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This paper studies a variant of ramified/branched optimal transportation problems. Given the distributions of production capacities and market sizes, a firm looks for an allocation of productions over factories, a distribution of sales across markets, and a transport path that delivers the product to maximize its profit. Mathematically, given any two measures $\mu$ and $\nu$ on $X$, and a payoff function $h$, the planner wants to minimize $\mathbf{M}_{\alpha }(T)-\int_{X}hd(\partial T)$ among all transport paths $T$ from $\tilde{\mu}$ to $\tilde{\nu}$ with $\tilde{\mu}\leq \mu $ and $\tilde{\nu}\leq \nu $, where $\mathbf{M}_{\alpha }$ is the standard cost functional used in ramified transportation. After proving the existence result, we provide a characterization of the boundary measures of the optimal solution. They turn out to be the original measures restricted on some Borel subsets up to a Delta mass on each connected component. Our analysis further finds that as the boundary payoff increases, the corresponding solution of the current problem converges to an optimal transport path, which is the solution of the standard ramified transportation., Comment: 23 pages

There is growing interest in promoting deformation twinning for plasticity in advanced materials, as highly organized twin boundaries are beneficial to better strength-ductility combination in contrast to disordered grain boundaries. Twinning deformation typically involves the kinetics of stacking faults, its interaction with dislocations, and dislocation - twin boundary interactions. While the latter has been intensively investigated, the dynamics of stacking faults has been less known. In this work, we report several new insights on the stacking fault behavior in twin induced plasticity from our meta-atom molecular dynamics simulation: The stacking fault interactions are dominated by dislocation reactions taking place spontaneously, different from the proposed mechanism in literatures; The competition among generating a single stacking fault, a twinning partial and a trailing partial dislocation is dependent on a unique parameter, i.e. stacking fault energy, which in turn determines deformation twinning behaviors. The complex twin-slip and twin-dislocation interactions demonstrate the dual role of deformation twins as both dislocation barrier and storage, potentially contributing to the high strength and ductility of advanced materials like TWIP steels where deformation twinning dominated plasticity accounts for the superb strength-ductility combination.

We report on the experimental observation of three dimensional self-deformation in an atmospheric micro discharge of the helium microjet through a tube into the ambient air upon a water electrode. The geometry of the discharge system is axial symmetric. While decreasing the discharge current, three dimensional collective motion of plasma filaments are directly observed. The three dimensional configuration of the discharge self changed from an axial symmetrical horn to a rectangular horn when the water acts as a cathode., Comment: 3 pages, 5 figures, accepted by Physics of plasmas

We studied the macro evolution of the micro atmospheric glow discharge generated between a micro argon jet into ambient air and static water. The micro discharge behaves similarly to a complex ecosystem. Non-linear behaviors are found for the micro discharge when the water acts as a cathode, different from the discharge when water behaves as an anode. Groups of snapshots of the micro discharge formed at different discharge currents are captured by an intensified charge-coupled device with controlled exposure time, and each group consisted of 256 images taken in succession. Edge detection methods are used to identify the water surface and then the total brightness is defined by adding up the signal counts over the area of the micro discharge. Motions of the water surface at different discharge currents show that the water surface lowers increasingly rapidly when the water acts as a cathode. In contrast, the water surface lowers at a constant speed when the water behaves as an anode. The light curves are similar to logistic growth curves, suggesting that a self-inhibition process occurs in the micro discharge. Meanwhile, the total brightness increases linearly during the same time when the water acts as an anode. Discharge-water interactions cause the micro discharge to evolve. The charged particle bomb process is probably responsible for the different behavior of the micro discharges when the water acts as cathode and anode., Comment: 5 pages, 5 figures, accepted by physics of plasmas

This study is designed to explore the two dimensional temperature maps of the atmospheric argon discharge consisting of pin-to-plane electrodes supplied by a high voltage DC source. After checking the stability of the micro discharge, the two dimensional image plane focused by a quartz lens was scanned by the fiber probe driven by a 3D Mobile Platform. The rotational and vibrational temperatures are calculated using nitrogen emissions collected by the high resolution spectrometer and high sensitive intensified charge coupled device (ICCD). The rotational temperature varies from 1558.15 K to 2621.14 K and vibrational temperature varies from 3010.38 K to 3774.69 K, indicating a great temperature gradient due to small discharge size. The temperature maps show a lateral expansion and a sharp truncation in the radial direction. A double layers discharge is identified, where an arc discharge coats the glow discharge., Comment: 5 pages, 5 figures. accepted by Physics of Plasmas