{"product_id":"9789811387500","title":"Gauge Invariance Approach to Acoustic Fields","description":"\u003ch1\u003eGauge Invariance Approach to Acoustic Fields\u003c\/h1\u003e \u003ch2\u003eGan, Woon Siong\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cdiv\u003e\n\u003cdiv\u003eThis book highlights the symmetry properties of acoustic fields and describes the gauge invariance approach, which can be used to reveal those properties. Symmetry is the key theoretical framework of metamaterials, as has been demonstrated by the successful fabrication of acoustical metamaterials.\u003cbr\u003e  \u003c\/div\u003e\n\u003cdiv\u003eThe book first provides the necessary theoretical background, which includes the covariant derivative, the vector potential, and invariance in coordinate transformation. This is followed by descriptions of global gauge invariance (isotropy), and of local gauge invariance (anisotropy). Sections on time reversal symmetry, reflection invariance, and invariance of finite amplitude waves round out the coverage.   \u003c\/div\u003e\n\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2019-08-16\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9789811387500\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-981-13-8751-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 169\u003c\/p\u003e ","brand":"Springer Nature Singapore","offers":[{"title":"Default Title","offer_id":47527046512780,"sku":"9789811387500","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789811387500.jpg?v=1776038120","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9789811387500","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}