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41.
A simple theoretical model is described for deriving a 1-dimensional equation for the spreading of a tracer in a steady flow at the field scale. The originality of the model is to use a stochastic appoach not in the 3-dimensional space but in the 1-D space of the stream tubes. The simplicity of calculation comes from the local relationship between permeability and velocity in a 1-D flow. The spreading of a tracer front is due to local variations in the cross-sectional area of the stream tubes, which induces randomness in travel time. The derived transport equation is averaged in the main flow direction. It differs from the standard dispersion equation. The roles of time and space variables are exchanged. This result can be explained by using the statistical theory of Continuous Time Random Walk instead of a standard Random Walk. However, the two equations are very close, since their solutions have the same first and second moments. Dispersivity is found to be equal to the product of the correlation length by the variance of the logarithm of permeability, a result similar to Gelhar's macrodispersion.Nomenclature
A
total cross-section area of the sample
-
C
(resident) concentration of tracer
-
D,D
*
dispersion coefficient
-
F
flux of tracer
-
G
probability distribution function for permeability in the stream-tube segments
-
I
tracer intensity (mass crossing a surface per unit time)
-
K
permeability
-
L
length of the medium
-
M
number of stream tubes in the medium
-
N
number of segments along a stream tube
-
P
pressure
-
Q
total flow rate in the sample
-
a
length of an elementary stream-tube segment
-
g
probability distribution function for permeability in the space
-
i, j
indices, tube numbers
-
q
flow rate in each stream tube
-
s
variable cross-section area of a stream tube
-
t, t
time
-
u
front velocity
-
x
space variable in the flow direction
-
small local variation in time
-
,
t
longitudinal, transverse dispersivity
-
porosity of the porous medium
-
correlation length in the permeability field
-
viscosity of the fluid
-
time for filling an elementary stream tube segment
-
standard deviation of a stochastic variable
-
probability distribution of arrival times (Gaussian) 相似文献
42.
43.
If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk
n
wherek
n+1
ck
n
then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG). 相似文献
44.
The surface pressure-molecular area curve of the mixed monolayer of 16-(9-anthroyloxy) palmitic acid (16AP) and fatty acid (palmitic or stearic acids) showed various kink points which indicated the phase transitions of the monolayer. On the basis of the surface phase rule, the phase diagrams of the mixed monolayer were elucidated. The bifunctional molecule, 16AP, takes two orientations in a monolayer state, that is, horizontal and vertical ones. Horizontally oriented 16AP and vertically oriented fatty acid form a mixed monolayer but this exhibits deviation from the ideal mixing, which was interpreted in terms of the surface regular solution theory. On the other hand, the 16AP molecule in the vertical state was found to be immiscible with the fatty acid molecule in a monolayer de spite both molecules being vertical to the surface and parallel to each other. This was caused by the participation of the 9-anthroyloxy moiety of 16AP in the interaction of 16AP and fatty acid in the hydrophobic region of the monolayer. 相似文献
45.
El-B. Yallaoui 《Periodica Mathematica Hungarica》1991,23(2):109-120
Let X be an abstract set and L a lattice of subsets of X. To each lattice regular measure µ, we associate two induced measures
and
on suitable lattices of the Wallman space IR(L) and another measure µ on the spaceIR(L). We will investigate the reflection of smoothness properties of p onto
,
and µ; and try to set some new criterion for repleteness and measure repleteness. 相似文献
46.
47.
Piotr Kacprzyk 《Mathematical Methods in the Applied Sciences》2013,36(3):313-322
Global existence of regular solutions to the Navier–Stokes equations coupled with the heat convection in a cylindrical pipe has already been shown. In this paper, we prove the existence of the global attractor to the equations and convergence of their solutions to a stationary one. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
48.
49.
In recent years, the utilization of machine learning and data mining techniques for intrusion detection has received great attention by both security research communities and intrusion detection system (IDS) developers. In intrusion detection, the most important constraints are the imbalanced class distribution, the scarcity of the labeled data, and the massive amounts of network flows. Moreover, because of the dynamic nature of the network flows, applying static learned models degrades the detection performance significantly over time. In this article, we propose a new semi‐supervised stream classification method for intrusion detection, which is capable of incremental updating using limited labeled data. The proposed method, called the incremental semi‐supervised flow network‐based IDS (ISF‐NIDS), relies on an incremental mixed‐data clustering, a new supervised cluster adjustment method, and an instance‐based learning. The ISF‐NIDS operates in real time and learns new intrusions quickly using limited storage and processing power. The experimental results on the KDD99, Moore, and Sperotto benchmark datasets indicate the superiority of the proposed method compared with the existing state‐of‐the‐art incremental IDSs. 相似文献
50.
Let G be a 2k-edge-connected graph with and let for every . A spanning subgraph F of G is called an L-factor, if for every . In this article, we show that if for every , then G has a k-edge-connected L-factor. We also show that if and for every , then G has a k-edge-connected L-factor. 相似文献