7,090 research outputs found
What is the number of spiral galaxies in compact groups
The distribution of morphological types of galaxies in compact groups is studied on plates from the 6 m telescope. In compact groups there are 57 percent galaxies of late morphological types (S + Irr), 23 percent lenticulars (SO) and 20 percent elliptical galaxies. The morphological content of compact groups is very nearly the same as in loose groups. There is no dependence of galaxy morphology on density in all compact groups (and possibly in loose groups). Genuine compact groups form only 60 percent of Hickson's list
Parabolic equations with the second order Cauchy conditions on the boundary
The paper studies some ill-posed boundary value problems on semi-plane for
parabolic equations with homogenuous Cauchy condition at initial time and with
the second order Cauchy condition on the boundary of the semi-plane. A class of
inputs that allows some regularity is suggested and described explicitly in
frequency domain. This class is everywhere dense in the space of square
integrable functions.Comment: 7 page
On the Mapping of Time-Dependent Densities onto Potentials in Quantum Mechanics
The mapping of time-dependent densities on potentials in quantum mechanics is
critically examined. The issue is of significance ever since Runge and Gross
(Phys. Rev. Lett. 52, 997 (1984)) established the uniqueness of the mapping,
forming a theoretical basis for time-dependent density functional theory. We
argue that besides existence (so called v-representability) and uniqueness
there is an important question of stability and chaos. Studying a 2-level
system we find innocent, almost constant densities that cannot be constructed
from any potential (non-existence). We further show via a Lyapunov analysis
that the mapping of densities on potentials has chaotic regions in this case.
In real space the situation is more subtle. V-representability is formally
assured but the mapping is often chaotic making the actual construction of the
potential almost impossible. The chaotic nature of the mapping, studied for the
first time here, has serious consequences regarding the possibility of using
TDDFT in real-time settings
Surface Impedance Determination via Numerical Resolution of the Inverse Helmholtz Problem
Assigning boundary conditions, such as acoustic impedance, to the frequency
domain thermoviscous wave equations (TWE), derived from the linearized
Navier-Stokes equations (LNSE) poses a Helmholtz problem, solution to which
yields a discrete set of complex eigenfunctions and eigenvalue pairs. The
proposed method -- the inverse Helmholtz solver (iHS) -- reverses such
procedure by returning the value of acoustic impedance at one or more unknown
impedance boundaries (IBs) of a given domain, via spatial integration of the
TWE for a given real-valued frequency with assigned conditions on other
boundaries. The iHS procedure is applied to a second-order spatial
discretization of the TWEs on an unstructured staggered grid arrangement. Only
the momentum equation is extended to the center of each IB face where pressure
and velocity components are co-located and treated as unknowns. The iHS is
finally closed via assignment of the surface gradient of pressure phase over
the IBs, corresponding to assigning the shape of the acoustic waveform at the
IB. The iHS procedure can be carried out independently for different
frequencies, making it embarrassingly parallel, and able to return the complete
broadband complex impedance distribution at the IBs in any desired frequency
range to arbitrary numerical precision. The iHS approach is first validated
against Rott's theory for viscous rectangular and circular ducts. The impedance
of a toy porous cavity with a complex geometry is then reconstructed and
validated with companion fully compressible unstructured Navier-Stokes
simulations resolving the cavity geometry. Verification against one-dimensional
impedance test tube calculations based on time-domain impedance boundary
conditions (TDIBC) is also carried out. Finally, results from a preliminary
analysis of a thermoacoustically unstable cavity are presented.Comment: As submitted to AIAA Aviation 201
Quasi-Optimal Filtering in Inverse Problems
A way of constructing a nonlinear filter close to the optimal Kolmogorov -
Wiener filter is proposed within the framework of the statistical approach to
inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions,
produces stable and efficient solutions by relying solely on the internal
resources of the inverse theory. The exact representation is given of the
Feasible Region for inverse solutions that follows from the statistical
consideration.Comment: 9 pages, 240 K
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