45 research outputs found
On 2D Viscoelasticity with Small Strain
An exact two-dimensional rotation-strain model describing the motion of
Hookean incompressible viscoelastic materials is constructed by the polar
decomposition of the deformation tensor. The global existence of classical
solutions is proved under the smallness assumptions only on the size of initial
strain tensor. The proof of global existence utilizes the weak dissipative
mechanism of motion, which is revealed by passing the partial dissipation to
the whole system.Comment: Different contributions of strain and rotation of the deformation are
studied for viscoelastic fluids of Oldroyd-B type in 2
Global Solutions for Incompressible Viscoelastic Fluids
We prove the existence of both local and global smooth solutions to the
Cauchy problem in the whole space and the periodic problem in the n-dimensional
torus for the incompressible viscoelastic system of Oldroyd-B type in the case
of near equilibrium initial data. The results hold in both two and three
dimensional spaces. The results and methods presented in this paper are also
valid for a wide range of elastic complex fluids, such as magnetohydrodynamics,
liquid crystals and mixture problems.Comment: We prove the existence of global smooth solutions to the Cauchy
problem for the incompressible viscoelastic system of Oldroyd-B type in the
case of near equilibrium initial dat
A blowup criterion for ideal viscoelastic flow
We establish an analog of the Beale-Kato-Majda criterion for singularities of
smooth solutions of the system of PDE arising in the Oldroyd model for ideal
viscoelastic flow
Geometrical properties of local dynamics in Hamiltonian systems: the Generalized Alignment Index (GALI) method
We investigate the detailed dynamics of multidimensional Hamiltonian systems
by studying the evolution of volume elements formed by unit deviation vectors
about their orbits. The behavior of these volumes is strongly influenced by the
regular or chaotic nature of the motion, the number of deviation vectors, their
linear (in)dependence and the spectrum of Lyapunov exponents. The different
time evolution of these volumes can be used to identify rapidly and efficiently
the nature of the dynamics, leading to the introduction of quantities that
clearly distinguish between chaotic behavior and quasiperiodic motion on
-dimensional tori. More specifically we introduce the Generalized Alignment
Index of order (GALI) as the volume of a generalized parallelepiped,
whose edges are initially linearly independent unit deviation vectors from
the studied orbit whose magnitude is normalized to unity at every time step.
The GALI is a generalization of the Smaller Alignment Index (SALI)
(GALI SALI). However, GALI provides significantly more
detailed information on the local dynamics, allows for a faster and clearer
distinction between order and chaos than SALI and works even in cases where the
SALI method is inconclusive.Comment: 45 pages, 10 figures, accepted for publication in Physica
Global existence for coupled systems of nonlinear wave and Klein-Gordon equations in three space dimensions
We consider the Cauchy problem for coupled systems of wave and Klein-Gordon
equations with quadratic nonlinearity in three space dimensions. We show global
existence of small amplitude solutions under certain condition including the
null condition on self-interactions between wave equations. Our condition is
much weaker than the strong null condition introduced by Georgiev for this kind
of coupled system. Consequently our result is applicable to certain physical
systems, such as the Dirac-Klein-Gordon equations, the Dirac-Proca equations,
and the Klein-Gordon-Zakharov equations.Comment: 31 pages. The final versio
Multidimensional Conservation Laws: Overview, Problems, and Perspective
Some of recent important developments are overviewed, several longstanding
open problems are discussed, and a perspective is presented for the
mathematical theory of multidimensional conservation laws. Some basic features
and phenomena of multidimensional hyperbolic conservation laws are revealed,
and some samples of multidimensional systems/models and related important
problems are presented and analyzed with emphasis on the prototypes that have
been solved or may be expected to be solved rigorously at least for some cases.
In particular, multidimensional steady supersonic problems and transonic
problems, shock reflection-diffraction problems, and related effective
nonlinear approaches are analyzed. A theory of divergence-measure vector fields
and related analytical frameworks for the analysis of entropy solutions are
discussed.Comment: 43 pages, 3 figure
Observation of Scaling Violations in Scaled Momentum Distributions at HERA
Charged particle production has been measured in deep inelastic scattering
(DIS) events over a large range of and using the ZEUS detector. The
evolution of the scaled momentum, , with in the range 10 to 1280
, has been investigated in the current fragmentation region of the Breit
frame. The results show clear evidence, in a single experiment, for scaling
violations in scaled momenta as a function of .Comment: 21 pages including 4 figures, to be published in Physics Letters B.
Two references adde
D* Production in Deep Inelastic Scattering at HERA
This paper presents measurements of D^{*\pm} production in deep inelastic
scattering from collisions between 27.5 GeV positrons and 820 GeV protons. The
data have been taken with the ZEUS detector at HERA. The decay channel
(+ c.c.) has been used in the study. The
cross section for inclusive D^{*\pm} production with
and is 5.3 \pms 1.0 \pms 0.8 nb in the kinematic region
{ GeV and }. Differential cross
sections as functions of p_T(D^{*\pm}), and are
compared with next-to-leading order QCD calculations based on the photon-gluon
fusion production mechanism. After an extrapolation of the cross section to the
full kinematic region in p_T(D^{*\pm}) and (D^{*\pm}), the charm
contribution to the proton structure function is
determined for Bjorken between 2 10 and 5 10.Comment: 17 pages including 4 figure
Observation of Events with an Energetic Forward Neutron in Deep Inelastic Scattering at HERA
In deep inelastic neutral current scattering of positrons and protons at the center of mass energy of 300 GeV, we observe, with the ZEUS detector, events with a high energy neutron produced at very small scattering angles with respect to the proton direction. The events constitute a fixed fraction of the deep inelastic, neutral current event sample independent of Bjorken x and Q2 in the range 3 · 10-4 \u3c xBJ \u3c 6 · 10-3 and 10 \u3c Q2 \u3c 100 GeV2