824 research outputs found
Maximizing Neumann fundamental tones of triangles
We prove sharp isoperimetric inequalities for Neumann eigenvalues of the
Laplacian on triangular domains.
The first nonzero Neumann eigenvalue is shown to be maximal for the
equilateral triangle among all triangles of given perimeter, and hence among
all triangles of given area. Similar results are proved for the harmonic and
arithmetic means of the first two nonzero eigenvalues
Influence of diffraction on the spectrum and wavefunctions of an open system
In this paper, we demonstrate the existence and significance of diffractive
orbits in an open microwave billiard, both experimentally and theoretically.
Orbits that diffract off of a sharp edge of the system are found to have a
strong influence on the transmission spectrum of the system, especially in the
regime where there are no stable classical orbits. On resonance, the
wavefunctions are influenced by both classical and diffractive orbits. Off
resonance, the wavefunctions are determined by the constructive interference of
multiple transient, nonperiodic orbits. Experimental, numerical, and
semiclassical results are presented.Comment: 27 pages, 29 figures, and 3 tables. Submitted to Physical Review E. A
copy with higher resolution figures is available at
http://monsoon.harvard.edu/~hersch/papers.htm
Observation of diffractive orbits in the spectrum of excited NO in a magnetic field
We investigate the experimental spectra of excited NO molecules in the
diamagnetic regime and develop a quantitative semiclassical framework to
account for the results. We show the dynamics can be interpreted in terms of
classical orbits provided that in addition to the geometric orbits, diffractive
effects are appropriately taken into account. We also show how individual
orbits can be extracted from the experimental signal and use this procedure to
reveal the first experimental manifestation of inelastic diffractive orbits.Comment: 4 fig
Pom1 gradient buffering through intermolecular auto-phosphorylation.
Concentration gradients provide spatial information for tissue patterning and cell organization, and their robustness under natural fluctuations is an evolutionary advantage. In rod-shaped Schizosaccharomyces pombe cells, the DYRK-family kinase Pom1 gradients control cell division timing and placement. Upon dephosphorylation by a Tea4-phosphatase complex, Pom1 associates with the plasma membrane at cell poles, where it diffuses and detaches upon auto-phosphorylation. Here, we demonstrate that Pom1 auto-phosphorylates intermolecularly, both in vitro and in vivo, which confers robustness to the gradient. Quantitative imaging reveals this robustness through two system's properties: The Pom1 gradient amplitude is inversely correlated with its decay length and is buffered against fluctuations in Tea4 levels. A theoretical model of Pom1 gradient formation through intermolecular auto-phosphorylation predicts both properties qualitatively and quantitatively. This provides a telling example where gradient robustness through super-linear decay, a principle hypothesized a decade ago, is achieved through autocatalysis. Concentration-dependent autocatalysis may be a widely used simple feedback to buffer biological activities
Mesoscopic scattering in the half-plane: squeezing conductance through a small hole
We model the 2-probe conductance of a quantum point contact (QPC), in linear
response. If the QPC is highly non-adiabatic or near to scatterers in the open
reservoir regions, then the usual distinction between leads and reservoirs
breaks down and a technique based on scattering theory in the full
two-dimensional half-plane is more appropriate. Therefore we relate conductance
to the transmission cross section for incident plane waves. This is equivalent
to the usual Landauer formula using a radial partial-wave basis. We derive the
result that an arbitrarily small (tunneling) QPC can reach a p-wave channel
conductance of 2e^2/h when coupled to a suitable reflector. If two or more
resonances coincide the total conductance can even exceed this. This relates to
recent mesoscopic experiments in open geometries. We also discuss reciprocity
of conductance, and the possibility of its breakdown in a proposed QPC for atom
waves.Comment: 8 pages, 3 figures, REVTeX. Revised version (shortened), accepted for
publication in PR
On the lowest eigenvalue of Laplace operators with mixed boundary conditions
In this paper we consider a Robin-type Laplace operator on bounded domains.
We study the dependence of its lowest eigenvalue on the boundary conditions and
its asymptotic behavior in shrinking and expanding domains. For convex domains
we establish two-sided estimates on the lowest eigenvalues in terms of the
inradius and of the boundary conditions
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