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Peng Qu

Publications and source records attributed to Peng Qu.

26 records · Page 2Linked to original sources
arXiv2022

Subsonic time-periodic solution to compressible Euler equations with damping in a bounded domain

In this paper, we consider the one-dimensional isentropic compressible Euler equations with linear damping $β(t,x)ρu$ in a bounded domain, which can be used to describe the process of compressible flows through a porous medium.~And the model is imposed a dissipative subsonic time-periodic boundary condition.~Our main results reveal that the time-periodic boundary can trigger a unique subsonic time-periodic smooth solution which is stable under small perturbations on initial data. Moreover, the time-periodic solution possesses higher regularity and stability provided a higher regular boundary condition.

math.AP↗
arXiv2022

Sharp non-uniqueness for the 3D hyperdissipative Navier-Stokes equations: above the Lions exponent

We study the 3D hyperdissipative Navier-Stokes equations on the torus, where the viscosity exponent $α$ can be larger than the Lions exponent $5/4$. It is well-known that, due to Lions [55], for any $L^2$ divergence-free initial data, there exist unique smooth Leray-Hopf solutions when $α\geq 5/4$. We prove that even in this high dissipative regime, the uniqueness would fail in the supercritical spaces $L^γ_tW^{s,p}_x$, in view of the generalized Ladyženskaja-Prodi-Serrin condition. The non-uniqueness is proved in the strong sense and, in particular, yields the sharpness at two endpoints $(3/p+1-2α, \infty, p)$ and $(2α/γ+1-2α, γ, \infty)$. Moreover, the constructed solutions are allowed to coincide with the unique Leray-Hopf solutions near the initial time and, more delicately, admit the partial regularity outside a fractal set of singular times with zero Hausdorff $\mathcal{H}^{η_*}$ measure, where $η_*>0$ is any given small positive constant. These results also provide the sharp non-uniqueness in the supercritical Lebesgue and Besov spaces. Furthermore, the strong vanishing viscosity result is obtained for the hyperdissipative Navier-Stokes equations.

math.AP↗
arXiv2018

Hierarchical Macro Strategy Model for MOBA Game AI

The next challenge of game AI lies in Real Time Strategy (RTS) games. RTS games provide partially observable gaming environments, where agents interact with one another in an action space much larger than that of GO. Mastering RTS games requires both strong macro strategies and delicate micro level execution. Recently, great progress has been made in micro level execution, while complete solutions for macro strategies are still lacking. In this paper, we propose a novel learning-based Hierarchical Macro Strategy model for mastering MOBA games, a sub-genre of RTS games. Trained by the Hierarchical Macro Strategy model, agents explicitly make macro strategy decisions and further guide their micro level execution. Moreover, each of the agents makes independent strategy decisions, while simultaneously communicating with the allies through leveraging a novel imitated cross-agent communication mechanism. We perform comprehensive evaluations on a popular 5v5 Multiplayer Online Battle Arena (MOBA) game. Our 5-AI team achieves a 48% winning rate against human player teams which are ranked top 1% in the player ranking system.

cs.MA↗
arXiv2017

A pico-Tesla magnetic sensor with PZT bimorph and permanent magnet proof mass

Ferromagnetic-ferroelectric composites have attracted interests in recent years for use as magnetic field sensors. The sensing is based on magneto-electric (ME) coupling between the electric and magnetic subsystems and is mediated by mechanical strain. Such sensors for AC magnetic fields require a bias magnetic field to achieve pT-sensitivity. Here we discuss measurements and theory for a novel passive, AC magnetic sensor that does not require a bias magnetic field and is based on a PZT bimorph with a permanent magnet proof mass. Mechanical strain on the PZT bimorph in this case is produced by interaction between the applied AC magnetic field and remnant magnetization of the permanent magnet, resulting in an induced voltage across PZT. Our studies have been performed on sensors with a bimorph of oppositely poled PZT platelets and a NdFeB permanent magnet proof mass. Magnetic floor noise N on the order of 100 pT per sqrHz and 10 nT per sqrHz are measured at 1 Hz and 10 Hz, respectively. When the AC magnetic field is applied at the bending resonance of 40 Hz for the bimorph, the measured N 700 pT per sqrHz. We also discuss a theory for the magneto-electro-mechanical coupling at low frequency and bending resonance in the sensor and theoretical estimates of ME voltage coefficients are in very good agreement with the data.

physics.app-ph↗
arXiv2017

Singularity formation and global existence of classical solutions for one dimensional rotating shallow water system

We study classical solutions of one dimensional rotating shallow water system which plays an important role in geophysical fluid dynamics. The main results contain two contrasting aspects. First, when the solution crosses certain threshold, we prove finite-time singularity formation for the classical solutions by studying the weighted gradients of Riemann invariants and utilizing conservation of physical energy. In fact, the singularity formation will take place for a large class of ${C}^1$ initial data whose gradients and physical energy can be arbitrarily small and higher order derivatives should be large. Second, when the initial data have constant potential vorticity, global existence of small classical solutions is established via studying an equivalent form of a quasilinear Klein-Gordon equation satisfying certain null conditions. In this global existence result, the smallness condition is in terms of the higher order Sobolev norms of the initial data.

math.AP↗
arXiv2016

Global Entropy Solutions to Weakly Nonlinear Gas Dynamics

Entropy weak solutions with bounded periodic initial data are considered for the system of weakly nonlinear gas dynamics. Through a modified Glimm scheme, an approximate solution sequence is constructed, and then a priori estimates are provided with the methods of approximate characteristics and approximate conservation laws, which gives not only the existence and uniqueness but also the uniform total variation bounds for the entropy solutions.

math.AP↗
arXiv2015

Global classical solutions to partially dissipative hyperbolic systems violating the Kawashima condition

This paper considers the Cauchy problem for the quasilinear hyperbolic system of balance laws in $\mathbb{R}^d$, $d\ge 2$. The system is partially dissipative in the sense that there is an eigen-family violating the Kawashima condition. By imposing certain supplementary degeneracy conditions with respect to the non-dissipative eigen-family, global unique smooth solutions near constant equilibria are constructed. The proof is based on the introduction of the partially normalized coordinates, a delicate structural analysis, a family of scaled energy estimates with minimum fractional derivative counts and a refined decay estimates of the dissipative components of the solution.

math.AP↗