Smoothed Boundary Method for Solving Partial Differential Equations with General Boundary Conditions on Complex Boundaries

In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential equation is valid and smoothly but rapidly varying values on the boundary where boundary conditions are imposed is used to modify the original differential equations. The mathematical derivations are straight forward, and generically applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions, (2) the diffusion equation with surface diffusion, (3) the mechanical equilibrium equation, and (4) the equation for phase transformation with additional boundaries. The solutions for a few of these cases are validated against corresponding analytical and semi-analytical solutions. The potential of the approach is demonstrated with five applications: surface-reaction diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces, and a self-propelling droplet.Comment: A better smooth algorithm has been developed and tested, will soon replace Eq. 58 in page 16. We have also developed a level-set moving boundary SBM method, and it will replace the Navier-Stokes-Cahn-Hilliard type domain parameter tracking method in Section 5.

Particle-Level Modeling of the Charge-Discharge Behavior of Nanoparticulate Phase-Separating Li-Ion Battery Electrodes

In nanoparticulate phase-separating electrodes, phase separation inside the particles can be hindered during their charge/discharge cycles even when a thermodynamic driving force for phase separation exists. In such cases, particles may (de)lithiate discretely in a process referred to as mosaic instability. This instability could be the key to elucidating the complex charge/discharge dynamics in nanoparticulate phase-separating electrodes. In this paper, the dynamics of the mosaic instability is studied using Smoothed Boundary Method simulations at the particle level, where the concentration and electrostatic potential fields are spatially resolved around individual particles. Two sets of configurations consisting of spherical particles with an identical radius are employed to study the instability in detail. The effect of an activity-dependent exchange current density on the mosaic instability, which leads to asymmetric charge/discharge, is also studied. While we show that our model reproduces the results of a porous-electrode model for the simple setup studied here, it is a powerful framework with the capability to predict the detailed dynamics in three-dimensional complex electrodes and provides further insights into the complex dynamics that result from the coupling of electrochemistry, thermodynamics, and transport kinetics

Loss of vesicular dopamine release precedes tauopathy in degenerative dopaminergic neurons in a Drosophila model expressing human tau.

While a number of genome-wide association studies have identified microtubule-associated protein tau as a strong risk factor for Parkinson's disease (PD), little is known about the mechanism through which human tau can predispose an individual to this disease. Here, we demonstrate that expression of human wild-type tau is sufficient to disrupt the survival of dopaminergic neurons in a Drosophila model. Tau triggers a synaptic pathology visualized by vesicular monoamine transporter-pHGFP that precedes both the age-dependent formation of tau-containing neurofibrillary tangle-like pathology and the progressive loss of DA neurons, thereby recapitulating the pathological hallmarks of PD. Flies overexpressing tau also exhibit progressive impairments of both motor and learning behaviors. Surprisingly, contrary to common belief that hyperphosphorylated tau could aggravate toxicity, DA neuron degeneration is alleviated by expressing the modified, hyperphosphorylated tau(E14). Together, these results show that impairment of VMAT-containing synaptic vesicle, released to synapses before overt tauopathy may be the underlying mechanism of tau-associated PD and suggest that correction or prevention of this deficit may be appropriate targets for early therapeutic intervention

The characterization of collapsin response mediator protein-1 (CRMP-1) for Arp2/3 dependent actin structures

The actin cytoskeleton, composed of actin and its binding proteins, drives cell motility, determines cell shape, and is necessary for strong cell-matrix and cell-cell adhesion. Consistent with its critical function in cell physiology, actin assembly is highly regulated. One of the key factors controlling actin assembly is the actin nucleator, the Arp2/3 complex. Upon the hierarchical regulation of the activity of the Arp2/3 complex, the cell can build the correct actin framework spatially and temporally in response to different cellular signals. Understanding the molecular mechanism of how Arp2/3 is regulated would provide crucial insights into how actin polymerization is normally controlled to direct cell movements and also insights into how misregulation of actin assembly can cause disease such as metastasis. Even though many factors have been shown to contribute to Arp2/3 dependent actin assembly, these known factors are not sufficient to account for Arp2/3 mediated actin assembly detected in cells, implying there are still missing factors that contribute to this reaction. The bacterial pathogen Listeria monocytogenes, for example, uses host Arp2/3 to assemble an actin comet tail. We used Listeria as a tool to screen brain cytosol for new factors that promote comet tail assembly. We identified Collapsin Response Mediator Protein-1 (CRMP-1) as a new factor for Arp2/3 dependent actin polymerization. CRMP-1 is essential for Listeria monocytogenes actin tail formation, as well as for actin filament accumulation inside MDCK epithelial cells. CRMP-1 acts as an enhancer for Arp2/3 complex in the Listeria system; yet CRMP-1 works with EVL as a novel Arp2/3 activator in the mammalian system. Perturbing CRMP-1 function results in the loss of actin assembly in both systems. CRMP-1 belongs to CRMP family which has been long studied as a microtubule binding protein. Our results reveal a potential new role for this whole family: a factor that crosstalk between actin and microtubule cytoskeleton

Development of a compact DFB laser interferometer for high-speed inline displacement measurement

A compact fiber laser interferometer, capable of precise displacement measurements, was devised using a 1550 nm DFB laser for frequency modulation up to 300 kHz. The system comprises a fiber laser, a fiber-optic interferometer, and a wavelength modulation system. The presented method offers nanometer-scale precision and incorporates a hydrogen cyanide (HCN) gas cell for monitoring the laser's central wavelength. A technique to compensate for modulation depth has been developed to maintain a consistent modulation depth over extensive measurement ranges. Preliminary trials reveal a measurement bias of less than 40 nm achieved over a 300 mm range at a speed of 100 mm/s compared to a calibrated interferometer. This approach proves beneficial for high-precision measurements for inline semiconductor manufacturing processes

Applying Sequential Pattern Mining to Generate Block for Scheduling Problems

The main idea in this paper is using sequential pattern mining to find the information which is helpful for finding high performance solutions. By combining this information, it is defined as blocks. Using the blocks to generate artificial chromosomes (ACs) could improve the structure of solutions. Estimation of Distribution Algorithms (EDAs) is adapted to solve the combinatorial problems. Nevertheless many of these approaches are advantageous for this application, but only some of them are used to enhance the efficiency of application. Generating ACs uses patterns and EDAs could increase the diversity. According to the experimental result, the algorithm which we proposed has a better performance to solve the permutation flow-shop problems

Applying Sequential Pattern Mining to Generate Block for Scheduling Problems

The main idea in this paper is using sequential pattern mining to find the information which is helpful for finding high performance solutions. By combining this information, it is defined as blocks. Using the blocks to generate artificial chromosomes (ACs) could improve the structure of solutions. Estimation of Distribution Algorithms (EDAs) is adapted to solve the combinatorial problems. Nevertheless many of these approaches are advantageous for this application, but only some of them are used to enhance the efficiency of application. Generating ACs uses patterns and EDAs could increase the diversity. According to the experimental result, the algorithm which we proposed has a better performance to solve the permutation flow-shop problems

Applying Sequential Pattern Mining to Generate Block for Scheduling Problems

The main idea in this paper is using sequential pattern mining to find the information which is helpful for finding high performance solutions. By combining this information, it is defined as blocks. Using the blocks to generate artificial chromosomes (ACs) could improve the structure of solutions. Estimation of Distribution Algorithms (EDAs) is adapted to solve the combinatorial problems. Nevertheless many of these approaches are advantageous for this application, but only some of them are used to enhance the efficiency of application. Generating ACs uses patterns and EDAs could increase the diversity. According to the experimental result, the algorithm which we proposed has a better performance to solve the permutation flow-shop problems