891 research outputs found
Levi umbilical surfaces in complex space
We define a complex connection on a real hypersurface of \C^{n+1} which is
naturally inherited from the ambient space. Using a system of Codazzi-type
equations, we classify connected real hypersurfaces in \C^{n+1}, ,
which are Levi umbilical and have non zero constant Levi curvature. It turns
out that such surfaces are contained either in a sphere or in the boundary of a
complex tube domain with spherical section.Comment: 18 page
Monte-Carlo simulation of events with Drell-Yan lepton pairs from antiproton-proton collisions
The complete knowledge of the nucleon spin structure at leading twist
requires also addressing the transverse spin distribution of quarks, or
transversity, which is yet unexplored because of its chiral-odd nature.
Transversity can be best extracted from single-spin asymmetries in fully
polarized Drell-Yan processes with antiprotons, where valence contributions are
involved anyway. Alternatively, in single-polarized Drell-Yan the transversity
happens convoluted with another chiral-odd function, which is likely to be
responsible for the well known (and yet unexplained) violation of the Lam-Tung
sum rule in the corresponding unpolarized cross section. We present Monte-Carlo
simulations for the unpolarized and single-polarized Drell-Yan at different center-of-mass energies in both
configurations where the antiproton beam hits a fixed proton target or it
collides on another proton beam. The goal is to estimate the minimum number of
events needed to extract the above chiral-odd distributions from future
measurements at the HESR ring at GSI. It is important to study the feasibility
of such experiments at HESR in order to demonstrate that interesting spin
physics can be explored already using unpolarized antiprotons.Comment: Deeply revised text with improved discussion of kinematics and
results; added one table; 12 figures. Accepted for publication in Phys. Rev.
The Finite Field Kakeya Problem
A Besicovitch set in AG(n,q) is a set of points containing a line in every
direction. The Kakeya problem is to determine the minimal size of such a set.
We solve the Kakeya problem in the plane, and substantially improve the known
bounds for n greater than 4.Comment: 13 page
Variety of idempotents in nonassociative algebras
In this paper, we study the variety of all nonassociative (NA) algebras from
the idempotent point of view. We are interested, in particular, in the spectral
properties of idempotents when algebra is generic, i.e. idempotents are in
general position. Our main result states that in this case, there exist at
least nontrivial obstructions (syzygies) on the Peirce spectrum of a
generic NA algebra of dimension . We also discuss the exceptionality of the
eigenvalue which appears in the spectrum of idempotents in
many classical examples of NA algebras and characterize its extremal properties
in metrised algebras.Comment: 27 pages, 1 figure, submitte
Elastic turbulence in curvilinear flows of polymer solutions
Following our first report (A. Groisman and V. Steinberg, \sl Nature , 53 (2000)) we present an extended account of experimental observations of
elasticity induced turbulence in three different systems: a swirling flow
between two plates, a Couette-Taylor (CT) flow between two cylinders, and a
flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of
width of the region available for flow to radius of curvature of the
streamlines. The experiments were carried out with dilute solutions of high
molecular weight polyacrylamide in concentrated sugar syrups. High polymer
relaxation time and solution viscosity ensured prevalence of non-linear elastic
effects over inertial non-linearity, and development of purely elastic
instabilities at low Reynolds number (Re) in all three flows. Above the elastic
instability threshold, flows in all three systems exhibit features of developed
turbulence. Those include: (i)randomly fluctuating fluid motion excited in a
broad range of spatial and temporal scales; (ii) significant increase in the
rates of momentum and mass transfer (compared to those expected for a steady
flow with a smooth velocity profile). Phenomenology, driving mechanisms, and
parameter dependence of the elastic turbulence are compared with those of the
conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure
q-breathers in Discrete Nonlinear Schroedinger lattices
-breathers are exact time-periodic solutions of extended nonlinear systems
continued from the normal modes of the corresponding linearized system. They
are localized in the space of normal modes. The existence of these solutions in
a weakly anharmonic atomic chain explained essential features of the
Fermi-Pasta-Ulam (FPU) paradox. We study -breathers in one- two- and
three-dimensional discrete nonlinear Sch\"{o}dinger (DNLS) lattices --
theoretical playgrounds for light propagation in nonlinear optical waveguide
networks, and the dynamics of cold atoms in optical lattices. We prove the
existence of these solutions for weak nonlinearity. We find that the
localization of -breathers is controlled by a single parameter which depends
on the norm density, nonlinearity strength and seed wave vector. At a critical
value of that parameter -breathers delocalize via resonances, signaling a
breakdown of the normal mode picture and a transition into strong mode-mode
interaction regime. In particular this breakdown takes place at one of the
edges of the normal mode spectrum, and in a singular way also in the center of
that spectrum. A stability analysis of -breathers supplements these
findings. For three-dimensional lattices, we find -breather vortices, which
violate time reversal symmetry and generate a vortex ring flow of energy in
normal mode space.Comment: 19 pages, 9 figure
Nonlinear management of the angular momentum of soliton clusters
We demonstrate an original approach to acquire nonlinear control over the
angular momentum of a cluster of solitary waves. Our model, derived from a
general description of nonlinear energy propagation in dispersive media, shows
that the cluster angular momentum can be adjusted by acting on the global
energy input into the system. The phenomenon is experimentally verified in
liquid crystals by observing power-dependent rotation of a two-soliton cluster.Comment: 4 pages, 3 figure
3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations
The equivalence problem for second order ODEs given modulo point
transformations is solved in full analogy with the equivalence problem of
nondegenerate 3-dimensional CR structures. This approach enables an analog of
the Feffereman metrics to be defined. The conformal class of these (split
signature) metrics is well defined by each point equivalence class of second
order ODEs. Its conformal curvature is interpreted in terms of the basic point
invariants of the corresponding class of ODEs
On the universality of the Discrete Nonlinear Schroedinger Equation
We address the universal applicability of the discrete nonlinear Schroedinger
equation. By employing an original but general top-down/bottom-up procedure
based on symmetry analysis to the case of optical lattices, we derive the most
widely applicable and the simplest possible model, revealing that the discrete
nonlinear Schroedinger equation is ``universally'' fit to describe light
propagation even in discrete tensorial nonlinear systems and in the presence of
nonparaxial and vectorial effects.Comment: 6 Pages, to appear in Phys. Rev.
Fermion Doubling and a Natural Solution of the Strong CP Problem
We suggest the fermion doubling for all quarks and leptons. It is a
generalization of the neutrino doubling of the seesaw mechanism. The new quarks
and leptons are singlets and carry the electromagnetic charges of their
lighter counterparts. An {\it anomaly free global symmetry} or a
discrete symmetry can be introduced to restrict the Yukawa couplings. The form
of mass matrix is belonging to that of Nelson and Barr even though our model
does not belong to Barr's criterion. The weak CP violation of the
Kobayashi-Maskawa form is obtained through the spontaneous breaking of CP
symmetry at high energy scale. The strong CP solution is through a specific
form of the mass matrix. At low energy, the particle content is the same as in
the standard model. For a model with a global symmetry, in addition there
exists a massless majoron.Comment: SNUTP 93-68, 19 pages 1 TeX figure, ReVTeX 3.
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