14,538 research outputs found
Complex Energy Method for Scattering Processes
A method for solving few-body scattering equations is proposed and examined.
The solution of the scattering equations at complex energies is analytically
continued to get scattering T-matrix with real positive energy. Numerical
examples document that the method works well for two-nucleon scattering and
three-nucleon scattering, if the set of complex energies is properly chosen.Comment: 6 pages, no figures, resubmitted to Prog. Theor. Phy
Phase equilibria of polydisperse hydrocarbons: moment free energy method analysis
We analyze the phase equilibria of systems of polydisperse hydrocarbons by
means of the recently introduced moment method. Hydrocarbons are modelled with
the Soave-Redlick-Kwong and Peng-Robinson equations of states. Numerical
results show no particular qualitative difference between the two equations of
states. Furthermore, in general the moment method proves to be an excellent
method for solving phase equilibria of polydisperse systems, showing excellent
agreement with previous results and allowing a great improvement in generality
of the numerical scheme and speed of computation.Comment: 12 pages, 2 figure
Stability of structural rings under uniformly distributed radial loads
Energy method analysis establishes parameters governing stability of circular rings acted upon by constant, uniformly distributed loads. Energy method is used so that nonlinear behavior of structure before buckling can be accounted for. Method affords conceptually superior basis for analyzing the axisymmetric deviation mode
The discrete energy method in numerical relativity: Towards long-term stability
The energy method can be used to identify well-posed initial boundary value
problems for quasi-linear, symmetric hyperbolic partial differential equations
with maximally dissipative boundary conditions. A similar analysis of the
discrete system can be used to construct stable finite difference equations for
these problems at the linear level. In this paper we apply these techniques to
some test problems commonly used in numerical relativity and observe that while
we obtain convergent schemes, fast growing modes, or ``artificial
instabilities,'' contaminate the solution. We find that these growing modes can
partially arise from the lack of a Leibnitz rule for discrete derivatives and
discuss ways to limit this spurious growth.Comment: 18 pages, 22 figure
Effective free energy method for nematic liquid crystals in contact with structured substrates
We study the phase behavior of a nematic liquid crystal confined between a
flat substrate with strong anchoring and a patterned substrate whose structure
and local anchoring strength we vary. By first evaluating an effective surface
free energy function characterizing the patterned substrate we derive an
expression for the effective free energy of the confined nematic liquid
crystal. Then we determine phase diagrams involving a homogeneous state in
which the nematic director is almost uniform and a hybrid aligned nematic state
in which the orientation of the director varies through the cell. Direct
minimization of the free energy functional were performed in order to test the
predictions of the effective free energy method. We find remarkably good
agreement between the phase boundaries calculated from the two approaches. In
addition the effective energy method allows one to determine the energy
barriers between two states in a bistable nematic device.Comment: 10 pages, 7 figures, submitte
Long time Solutions for a Burgers-Hilbert Equation via a Modified Energy Method
We consider an initial value problem for a quadratically nonlinear inviscid
Burgers-Hilbert equation that models the motion of vorticity discontinuities.
We use a modified energy method to prove the existence of small, smooth
solutions over cubically nonlinear time-scales
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