144,112 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
A refined invariant subspace method and applications to evolution equations
The invariant subspace method is refined to present more unity and more
diversity of exact solutions to evolution equations. The key idea is to take
subspaces of solutions to linear ordinary differential equations as invariant
subspaces that evolution equations admit. A two-component nonlinear system of
dissipative equations was analyzed to shed light on the resulting theory, and
two concrete examples are given to find invariant subspaces associated with
2nd-order and 3rd-order linear ordinary differential equations and their
corresponding exact solutions with generalized separated variables.Comment: 16 page
Extension of Hereditary Symmetry Operators
Two models of candidates for hereditary symmetry operators are proposed and
thus many nonlinear systems of evolution equations possessing infinitely many
commutative symmetries may be generated. Some concrete structures of hereditary
symmetry operators are carefully analyzed on the base of the resulting general
conditions and several corresponding nonlinear systems are explicitly given out
as illustrative examples.Comment: 13 pages, LaTe
A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations
A Hamiltonian pair with arbitrary constants is proposed and thus a sort of
hereditary operators is resulted. All the corresponding systems of evolution
equations possess local bi-Hamiltonian formulation and a special choice of the
systems leads to the KdV hierarchy. Illustrative examples are given.Comment: 8 pages, late
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
Non-Abelian Discrete Symmetries and Neutrino Masses: Two Examples
Two recent examples of non-Abelian discrete symmetries (S_3 and A_4) in
understanding neutrino masses and mixing are discussed.Comment: 16 pages, no figure, invited contribution to NJP focus issue on
neutrino
Finite dimensional integrable Hamiltonian systems associated with DSI equation by Bargmann constraints
The Davey-Stewartson I equation is a typical integrable equation in 2+1
dimensions. Its Lax system being essentially in 1+1 dimensional form has been
found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the
present paper, this essentially 1+1 dimensional Lax system is further
nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann
constraints. It is shown that the resulting 1+0 dimensional Hamiltonian systems
are completely integrable in Liouville sense by finding a full set of integrals
of motion and proving their functional independence.Comment: 10 pages, in LaTeX, to be published in J. Phys. Soc. Jpn. 70 (2001
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A hybrid stabilization technique for simulating water wave - Structure interaction by incompressible Smoothed Particle Hydrodynamics (ISPH) method
The Smoothed Particle Hydrodynamics (SPH) method is emerging as a potential tool for studying water wave related problems, especially for violent free surface flow and large deformation problems. The incompressible SPH (ISPH) computations have been found not to be able to maintain the stability in certain situations and there exist some spurious oscillations in the pressure time history, which is similar to the weakly compressible SPH (WCSPH). One main cause of this problem is related to the non-uniform and clustered distribution of the moving particles. In order to improve the model performance, the paper proposed an efficient hybrid numerical technique aiming to correct the ill particle distributions. The correction approach is realized through the combination of particle shifting and pressure gradient improvement. The advantages of the proposed hybrid technique in improving ISPH calculations are demonstrated through several applications that include solitary wave impact on a slope or overtopping a seawall, and regular wave slamming on the subface of open-piled structure
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
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