{"id":397,"date":"2012-06-17T19:04:01","date_gmt":"2012-06-17T23:04:01","guid":{"rendered":"http:\/\/blogs.vassar.edu\/diffractionsymmetries\/?page_id=397"},"modified":"2013-07-02T10:11:04","modified_gmt":"2013-07-02T14:11:04","slug":"symmetry-library-3","status":"publish","type":"page","link":"https:\/\/pages.vassar.edu\/diffractionsymmetries\/symmetry-library-3\/","title":{"rendered":"Symmetry Library"},"content":{"rendered":"

Symmetry patterns\u00a0 of group \u201cC\u201d<\/strong><\/em><\/p>\n

Symmetry Group\u00a0C\u221e:\u00a0<\/span><\/em><\/strong>This is an image of\u00a0C. elegans<\/em> in a circular shape. Once taken, the image is imported into Mathematica, where a specific code is used to form the diffraction image.\u00a0Examining the diffraction image, we can conclude that \u00a0it has\u00a0a\u00a0linear element, which contains an Inversion Center. Thus the diffraction image possesses symmetry by using the rules of Group theory. This symmetry can be classified under the C infinity group. The matrix is composed from the diffraction image.<\/p>\n

\u00a0C. elegans \u00a0<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0Diffraction Image<\/span><\/p>\n

\"\"<\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\"\"<\/a><\/p>\n

matrix\u00a0<\/span><\/p>\n

\"\begin{bmatrix}<\/p>\n

 <\/p>\n

Symmetry Group C1<\/span><\/strong><\/em>:<\/span><\/strong>\u00a0\u00a0Once an image of the\u00a0C. elegans<\/em>\u00a0is taken, the image is imported into Mathematica, where a specific code is used to form the diffraction image. This diffraction image is classified under the symmetry group C1. This is interpreted as a nonlinear element that doesn\u2019t contain multiple c3, a reflection plane, or proper rotational axis. The diffraction image also does not contain an inversion center.\u00a0Examining the diffraction image, we can conclude the C. elegans<\/em>\u00a0has a unique shape that is classified under diffraction image from the\u00a0C. elegans<\/em>\u00a0possessive symmetry by using the rules of symmetry under Group theory. This symmetry can be classified under the C1. The matrix is composed from the diffraction image.<\/p>\n

 <\/p>\n

C. elegans \u00a0<\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Diffraction Image<\/p>\n

\"\"<\/a>\"\"<\/a><\/p>\n

matrix<\/span><\/p>\n

\"\begin{bmatrix}<\/p>\n

Symmetry Group C2v:<\/span><\/em><\/strong> <\/strong>\u00a0The C. elegan<\/em> shown below is in shape in a classical “C” shape.\u00a0The image is imported into Mathematica where a specific code is used to form the diffraction image. Examining the diffraction image we can conclude the diffraction image from the\u00a0C. elegan<\/em>\u00a0possessive symmetry by using the rules of symmetry under Group theory.\u00a0The diffraction pattern from the C. elegan<\/em>\u00a0has a\u00a0linear element that does not include multiple C3 or horizontal perpendicular axes. However it does contain a proper rotational, and vertical reflection plane. This symmetry can be classified under the C2v group. The matrix is composed from the diffraction image.<\/p>\n

C. elegans<\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Diffraction Image<\/span><\/p>\n

\"\"<\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\"\"<\/a><\/p>\n

matrix<\/span><\/p>\n

 <\/p>\n

\"\begin{bmatrix}<\/p>\n

Symmetry Group\u00a0<\/span><\/em><\/strong>C2:\u00a0<\/span>This is an image of a\u00a0C. elegan<\/em>\u00a0in a sinusoidal shape. Once taken, the image is imported into Mathematica where a specific code is used to form the diffraction image.\u00a0Examining the diffraction image we can conclude it has\u00a0a\u00a0linear, that element that does not include multiple C3 or horizontal axis perpendicular axes. However, it has a proper rotational and vertical reflection plane.\u00a0Thus the diffraction image possesses symmetry by using the rules of Group theory. This symmetry can be classified under the C 2 group. The matrix is composed from the diffraction image.<\/p>\n

C. elegans\u00a0\u00a0<\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0Diffraction Image\u00a0<\/span><\/p>\n

\"\"<\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\"\"<\/a><\/p>\n

Matrix<\/span><\/p>\n

\"\begin{bmatrix}<\/p>\n

Symmetry pattern of \u00a0Group \u201cD\u201d<\/strong><\/em><\/p>\n

Symmetry Group D\u221e<\/span><\/em><\/strong>: This<\/em><\/strong> is an image of a\u00a0C. elegan<\/em>\u00a0in a linear shape. Once taken, the image is imported into Mathematica where a specific code is used to form the diffraction image.\u00a0Examining the diffraction image we can conclude it has\u00a0a\u00a0linear element, which contains an Inversion Center. Thus the diffraction image possesses symmetry by using the rules of Group theory. This symmetry can be classified under the D infinity group. The matrix is composed from the diffraction image.<\/p>\n

C. elegans\u00a0<\/span>\u00a0\u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0Diffraction Image\u00a0<\/span><\/p>\n

\"\"<\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\"\"<\/a><\/p>\n

Matrix<\/span><\/p>\n

\"\begin{bmatrix}<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Symmetry patterns\u00a0 of group \u201cC\u201d Symmetry Group\u00a0C\u221e:\u00a0This is an image of\u00a0C. elegans in a circular shape. Once taken, the image is imported into Mathematica, where a specific code is used to form the diffraction image.\u00a0Examining the diffraction image, we can … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2480,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-397","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/diffractionsymmetries\/wp-json\/wp\/v2\/pages\/397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/diffractionsymmetries\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pages.vassar.edu\/diffractionsymmetries\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/diffractionsymmetries\/wp-json\/wp\/v2\/users\/2480"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/diffractionsymmetries\/wp-json\/wp\/v2\/comments?post=397"}],"version-history":[{"count":36,"href":"https:\/\/pages.vassar.edu\/diffractionsymmetries\/wp-json\/wp\/v2\/pages\/397\/revisions"}],"predecessor-version":[{"id":412,"href":"https:\/\/pages.vassar.edu\/diffractionsymmetries\/wp-json\/wp\/v2\/pages\/397\/revisions\/412"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/diffractionsymmetries\/wp-json\/wp\/v2\/media?parent=397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}