Quantitative Properties on the Steady States to A Schr\"odinger-Poisson-Slater System

A relatively complete picture on the steady states of the following Schr$\ddot{o}$dinger-Poisson-Slater (SPS) system \begin{cases} -\Delta Q+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R}^{3}\\ Q(x)\to0, & \mbox{as }x\to\infty,\\ -\Delta V=Q^{2}, & \text{in }\mathbb{R}^{3}\\ V(x)\to0 & \mbox{as }x\to\infty. \end{cases} is given in this paper: existence, uniqueness, regularity and asymptotic behavior at infinity, where $C_{S}>0$ is a constant. To the author's knowledge, this is the first uniqueness result on SPS system

Liouville Type Theorem For A Nonlinear Neumann Problem

Consider the following nonlinear Neumann problem $$\begin{cases} \text{div}\left(y^{a}\nabla u(x,y)\right)=0, & \text{for }(x,y)\in\mathbb{R}_{+}^{n+1}\\ \lim_{y\rightarrow0+}y^{a}\frac{\partial u}{\partial y}=-f(u), & \text{on }\partial\mathbb{R}_{+}^{n+1},\\ u\ge0 & \text{in }\mathbb{R}_{+}^{n+1}, \end{cases}$$ $a\in(-1,1)$. A Liouville type theorem and its applications are given under suitable conditions on $f$. Our tool is the famous moving plane method.Comment: This paper has been withdrawn by the author due to a poor writin

Deep Learning Convective Flow Using Conditional Generative Adversarial Networks

We developed a general deep learning framework, FluidGAN, that is capable of learning and predicting time-dependent convective flow coupled with energy transport. FluidGAN is thoroughly data-driven with high speed and accuracy and satisfies the physics of fluid without any prior knowledge of underlying fluid and energy transport physics. FluidGAN also learns the coupling between velocity, pressure and temperature fields. Our framework could be used to learn deterministic multiphysics phenomena where the underlying physical model is complex or unknown

Electrolysis-based Parylene Balloon Actuators for Movable Neural Probes

In order to track a specific neuron and keep good sampling neural signals during chronic implantation, the neural probes are highly desired to have moving capability. This paper presents a novel electrolysis-based parylene balloon actuator fabricated with MEMS technology. The actuator is integrated with silicon probe to make it movable. A new fabrication technology has been developed to build a parylene balloon structure with silicon spring structure, electrolysis electrodes and electrolyte inside. By applying little current to electrolysis electrodes, high pressure is generated inside the parylene balloon by electrolysis. The spring structure is stretched with the parylene balloon expansion. Therefore the neural probe is moved by the actuation. The electrolysis actuator can generate large stain and pressure, requires modest electrical power and produces minimal heat. Due to the large volume expansion obtained via electrolysis, the small actuator can create a large force. The new electrolysis actuators for movable neural probes have been fabricated and validated

CO preferential oxidation in a novel Au@ZrO₂ flow-through catalytic membrane reactor with high stability and efficiency

CO preferential oxidation (CO-PROX) achieves much interest as a strategy to remove trace CO in reformed gases for hydrogen utilization. Herein, we reported a novel Au@ZrO₂ catalytic membrane reactor by embedding gold nano-particles in ZrO₂ hollow fiber membrane for CO-PROX. The flow-through catalytic membrane exhibited high catalytic activity and oxygen selectivity, which gave a turnover frequency of 4.73 s⁻¹ at 60 °C, 2–3 times higher than conventional catalyst pellets. CO conversion of >95% was achieved over the catalytic membrane, which maintained great operational stability during 500-h operation even CO₂ and H₂O were added in the feed stream. The excellent catalytic performance of the flow-through catalytic membrane makes gold catalyst possible for practical application in the removal of CO from hydrogen