Radial Shearing Interferometer

Radial shearing interferometer (RSI) is one of the most powerful tools in many domains, especially in optical testing. RSI has compact size and good vibration immunity, which is adaptive to various environments, due to its common-path configuration. Moreover, it is very convenient application because no plane referencing wavefront is needed. The disadvantages of the conventional RSIs are that the distorted wavefront is hard to extract quickly and accurately from one radial shearography due to the phase extract algorithm is complex. Fortunately, the new RSIs can receive benefits from the accuracy of the methods of phase-shifting interferometry, and phase-shifting shearography is more sensitive than simple digital shearography. There are two mainly trend to the RSIs based on phase-shifting technique, i.e. instantaneous phase-shifting and compact size. In this chapter, a development process of RSI will be introduced briefly firstly, and then the some new RSIs based phase-shifting techniques in our work will be described in following parts, including initial RSI by using four-step polarization phase-shifting, modal wavefront reconstruction method for RSI with lateral shear and a new kind of compact RSI based micro-optics technique

Modal test and finite element analysis of a turbine disk

Experimental modal analysis of a turbine disk was conducted with the hammering method. The first five modals were obtained, matches well with calculation results of ANSYS, and proves the effectiveness of the experiment, provides a reference for further improvement of a certain engine

Invariant subspaces of the direct sum of forward and backward shifts on vector-valued Hardy spaces

Let $S_{E}$ be the shift operator on vector-valued Hardy space $H_{E}^{2}.$ Beurling-Lax-Halmos Theorem identifies the invariant subspaces of $S_{E}$ and hence also the invariant subspaces of the backward shift $S_{E}^{\ast}.$ In this paper, we study the invariant subspaces of $S_{E}\oplus S_{F}^{\ast}.$ We establish a one-to-one correspondence between the invariant subspaces of $S_{E}\oplus S_{F}^{\ast}$ and a class of invariant subspaces of bilateral shift $B_{E}\oplus B_{F}$ which were described by Helson and Lowdenslager. As applications, we express invariant subspaces of $S_{E}\oplus S_{F}^{\ast}$ as kernels or ranges of mixed Toeplitz operators and Hankel operators with partial isometry-valued symbols. Our approach greatly extends and gives different proofs of the results of C\^{a}mara and Ross, and Timotin where the case with one dimensional $E$ and $F$ was considered

ReZero: Region-customizable Sound Extraction

We introduce region-customizable sound extraction (ReZero), a general and flexible framework for the multi-channel region-wise sound extraction (R-SE) task. R-SE task aims at extracting all active target sounds (e.g., human speech) within a specific, user-defined spatial region, which is different from conventional and existing tasks where a blind separation or a fixed, predefined spatial region are typically assumed. The spatial region can be defined as an angular window, a sphere, a cone, or other geometric patterns. Being a solution to the R-SE task, the proposed ReZero framework includes (1) definitions of different types of spatial regions, (2) methods for region feature extraction and aggregation, and (3) a multi-channel extension of the band-split RNN (BSRNN) model specified for the R-SE task. We design experiments for different microphone array geometries, different types of spatial regions, and comprehensive ablation studies on different system configurations. Experimental results on both simulated and real-recorded data demonstrate the effectiveness of ReZero. Demos are available at https://innerselfm.github.io/rezero/.Comment: 13 pages, 11 figure

Higher order isometric shift operator on the de Branges-Rovnyak space

The de Branges-Rovnyak space $H(b)$ is generated by a bounded analytic function $b$ in the unit ball of $H^\infty$. When $b$ is a nonextreme point, the space $H(b)$ is invariant by the forward shift operator $M_z$. We show that the $H(b)$ spaces provide model spaces for expansive quasi-analytic $2n$-isometric operators $T$ with $T^*T - I$ being rank one. Then we describe the invariant subspaces of the $2n$-isometric forward shift operator $M_z$ on $H(b)$

Three-dimensional modelling on the hydrodynamics of a circulating fluidised bed

The rapid depletion of oil and the environmentalimpact of combustion has motivated the search for cleancombustion technologies. Fluidised bed combustion (FBC)technology works by suspending a fuel over a fast air inletwhilst sustaining the required temperatures. Using biomassor a mixture of coal/biomass as the fuel, FBC provides alow-carbon combustion technology whilst operating at lowtemperatures. Understanding the hydrodynamic processes influidised beds is essential as the flow behaviours causing heatdistributions and mixing determine the combustion processes.The inlet velocities and different particle sizes influence theflow behaviour significantly, particularly on the transitionfrom bubbling to fast fluidising regimes. Computationalmodelling has shown great advancement in its predictive capabilityand reliability over recent years. Whilst 3D modellingis preferred over 2D modelling, the majority of studies use2D models for multiphase models due to computational costconsideration. In this paper, two-fluid modelling (TFM) isused to model a 3D circulating fluidised bed (CFB) initiallyfocussing on fluid catalytic cracker (FCC) particles. Thetransition from bubbling to fast fluidisation over a rangeof velocities is explored, whilst the effects on the bubblediameter, particle distributions and bed expansion for differentparticle properties including particle sizes are compared. Dragmodels are also compared to study the effects of particleclustering at the meso-scale