◽  
The Other ◽  
Small Diffusion ◽  
Secondary Ion ◽  
Thick Layers

ABSTRACTDopant elements, B and Ga, P, As and Sb, and Ge as well, have been implanted into thick (350–400 nm) layers of TiSi2 prepared by Ti-Si reaction. Both B and Sb appear to be immobile, this behavior is thought to result from very small solid solubilities, rather than from very small diffusion coefficients. The other elements display about the same behavior, with detectable grain boundary diffusion at temperatures as low as 600°C, and lattice diffusion becoming considerable at 750°C, so that with the cooperation of both phenomena almost complete homogenisation of these relatively thick layers occurs in 30 minutes at 800°C. Germanium is used in lieu of a Si radioactive tracer because it can be analyzed by Secondary Ion Mass Spectroscopy. Its behavior is thought to imply that there is little equilibrium adsorption of the dopant elements at the Si/TiSi2 interface. The comparable values of the diffusion coefficients for the mobile elements confirm the anticipation that the dopants move as substitutional atoms on the Si sublattice. Results obtained with some samples implanted with both dopant and Ti indicate that in these silicon-saturated suicide layers the diffusion process is not significantly affected by small changes in stoichiometry.

NON-TURING MECHANISM OF SELF-SUSTAINED STRUCTURE FORMATION

2013 ◽  
Vol 23 (02) ◽  
pp. 1350037
Author(s):  
ANDREY YU. VERISOKIN ◽  
DARYA V. VERVEYKO
Keyword(s):  
Mathematical Model ◽  
Phase Space ◽  
Structure Formation ◽  
Spatial Patterns ◽  
Diffusion Coefficients ◽  
Small Diffusion ◽  
Spatial Phase ◽  
Local Rotation ◽  
Turing Mechanism ◽  
Large Diffusion

We study the mechanism of experimentally observed phase waves and clusters in yeast extracts (cells with destroyed membranes) placed into the unstirred medium (gel). As a mathematical model, the distributed Selkov system is used, since it describes the key step of glycolytic reaction cascade — the phosphofructokinase-catalyzed reaction. We argue that the emergence of spatial phase clusters does not correspond to the Turing mechanism because diffusion coefficients used for two considered reagents are taken as equal. We show that the actual background of this phenomenon is connected with various local rotation velocities in phase space. In this case, large diffusion coefficients stabilize spatial patterns and small diffusion provides an asynchronous regime only.

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