An Analysis of Thickness-shear Vibrations of an Annular Plate with the Mindlin Plate Equations

The Mindlin plate equations with the consideration of thickness-shear deformation as an independent variable have been used for the analysis of vibrations of quartz crystal resonators of both rectangular and circular types. The Mindlin or Lee plate theories that treat thickness-shear deformation as an independent higher-order vibration mode in a coupled system of two-dimensional variables are the choice of theory for analysis. For circular plates, we derived the Mindlin plate equations in a systematic manner as demonstrated by Mindlin and others and obtained the truncated two-dimensional equations of closely coupled modes in polar coordinates. We simplified the equations for vibration modes in the vicinity of fundamental thickness-shear frequency and validated the equations and method. To explore newer structures of quartz crystal resonators, we utilized the Mindlin plate equations for the analysis of annular plates with fixed inner and free outer edges for frequency spectra. The detailed analysis of vibrations of circular plates for the normalized frequency versus dimensional parameters provide references for optimal selection of parameters based on the principle of strong thickness-shear mode and minimal presence of other modes to enhance energy trapping through maintaining the strong and pure thickness-shear vibrations insensitive to some complication factors such as thermal and initial stresses.Comment: Paper to be presented to the 2015 IEEE International Frequency Control Symposium and European Frequency and Time Forum, Denver, CO, USA. April 12-16, 201

Sharing, Teaching and Aligning: Knowledgeable Transfer Learning for Cross-Lingual Machine Reading Comprehension

In cross-lingual language understanding, machine translation is often utilized to enhance the transferability of models across languages, either by translating the training data from the source language to the target, or from the target to the source to aid inference. However, in cross-lingual machine reading comprehension (MRC), it is difficult to perform a deep level of assistance to enhance cross-lingual transfer because of the variation of answer span positions in different languages. In this paper, we propose X-STA, a new approach for cross-lingual MRC. Specifically, we leverage an attentive teacher to subtly transfer the answer spans of the source language to the answer output space of the target. A Gradient-Disentangled Knowledge Sharing technique is proposed as an improved cross-attention block. In addition, we force the model to learn semantic alignments from multiple granularities and calibrate the model outputs with teacher guidance to enhance cross-lingual transferability. Experiments on three multi-lingual MRC datasets show the effectiveness of our method, outperforming state-of-the-art approaches.Comment: emnlp 202

Thickness-shear Frequencies of an Infinite Quartz Plate with Material Property Variation Along the Thickness

Properties of the quartz crystal blank of a resonator is assumed homogeneous, uniform, and perfect in design, manufacturing, and applications. As end products, quartz crystal resonators are frequently exposed to gases and liquids which can cause surface damage and internal degradation of blanks under increasingly hostile conditions. The combination of service conditions and manufacturing process including chemical etching and polishing can inevitably modify the surface of quartz crystal blanks with changes of material properties, raising the question of what will happen to vibrations of quartz crystal resonators of thickness-shear type if such modifications to blanks are to be evaluated for sensitive applications. Such questions have been encountered in other materials and structures with property variations either on purpose or as the effect of environmental or natural processes commonly referred to as functionally graded materials, or FGMs. Analyses have been done in applications as part of studies on FGMs in structural as well as in acoustic wave device applications. A procedure based on series solutions has been developed in the evaluation of frequency changes and features in an infinite quartz crystal plate of AT-cut with the symmetric material variation pattern given in a cosine function with the findings that the vibration modes are now closely coupled. These results can be used in the evaluation of surface damage and corrosion of quartz crystal blanks of resonators in sensor applications or development of new structures of resonators.Comment: This is to be presented and published with the 2014 IEEE International Frequency Control Symposium, May 19-22, 2014, Taipei International Convention Center, Taipe

Towards Understanding Cross and Self-Attention in Stable Diffusion for Text-Guided Image Editing

Deep Text-to-Image Synthesis (TIS) models such as Stable Diffusion have recently gained significant popularity for creative Text-to-image generation. Yet, for domain-specific scenarios, tuning-free Text-guided Image Editing (TIE) is of greater importance for application developers, which modify objects or object properties in images by manipulating feature components in attention layers during the generation process. However, little is known about what semantic meanings these attention layers have learned and which parts of the attention maps contribute to the success of image editing. In this paper, we conduct an in-depth probing analysis and demonstrate that cross-attention maps in Stable Diffusion often contain object attribution information that can result in editing failures. In contrast, self-attention maps play a crucial role in preserving the geometric and shape details of the source image during the transformation to the target image. Our analysis offers valuable insights into understanding cross and self-attention maps in diffusion models. Moreover, based on our findings, we simplify popular image editing methods and propose a more straightforward yet more stable and efficient tuning-free procedure that only modifies self-attention maps of the specified attention layers during the denoising process. Experimental results show that our simplified method consistently surpasses the performance of popular approaches on multiple datasets

Thickness-shear Vibration Frequencies of an Infinite Plate with a Generalized Material Property Grading along the Thickness

For quartz crystal resonators of thickness-shear type, the vibration frequency and mode shapes, which are key features of resonators in circuit applications, reflect the basic material and structural properties of the quartz plate and its variation with time under various factors such as erosive gases and liquids that can cause surface and internal damages and degradation of crystal blanks. The accumulated effects eventually will change the surface conditions in terms of elastic constants and stiffness and more importantly, the gradient of such properties along the thickness. This is a typical functionally graded materials (FGM) structure and has been studied extensively for structural applications under multiple loadings such as thermal and electromagnetic fields in recent years. For acoustic wave resonators, such studies are equally important and the wave propagation in FGM structures can be used in the evaluation and assessment of performance, reliability, and life of sensors based on acoustic waves such as the quartz crystal microbalances (QCM). Now we studied the thickness-shear vibrations of FGM plates with properties of AT-cut quartz crystal varying along the thickness in a general pattern represented by a trigonometric function with both sine and cosine functions of the thickness coordinate. The solutions are obtained by using Fourier expansion of the plate deformation. We also obtained the frequency changes of the fundamental and overtone modes which are strongly coupled for the evaluation of resonator structures with property variation or design to take advantages of FGM in novel applications.Comment: Paper for the proceedings of the 2015 IEEE International Frequency Control Symposium and the European Frequency and Time Forum, Denver, CO, USA. April 12-16, 201