1,047 research outputs found
Hamiltonian structure of peakons as weak solutions for the modified Camassa-Holm equation
The modified Camassa-Holm (mCH) equation is a bi-Hamiltonian system
possessing -peakon weak solutions, for all , in the setting of an
integral formulation which is used in analysis for studying local
well-posedness, global existence, and wave breaking for non-peakon solutions.
Unlike the original Camassa-Holm equation, the two Hamiltonians of the mCH
equation do not reduce to conserved integrals (constants of motion) for
-peakon weak solutions. This perplexing situation is addressed here by
finding an explicit conserved integral for -peakon weak solutions for all
. When is even, the conserved integral is shown to provide a
Hamiltonian structure with the use of a natural Poisson bracket that arises
from reduction of one of the Hamiltonian structures of the mCH equation. But
when is odd, the Hamiltonian equations of motion arising from the conserved
integral using this Poisson bracket are found to differ from the dynamical
equations for the mCH -peakon weak solutions. Moreover, the lack of
conservation of the two Hamiltonians of the mCH equation when they are reduced
to -peakon weak solutions is shown to extend to -peakon weak solutions
for all . The connection between this loss of integrability structure
and related work by Chang and Szmigielski on the Lax pair for the mCH equation
is discussed.Comment: Minor errata in Eqns. (32) to (34) and Lemma 1 have been fixe
Derivation of the Lindblad Generator Structure by use of the It\^o Stochastic Calculus
We use the It\^o stochastic calculus to give a simple derivation of the
Lindblad form for the generator of a completely positive density matrix
evolution, by specialization from the corresponding global form for a
completely positive map. As a by-product, we obtain a generalized generator for
a completely positive stochastic density matrix evolution.Comment: Plain TEX, no figures or table
Increase in Skin Surface Lipids During Nutritional Rehabilitation of Male Alcoholics**From the Division of Dermatology, Case-Western Reserve University, Cleveland, Ohio 44106.
Skin surface lipid production was studied in a group of chronic alcoholics during a period when alcohol was replaced by a balanced diet. All subjects studied had abnormal liver function tests at the start and these returned to normal during the study. A statistically significant increase in skin surface lipid production occurred during the period of observation. Although several explanations are available, the reason for this increase is unknown
Efficient table-top dual-wavelength beamline for ultrafast transient absorption spectroscopy in the soft X-ray region.
We present a table-top beamline providing a soft X-ray supercontinuum extending up to 370 eV from high-order harmonic generation with sub-13 fs 1300 nm driving pulses and simultaneous production of sub-5 fs pulses centered at 800 nm. Optimization of high harmonic generation in a long and dense gas medium yields a photon flux of ~ 1.4 × 106 photons/s/1% bandwidth at 300 eV. The temporal resolution of X-ray transient absorption experiments with this beamline is measured to be 11 fs for 800 nm excitation. This dual-wavelength approach, combined with high flux and high spectral and temporal resolution soft X-ray absorption spectroscopy, is a new route to the study of ultrafast electronic dynamics in carbon-containing molecules and materials at the carbon K-edge
Gastrointestinal helminths of Choerophryne proboscidea and Xenorhina parkerorum (Anura: Microhylidae) from Papua New Guinea
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