119,653 research outputs found
A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations
A bi-Hamiltonian formulation is proposed for triangular systems resulted by
perturbations around solutions, from which infinitely many symmetries and
conserved functionals of triangular systems can be explicitly constructed,
provided that one operator of the Hamiltonian pair is invertible. Through our
formulation, four examples of triangular systems are exhibited, which also show
that bi-Hamiltonian systems in both lower dimensions and higher dimensions are
many and varied. Two of four examples give local 2+1 dimensional bi-Hamiltonian
systems and illustrate that multi-scale perturbations can lead to
higher-dimensional bi-Hamiltonian systems.Comment: 16 pages, to appear in J. Math. Phy
Triplicity of Quarks and Leptons
Quarks come in three colors and have electric charges in multiples of
one-third. There are also three families of quarks and leptons. Whereas the
first two properties can be understood in terms of unification symmetries such
as SU(5), SO(10), or E_6, why there should only be three families remains a
mystery. I propose how all three properties involving the number three are
connected in a fivefold application of the gauge symmetry SU(3).Comment: 10 pages, including 2 figure
Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras
Polynomial-in-time dependent symmetries are analysed for polynomial-in-time
dependent evolution equations. Graded Lie algebras, especially Virasoro
algebras, are used to construct nonlinear variable-coefficient evolution
equations, both in 1+1 dimensions and in 2+1 dimensions, which possess
higher-degree polynomial-in-time dependent symmetries. The theory also provides
a kind of new realisation of graded Lie algebras. Some illustrative examples
are given.Comment: 11 pages, latex, to appear in J. Phys. A: Math. Ge
Distribution of the second virial coefficients of globular proteins
George and Wilson [Acta. Cryst. D 50, 361 (1994)] looked at the distribution
of values of the second virial coefficient of globular proteins, under the
conditions at which they crystallise. They found the values to lie within a
fairly narrow range. We have defined a simple model of a generic globular
protein. We then generate a set of proteins by picking values for the
parameters of the model from a probability distribution. At fixed solubility,
this set of proteins is found to have values of the second virial coefficient
that fall within a fairly narrow range. The shape of the probability
distribution of the second virial coefficient is Gaussian because the second
virial coefficient is a sum of contributions from different patches on the
protein surface.Comment: 5 pages, including 3 figure
A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks
I reanalyze the hydrodynamic theory of fluid, polar ordered flocks. I find
new linear terms in the hydrodynamic equations which slightly modify the
anisotropy, but not the scaling, of the damping of sound modes. I also find
that the nonlinearities allowed {\it in equilibrium} do not stabilize long
ranged order in spatial dimensions ; in accord with the Mermin-Wagner
theorem. Nonequilibrium nonlinearities {\it do} stabilize long ranged order in
, as argued by earlier work. Some of these were missed by earlier work; it
is unclear whether or not they change the scaling exponents in .Comment: 6 pages, no figures. arXiv admin note: text overlap with
arXiv:0909.195
Moments of Wigner function and Renyi entropies at freeze-out
Relation between Renyi entropies and moments of the Wigner function,
representing the quantum mechanical description of the M-particle
semi-inclusive distribution at freeze-out, is investigated. It is shown that in
the limit of infinite volume of the system, the classical and quantum
descriptions are equivalent. Finite volume corrections are derived and shown to
be small for systems encountered in relativistic heavy ion collisions.Comment: 15 pages, one figur
Observation of fractional quantum Hall effect in an InAs quantum well
The two-dimensional electron system in an InAs quantum well has emerged as a
prime candidate for hosting exotic quasi-particles with non-Abelian statistics
such as Majorana fermions and parafermions. To attain its full promise,
however, the electron system has to be clean enough to exhibit
electron-electron interaction phenomena. Here we report the observation of
fractional quantum Hall effect in a very low disorder InAs quantum well with a
well-width of 24 nm, containing a two-dimensional electron system with a
density cm and low-temperature mobility cm/Vs. At a temperature of mK and T, we
observe a deep minimum in the longitudinal resistance, accompanied by a nearly
quantized Hall plateau at Landau level filling factor
- …