148,703 research outputs found
Equation-free dynamic renormalization in a glassy compaction model
Combining dynamic renormalization with equation-free computational tools, we
study the apparently self-similar evolution of void distribution dynamics in
the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev.
Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches,
forward as well as backward in time.Comment: 4 pages, 4 figures (Minor Modifications; Submitted Version
Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows
We are concerned with globally defined entropy solutions to the Euler
equations for compressible fluid flows in transonic nozzles with general
cross-sectional areas. Such nozzles include the de Laval nozzles and other more
general nozzles whose cross-sectional area functions are allowed at the nozzle
ends to be either zero (closed ends) or infinity (unbounded ends). To achieve
this, in this paper, we develop a vanishing viscosity method to construct
globally defined approximate solutions and then establish essential uniform
estimates in weighted norms for the whole range of physical adiabatic
exponents , so that the viscosity approximate solutions
satisfy the general compensated compactness framework. The viscosity
method is designed to incorporate artificial viscosity terms with the natural
Dirichlet boundary conditions to ensure the uniform estimates. Then such
estimates lead to both the convergence of the approximate solutions and the
existence theory of globally defined finite-energy entropy solutions to the
Euler equations for transonic flows that may have different end-states in the
class of nozzles with general cross-sectional areas for all . The approach and techniques developed here apply to other problems
with similar difficulties. In particular, we successfully apply them to
construct globally defined spherically symmetric entropy solutions to the Euler
equations for all .Comment: 32 page
Exactness of the Original Grover Search Algorithm
It is well-known that when searching one out of four, the original Grover's
search algorithm is exact; that is, it succeeds with certainty. It is natural
to ask the inverse question: If we are not searching one out of four, is
Grover's algorithm definitely not exact? In this article we give a complete
answer to this question through some rationality results of trigonometric
functions.Comment: 8 pages, 2 figure
Strongly nonlinear waves in capillary electrophoresis
In capillary electrophoresis, sample ions migrate along a micro-capillary
filled with a background electrolyte under the influence of an applied electric
field. If the sample concentration is sufficiently high, the electrical
conductivity in the sample zone could differ significantly from the
background.Under such conditions, the local migration velocity of sample ions
becomes concentration dependent resulting in a nonlinear wave that exhibits
shock like features. If the nonlinearity is weak, the sample concentration
profile, under certain simplifying assumptions, can be shown to obey Burgers'
equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which
has an exact analytical solution for arbitrary initial condition.In this paper,
we use a numerical method to study the problem in the more general case where
the sample concentration is not small in comparison to the concentration of
background ions. In the case of low concentrations, the numerical results agree
with the weakly nonlinear theory presented earlier, but at high concentrations,
the wave evolves in a way that is qualitatively different.Comment: 7 pages, 5 figures, 1 Appendix, 2 videos (supplementary material
Early Time Dynamics of Gluon Fields in High Energy Nuclear Collisions
Nuclei colliding at very high energy create a strong, quasi-classical gluon
field during the initial phase of their interaction. We present an analytic
calculation of the initial space-time evolution of this field in the limit of
very high energies using a formal recursive solution of the Yang-Mills
equations. We provide analytic expressions for the initial chromo-electric and
chromo-magnetic fields and for their energy-momentum tensor. In particular, we
discuss event-averaged results for energy density and energy flow as well as
for longitudinal and transverse pressure of this system. For example, we find
that the ratio of longitudinal to transverse pressure very early in the system
behaves as where
is the longitudinal proper time, is related to the saturation scales
of the two nuclei, and with a scale to
be defined later. Our results are generally applicable if .
As already discussed in a previous paper, the transverse energy flow of
the gluon field exhibits hydrodynamic-like contributions that follow transverse
gradients of the energy density . In addition, a
rapidity-odd energy flow also emerges from the non-abelian analog of Gauss' Law
and generates non-vanishing angular momentum of the field. We will discuss the
space-time picture that emerges from our analysis and its implications for
observables in heavy ion collisions.Comment: 26 pages, 9 figure
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