Chemical surface tuning of zinc metal anode toward stable,dendrite-less aqueous zinc-ion batteries

The commercialization of Zn batteries is confronted with urgent challenges in the metal anode,such as dendrite formation,capacity loss,and cracking or dissolution.Here,surface interfacial engineering of the Zn anode is introduced for achieving safety and dendritic-free cycling for high-performance aqueous Zn batteries through a simple but highly effective chemical etching-substitution method.The chemical modification induces a rough peak-valley surface with a thin fluorine-rich interfacial layer on the Zn anode surface,which regulates the growth orientation via guiding uniform Zn plating/stripping,significantly enhances accessibility to aqueous electrolytes and improves wettability by reducing surface energy.As a result,such a synergetic surface effect enables uniform Zn plating/stripping with low polarization of 29 m V at a current density of 0.5 m A cm^(-2) with stable cyclic performance up to 1000 h.Further,a full cell composed of a fluorine-substituted Zn anode coupled with aβ-MnO_(2)or Ba-V_(6)O_(13)cathode demonstrates improved capacity retention to 1000 cycles compared to the pristine-Zn cells.The proposed valley deposition model provides the practical direction of surface-modified interfacial chemistries for improving the electrochemical properties of multivalent metal anodes via surface tuning.

Geometric Proof of Riemann Conjecture

This paper proves Riemann conjecture (RH), i.e., that all the zeros in critical region of Riemann ξ -function lie on symmetric line σ =1/2 . Its proof is based on two important properties: the symmetry and alternative oscillation for ξ = u + iv . Denote . Riemann proved that u is real and v ≡ 0 for β =0 (the symmetry). We prove that the zeros of u and v for β > 0 are alternative, so u (t,0) is the single peak. A geometric model was proposed. is called the root-interval of u (t,β) , if |u| > 0 is inside Ij and u = 0 is at its two ends. If |u (t,β)| has only one peak on each Ij, which is called the single peak, else called multiple peaks (it will be proved that the multiple peaks do not exist). The important expressions of u and v for β > 0 were derived. By , the peak u (t,β) will develop toward its convex direction. Besides, ut (t,β) has opposite signs at two ends t = tj , tj+1 of Ij , also does, then there exists some inner point t′ such that v (t′,β) = 0. Therefore {|u|,|v|/β} in Ij form a peak-valley structure such that has positive lower bound independent of t ∈ Ij (i.e. RH holds in Ij ). As u (t,β) does not have the finite condensation point (unless u = const.), any finite t surely falls in some Ij , then holds for any t (RH is proved). Our previous paper “Local geometric proof of Riemann conjecture” (APM, V.10:8, 2020) has two defects, this paper has amended these defects and given a complete proof of RH.

Local Geometric Proof of Riemann Conjecture

Riemann hypothesis (RH) is a difficult problem. So far one doesn’t know how to go about it. Studying ζ and using analysis method likely are two incor-rect guides. Actually, a unique hope may study Riemann function , , by geometric analysis, which has the symmetry: v=0 if β=0, and basic expression . We show that |u| is single peak in each root-interval of u for fixed β ∈(0,1/2]. Using the slope ut, we prove that v has opposite signs at two end-points of Ij. There surely exists an inner point such that , so {|u|,|v|/β} form a local peak-valley structure, and have positive lower bound in Ij. Because each t must lie in some Ij, then ||ξ|| > 0 is valid for any t (i.e. RH is true). Using the positivity of Lagarias (1999), we show the strict monotone for β > β0 ≥ 0 , and the peak-valley structure is equiva-lent to RH, which may be the geometric model expected by Bombieri (2000). This research follows Liuhui’s methodology: “Computing can detect the un-known and method”.

The Symmetry of Riemann <i>ξ</i>-Function

To prove RH, studying ζ and using pure analysis method likely are two kinds of the incorrect guide. Actually, a unique hope may study Riemann function by geometric analysis, which has the symmetry: v = 0 if β = 0, and Assume that |u| is single peak in each root-interval of u for any fixed β ∈ (0,1/2], using the slope ut of the single peak, we prove that v has opposite signs at two end-points of Ij, there surely is an inner point so that v = 0, so {|u|,|v|/β}form a local peak-valley structure, and have positive lower bound in Ij. Because each t must lie in some Ij , then ||ξ|| > 0 is valid for any t. In this way, the summation process of ξ is avoided. We have proved the main theorem: Assume that u (t, β) is single peak, then RH is valid for any . If using the equivalence of Lagarias (1999), the assumption of single peak can be canceled. Therefore our new thinking is that we have found the local peak-valley structure of ξ, which may be the geometry structure expected by Bombieri (2000), and proposed a basic framework of proving RH by geometric analysis.

An optimization strategy of controlled electric vehicle charging considering demand side response and regional wind and photovoltaic

Renewable energy,such as wind and photovoltaic(PV),produces intermittent and variable power output.When superimposed on the load curve,it transforms the load curve into a‘load belt’,i.e.a range.Furthermore,the large scale development of electric vehicle(EV)will also have a significant impact on power grid in general and load characteristics in particular.This paper aims to develop a controlled EV charging strategy to optimize the peak-valley difference of the grid when considering the regional wind and PV power outputs.The probabilistic model of wind and PV power outputs is developed.Based on the probabilistic model,the method of assessing the peak-valley difference of the stochastic load curve is put forward,and a two-stage peak-valley price model is built for controlled EV charging.On this basis,an optimization model is built,in which genetic algorithms are used to determine the start and end time of the valley price,as well as the peak-valley price.Finally,the effectiveness and rationality of the method are proved by the calculation result of the example.

Actual wellbore tortuosity evaluation using a new quasi-three-dimensional approach

The irregular wellbore trajectory caused by the wellbore deviation and fluctuation makes a significant effect on the torque and drag in extending and direction drilling,especially for wellbore trajectory with obvious deviation in the drilling direction.As a consequence,a new quasi-three-dimensional wellbore tortuosity evaluation method is developed.The new method incorporates the effect of fluctuation frequency and amplitude of oscillating wellbore trajectory;a weight coefficient index that quantifies the effect of tortuosity of one segment trajectory to the entire trajectory;a‘Peak-Valley’principle that can decompose the irregular wellbore trajectory in various scale lengths.The studies show that the deflection angle between the segments of tortuous wellbore increases the torque and drag by strengthening the contact behaviors between the drillstring and borehole.Therefore,the deflection angle is introduced to quantify the effect of deviation in the drilling direction on wellbore tortuosity.The evaluation results of two field cases demonstrate the new method which is adapted to the wellbore trajectory fluctuating with various characteristics and can reflect the actual state of wellbore tortuosity with severe oscillation more effectively and accurately.