Related papers: Computation of Spiral Spectra
The second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane, limiting half-space, makes harmonious oscillations in the plane. The kinetic equation with modelling integral of collisions in the form…
Disc spectra from highly luminous black hole binaries are observed to be rather simple, despite theoretical predictions to the contrary. We collate the disc-dominated spectra from multiple observations of 10 separate sources, and show that…
The spiral core instability, observed in large aspect ratio Rayleigh-Benard convection, is studied numerically in the framework of the Swift-Hohenberg equation coupled to a large-scale flow. It is shown that the instability leads to…
We investigate existence, stability, and instability of anchored rotating spiral waves in a model for geometric curve evolution. We find existence in a parameter regime limiting on a purely eikonal curve evolution. We study stability and…
The method of second order relative spectra has been shown to reliably approximate the discrete spectrum for a self-adjoint operator. We extend the method to normal operators and find optimal convergence rates for eigenvalues and…
We establish Strichartz estimates, including estimates involving spatial derivatives, for radial wave equations with potentials in similarity variables. This is accomplished for all spatial dimensions $d\geq 3$ and almost all regularities…
We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…
The eigenvalue problem for radial potentials is considered in a space whose spatial coordinates satisfy the SU(2) Lie algebra. As the consequence, the space has a lattice nature and the maximum value of momentum is bounded from above. The…
We derive an analytical expression for the scattering of a scalar wave from a perfectly conducting self-affine one dimensional surface in the framework of the Kirchhoff approximation. We show that most of the results can be recovered via a…
Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries.…
Let G be a simple connected graph of order n with degree sequence d_1, d_2, ..., d_n in non-increasing order. The spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer L at most n, we give…
We examine the properties of spiral shocks from a steady, adiabatic, non-axisymmetric accretion disk around a compact star in binary. We first time incorporate all the possible influences from binary through adopting the Roche potential and…
Eigenvalue spectrum has been a long term unsolved problem for plasma physicists. In this paper, some numerical calculations are conducted about the minimum eigenvalues of the linearized Rosenbluth collision operator and the differential…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
We present eigenvalue decay estimates of integral operators associated with compositional dot-product kernels. The estimates improve on previous ones established for power series kernels on spheres. This allows us to obtain the volumes of…
We investigate the dispersive properties of solutions to the Schr\"odinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay at infinity, then we show that the Schr\"odinger flow on…
Transonic discs with accretion rates relevant to intrinsically bright Galactic X-ray sources ($L\approx 10^{38}$-$10^{39} {\rm erg s}^{-1}$) exhibit a time dependent cyclic behaviour due to the onset of a thermal instability driven by…
Theoretical models of protoplanetary disks including stellar irradiation often show a spontaneous amplification of scale height perturbations, produced by the enhanced absorption of starlight in enlarged regions. In turn, such regions cast…