11,233 research outputs found
A class of equations with peakon and pulson solutions (with an Appendix by Harry Braden and John Byatt-Smith)
We consider a family of integro-differential equations depending upon a
parameter as well as a symmetric integral kernel . When and
is the peakon kernel (i.e. up to rescaling) the
dispersionless Camassa-Holm equation results, while the Degasperis-Procesi
equation is obtained from the peakon kernel with . Although these two
cases are integrable, generically the corresponding integro-PDE is
non-integrable. However,for the family restricts to the pulson family of
Fringer & Holm, which is Hamiltonian and numerically displays elastic
scattering of pulses. On the other hand, for arbitrary it is still possible
to construct a nonlocal Hamiltonian structure provided that is the peakon
kernel or one of its degenerations: we present a proof of this fact using an
associated functional equation for the skew-symmetric antiderivative of .
The nonlocal bracket reduces to a non-canonical Poisson bracket for the peakon
dynamical system, for any value of .Comment: Contribution to volume of Journal of Nonlinear Mathematical Physics
in honour of Francesco Caloger
How Close to Two Dimensions Does a Lennard-Jones System Need to Be to Produce a Hexatic Phase?
We report on a computer simulation study of a Lennard-Jones liquid confined
in a narrow slit pore with tunable attractive walls. In order to investigate
how freezing in this system occurs, we perform an analysis using different
order parameters. Although some of the parameters indicate that the system goes
through a hexatic phase, other parameters do not. This shows that to be certain
whether a system has a hexatic phase, one needs to study not only a large
system, but also several order parameters to check all necessary properties. We
find that the Binder cumulant is the most reliable one to prove the existence
of a hexatic phase. We observe an intermediate hexatic phase only in a
monolayer of particles confined such that the fluctuations in the positions
perpendicular to the walls are less then 0.15 particle diameters, i. e. if the
system is practically perfectly 2d
Helical states of nonlocally interacting molecules and their linear stability: geometric approach
The equations for strands of rigid charge configurations interacting
nonlocally are formulated on the special Euclidean group, SE(3), which
naturally generates helical conformations. Helical stationary shapes are found
by minimizing the energy for rigid charge configurations positioned along an
infinitely long molecule with charges that are off-axis. The classical energy
landscape for such a molecule is complex with a large number of energy minima,
even when limited to helical shapes. The question of linear stability and
selection of stationary shapes is studied using an SE(3) method that naturally
accounts for the helical geometry. We investigate the linear stability of a
general helical polymer that possesses torque-inducing non-local
self-interactions and find the exact dispersion relation for the stability of
the helical shapes with an arbitrary interaction potential. We explicitly
determine the linearization operators and compute the numerical stability for
the particular example of a linear polymer comprising a flexible rod with a
repeated configuration of two equal and opposite off-axis charges, thereby
showing that even in this simple case the non-local terms can induce
instability that leads to the rod assuming helical shapes.Comment: 34 pages, 9 figure
Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction
In the paper we construct an hierarchy of integrable Hamiltonian systems
which describe the variation of n-wave envelopes in nonlinear dielectric
medium. The exact solutions for some special Hamiltonians are given in terms of
elliptic functions of the first kind.Comment: 17 page
-Strands
A -strand is a map for a Lie
group that follows from Hamilton's principle for a certain class of
-invariant Lagrangians. The SO(3)-strand is the -strand version of the
rigid body equation and it may be regarded physically as a continuous spin
chain. Here, -strand dynamics for ellipsoidal rotations is derived as
an Euler-Poincar\'e system for a certain class of variations and recast as a
Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as
for a perfect complex fluid. For a special Hamiltonian, the -strand is
mapped into a completely integrable generalization of the classical chiral
model for the SO(3)-strand. Analogous results are obtained for the
-strand. The -strand is the -strand version of the
Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical
sorting. Numerical solutions show nonlinear interactions of coherent wave-like
solutions in both cases. -strand equations on the
diffeomorphism group are also introduced and shown
to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc
Bioethanol from Germinated Grains.
The most well-known way to produce bioethanol is by the enzymatic hydrolysis and fermentation of starch. In a new project “BioConcens” (2007) sponsored by DARCOF (DAnish Research Center for Organic Food and farming) one aim is to develop a combined ethanol and biogas production for use in organic farming using starch containing biomass. Natural enzymes from cereals will be used for hydrolysis of starch to glucose in accordance with technology in brewing technology. Commercial enzymes are often produced from gene-modified organisms and will therefore not be used in the suggested organic context or process.
A preliminary study was performed in which grains of wheat, rye, and barley were germinated using traditional methods applied in malting for beer production. During malting the amylase enzymes present in the grain are activated (autoamylolytic effect). Three steps were applied in the malting process; steeping, germination, and drying of the grains. After malting the grains were milled and mixed with water to 13% DM, cooked at 57.5C for 2 hours (to activate the enzymes), and cooled to 30C before adding Bakers Yeast.
The results of this study indicate that efficient hydrolysis of starch can be achieved by activation of autoamylolytic enzymes in cereal grains after a malting process. The ethanol yields obtained in the autoamylolytic hydrolysis was comparable (or slightly higher) to that of reference experiments using commercial enzymes (amylases). The highest ethanol yield was obtained with wheat (0.34 g/g DM grain), followed by barley (0.31 g/g DM grain), and rye (0.29 g/g DM grain)
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