Search results for "BIF"
showing 10 items of 539 documents
Axisymmetric solutions for a chemotaxis model of Multiple Sclerosis
2018
In this paper we study radially symmetric solutions for our recently proposed reaction–diffusion–chemotaxis model of Multiple Sclerosis. Through a weakly nonlinear expansion we classify the bifurcation at the onset and derive the amplitude equations ruling the formation of concentric demyelinating patterns which reproduce the concentric layers observed in Balò sclerosis and in the early phase of Multiple Sclerosis. We present numerical simulations which illustrate and fit the analytical results.
On the stability of bifurcation branches in thermal ignition
1984
A method is given to determine the stability of stationary solutions of the thermal ignition equation for the case ofn-dimensional spherical symmetry, together with the number of unstable modes. For sufficiently high temperature and activation temperature this number is arbitrarily large. Some numerical results on the solutions and their stability are reported.
Lusternik-Schnirelmann Critical Values and Bifurcation Problems
1987
We present a method to calculate bifurcation branches for nonlinear two point boundary value problems of the following type $$ \{ _{u(a) = u(b) = 0,}^{ - u'' = \lambda G'(u)} $$ (1.1) where G : R → R is a smooth mapping. This problem can be formulated equivalently as $$ g' \left(u \right)= \mu u, $$ (1.2) where $$ g \left(u \right)= \overset{b} {\underset{a} {\int}} G \left(u \left(t \right) \right) dt $$ (1.3) and μ = 1/λ. Solutions of this problem can be found by locating the critical points of the functional g : H → R on the spheres \(S_r= \lbrace x \in H \mid \;\parallel x \parallel =r \rbrace, r >0.\) (The Lagrange multiplier theorem.)
Intermittent-Type Chaos in Nonsinusoidal Driven Oscillators
2000
The intermittent-type chaos occurring in rf- and dc- nonsinusoidal driven oscillators is investigated analytically and numerically. The attention is focused on a general class of oscillators in which the total potential VRP(,r) is the Remoissenet-Peyrard potential which has constant amplitude and is 2π-periodic in , and whose shape can be varied as a function of parameter r ( |r| < 1). A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. The parameter regions of chaotic behaviour predicted by the theore…
Domain wall dynamics in an optical Kerr cavity
2004
An anisotropic (dichroic) optical cavity containing a self-focusing Kerr medium is shown to display a bifurcation between static --Ising-- and moving --Bloch-- domain walls, the so-called nonequilibrium Ising-Bloch transition (NIB). Bloch walls can show regular or irregular temporal behaviour, in particular, bursting and spiking. These phenomena are interpreted in terms of the spatio-temporal dynamics of the extended patterns connected by the wall, which display complex dynamical behaviour as well. Domain wall interaction, including the formation of bound states is also addressed.
Unitarity, Becchi-Rouet-Stora-Tyutin symmetry, and Ward identities in orbifold gauge theories
2004
We discuss the use of BRST symmetry and the resulting Ward identities as consistency checks for orbifold gauge theories in an arbitrary number of dimensions. We demonstrate that both the usual orbifold symmetry breaking and the recently proposed Higgsless symmetry breaking are consistent with the nilpotency of the BRST transformation. The corresponding Ward identities for four-point functions of the theory engender relations among the coupling constants that are equivalent to the sum rules from tree level unitarity. We present the complete set of these sum rules also for inelastic scattering and discuss applications to six-dimensional models and to incomplete matter multiplets on orbifold f…
Experimental approach to transverse wave-number selection in cavity nonlinear optics
2004
Spontaneous transverse pattern formation is experimentally studied in a ${\text{BaTiO}}_{3}$ photorefractive oscillator under degenerate four-wave mixing conditions. A near self-imaging resonator of high Fresnel number and quasi-one-dimensional in the transverse plane is used. A fine control technique of the cavity detuning, $\ensuremath{\Omega}$, is described. It allows a precise study of the relation of $\ensuremath{\Omega}$ with the transverse wave number ${k}_{\ensuremath{\perp}}$ of the roll patterns selected by the system. The law ${k}_{\ensuremath{\perp}}^{2}=\ensuremath{-}\ensuremath{\Omega}∕a$ is verified, which evidences that wave-number selection is mainly dictated by the cavity …
Rich dynamics and anticontrol of extinction in a prey-predator system
2019
This paper reveals some new and rich dynamics of a two-dimensional prey-predator system and to anticontrol the extinction of one of the species. For a particular value of the bifurcation parameter, one of the system variable dynamics is going to extinct, while another remains chaotic. To prevent the extinction, a simple anticontrol algorithm is applied so that the system orbits can escape from the vanishing trap. As the bifurcation parameter increases, the system presents quasiperiodic, stable, chaotic and also hyperchaotic orbits. Some of the chaotic attractors are Kaplan-Yorke type, in the sense that the sum of its Lyapunov exponents is positive. Also, atypically for undriven discrete sys…
A Model of Comprehensive Unification
2017
Comprehensive – that is, gauge and family – unification using spinors has many attractive features, but it has been challenged to explain chirality. Here, by combining an orbifold construction with more traditional ideas, we address that difficulty. Our candidate model features three chiral families and leads to an acceptable result for quantitative unification of couplings. A potential target for accelerator and astronomical searches emerges.
Transition to turbulence in toroidal pipes
2011
AbstractIncompressible flow in toroidal pipes of circular cross-section was investigated by three-dimensional, time-dependent numerical simulations using a finite volume method. The computational domain included a whole torus and was discretized by up to ${\ensuremath{\sim} }11. 4\ensuremath{\times} 1{0}^{6} $ nodes. Two curvatures $\delta $ (radius of the cross-section/radius of the torus), namely 0.3 and 0.1, were examined; a streamwise forcing term was imposed, and its magnitude was made to vary so that the bulk Reynolds number ranged between ${\ensuremath{\sim} }3500$ and ${\ensuremath{\sim} }14\hspace{0.167em} 700$. The results were processed by different techniques in order to confirm…