200,004 research outputs found
Renormalization Group Method and Reductive Perturbation Method
It is shown that the renormalization group method does not necessarily
eliminate all secular terms in perturbation series to partial differential
equations and a functional subspace of renormalizable secular solutions
corresponds to a choice of scales of independent variables in the reductive
perturbation method.Comment: 5 pages, late
Derivation of Amplitude Equations by Renormalization Group Method
A proper formulation in the perturbative renormalization group method is
presented to deduce amplitude equations. The formulation makes it possible not
only avoiding a serious difficulty in the previous reduction to amplitude
equations by eliminating all of the secular terms but also consistent
derivation of higher-order correction to amplitude equations.Comment: 6 page, revte
Optical study of phase transitions in single-crystalline RuP
RuP single crystals of MnP-type orthorhombic structure were synthesized by
the Sn flux method. Temperature-dependent x-ray diffraction measurements reveal
that the compound experiences two structural phase transitions, which are
further confirmed by enormous anomalies shown in temperature-dependent
resistivity and magnetic susceptibility. Particularly, the resistivity drops
monotonically upon temperature cooling below the second transition, indicating
that the material shows metallic behavior, in sharp contrast with the
insulating ground state of polycrystalline samples. Optical conductivity
measurements were also performed in order to unravel the mechanism of these two
transitions. The measurement revealed a sudden reconstruction of band structure
over a broad energy scale and a significant removal of conducting carriers
below the first phase transition, while a charge-density-wave-like energy gap
opens below the second phase transition.Comment: 5 pages, 6 figure
Regularizing effect and local existence for non-cutoff Boltzmann equation
The Boltzmann equation without Grad's angular cutoff assumption is believed
to have regularizing effect on the solution because of the non-integrable
angular singularity of the cross-section. However, even though so far this has
been justified satisfactorily for the spatially homogeneous Boltzmann equation,
it is still basically unsolved for the spatially inhomogeneous Boltzmann
equation. In this paper, by sharpening the coercivity and upper bound estimates
for the collision operator, establishing the hypo-ellipticity of the Boltzmann
operator based on a generalized version of the uncertainty principle, and
analyzing the commutators between the collision operator and some weighted
pseudo differential operators, we prove the regularizing effect in all (time,
space and velocity) variables on solutions when some mild regularity is imposed
on these solutions. For completeness, we also show that when the initial data
has this mild regularity and Maxwellian type decay in velocity variable, there
exists a unique local solution with the same regularity, so that this solution
enjoys the regularity for positive time
A three-dimensional algebraic grid generation scheme for gas turbine combustors with inclined slots
A 3D algebraic grid generation scheme is presented for generating the grid points inside gas turbine combustors with inclined slots. The scheme is based on the 2D transfinite interpolation method. Since the scheme is a 2D approach, it is very efficient and can easily be extended to gas turbine combustors with either dilution hole or slot configurations. To demonstrate the feasibility and the usefulness of the technique, a numerical study of the quick-quench/lean-combustion (QQ/LC) zones of a staged turbine combustor is given. Preliminary results illustrate some of the major features of the flow and temperature fields in the QQ/LC zones. Formation of co- and counter-rotating bulk flow and shape temperature fields can be observed clearly, and the resulting patterns are consistent with experimental observations typical of the confined slanted jet-in-cross flow. Numerical solutions show the method to be an efficient and reliable tool for generating computational grids for analyzing gas turbine combustors with slanted slots
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