6,074 research outputs found
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
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
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
Screening Effects in Superfluid Nuclear and Neutron Matter within Brueckner Theory
Effects of medium polarization are studied for pairing in neutron and
nuclear matter. The screening potential is calculated in the RPA limit,
suitably renormalized to cure the low density mechanical instability of nuclear
matter. The selfenergy corrections are consistently included resulting in a
strong depletion of the Fermi surface. All medium effects are calculated based
on the Brueckner theory. The gap is determined from the generalized gap
equation. The selfenergy corrections always lead to a quenching of the gap,
which is enhanced by the screening effect of the pairing potential in neutron
matter, whereas it is almost completely compensated by the antiscreening effect
in nuclear matter.Comment: 8 pages, 6 Postscript figure
Dense Quarks, and the Fermion Sign Problem, in a SU(N) Matrix Model
We study the effect of dense quarks in a SU(N) matrix model of deconfinement.
For three or more colors, the quark contribution to the loop potential is
complex. After adding the charge conjugate loop, the measure of the matrix
integral is real, but not positive definite. In a matrix model, quarks act like
a background Z(N) field; at nonzero density, the background field also has an
imaginary part, proportional to the imaginary part of the loop. Consequently,
while the expectation values of the loop and its complex conjugate are both
real, they are not equal. These results suggest a possible approach to the
fermion sign problem in lattice QCD.Comment: 9 pages, 3 figure
Equilibrium molecular energies used to obtain molecular dissociation energies and heats of formation within the bond-order correlation approach
Ab initio calculations including electron correlation are still extremely
costly except for the smallest atoms and molecules. Therefore, our purpose in
the present study is to employ a bond-order correlation approach to obtain, via
equilibrium molecular energies, molecular dissociation energies and heats of
formation for some 20 molecules containing C, H, and O atoms, with a maximum
number of electrons around 40. Finally, basis set choice is shown to be
important in the proposed procedure to include electron correlation effects in
determining thermodynamic properties. With the optimum choice of basis set, the
average percentage error for some 20 molecules is approximately 20% for heats
of formation. For molecular dissociation energies the average error is much
smaller: ~0.4.Comment: Mol. Phys., to be publishe
Mass gap in the 2D O(3) non-linear sigma model with a theta=pi term
By analytic continuation to real theta of data obtained from numerical
simulation at imaginary theta we study the Haldane conjecture and show that the
O(3) non-linear sigma model with a theta term in 2 dimensions becomes massless
at theta=3.10(5). A modified cluster algorithm has been introduced to simulate
the model with imaginary theta. Two different definitions of the topological
charge on the lattice have been used; one of them needs renormalization to
match the continuum operator. Our work also offers a successful test for
numerical methods based on analytic continuation.Comment: Latex file, 4 pages. To appear in PRD; it contains the justification
of analicity, more details about the fits, more references, et
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