非线性扩散和波阻尼传播：弱解和统计turbulence行为

Formal expansions in stochastic model for wave turbulence 2: method of diagram decomposition (complete version)

In this paper we continue to study small amplitude solutions of the damped cubic NLS equation, driven by a random force (the study was initiated in our previous work [A.Dymov, S.Kuksin, Comm. Math. Phys.'2021] and continued in [A.Dymov, S.Kuksin, A.Maiocchi, S.Vladuts, arXiv:2104.11967]). We write solutions of the equation as formal series in the amplitude and discuss the behaviour of this series under the wave turbulence limit, when the amplitude goes to zero, while the space-period goes to infinity.

阻尼机械振荡器系统中二进制信号的传播

On the propagation of binary signals in damped mechanical systems of oscillators

利用非线性超传输过程，在离散半无限耦合振荡器链中高效传输二进制信息，并通过线性串联多个机械系统来最小化或避免阻尼导致的信息损失。

Construction of quasimodes for non-selfadjoint operators via propagation of Hagedorn wave-packets

We construct quasimodes for some non-selfadjoint semiclassical operators at the boundary of the pseudo-spectrum using propagation of Hagedorn wave-packets. Assuming that the imaginary part of the principal symbol of the operator is non-negative and vanishes on certain points of the phase-space satisfying a subelliptic finite-type condition, we construct quasimodes that concentrate on these non-damped points. More generally, we apply this technique to construct quasimodes for non-selfadjoint semiclassical perturbations of the harmonic oscillator that concentrate on non-damped periodic orbits or…

关于二维重力波的波湍流理论，II：随机性的传播

On the wave turbulence theory of 2D gravity waves, II: propagation of randomness

本文结合能量估计、标准形及概率组合方法，构造了大环面上随机初值二维重力水波的长时间解，首次获得适用于波湍流的大能量、小局部能量情形正则性结果。

On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillations

We study the time-harmonic Galbrun equation describing the propagation of sound in the presence of a steady background flow. With additional rotational and gravitational terms these equations are also fundamental in helio- and asteroseismology as a model for stellar oscillations. For a simple damping model we prove well-posedness of these equations, i.e. uniqueness, existence, and stability of solutions under mild conditions on the parameters (essentially subsonic flows). The main tool of our analysis is a generalized Helmholtz decomposition.

亚临界情形下离散湍流方程的动力学近似

Kinetic approximation for equations of discrete turbulence in the subcritical case

本文在亚临界标度下为环面上阻尼/驱动三次NLS方程的能谱动力学近似提供了新证明，将已有拟解结果推广到精确解，且不依赖Feynman图而采用累积量归纳分析。

二维湍流中傅里叶模的随机建模

Stochastic modeling of Fourier modes in two-dimensional turbulence via filtered white noise

本文通过滤波白噪声建模二维湍流的傅里叶模，发现典型时间相关长度并提出随机模型，利用直接数值模拟比较被动示踪物的输运与随机模型的有效扩散。