8,342 research outputs found

    Renormalization and blow up for charge one equivariant critical wave maps

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    We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

    Nondispersive solutions to the L2-critical half-wave equation

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    We consider the focusing L2L^2-critical half-wave equation in one space dimension i∂tu=Du−∣u∣2u, i \partial_t u = D u - |u|^2 u, where DD denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold M∗>0M_* > 0 such that all H1/2H^{1/2} solutions with ∄u∄L2<M∗\| u \|_{L^2} < M_* extend globally in time, while solutions with ∄u∄L2≄M∗\| u \|_{L^2} \geq M_* may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass ∄u0∄L2=M∗\| u_0 \|_{L^2} = M_*. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy E0>0E_0 >0 and the linear momentum P0∈RP_0 \in \R. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for L2L^2-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page

    Color television study Final report, Nov. 1965 - Mar. 1966

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    Color television camera for transmission from lunar and earth orbits and lunar surfac

    Electron-vibration interaction in single-molecule junctions: from contact to tunneling regime

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    Point contact spectroscopy on a H2O molecule bridging Pt electrodes reveals a clear crossover between enhancement and reduction of the conductance due to electron-vibration interaction. As single channel models predict such a crossover at transmission probability of t=0.5, we used shot noise measurements to analyze the transmission and observed at least two channels across the junction where the dominant channel has t=0.51+/-0.01 transmission probability at the crossover conductance, which is consistent with the predictions for single-channel models.Comment: 4 pages, 1 table, 4 figure

    Lesbian and bisexual women's experiences of sexuality-based discrimination and their appearance concerns

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    Lesbian and bisexual women frequently experience sexuality-based discrimination, which is often based on others' judgements about their appearance. This short article aims to explore whether there is a relationship between lesbian and bisexual women's experiences of sexuality-based discrimination and their satisfaction with the way that they look. Findings from an online survey suggest that discrimination is negatively related to appearance satisfaction for lesbian women, but not for bisexual women. It is argued that this difference exists because lesbian appearance norms are more recognisable and distinctive than bisexual women's appearance norms

    Free Versus Constrained Evolution of the 2+1 Equivariant Wave Map

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    We compare the numerical solutions of the 2+1 equivariant Wave Map problem computed with the symplectic, constraint respecting Rattle algorithm and the well known fourth order Runge-Kutta method. We show the advantages of the Rattle algorithm for constrained system compared to the free evolution with the Runge-Kutta method. We also present an expression, which represents the energy loss due to constraint violation. Taking this expression into account we can achieve energy conservation for the Runge-Kutta scheme, which is better than with the Rattle method. Using the symplectic scheme with constraint enforcement we can reproduce previous calculations of the equivariant case without imposing the symmetry explicitly, thereby confirming that the critical behaviour is stable.Comment: 16 pages, 8 figures. Formula for the scaling function on p. 13 corrected and two typos eliminated; otherwise agrees with the published pape
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