The blue curve shows the classic Van Hove singularities (the discontinuities in the DOS). The right panel shows that after introduction of disorder in the force constants, the reduced DOS exhibits a boson peak (pink curve). The histogram is established from numerical calculations of eigenvalues in 25 instances of a 23 × 23 × 23 lattice. The middle panel shows the evolution of energy levels for interpolations of the dynamical matrix between the two systems. To avoid crowding of the picture, the system size is only 5 × 5 × 5 here. The modes lying closest to the transverse acoustic Van Hove singularity are marked in red to allow easier tracing. Researchers have known for more than four decades that the density of vibrational states (DOS) of amorphous materials differs in a characteristic way from that of crystalline ones. In crystals, the low frequency DOS, g ( ω ), follows the so-called Debye model well that is, by simple counting of possible sound waves compatible with the boundary conditions one obtains the frequency dependence of the DOS, g ( ω ) ∝ ω 2. In contrast, amorphous materials show an excess contribution at low frequencies. Man and woman looking at smartphone graphic, Landscape architecture Architectural drawing People Art, old people, tshirt, people png 500x750px Architectural rendering Architectural Presentation Architectural drawing, Skateboard Mockup, plan, electric Blue png 564x846px Architectural designer Architectural drawing Drafter, construction planning, electronics, building png 1000x704px Building Architectural drawing Sketch, building, building, condominium png 960x582px plan Architecture Architectural plan Architectural drawing, design, angle, text png 675x1230px collage with white background, Visualization Architectural rendering Architecture SketchUp, people, 3D Computer Graphics, people png 1400x1068px holding binoculars, Architecture montage graphy Architectural rendering, people Looking Down, arm, silhouette png 378x1280px Adobe shop Person Design, People ARCHITECTURAL, photomontage, human png 438x1000px Rendering Person, 3D Computer Graphics, people png 940圆27px compass with documents illustration, Architecture Architectural engineering, Construction engineer desk, angle, construction Tools png 1121x1006px plan Architecture, top view, angle, animals png 1385x577px Architectural drawing Architecture Sketch, Hand-painted city building, white and blue building illustration, watercolor Painting, angle png 874x537px Building Architectural engineering House, the modern huizhou architecture, angle, building png 995x820px Architectural plan House plan, design, angle, building png 1000圆80px, people, people, presentation png 1500x2250px 2.65MB.Architecture Architectural plan Drawing, architecture, building, plan png 1461x1461px 1.16MB.Architectural drawing Architecture Illustration, people, illustration of people, watercolor Painting, angle png 564x795px rendering Architecture Drawing, sitting man, tshirt, 3D Computer Graphics png 528x900px Architectural drawing, SKETCHES, angle, building png 1128x847px Architectural plan Landscape architecture, Tree Plan, round green, watercolor Painting, leaf Vegetable png 900x900px 1.37MB.blue and white house illustration, Architectural rendering Architecture Villa Architectural designer, houses, angle, building png 534x480px Rendering, daughter, white, child png 800x1200px plan Blueprint Architecture Drawing, building, building, plan png 840x597px architecture Architectural drawing Sketch, design, angle, building png 1000x763px is usually identified in a reduced DOS representation, g ( ω ) / ω 2 vs ω, which shows a peak which can be detected experimentally by methods like inelastic neutron scattering or nuclear inelastic scattering.
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