1,907 research outputs found
Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion
In this work we study the effect of density dependent nonlinear diffusion on
pattern formation in the Lengyel--Epstein system. Via the linear stability
analysis we determine both the Turing and the Hopf instability boundaries and
we show how nonlinear diffusion intensifies the tendency to pattern formation;
%favors the mechanism of pattern formation with respect to the classical linear
diffusion case; in particular, unlike the case of classical linear diffusion,
the Turing instability can occur even when diffusion of the inhibitor is
significantly slower than activator's one. In the Turing pattern region we
perform the WNL multiple scales analysis to derive the equations for the
amplitude of the stationary pattern, both in the supercritical and in the
subcritical case. Moreover, we compute the complex Ginzburg-Landau equation in
the vicinity of the Hopf bifurcation point as it gives a slow spatio-temporal
modulation of the phase and amplitude of the homogeneous oscillatory solution.Comment: Accepted for publication in Acta Applicandae Mathematica
Pattern formation driven by cross--diffusion in a 2D domain
In this work we investigate the process of pattern formation in a two
dimensional domain for a reaction-diffusion system with nonlinear diffusion
terms and the competitive Lotka-Volterra kinetics. The linear stability
analysis shows that cross-diffusion, through Turing bifurcation, is the key
mechanism for the formation of spatial patterns. We show that the bifurcation
can be regular, degenerate non-resonant and resonant. We use multiple scales
expansions to derive the amplitude equations appropriate for each case and show
that the system supports patterns like rolls, squares, mixed-mode patterns,
supersquares, hexagonal patterns
Monads in Double Categories
We extend the basic concepts of Street's formal theory of monads from the
setting of 2-categories to that of double categories. In particular, we
introduce the double category Mnd(C) of monads in a double category C and
define what it means for a double category to admit the construction of free
monads. Our main theorem shows that, under some mild conditions, a double
category that is a framed bicategory admits the construction of free monads if
its horizontal 2-category does. We apply this result to obtain double
adjunctions which extend the adjunction between graphs and categories and the
adjunction between polynomial endofunctors and polynomial monads.Comment: 30 pages; v2: accepted for publication in the Journal of Pure and
Applied Algebra; added hypothesis in Theorem 3.7 that source and target
functors preserve equalizers; on page 18, bottom, in the statement concerning
the existence of a left adjoint, "if and only if" was replaced by "a
sufficient condition"; acknowledgements expande
Double Adjunctions and Free Monads
We characterize double adjunctions in terms of presheaves and universal
squares, and then apply these characterizations to free monads and
Eilenberg--Moore objects in double categories. We improve upon our earlier
result in "Monads in Double Categories", JPAA 215:6, pages 1174-1197, 2011, to
conclude: if a double category with cofolding admits the construction of free
monads in its horizontal 2-category, then it also admits the construction of
free monads as a double category. We also prove that a double category admits
Eilenberg--Moore objects if and only if a certain parameterized presheaf is
representable. Along the way, we develop parameterized presheaves on double
categories and prove a double-categorical Yoneda Lemma.Comment: 52 page
Studies of Radiative Penguin B Decays at BaBar
We summarize results on a number of observations of penguin dominated
radiative decays of the B meson. Such decays are forbidden at tree level and
proceed via electroweak loops. As such they may be sensitive to physics beyond
the standard model. The observations have been made at the BaBar experiment at
PEP-II, the asymmetric B factory at SLAC.Comment: 3 pages, 5 figure
Turing pattern formation in the Brusselator system with nonlinear diffusion
In this work we investigate the effect of density dependent nonlinear
diffusion on pattern formation in the Brusselator system. Through linear
stability analysis of the basic solution we determine the Turing and the
oscillatory instability boundaries. A comparison with the classical linear
diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern
formation. We study the process of pattern formation both in 1D and 2D spatial
domains. Through a weakly nonlinear multiple scales analysis we derive the
equations for the amplitude of the stationary patterns. The analysis of the
amplitude equations shows the occurrence of a number of different phenomena,
including stable supercritical and subcritical Turing patterns with multiple
branches of stable solutions leading to hysteresis. Moreover we consider
traveling patterning waves: when the domain size is large, the pattern forms
sequentially and traveling wavefronts are the precursors to patterning. We
derive the Ginzburg-Landau equation and describe the traveling front enveloping
a pattern which invades the domain. We show the emergence of radially symmetric
target patterns, and through a matching procedure we construct the outer
amplitude equation and the inner core solution.Comment: Physical Review E, 201
On the numerical closeness of the effective phenomenological electroweak mixing angle and the \MS parameter
It happens that and are equal with 0.1% accuracy, though
they are split by radiative corrections and a natural estimate for their
difference is 1%. This degeneracy occurs only for value close to
170\GeV, so no deep physical reason can be attributed to it. However, another
puzzle of the Standard Model, the degeneracy of s_\Eff^2 and , is not
independent of the previous one since a good physical reason exists for
s_\Eff^2 and degeneracy. We present explicit formulas which relate
these three angles.Comment: 10 pages, latex, 3 figures included; published on MPLA. A few
numerical estimates are improved; journal-ref is adde
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