9,387 research outputs found
Self-adjoint symmetry operators connected with the magnetic Heisenberg ring
We consider symmetry operators a from the group ring C[S_N] which act on the
Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We
investigate such symmetry operators a which are self-adjoint (in a sence
defined in the paper) and which yield consequently observables of the
Heisenberg model. We prove the following results: (i) One can construct a
self-adjoint idempotent symmetry operator from every irreducible character of
every subgroup of S_N. This leads to a big manifold of observables. In
particular every commutation symmetry yields such an idempotent. (ii) The set
of all generating idempotents of a minimal right ideal R of C[S_N] contains one
and only one idempotent which ist self-adjoint. (iii) Every self-adjoint
idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k
which are also self-adjoint and pairwise orthogonal. We give a computer
algorithm for the calculation of such decompositions. Furthermore we present 3
additional algorithms which are helpful for the calculation of self-adjoint
operators by means of discrete Fourier transforms of S_N. In our investigations
we use computer calculations by means of our Mathematica packages PERMS and
HRing.Comment: 13 page
The structure of algebraic covariant derivative curvature tensors
We use the Nash embedding theorem to construct generators for the space of
algebraic covariant derivative curvature tensors
The large core limit of spiral waves in excitable media: A numerical approach
We modify the freezing method introduced by Beyn & Thuemmler, 2004, for
analyzing rigidly rotating spiral waves in excitable media. The proposed method
is designed to stably determine the rotation frequency and the core radius of
rotating spirals, as well as the approximate shape of spiral waves in unbounded
domains. In particular, we introduce spiral wave boundary conditions based on
geometric approximations of spiral wave solutions by Archimedean spirals and by
involutes of circles. We further propose a simple implementation of boundary
conditions for the case when the inhibitor is non-diffusive, a case which had
previously caused spurious oscillations.
We then utilize the method to numerically analyze the large core limit. The
proposed method allows us to investigate the case close to criticality where
spiral waves acquire infinite core radius and zero rotation frequency, before
they begin to develop into retracting fingers. We confirm the linear scaling
regime of a drift bifurcation for the rotation frequency and the core radius of
spiral wave solutions close to criticality. This regime is unattainable with
conventional numerical methods.Comment: 32 pages, 17 figures, as accepted by SIAM Journal on Applied
Dynamical Systems on 20/03/1
Transition from rotating waves to modulated rotating waves on the sphere
We study non-resonant and resonant Hopf bifurcation of a rotating wave in
SO(3)-equivariant reaction-diffusion systems on a sphere. We obtained reduced
differential equations on so(3), the characterization of modulated rotating
waves obtained by Hopf bifurcation of a rotating wave, as well as results
regarding the resonant case. Our main tools are the equivariant center manifold
reduction and the theory of Lie groups and Lie algebras, especially for the
group SO(3) of all rigid rotations on a sphere
Moist turbulent Rayleigh-Benard convection with Neumann and Dirichlet boundary conditions
Turbulent Rayleigh-Benard convection with phase changes in an extended layer
between two parallel impermeable planes is studied by means of
three-dimensional direct numerical simulations for Rayleigh numbers between
10^4 and 1.5\times 10^7 and for Prandtl number Pr=0.7. Two different sets of
boundary conditions of temperature and total water content are compared:
imposed constant amplitudes which translate into Dirichlet boundary conditions
for the scalar field fluctuations about the quiescent diffusive equilibrium and
constant imposed flux boundary conditions that result in Neumann boundary
conditions. Moist turbulent convection is in the conditionally unstable regime
throughout this study for which unsaturated air parcels are stably and
saturated air parcels unstably stratified. A direct comparison of both sets of
boundary conditions with the same parameters requires to start the turbulence
simulations out of differently saturated equilibrium states. Similar to dry
Rayleigh-Benard convection the differences in the turbulent velocity
fluctuations, the cloud cover and the convective buoyancy flux decrease across
the layer with increasing Rayleigh number. At the highest Rayleigh numbers the
system is found in a two-layer regime, a dry cloudless and stably stratified
layer with low turbulence level below a fully saturated and cloudy turbulent
one which equals classical Rayleigh-Benard convection layer. Both are separated
by a strong inversion that gets increasingly narrower for growing Rayleigh
number.Comment: 19 pages, 13 Postscript figures, Figures 10,11,12,13, in reduced
qualit
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