16,513 research outputs found
Resource Letter TF-1: Turbulence in Fluids
This Resource Letter provides a guide to the literature on fully developed
turbulence in fluids. It is restricted to mechanically driven turbulence in an
incompressible fluid described by the Navier-Stokes equations of hydrodynamics,
and places greatest emphasis on fundamental physical questions. Journal
articles and books are cited for the following topics: The Navier-Stokes
equations, qualitative aspects of turbulence, the 1941 Kolmogorov theory,
intermittency and small scale structure, time correlations and pressure; with
brief mention of two-dimensional turbulence, passive scalars in turbulence, and
the turbulent boundary layer,Comment: 38 pages LaTeX, no figures. To appear in American Journal of Physic
What is General Relativity?
General relativity is a set of physical and geometric principles, which lead
to a set of (Einstein) field equations that determine the gravitational field,
and to the geodesic equations that describe light propagation and the motion of
particles on the background. But open questions remain, including: What is the
scale on which matter and geometry are dynamically coupled in the Einstein
equations? Are the field equations valid on small and large scales? What is the
largest scale on which matter can be coarse grained while following a geodesic
of a solution to Einstein's equations? We address these questions. If the field
equations are causal evolution equations, whose average on cosmological scales
is not an exact solution of the Einstein equations, then some simplifying
physical principle is required to explain the statistical homogeneity of the
late epoch Universe. Such a principle may have its origin in the dynamical
coupling between matter and geometry at the quantum level in the early
Universe. This possibility is hinted at by diverse approaches to quantum
gravity which find a dynamical reduction to two effective dimensions at high
energies on one hand, and by cosmological observations which are beginning to
strongly restrict the class of viable inflationary phenomenologies on the
other. We suggest that the foundational principles of general relativity will
play a central role in reformulating the theory of spacetime structure to meet
the challenges of cosmology in the 21st century.Comment: 18 pages. Invited article for Physica Scripta Focus issue on 21st
Century Frontiers. v2: Appendix amended, references added. v3: Small
corrections, references added, matches published versio
Uniformity of Cosmic Microwave Background as a Non-Inflationary Geometrical Effect
The conventional CDM cosmological model supplemented by the
inflation concept describes the Universe very well. However, there are still a
few concerns: new Planck data impose constraints on the shape of the inflaton
potential, which exclude a lot of inflationary models; dark matter is not
detected directly, and dark energy is not understood theoretically on a
satisfactory level. In this brief sketch we investigate an alternative
cosmological model with spherical spatial geometry and an additional perfect
fluid with the constant parameter in the linear equation of
state. It is demonstrated explicitly that in the framework of such a model it
is possible to satisfy the supernovae data at the same level of accuracy as
within the CDM model and at the same time suppose that the observed
cosmic microwave background (CMB) radiation originates from a very limited
space region. This is ensured by introducing an additional condition of light
propagation between the antipodal points during the age of the Universe.
Consequently, the CMB uniformity can be explained without the inflation
scenario. The corresponding drawbacks of the model with respect to its
comparison with the CMB data are also discussed.Comment: 23 pages, 4 figure
Clock and induction model for somitogenesis
After many years of research, somitogenesis is still one of the major unresolved problems in developmental biology. Recent experimental findings show a novel type of pattern formation in which a signal sweeps along the presomitic mesoderm and narrows simultaneously as a new somite is formed. The signal then residues in the posterior half of the new somite, and another wave begins to sweep up from the caudal end. This behaviour is not easily explained by the existing theoretical models. We present a new model for somitogenesis that can account for this behaviour and is consistent with previous experimental observations. Dev Den;217:415-420. © 2000 Wiley-Liss, Inc
Some open problems in mathematical two-dimensional conformal field theory
We discuss some open problems in a program of constructing and studying
two-dimensional conformal field theories using the representation theory of
vertex operator algebras.Comment: 16 pages. Typos are corrected and some sentences are adjusted. Final
version to appear in the proceedings of the Conference on Lie Algebras,
Vertex Operator Algebras, and Related Topics, held at University of Notre
Dame, Notre Dame, Indiana, August 14-18, 201
Cosmology at the Turn of Centuries
A brief review of the present-day development of cosmology is presented for
mixed physical audience. The universe history is briefly described. Unsolved
problems are discussed, in particular, the mystery of the cosmological constant
and dark energy, the problems of dark matter, and baryogenesis. A brief
discussion of the cosmological role of neutrinos is also given.Comment: 20 pages, Invited talk presented at the International Conference
I.Ya. Pomeranchuk and Physics at the Turn of Centuries, January 24-28, 2003,
Moscow, Russia. A comment on spectral index of inflationary perturbations and
one reference are adde
Dynamics of vorticity
Remarks are made about the status of research on the role of vorticity in fluid dynamics and some unsolved problems of current interest are described
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