Institute of Applied Physics and Computational Mathematics

Abstract The self-generated magnetic field coupled with the growth of multimode ablative Rayleigh–Taylor instability (ARTI) is investigated by numerical simulations with Nernst effects, resistivity and magnetized heat conduction taken into account. It is found that intense magnetic fields about 1 kT can be generated in multimode ARTI via the Biermann-battery source and the Nernst amplification. The enhancement of the self-similar growing coefficient α b caused by self-generated magnetic fields is attributed to the reinforcement of the vorticity inside the bubbles. It is also found that α b is enhanced more significantly in cases where the perturbation spectra contain more short-wavelength components. The formula for the dependence of α b on the initial perturbation amplitude proposed in Zhang et al (2018 Phys. Rev. Lett. 121 185002) remains applicable, but requires a modified coefficient to account for the attenuation of ablative stabilization due to self-generated magnetic fields.

This paper focuses on investigating the dynamic behavior of the three-dimensional globally modified Navier–Stokes equations with memory term, based on the general framework of dynamical systems arising from differential equations with delay terms. The method we employed diverges from previous approaches investigating the dynamic behavior of equations with memory term by Dafermos transformations. First, we use the classical Galerkin method to prove the well-posedness of the solutions to the transformation equation. Subsequently, by constructing an appropriate linear mapping, we demonstrated the existence of solutions to the original equation, thereby the semigroup generated by the original equation is established in phase space V × L D ( A ) 2 . Lastly, by showing the existence of bounded absorbing sets for the semigroup and its asymptotic compactness, the existence of global attractors is proved.

In the field of speech recognition, end-to-end models are gradually replacing traditional and hybrid approaches. Their main principle is autoregressive decoding, where the output sequence is formed from left to right. However, it has not yet been proven that this method provides the best results in converting speech to text. Moreover, end-toend models rely solely on the previous context, which complicates the processing of unclear or distorted sounds. In this regard, the insertion method was proposed, which does not use autoregressive decoding and generates output data in an arbitrary order. This paper examines a Kazakh speech recognition model trained using the insertion method and Connectionist Temporal Classification (CTC). The experiments conducted showed that this method improves recognition accuracy. Unlike autoregressive models, the Insertion method provides greater flexibility in processing sequences, as it does not require a strict order for generating output data. This reduces decoding delays and makes the model more robust to poorly pronounced words. Furthermore, combining the Insertion method with CTC improves the alignment of audio data and text transcription. This is especially important for agglutinative languages such as Kazakh. According to the experimental results, the recognition accuracy of the proposed model reached 10.2%, making it competitive today.