Random attractor for the 2D stochastic nematic liquid crystals flows with multiplicative noise

Under non-periodic boundary conditions, we consider the long-time behavior for stochastic 2D nematic liquid crystals flows with velocity and orientations perturbed by additive noise and multiplicative noise respectively. It is the first result for the long-time behavior of stochastic nematic liquid crystals under Dirichlet boundary condition for velocity field and Neumann boundary condition for orientation field.Comment: arXiv admin note: text overlap with arXiv:cond-mat/0211455 by other author

Random attractor of the 3D viscous primitive equations driven by fractional noises

We develop a new and general method to prove the the existence of the random attractor (strong attractor) for the primitive equations (PEs) of large-scale ocean and atmosphere dynamics under $non$-$periodic$ boundary conditions and driven by infinite-dimensional additive fractional Wiener processes. In contrast to our new method, the common method, compact Sobolev embedding theorem, is to obtain the uniform $a$ $priori$ estimates in some Sobolev space whose regularity is high enough. But this is very complicated for the 3D stochastic PEs with the $non$-$periodic$ boundary conditions. Therefore, the existence of universal attractor ( weak attractor) was established in previous work. The main idea of our method is that we first derive that $\mathbb{P}$-almost surely the solution operator of stochastic PEs is compact. Then we construct a compact absorbing set by virtue of the compact property of the the solution operator and the existence of a absorbing set. We should point out that our method has some advantages over the common method of using compact Sobolev embedding theorem, i.e., if the random attractor in some Sobolev space do exist in view of the common method, our method would then further implies the existence of random attractor in this space. The present work provides a general way for proving the existence of random attractor for common classes of dissipative stochastic partial differential equations and improves the existing results concerning random attractor of stochastic PEs. In a forth coming paper, we use this new method to prove the existence of strong attractor for the stochastic moist primitive equations, improving the results, the existence of weak (universal) attractor of the deterministic model.Comment: arXiv admin note: text overlap with arXiv:1409.0423 by other author

Large deviations for nematic liquid crystals driven by pure jump noise

In this paper, we establish a large deviation principle for a stochastic evolution equation which describes the system governing the nematic liquid crystals driven by pure jump noise. The proof is based on the weak convergence approach.Comment: arXiv admin note: text overlap with arXiv:1706.05056 by other author

The asymptotic behavior of primitive equations with multiplicative noise

This paper is concerned with the existence of invariant measure for 3D stochastic primitive equations driven by linear multiplicative noise under non-periodic boundary conditions. The common method is to apply Sobolev imbedding theorem to proving the tightness of the distribution of the solution. However, this method fails because of the non-linearity and non-periodic boundary conditions of the stochastic primitive equations. To overcome the difficulties, we show the existence of random attractor by proving the compact property and the regularity of the solution operator. Then we show the existence of invariant measure.Comment: arXiv admin note: text overlap with arXiv:1604.0537

A moderate deviation principle for 2D stochastic primitive equations

In this paper, we establish a central limit theorem and a moderate deviations for 2D stochastic primitive equations with multiplicative noise. The proof is mainly based on the weak convergence approach

Asymptotic behavior of 3-D stochastic primitive equations of large-scale moist atmosphere with additive noise

Using a new and general method, we prove the existence of random attractor for the three dimensional stochastic primitive equations defined on a manifold \D\subset\R^3 improving the existence of weak attractor for the deterministic model. Furthermore, we show the existence of the invariant measure

The charged top-pion production associated with the bottom quark pair as a probe of the topcolor-assisted technicolor model at the LHC

The topcolor-assisted technicolor (TC2) model predicts the existence of the charged top-pions ($\pi_t^\pm$), whose large couplings with the third generation fermions will induce the charged top-pion production associated with the bottom and anti-bottom quark pair at the CERN Large Hadron Collider (LHC) through the parton processes $c\bar b \to \pi_t^+ b \bar b$ and $u\bar d(c\bar s) \to \pi_t^+ b \bar b$. In this paper we examine these productions and find that, due to the small Standard Model backgrounds, their production rates can exceed the $3\sigma$ sensitivity of the LHC in a large part of parameter space, so these processes may serve as a good probe for the TC2 model.Comment: 10 pages, 5 figures; negligible changes in the text, notations for curves in Fig. 3a and Fig. 3b changed, references adde

Exponential stability of 3D stochastic primitive equations driven by fractional noise

In this article, we study the stability of solutions to 3D stochastic primitive equations driven by fractional noise. Since the fractional Brownian motion is essentially different from Brownian motion, lots of stochastic analysis tools are not available to study the exponential stability for the stochastic systems. Therefore, apart from the standard method for the case of Brownian motion, we develop a new method to show that 3D stochastic primitive equations driven by fractional noise converge almost surely exponentially to the stationary solutions. This method may be applied to other stochastic hydrodynamic equations and other noises including Brownian motion and L\'evy noise

Low Latency End-to-End Streaming Speech Recognition with a Scout Network

The attention-based Transformer model has achieved promising results for speech recognition (SR) in the offline mode. However, in the streaming mode, the Transformer model usually incurs significant latency to maintain its recognition accuracy when applying a fixed-length look-ahead window in each encoder layer. In this paper, we propose a novel low-latency streaming approach for Transformer models, which consists of a scout network and a recognition network. The scout network detects the whole word boundary without seeing any future frames, while the recognition network predicts the next subword by utilizing the information from all the frames before the predicted boundary. Our model achieves the best performance (2.7/6.4 WER) with only 639 ms latency on the test-clean and test-other data sets of Librispeech

Global well-posedness of stochastic nematic liquid crystals with random initial and random boundary conditions driven by multiplicative noise

The flow of nematic liquid crystals can be described by a highly nonlinear stochastic hydrodynamical model, thus is often influenced by random fluctuations, such as uncertainty in specifying initial conditions and boundary conditions. In this article, we consider the $2$-D stochastic nematic liquid crystals with the velocity field perturbed by affine-linear multiplicative white noise, with random initial data and random boundary conditions. Our main objective is to establish the global well-posedness of the stochastic equations under certain sufficient Malliavin regularity of the initial conditions and the boundary conditions. The Malliavin calculus techniques play important roles in proving the global existence of the solutions to the stochastic nematic liquid crystal models with random initial and random boundary conditions. It should be pointed out that the global well-posedness is also true when the stochastic system is perturbed by the noise on the boundary