8,849 research outputs found
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
Complex singularities and PDEs
In this paper we give a review on the computational methods used to
characterize the complex singularities developed by some relevant PDEs. We
begin by reviewing the singularity tracking method based on the analysis of the
Fourier spectrum. We then introduce other methods generally used to detect the
hidden singularities. In particular we show some applications of the Pad\'e
approximation, of the Kida method, and of Borel-Polya method. We apply these
techniques to the study of the singularity formation of some nonlinear
dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of
the 2D KP equation, and to Navier-Stokes equation for high Reynolds number
incompressible flows in the case of interaction with rigid boundaries
Two relaxation times and thermal nonlinear waves along wires with lateral heat exchange
We propose a model for studying several nonlinear waves for heat transport along a cylindrical system with lateral non-linear heat transfer to the environment. We consider relaxational equations, each with its own relaxation time, for longitudinal heat transfer and for lateral heat transfer across the wall. We consider two kinds of nonlinear lateral heat transport: radiative heat transport, and flux-limited heat transport. This work generalizes our previous studies in which the relaxation time for the lateral heat transfer was considered equal to that of the longitudinal heat flux. We explore the influence of both relaxation times on the propagation speed of linear and nonlinear waves, and on the form of nonlinear waves
Nonlinear Thermal Transport with Inertia in Thin Wires: Thermal Fronts and Steady States
In a series of papers we have obtained results for nonlinear heat transport when thin wires exchange heat non-linearly with the surroundings, with particular attention to propagating solitons. Here we obtain and discuss new results related to the propagation of nonlinear heat fronts and some conceptual aspects referring to the application of the second principle of thermodynamics to some nonlinear steady states related to non-propagating solitons
A Mathematical Analysis of the Intermediate Behaviour of the Energy Cascades of Quantum Turbulence
We propose a mathematical interpolation between several regimes of energy cascade in quantum turbulence in He II. On the basis of a physical interpretation of such mathematical expression we discuss in which conditions it is expected to appear an intermediate k(2) regime (equipartition regime) in the transition region between the hydrodynamic regime and the Kelvin wave regime (namely, between the k(-5/3) and k(-1) regions in coflow situations and between the k(-3) and k(-1) regions in counterflow situations). It is seen that if the energy rate transfer from the hydrodynamic region to the Kelvin wave region is sufficiently slow, such equipartition region will be present, but for higher values of such energy rate transfer it will disappear. For high rates of the energy rate transfer, the transition regime between the hydrodynamic and the Kelvin wave regimes will be monotonous, characterized by a negative exponent of k between -5/3 and -1 (or between -3 and -1), instead of the positive 2 exponent of the equipartition regime
Matter-wave dark solitons in boxlike traps
Motivated by the experimental development of quasihomogeneous Bose-Einstein condensates confined in boxlike traps, we study numerically the dynamics of dark solitons in such traps at zero temperature. We consider the cases where the side walls of the box potential rise either as a power law or a Gaussian. While the soliton propagates through the homogeneous interior of the box without dissipation, it typically dissipates energy during a reflection from a wall through the emission of sound waves, causing a slight increase in the soliton's speed. We characterize this energy loss as a function of the wall parameters. Moreover, over multiple oscillations and reflections in the boxlike trap, the energy loss and speed increase of the soliton can be significant, although the decay eventually becomes stabilized when the soliton equilibrates with the ambient sound field
Comparative electrochemical behavior of Prussian blue analogues as a host electrode for rare earth element recovery
In this paper, electrodeposited films belonging to the Prussian Blue Analogues (PBAs) family, namely, nickel-hexacyanoferrate (NiHCF) and copper-hexacyanoferrate (CuHCF), were employed as a host material for rare earth elements (REE), and the reported insertion/release study reveals a recovery capability for such valuable metals. The ion insertion/release was accomplished by adopting an electrochemically-driven process. A reversible intercalation was observed while considering both heavy and ligth rare earth elements. The amount of REEs inserted/released over the process and its kinetic evolution during the process were also studied by a chemometric approach. For CuHCF, it was seen that the intercalation of heavy rare earth elements occurs easily respect to the light ones, suggesting a possible selectivity among these ions
Vortex density waves and high-frequency second sound in superfluid turbulence hydrodynamics
In this paper we show that a recent hydrodynamical model of superfluid
turbulence describes vortex density waves and their effects on the speed of
high-frequency second sound. In this frequency regime, the vortex dynamics is
not purely diffusive, as for low frequencies, but exhibits ondulatory features,
whose influence on the second sound is here explored.Comment: 8 page
Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions
Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes
equations are considered for the case of the two-dimensional uniform flow past
an impulsively-started circular cylinder. We show how Prandtl's solution
develops a finite time separation singularity. On the other hand Navier-Stokes
solution is characterized by the presence of two kinds of viscous-inviscid
interactions that can be detected by the analysis of the enstrophy and of the
pressure gradient on the wall. Moreover we apply the complex singularity
tracking method to Prandtl and Navier-Stokes solutions and analyze the previous
interactions from a different perspective
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