A three‐dimensional theory is described for field‐scale Fickian dispersion in anisotropic porous media due to the spatial variability of hydraulic conductivities. The study relies partly on earlier work by authors attributes which are briefly reviewed. It leads results differ important ways from theoretical conclusions about media. We express tensor D as sum a local component d and Δ. assumed be independent velocity (which most appropriate if it represents molecular diffusion) its principal...

Certain topics in research and advancements medical diagnostics may benefit from improved temporal spatial resolution during non-invasive optical imaging of living tissue. However, so far no technique can generate entirely diffraction-limited tomographic volumes with a single data acquisition, if the target moves or changes rapidly, such as human retina. Additionally, presence aberrations represent further difficulties. We show that simple interferometric setup-based on parallelized...

We present a formal perturbation expansion for the large scale effective drift velocity and diffusion matrix of medium with stationary random velocity, $V(x)$, constant nonrandom matrix, a, on small scale. If $\mu $ denotes mean we express $V(x)$ as + \varepsilon U(x)$, then is in powers $\varepsilon $, U fixed. obtain explicit expressions up to second order which generalize standard formulae case $a \ne 0$.

We perform a set of detailed numerical simulations single-phase, fully saturated flow in stochastically generated, three-dimensional pore structures with diverse porosities (\ensuremath{\phi}) and degrees connectivity, analyze the probability density functions (PDFs) sizes, $S$, vertical velocity components, $w$, which are aligned mean direction. Both PDFs markedly skewed pronounced positive tails. This feature PDF is dictated by structure determines shortest travel times, one key transport...

Background Optical coherence tomography (OCT) is a noninvasive morphological method for investigating human skin. It allows high-resolution in vivo imaging of inflammatory skin diseases and tumours. Because it newly developed method, systematic studies on standardization evaluation factors influencing the representation have not yet been performed. Objectives In this study, normal was treated with various external stimuli which induce changes function morphology. Changes stratum corneum...

We introduce a stochastic model of flow through highly heterogeneous, composite porous media that greatly improves estimates pressure head statistics. Composite consist disjoint blocks permeable materials, each block comprising single material type. Within medium, hydraulic conductivity can be represented pair random processes: (1) boundary process determines arrangement and extent (2) stationary defines within given block. obtain second‐order statistics for in the then contrast them with...

Abstract Drylands cover over 40% of the global land area and are home to more than 2 billion humans. Here, we use terrestrial water storage (TWS) anomaly data derived from GRACE satellites assess changes globally find that drylands lost ~15.9 ± 9.1 mm between April 2002 January 2017. The TWS trends significant apparent in dry regions humid regions. decrease occurred mainly hyperarid arid Exact causes observed declines remain elusive due anthropogenic withdrawals, atmospheric demand...

Heterogeneous flows are observed to result from variations in the geometry and topology of pore structures within stochastically generated three dimensional porous media. A stochastic procedure generates media comprising complex networks connected pores. Inside each space, Navier-Stokes equations numerically integrated until steady state velocity pressure fields attained. The intricate exert spatially variable resistance on fluid, resulting have a wide range magnitudes directions. Spatially...

Volumetric imaging of dynamic processes with microscopic resolution holds a huge potential in biomedical research and clinical diagnosis. Using supercontinuum light sources high numerical aperture (NA) objectives, optical coherence tomography (OCT) achieves is well suited for cellular subcellular structures biological tissues. Currently, the speed OCT (mOCT) limited by line-scan rate spectrometer camera ranges from 30 to 250 kHz. This not fast enough volumetric vivo limits endoscopic...

In this opinion paper we contend that high‐resolution characterization, monitoring, and prediction are the key elements to advancing reducing uncertainty in our understanding of subsurface processes at basin scales. First, advocate recently developed tomographic surveying is an effective approach for characterizing field‐scale subsurface. Fusion different types surveys further enhances characterization. A appropriate scale many water resources management purposes. We thereby propose...

Summary In this paper, we study single phase, steady-state flow in bounded, heterogeneous reservoirs. We derive general equations governing the statistical moments of quantities by perturbation expansions. These may be used to construct confidence intervals for quantities. Due their mathematical complexity, solve moment differential (MDEs) numerical technique finite differences. The MDE approach renders flexibility handling complex configurations, different boundary conditions, various...

We develop probabilities and statistics for the parameters of Darcy flows through saturated porous media composed units different materials. Our probability model has two levels. On local level, a medium is disjoint, statistically homogeneous volumes (or blocks) each which consists single type material. larger scale, an arrangement blocks whose extent location are uncertain. Using this two‐scaled model, we derive general formulae distribution hydraulic conductivity its mean; then...

Existing stochastic models of unsaturated flow and transport are usually developed using the simple Gardner‐Russo constitutive relationship though it is generally accepted that more complex van Genuchten Brooks‐Corey relationships may perform better in describing experimental data. In this paper, we develop first‐order for gravity‐dominated second‐order stationary media with both relationships. These also account spatial variability effective water content, while neglected most existing...

Abstract Given partially ordered sets (posets) $$(P, \le _P)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>P</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mo>≤</mml:mo> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$(P', _{P'})$$ <mml:msup> <mml:mo>′</mml:mo> </mml:msup> , we say that $$P'$$ contains a copy of P if for some injective function $$f:P\rightarrow P'$$ <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mo>→</mml:mo> any $$A,...

In this study we develop a first‐order, nonstationary stochastic model for steady state, unsaturated flow in randomly heterogeneous media. The is applicable to the entire domain of bounded vadose zone, unlike most existing models. Because its nonstationarity, solve it by numerical technique finite differences, which renders flexibility handling different boundary conditions, input covariance structures, and soil constitutive relationships. We illustrate results one two dimensions soils...

We analyze flow in heterogeneous media composed of multiple materials whose hydraulic properties and geometries are uncertain. Our analysis relies on the composite theory Winter Tartakovsky [2000 , 2002 ], which allows one to derive solve moment equations even when medium is highly heterogeneous. use numerical solutions Darcy flows through a representative investigate robustness perturbation approximations porous with total log conductivity variances as high 20. also relative importance two...

Many of hydrogeology's most fundamental questions remain unresolved today, a hundred years after the basic governing equations for groundwater flow and transport were formulated. This paper provides brief overview field outlines future directions, with special emphasis on uncertainty quantification.

Key Points Computational experiments are used to develop generalized pedotransfer functions Kozeny eqn gives good estimates of permeability for porosities in a normal range Power laws give better across wider ranges porosity