PPT-ECE 340 Lecture 3 Crystals and Lattices

Online reference httpecewwwcoloradoedu bartbook Crystal Lattices Periodic arrangement of atoms Repeated unit cells solidstate Stuffing atoms into unit cells Diamond Si and zinc . Identify the plane intercepts on the x y and axes 2 Specify intercepts in fractional coordinates 3 Take the reciprocals of the fractional intercepts brPage 8br Miller Indices for Planes Illustration Consider the plane in pink which is one of an infi However computational aspects of lattices were not investigated much until the early 1980s when they were successfully employed for breaking several proposed cryptosystems among many other applications It was not until the late 1990s that lattices w By Le . Mond. & Malachi. KWL. What we know:. They are . c. o. l. o. u. r. f. u. l. They are very strong. Some are worshiped. They are found all over the world. There made out of little minerals. Can We Solve Ideal Lattice Problems Efficiently?. Craig Gentry. IBM T.J. Watson. Workshop on Lattices with Symmetry. Can we efficiently break lattices with certain types of symmetry?. If a lattice has an orthonormal basis, can we find it?. PHY 752 Spring 2015 -- Lecture 1. 1. PHY 752 Electrodynamics. 11-11:50 AM MWF Olin 107. Plan for Lecture 1:. Reading: Chapters 1-2 in . Marder’s. text. Course structure and expectations. Crystal structures. Minkowski’s. Theorem. Chapter 2. Preface. A lattice point is a point in R. d . with integer coordinates.. Later we will talk about general lattice point.. Lattice Point. Let C ⊆ R. d. be symmetric around the origin, convex, bounded and suppose that volume(C)>2. China Summer School on Lattices and Cryptography, June 2014. Starting Point: Linear Equations. Easy to solve a linear system of equations. Given . A. , . b. , find . s. S. olved using Gaussian elimination, Cramer rule, etc.. recrystallisation. . . Step 1. Dissolve the impure. Crystals. Just enough hot water. to do the job. Step 2. Hot filtration . with suction. Takes out non-soluble . impurities. Step 3. Crystals allowed . Neil Conway. UC Berkeley. Joint work with:. Peter Alvaro, Peter . Bailis. ,. David Maier, Bill Marczak,. Joe Hellerstein, . Sriram. . Srinivasan. Basho Chats #004. June 27, 2012. Programming. Distributed Programming. Zakopane. 2009. Introduction . to. Crystallography. H. Böhm. Institut für Geowissenschaften. Universität Mainz. Germany. Definition. Crystallography. :. It is dedicated to the study of matter on the atomic scale, to the structural characteristics of matter and its relation to physical and chemical properties.. Thermotropic. . (temperature dependent). Lyotropic. (concentration dependent). Metallotropic. Nematic. Smectic. Cholesteric. Various forms depending on concentration. Thermotropic. Liquid Crystals. By Ben Grober. Outline. Goals. Background. Crystals. Birefringence. Samples. Method. Senarmont. Method. Results. Discussion. Goals. Accurately measure phase retardation of anisotropic crystal. Calculate birefringence of . China Summer School on Lattices and Cryptography, June 2014. Starting Point: Linear Equations. Easy to solve a linear system of equations. Given . A. , . b. , find . s. S. olved using Gaussian elimination, Cramer rule, etc.. Craig Gentry. IBM T.J. Watson. Workshop on Lattices with Symmetry. Can we efficiently break lattices with certain types of symmetry?. If a lattice has an orthonormal basis, can we find it?. Can we break “ideal lattices” – lattices for ideals in number fields – by combining geometry with algebra?.