8,342 research outputs found
Renormalization and blow up for charge one equivariant critical wave maps
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
We consider the focusing -critical half-wave equation in one space
dimension where denotes the
first-order fractional derivative. Standard arguments show that there is a
critical threshold such that all solutions with extend globally in time, while solutions with 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 . More precisely, we construct a
family of minimal mass blowup solutions that are parametrized by the energy
and the linear momentum . In particular, our main result
(and its proof) can be seen as a model scenario of minimal mass blowup for
-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page
Color television study Final report, Nov. 1965 - Mar. 1966
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
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
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
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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