We introduce a mathematical model, which describes the charge inversion phenomena in systems with a charged wall or boundary. This model may prove helpful in understanding semiconductor devices, ion channels, and electrochemical systems like batteries that depend on complex distributions of charge for their function. The mathematical model is derived using the energy variational approach that takes into account ion difusion, electrostatics, finite size effects, and specific boundary behavior. In ion dynamic theory, a wellknown system of equations is the Poisson-Nernst-Planck (PNP) equation that includes entropic and electrostatic energy. The PNP type of equation can also be derived by the energy variational approach. However, the PNP equations have not produced the charge inversion/layering in charged wall situations presumably because the conventional PNP does not include the finite size of ions and other physical features needed to create the charge inversion. In this paper, we investigate the key features needed to produce the charge inversion phenomena using a mathematical model, the energy variational approach. One of the key features is a finite size (finite volume) effect, which is an unavoidable property of ions important for their dynamics on small scales. The other is an interfacial constraint to capture the spatial variation of electroneutrality in systems with charged walls. The interfacial constraint is established by the difusive interface approach that approximately describes the boundary effect produced by the charged wall. The energy variational approach gives us a mathematically self-consistent way to introduce the interfacial constraint. We mainly discuss those two key features in this paper. Employing the energy variational approach, we derive a non-local partial diferential equation with a total energy consisting of the entropic energy, electrostatic energy, repulsion energy representing the excluded volume effect, and the contribution of an interfacial constraint related to overall electroneutrality between bulk/bath and wall. The resulting mathematical model produces the charge inversion phenomena near charged walls. We compare the computational results of the mathematical model to those of Monte-Carlo computations.

Three different iteration methods for a three-dimensional coordinate-transformed saturated–unsaturated flow model are compared in this study. The Picard and Newton iteration methods are the common approaches for solving Richards’ equation. The Picard method is simple to implement and cost-efficient (on an individual iteration basis). However it converges slower than the Newton method. On the other hand, although the Newton method converges faster, it is more complex to implement and consumes more CPU resources per iteration than the Picard method. The comparison of the two methods in finite-element model (FEM) for saturated–unsaturated flow has been well evaluated in previous studies. However, two iteration methods might exhibit different behavior in the coordinate-transformed finite-difference model (FDM). In addition, the Newton–Krylov method could be a suitable alternative for the coordinate-transformed FDM because it requires the evaluation of a 19-point stencil matrix. The formation of a 19-point stencil is quite a complex and laborious procedure. Instead, the Newton–Krylov method calculates the matrix–vector product, which can be easily approximated by calculating the differences of the original nonlinear function. In this respect, the Newton–Krylov method might be the most appropriate iteration method for coordinate-transformed FDM. However, this method involves the additional cost of taking an approximation at each Krylov iteration in the Newton–Krylov method. In this paper, we evaluated the efficiency and robustness of three iteration methods—the Picard, Newton, and Newton–Krylov methods—for simulating saturated–unsaturated flow through porous media using a three-dimensional coordinate-transformed FDM.

In this study, we defined risk capital as the contingency fee or insurance premium that a brownfields redeveloper needs to set aside from the sale of each house in case they need to repurchase it at a later date because the indoor air has been detrimentally affected by subsurface contamination. The likelihood that indoor air concentrations will exceed a regulatory level subject to subsurface heterogeneity and source zone location uncertainty is simulated by a physics-based hydrogeological model using Monte Carlo realizations, yielding the probability of failure. The cost of failure is the future value of the house indexed to the stochastic US National Housing index. The risk capital is essentially the probability of failure times the cost of failure with a surcharge to compensate the developer against hydrogeological and financial uncertainty, with the surcharge acting as safety loading reflecting the developers' level of risk aversion. We review five methodologies taken from the actuarial and financial literature to price the risk capital for a highly stylized brownfield redevelopment project, with each method specifically adapted to accommodate our notion of the probability of failure. The objective of this paper is to develop an actuarially consistent approach for combining the hydrogeological and financial uncertainty into a contingency fee that the brownfields developer should reserve (i.e. the risk capital) in order to hedge their risk exposure during the project. Results indicate that the price of the risk capital is much more sensitive to hydrogeological rather than financial uncertainty. We use the Capital Asset Pricing Model to estimate the risk-adjusted discount rate to depreciate all costs to present value for the brownfield redevelopment project. A key outcome of this work is that the presentation of our risk capital valuation methodology is sufficiently generalized for application to a wide variety of engineering projects.

A well-balanced shallow water flow model on quadtree cut cell grids is presented. The Cartesian cut cell method is applied due to its flexibility in treating curvilinear boundaries. In order to preserve a lake-at-rest and the positivity of water depths in drying/wetting zones, the hydrostatic reconstruction proposed by Audusse et al. [1] is implemented on cut cell grids. In addition, the gradient construction method on cut cells proposed by Causon et al. [8] is modified due to the spurious calculation when a solid boundary is nearly parallel to grids. The numerical schemes mentioned above are employed in Gerris which is open source free software and provides a shallow water solver on adaptive quadtree grids. The applied numerical schemes are validated using four test simulations: still water in an inclined domain; oscillation in a parabolic container; shock reflection by a circular cylinder; flash flood experiment in a model city. The simulation results are compared with analytical solutions, experiment data and the results simulated by other researchers.

Magnetic resonance electrical impedance tomography (MREIT) is a non-invasive method to visualize cross-sectional electrical conductivity and/or current density by measuring a magnetic flux density signal when an electrical current is injected into a subject. In the MREIT system, it is crucial to reduce the scan duration while maintaining spatial resolution and contrast for practical in vivo implementation. The purpose of the study is to optimize the measured magnetic flux density using an interleaved multiple-echo pulse sequence (injected current nonlinear encoding) that acquires each spatial position multiple times, although these pixels vary between echoes in their signal-to-noise ratio due to (a) T*₂ decay and (b) the current density passing through the pixel. Using the acquired multiple measured magnetic flux densities, the noise level for the measured magnetic flux density B_z at each pixel is estimated using the relationship between the intensity of the magnitude and the width of the injected current. We determine an optimal combination of the multiply acquired magnetic flux densities, which optimally reduces the random noise artifacts. We develop a new denoising technique and apply it to a recovered conductivity distribution with a known noise level of the recovered magnetic flux density, which is designed to provide a stable internal conductivity distribution, while sustaining resolution. The proposed method uses three key steps: the first step is optimizing the magnetic flux density by using the multiple-echo magnetic flux densities at each pixel, the second step is estimating the noise level of this optimized magnetic flux density and the third step is applying a denoising technique using the pixel-specific estimated noise level. Numerical simulation experiments using a three-dimensional cylindrical phantom model validated the proposed method. Multiple-echo B_z data were generated, including in short T*₂ or low spin-density regions, as a function of T*₂ and the temporal extent of the injected current. In the simulation experiment, comparing between an equally averaged and the optimized B_z methods, relative L₂-mode errors were 0.053 and 0.024, respectively. In an actual imaging experiment of an agarose gel filled with objects of various conductivities and shapes, we acquired six echoes per repetition time. The optimal weighting factors minimized the effects of noise in B_z, and provided reconstructed conductivity maps that suppressed noise artifacts that normally accumulate in the low signal-to-noise-ratio defect regions.

In this study, we observed asymmetric information flow between the stock market index and their component stocks using a transfer entropy measure. We found that the amount of information flow from an index to a stock is larger than from a stock to an index. This finding indicates that the market index is a major driving force in determining individual stocks. Interestingly, this asymmetry occurred in the same direction in every market studied from mature to emerging markets. However, the strength of the asymmetry was higher in mature markets than in emerging markets.

We investigated the express bus flow in Korea and its network topology. By using a gravity type model, we found that the bus flow between cities depends on the square root of the product of the population size of city A and the population size of city B. On the other hand, the total bus flow of a city depends on only its population size. These different dependences on population originate from the network property of the express bus network.

In a smart grid environment, data for the usage and control of power are transmitted over an Internet protocol (IP)-based network. This data contains very sensitive information about the user or energy service provider (ESP); hence, measures must be taken to prevent data manipulation. Mutual authentication between devices, which can prevent impersonation attacks by verifying the counterpart's identity, is a necessary process for secure communication. However, it is difficult to apply existing signature-based authentication in a smart grid system because smart meters, a component of such systems, are resource-constrained devices. In this paper, we consider a smart meter and propose an efficient mutual authentication protocol. The proposed protocol uses a matrix-based homomorphic hash that can decrease the amount of computations in a smart meter. To prove this, we analyze the protocol's security and performance.

We propose a model for macroautophagy and study the resulting dynamics of autophagy in a system isolated from its extra-cellular environment. It is found that the intracellular concentrations of autophagosomes and autolysosomes display oscillations with their own natural frequencies. Such oscillatory behaviors, which are interrelated to the dynamics of intracellular ATP, amino acids, and proteins, are consistent with the very recent biological observations. Implications of this theoretical study of autophagy are discussed, with regard to the possibility of guiding molecular studies of autophagy.