arXiv subjects

Zhipeng Duan

Publications and source records attributed to Zhipeng Duan.

5 recordsLinked to original sources

arXiv2025

Periodicity and finite complexity in higher real $K$-theories

In this paper, we establish periodicity results for higher real $K$-theories at all heights and for all finite subgroups of the Morava stabilizer group at the prime 2. We further analyze the $RO(G)$-periodicity lattice of the height-$h$ Lubin--Tate theory, proving new $RO(G)$-graded periodicities and explicit finiteness results for the $RO(G)$-graded homotopy groups of $E_h$. Together, these results provide a foundation for both the structural and computational study of higher real $K$-theories.

math.AT↗

arXiv2024

Vanishing lines in chromatic homotopy theory

We show that at the prime 2, for any height $h$ and any finite subgroup $G \subset \mathbb{G}_h$ of the Morava stabilizer group, the $RO(G)$-graded homotopy fixed point spectral sequence for the Lubin--Tate spectrum $E_h$ has a strong horizontal vanishing line of filtration $N_{h, G}$, a specific number depending on $h$ and $G$. It is a consequence of the nilpotence theorem that such homotopy fixed point spectral sequences all admit strong horizontal vanishing lines at some finite filtration. Here, we establish specific bounds for them. Our bounds are sharp for all the known computations of $E_h^{hG}$. Our approach involves investigating the effect of the Hill--Hopkins--Ravenel norm functor on the slice differentials. As a result, we also show that the $RO(G)$-graded slice spectral sequence for $(N_{C_2}^{G}\bar{v}_h)^{-1}BP^{(\!(G)\!)}$ shares the same horizontal vanishing line at filtration $N_{h, G}$. As an application, we utilize this vanishing line to establish a bound on the orientation order $Θ(h, G)$, the smallest number such that the $Θ(h, G)$-fold direct sum of any real vector bundle is $E_h^{hG}$-orientable.

math.AT↗

arXiv2024

$RO(G)$-graded homotopy fixed point spectral sequence for height $2$ Morava $E$-theory

We consider $G=Q_8,SD_{16},G_{24},$ and $G_{48}$ as finite subgroups of the Morava stabilizer group which acts on the height $2$ Morava $E$-theory $\mathbf{E}_2$ at the prime $2$. We completely compute the $G$-homotopy fixed point spectral sequences of $\mathbf{E}_2$. Our computation uses recently developed equivariant techniques since Hill, Hopkins, and Ravenel. We also compute the $(*-σ_i)$-graded $Q_8$- and $SD_{16}$-homotopy fixed point spectral sequences, where $σ_i$ is a non-trivial one-dimensional representation of $Q_8$.

math.AT↗

arXiv2021

A new approach to the thermodynamic analysis of gas power cycles

Engineering Thermodynamics has been the core course of many science and engineering majors around the world, including energy and power, mechanical engineering, civil engineering, aerospace, cryogenic refrigeration, food engineering, chemical engineering, and environmental engineering, among which gas power cycle is one of the important contents. However, many Engineering Thermodynamics textbooks focus only on evaluating the thermal efficiency of gas power cycle, while the important concept of specific cycle work is ignored. Based on the generalized temperature-entropy diagram for the gas power cycles proposed by the authors, an ideal Otto cycle and an ideal Miller-Diesel cycle are taking as examples for the thermodynamic analyses of gas power cycles. The optimum compression ratio (or the pressure ratio) for the maximum specific cycle work or the maximum mean effective pressure is analyzed and determined. The ideal Otto and the ideal Miller-Diesel cycles, and also other gas power cycles for movable applications, are concluded that the operation under the maximum specific cycle work or the maximum mean effective pressure, instead of under the higher efficiency, is more economic and more reasonable. We concluded that the very important concept, i.e., the optimum compression (or pressure) ratio for the gas power cycles, should be emphasized in the Engineering Thermodynamics teaching process and in the latter revised or the newly edited textbooks, in order to better guide the engineering applications.

physics.ed-ph↗

arXiv2019

Discussions of gas power cycle performance analysis method in the course of Engineering Thermodynamics

Engineering Thermodynamics has been the core course of many science and engineering majors at home and abroad, including energy and power, mechanical engineering, civil engineering, aerospace, cryogenic refrigeration, food engineering, chemical engineering, and environmental engineering, among which gas power cycle is one of the important contents. However, many Engineering Thermodynamics textbooks at home and abroad focus only on evaluating the thermal efficiency of gas power cycle, while the important concept of specific cycle net work is ignored. Taking an ideal Otto cycle and an ideal Brayton as examples, the optimum compression ratio (or the pressure ratio) and the maximum specific cycle net work are analyzed and determined. The ideal Otto and the ideal Brayton cycles, and also other gas power cycles, are concluded that the operation under the optimum compression/pressure ratio of the engine, instead of under the higher efficiency, is more economic and more reasonable. We concluded that the two very important concepts, i.e., the maximum specific cycle net work and the optimum compression (or pressure) ratio for the gas power cycles, should be emphasized in the Engineering Thermodynamics teaching process and the latter revised or the newly edited textbooks, in order to better guide the engineering applications. In the end, general T-s diagram is proposed for the gas power cycles.

physics.ed-ph↗