1,395 research outputs found

    The synthesis of boron carbide filaments final report

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    Synthesis, strength, crystal structure, and composite material formation of boron carbide whisker

    Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

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    We consider chaotic billiards in d dimensions, and study the matrix elements M_{nm} corresponding to general deformations of the boundary. We analyze the dependence of |M_{nm}|^2 on \omega = (E_n-E_m)/\hbar using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency \omega. We show that for dilations and translations of the boundary, |M_{nm}|^2 vanishes like \omega^4 as \omega -> 0, for rotations like \omega^2, whereas for generic deformations it goes to a constant. Such special cases lead to quasi-orthogonality of the eigenstates on the boundary.Comment: 4 pages, 3 figure

    Parametric Evolution for a Deformed Cavity

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    We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>. We describe how the parametric kernel P(n|m) = , also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.Comment: 13 pages, 8 figures, improved introduction, to be published in Phys. Rev.

    Study of the growth parameters involved in synthesizing boron carbide filaments Final report

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    Boron carbide whiskers - growth, mechanical properties and crystalline perfection, and incorporation in composite material

    Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems

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    Consider a time-dependent Hamiltonian H(Q,P;x(t))H(Q,P;x(t)) with periodic driving x(t)=Asin(Ωt)x(t)=A\sin(\Omega t). It is assumed that the classical dynamics is chaotic, and that its power-spectrum extends over some frequency range ω<ωcl|\omega|<\omega_{cl}. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for Ω<ωcl\Omega<\omega_{cl}, and a relatively small response otherwise, independently of the driving amplitude AA. We define a non-perturbative regime in the (Ω,A)(\Omega,A) space, where LRT fails, and demonstrate this failure numerically. For A>AprtA>A_{prt}, where AprtA_{prt}\propto\hbar, the system may have a relatively strong response for Ω>ωcl\Omega>\omega_{cl}, and the shape of the response function becomes AA dependent.Comment: 4 pages, 2 figures, revised version with much better introductio

    Localization in Strongly Chaotic Systems

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    We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across the energy shell and decay faster than exponentially outside the energy shell. Typically however, matrix elements are strongly correlated leading to deviations from such behavior.Comment: RevTeX, 5 pages + 3 postscript figures, submitted to Phys. Rev. Let

    The ENCODE (ENCyclopedia Of DNA Elements) Project

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    The ENCyclopedia Of DNA Elements (ENCODE) Project aims to identify all functional elements in the human genome sequence. The pilot phase of the Project is focused on a specified 30 megabases (∼1%) of the human genome sequence and is organized as an international consortium of computational and laboratory-based scientists working to develop and apply high-throughput approaches for detecting all sequence elements that confer biological function. The results of this pilot phase will guide future efforts to analyze the entire human genome
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