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Brian Berkowitz

Publications and source records attributed to Brian Berkowitz.

11 recordsLinked to original sources
PubMed2005

Morphogen gradient formation in a complex environment: an anomalous diffusion model.

Current models of morphogen-induced patterning assume that morphogens undergo normal, or Fickian, diffusion, although the validity of this assumption has never been examined. Here we argue that the interaction of morphogens with the complex extracellular surrounding may lead to anomalous diffusion. We present a phenomenological model that captures this interaction, and derive the properties of the morphogen profile under conditions of anomalous (non-Fickian) diffusion. In this context we consider the continuous time random walk formalism and extend its application to account for degradation of morphogen particles. We show that within the anomalous diffusion model, morphogen profiles are fundamentally distinct from the corresponding Fickian profiles. Differences were found in several key aspects, including the role of degradation in determining the profile, the rate by which it spreads in time and its long-term behavior. We analyze the effect of an abrupt change in the extracellular environment on the concentration profiles. Furthermore, we discuss the robustness of the morphogen distribution to fluctuations in morphogen production rate, and describe a feedback mechanism that can buffer such fluctuations. Our study also provides rigorous criteria to distinguish experimentally between Fickian and anomalous modes of morphogen transport.

Algorithms↗
PubMed2005

Exact effective transport dynamics in a one-dimensional random environment.

We study effective transport under linear equilibrium adsorption characterized by a spatially random retardation factor. In a stochastic framework, we present a methodology to quantify explicitly the impact of spatial disorder on effective transport dynamics. We derive an exact effective transport equation, which is equivalent to transport under linear kinetic adsorption characterized by a spectrum of adsorption times. The distribution of adsorption times is given explicitly in terms of the spatial disorder distribution. Furthermore, we find that effective transport is formally equivalent to a decoupled continuous time random walk. This observation and the explicit nature of the presented results allow for a mapping of the static disorder distribution on the transition time distribution.

Journal Article↗
PubMed2005

Magnetic resonance imaging and quantitative analysis of particle deposition in porous media.

Measurements of particle deposition and mobilization in water-saturated porous columns were performed using nuclear magnetic resonance imaging (MRI). The use of MRI enabled the acquisition of detailed, noninvasive measurements that quantify spatial and temporal evolution of particle transport patterns and porosity changes due to particle deposition. Measurements indicate that for the considered particle sizes and flow conditions significant particle deposition occurs at some distance into the column. Because identification of unique parametrizations for processes of particle straining, deposition, and detachment is complex and nonunique, a simple phenomenological model of particle deposition and porosity reduction is suggested. This model captures the essential features of the experimental measurements on spatial and temporal flow and deposition patterns.

Electromagnetic Fields↗
PubMed2005

Use of nanosized catalysts for transformation of chloro-organic pollutants.

A new method to transform anthropogenic, chloro-organic compounds (COC) by use of nanosized molecular catalysts immobilized in sol-gel matrixes is presented. COC represent a serious threat to soil and groundwater quality. Metalloporphyrinogens are nanometer sized molecules that are known to catalyze degradation of COC by reduction reactions. In the current study, metalloporphyrinogens were immobilized in sol--gel matrixes with pore throat diameters of nanometers. The catalytic activity of the matrix arrays for anaerobic reduction of tetrachloroethylene (PCE), trichloroethylene (TCE), and carbon tetrachloride (CT) was examined. Experiments were performed under conditions pertinent to groundwater systems, with titanium citrate and zero-valent iron as electron donors. All chloroorganic compounds were reduced in the presence of several sol-gel-metalloporphyrinogen hybrids (heterogeneous catalysts). For example, cobalt-5,10,15,20-(4-hydroxyphenyl)-21H,23H-porphine (TP(OH)P-Co) and cyanocobalamin (vitamin B12) reduced CT concentrations to less than 5% of their initial values in a matter of hours. Cyanocobalamin was found to reduce PCE to trace amounts in less than 48 h and TCE to less than 25% of its initial concentration in 144 h. The reactions were compared to their homogeneous (without sol-gel matrix) analogues. The reduction activity of COC for the homogeneous and heterogeneous systems ranged between similar reactivity in some cases to lower reduction rates for the heterogeneous system. These lower rates are, however, compensated by the ability to encapsulate and reuse the catalyst. Experiments with cyanocobalamin showed that the catalyst could be reused over at least 12 successive cycles of 24 h each.

Catalysis↗
PubMed2004

Quantitative characterization of pore-scale disorder effects on transport in "homogeneous" granular media.

Breakthrough curves (BTC) of a passive tracer in macroscopically homogeneous granular materials (well-sorted, unconsolidated sands or glass beads) were measured in a series of column experiments. The early and late arrival times are observed to differ systematically from theoretical predictions based on solution of the advective-dispersion equation for uniform porous media. We propose that subtle and residual pore-scale disorder effects in the porous media can account for these observations. We determine an ensemble-averaged distribution of particle transfer rates (based on a master equation for the local flux-averaged concentration) which incorporates these effects, and utilize it to calculate BTC that are in excellent agreement with the entire series of observations. Theoretical prediction of the dependence of the effective macroscopic parameters on measurable quantities is also in excellent agreement with the observations.

Journal Article↗
PubMed2003

Measurement and analysis of non-Fickian dispersion in heterogeneous porous media.

Contaminant breakthrough behavior in a variety of heterogeneous porous media was measured in laboratory experiments, and evaluated in terms of both the classical advection-dispersion equation (ADE) and the continuous time random walk (CTRW) framework. Heterogeneity can give rise to non-Fickian transport patterns, which are distinguished by "anomalous" early arrival and late time tails in breakthrough curves. Experiments were conducted in two mid-scale laboratory flow cells packed with clean, sieved sand of specified grain sizes. Three sets of experiments were performed, using a "homogeneous" packing, a randomly heterogeneous packing using sand of two grain sizes, and an exponentially correlated structure using sand of three grain sizes. Concentrations of sodium chloride tracer were monitored at the inflow reservoir and measured at the outflow reservoir. Breakthrough curves were then analyzed by comparison to fitted solutions from the ADE and CTRW formulations. In all three systems, including the "homogeneous" one, subtle yet measurable differences between Fickian and non-Fickian transport were observed. Quantitative analysis demonstrated that the CTRW theory characterized the full shape of the breakthrough curves far more effectively than the ADE.

Chemical Phenomena↗
PubMed2002

In situ remediation of groundwater contaminated by heavy- and transition-metal ions by selective ion-exchange methods.

Laboratory studies were conducted to investigate the feasibility of using ion-exchange resins in permeable reactive barriers (PRBs) for the remediation of groundwater contaminated by heavy and transition metals. Ion-exchange resins represent an essentially neglected class of materials which may, in addition to iron, activated carbon, and zeolites, prove effective for use in PRBs. Four resins were considered: two commercially available resins, Duolite GT-73 (Rohm and Haas) and Amberlite IRC-748 (Rohm and Haas), and two solvent-impregnated resins (SIRs). The SIRs were prepared from Amberlite IRA-96 (Rohm and Haas) and two different thiophosphoric extractants. All four resins are able to reduce cadmium, lead, and copper concentrations from 1000 microg/L (typical for contaminated groundwaters) to below 5 microg/L. Significantly, all of the resins are effective for the capture of cadmium, copper, and lead, even in the presence of CaCl2 and clay. Because of their high hydraulic conductivity, the use of these resins in clusters of wells, as an alternative to continuous walls, is considered in the design of effective PRBs. Numerical solution of the groundwater flow equations shows that, depending on the well configuration, most (or all) of the contaminated groundwater can pass through the resins. These results demonstrate the possibility of using selective ion-exchange resins as an effective, active material in PRBs for in situ groundwater remediation.

Ion Exchange↗
PubMed2002

Spatial behavior of anomalous transport.

We present a general derivation of one-dimensional spatial concentration distributions for anomalous transport regimes. Such transport can be captured in the framework of a continuous time random walk with a broad transition time distribution. This general theory includes a Fokker-Planck equation as a particular limiting case. All of the concentration profiles, as well as the associated temporal first passage time distributions, can be written in terms of a single special function (that belongs to the class of Fox functions). In addition, we consider the first two moments of the spatial concentration distributions, and determine not only their scaling behavior with time but also the coefficients and correction terms.

Journal Article↗
PubMedDate not supplied

Fluid flow and solute migration within the capillary fringe.

Laboratory experiments involving both homogeneous and heterogeneous porous media are used to demonstrate that fluid flow and solute transport will occur regularly in the capillary fringe (CF), including both vertical (upward as well as downward) and horizontal flow velocities. Horizontal flow above the water table appears to be limited primarily to the region of high water saturation (i.e., the CF), an observation supported by numerical modeling and consistent with the literature. Beyond observations presented in prior literature, it was observed that exchange of water within the CF with water below the water table is active, with flux both from the CF downward across the water table and from the region below the water table, upward into the CF. This flux is enhanced by the presence of physical heterogeneity. These findings strongly contrast the common conceptualization of predominantly downward vertical fluid flow through the unsaturated zone, with transition to fully three-dimensional flow only below the water table. Based on these observations, it is suggested that the CF may affect, far more significantly than is usually assumed, the natural geochemical and microbial conditions present in the region of transition from unsaturated to saturated ground water flow.

Geological Phenomena↗
PubMedDate not supplied

Computing "anomalous" contaminant transport in porous media: the CTRW MATLAB toolbox.

We describe the continuous time random walk (CTRW) MATLAB toolbox, a collection of MATLAB scripts and functions that compute breakthrough curves (BTCs) and one-dimensional/two-dimensional (1D/2D) resident concentration profiles for passive tracer dispersion. The transport model is based on the CTRW theory. CTRW includes as special cases the classical Fickian dispersion based advection-dispersion equation, multirate and mobile-immobile models, and the fractional-in-time derivative transport equation. Several models for treating the memory effects responsible for the anomalous character of dispersion have been implemented in the CTRW toolbox. In the current version of the toolbox, it is possible to solve explicitly for the forward problem (concentration prediction) in 1D and 2D and for the inverse problem (parameter identification from experimental BTC data) in 1D. Future extensions will include explicit treatment of sorbing tracers, simple subroutines for treating radial flow from wells, introduction of arbitrary initial conditions, treatment of heterogeneous domains by use of the Fokker-Planck with Memory equation, and treatment of transport in multidimensional systems.

Environmental Monitoring↗