controlling turbulence in the complex ginzburg landau equation abstract we suggest that diffusion induced turbulence in distributed dynamical systems near a supercritical hopf bifurcation can be controlled by means of global delayed feedback analytical and numerical investigations of this method for a system described by the complex ginzburg landau equation are performed suppression of phase and amplitude turbulence is found inside a window of delay times under increasing the intensity of the control signal

a theory for one dimensional asynchronous chemical waves we present a theory for an experimentally observed phenomenon of one dimensional asynchronous waves it has been proposed that two oppositely moving travelling wave states can localize an oscillatory core structure a class of even and odd parity localized solution of the same system has been explicitly shown it has been argued that a combination of these local and global states in an extended system can produce asynchronous waves we also produce numerical results in support of our analytic predictions

harmonic maps with defects two problems concerning maps with point singularities from a domain c 3 tos2 are solved the first is to determine the minimum energy of when the location and topological degree of the singularities are prescribed in the second problem is the unit ball and g is given on we show that the only cases in whichg x x minimizes the energy isg const org x rx withr a rotation extensions of these problems are also solved e g points are replaced by holes 3 s2 is replaced by n sn 1 or by n pn 1 the latter being appropriate for the theory of liquid crystals

density of smooth functions between two manifolds in sobolev spaces abstract we give some results concerning density or non density of smooth functions between two compact manifolds m n and n k in sobolev spaces w 1 p m n n k in particular we study the case n s k

multigrid one shot method for aerodynamic shape optimization the paper deals with a numerical method for aerodynamic shape optimization using simultaneous pseudo timestepping we have recently developed a method for the optimization problem in which stationary states are obtained by solving the pseudo stationary system of equations representing state costate and design equations the method requires no additional globalization techniques in the design space and a reduced sequential quadratic programming rsqp methods based preconditioner can be used for convergence acceleration the overall cost of computation is reduced up to 70the number of optimization iterations is comparatively large since we update the design parameters in each time step of state and costate runs in this paper we use a multigrid strategy to reduce the total number of optimization iterations keeping the idea of the one shot method design examples of drag reduction together with geometrical constraints for an rae2822 airfoil and an sct wing are included the total effort required for the convergence of the optimization problem is less than 2 times 4 times that of the forward simulation runs in two dimensions in three dimensions

a counterexample to the weak density of smooth maps between manifolds in sobolev spaces the present paper presents a counterexample to the sequential weak density of smooth maps between two manifolds m and n in the sobolev space w 1 p m n in the case p is an integer it has been shown see e g 6 that if p dim m is not an integer and the p th homotopy group p n of n is not trivial p denoting the largest integer less then p then smooth maps are not sequentially weakly dense in w 1 p m n on the other hand in the case p dim m is an integer examples have been provided where smooth maps are actually sequentially weakly dense in w 1 p m n with p n 0 although they are not dense for the strong convergence this is the case for instance for m b m the standard ball in r m and n s p the standard sphere of dimension p for which p n z the main result of this paper shows however that such a property does not holds for arbitrary manifolds n and integers p our counterexample deals with the case p 3 dim m 4 and n s 2 for which the homotopy group 3 s 2 z is related to the hopf fibration we construct explicitly a map which is not weakly approximable in w 1 3 m s 2 by maps in c m s 2 one of the central ingredients in our argument is related to issues in branched transportation and irrigation theory in the case of the exponent is critical which are possibly of independent interest as a byproduct of our method we also address some questions concerning the s 3 lifting problem for s 2 valued sobolev maps

solution of the euler equations for two dimensional transonic flow by a multigrid method the assumption of potential o w implies that the o w is irrotational this is not strictly correct when shock waves are present an exact description of transonic inviscid o w requires the solution of the euler equations the numerical solution of the euler equations for steady transonic o ws is therefore a problem of great interest to the aeronautical community it also presents a testing challenge to applied mathematicians and numerical analysts

connecting rational homotopy type singularities let n be a compact simply connected smooth riemannian manifold and for p 2 3 w 1 p r p 1 n be the sobolev space of measurable maps from r p 1 into n whose gradients are in l p the restriction of u to almost every p dimensional sphere s in r p 1 is in w 1 p s n and defines an homotopy class in p n white 1988 evaluating a fixed element z of hom p n r on this homotopy class thus gives a real number z u s the main result of the paper is that any w 1 p weakly convergent limit u of a sequence of smooth maps in c r p 1 n z u has a rectifiable poincare dual left gamma overrightarrow gamma theta right here is a a countable union of c 1 curves in r p 1 with hausdorff user1 mathcal h 1 measurable orientation overrightarrow gamma gamma to s p and density function r the intersection number between left gamma overrightarrow gamma theta right and s evaluates z u s for almost every p sphere s moreover we exhibit a non negative integer n z depending only on homotopy operation z such that int gamma left theta right p mathord left vphantom p left p n z right right kern nulldelimiterspace left p n z right d user1 mathcal h 1 infty even though the mass int gamma left theta right d user1 mathcal h 1 may be infinite we also provide cases of n p and z for which this rational power p p n z is optimal the construction of this poincare dual is based on 1 dimensional bubbling described by the notion of scans which was introduced in hardt and riviere 2003 we also describe how to generalize these results to r m for any m p 1 in which case the bubbling is described by an m p rectifiable set with orientation and density function determined by restrictions of the mappings to almost every oriented euclidean p sphere

on solitary wave solutions of ac driven complex ginzburg landau equation a new class of periodic solutions of modified complex ginzburg landau equation phase locked to a time dependent force by applying a nonfeedback mechanism for chaos control have been found the reported solutions are necessarily of the rational form containing trigonometric and hyperbolic functions

bifurcations and exact solutions of ac driven complex ginzburg landau equation in this paper we study the exact solutions of ac driven complex ginzburg landau equation under the given parameter conditions we apply the method of dynamical systems to analyze the dynamical behavior of the stationary solutions and their bifurcations depending on the parameters of systems all bounded exact solutions are obtained to guarantee the existence of those solutions the constraint parameter conditions are given

on exact solitary wave solutions of the nonlinear schrodinger equation with a source we use a fractional transformation to connect the travelling wave solutions of the nonlinear schrodinger equation nlse phase locked with a source to the elliptic equations satisfying f af f3 0 the solutions are necessarily of rational form containing both trigonometric and hyperbolic types as special cases bright and dark solitons as well as singular solitons are obtained in a suitable range of parameter values

a parallel two level domain decomposition based one shot method for shape optimization problems summary a two level domain decomposition method is introduced for general shape optimization problems constrained by the incompressible navier stokes equations the optimization problem is first discretized with a finite element method on an unstructured moving mesh that is implicitly defined without assuming that the computational domain is known and then solved by some one shot lagrange newton krylov schwarz algorithms in this approach the shape of the domain its corresponding finite element mesh the flow fields and their corresponding lagrange multipliers are all obtained computationally in a single solve of a nonlinear system of equations highly scalable parallel algorithms are absolutely necessary to solve such an expensive system the one level domain decomposition method works reasonably well when the number of processors is not large aiming for machines with a large number of processors and robust nonlinear convergence we introduce a two level inexact newton method with a hybrid two level overlapping schwarz preconditioner as applications we consider the shape optimization of a cannula problem and an artery bypass problem in 2d numerical experiments show that our algorithm performs well on a supercomputer with over 1000 processors for problems with millions of unknowns copyright 2014 john wiley sons ltd

topology of sobolev mappings ii this paper addresses some topological and analytical issues concern ing sobolev mappings between compact riemannian manifolds among the results we obtained are unified proofs of various generalizations of results obtained in a recent work of brezis and li in particular we solved two conjectures in bl we also give a topological obstruction for the weak sequential density of smooth maps in a given sobolev mapping space finally we show a necessary and suf ficient topological condition under which the smooth maps are strongly dense in the sobolev spaces the earlier result theorem 1 of b2 was shown to be not correct

the jacobian the square root and the set abstract in these notes we wish to present a new approach to the problem of prescribing jacobian determinants in dimension two we restrict ourselves to the case the datum is a finite sum of dirac masses the main point is to show that we may relate this problem to the search of harmonic maps into a singular space shaped as the symbol the later problem in turn is closely linked to questions in complex analysis a large part of the paper is devoted to a presentation of these mathematical objects and their connections

strong resonances of spatially distributed oscillators a laboratory to study patterns and defects abstract this paper describes phenomena which arise in a continuous system of coupled oscillators subject to a strongly resonant forcing we show that the temporal forcing induces a new type of instability leading to the formation of spatial patterns such as stripes hexagons and spatio temporal intermittent states reminiscent of chemical and magnetical systems we also report the existence of localized states where the instability is confined in the core of a defect leading to an increased mobility and diffusive behaviour of the defect

multiphase patterns in periodically forced oscillatory systems periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency we study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency the 4 1 resonance these systems possess four coexisting stable states corresponding to uniform oscillations with successive phase shifts of pi 2 using an amplitude equation approach near a hopf bifurcation to uniform oscillations we study front solutions connecting different phase states these solutions divide into two groups pi fronts separating states with a phase shift of pi and pi 2 fronts separating states with a phase shift of pi 2 we find a type of front instability where a stationary pi front open quotes decomposes close quotes into a pair of traveling pi 2 fronts as the forcing strength is decreased the instability is degenerate for an amplitude equation with cubic nonlinearities at the instability point a continuous family of pair solutions exists consisting of pi 2 fronts separated by distances ranging from zero to infinity quintic nonlinearities lift the degeneracy at the instability point but do not change the basic nature of the instability we conjecture the existence of similar instabilities in higher 2n 1 resonances n 3 4 hor ellipsis where stationarymore pi fronts decompose into ital n traveling pi n fronts the instabilities designate transitions from stationary two phase patterns to traveling 2n phase patterns as an example we demonstrate with a numerical solution the collapse of a four phase spiral wave into a stationary two phase pattern as the forcing strength within the 4 1 resonance is increased copyright ital 1999 ital the american physical society less

lorentzian type soliton solutions of ac driven complex ginzburg landau equation abstract fractional transform solutions of modified complex ginzburg landau equation phase locked to a time dependent force have been found the reported solutions are necessarily of the lorentzian type containing trigonometric hyperbolic and pure cnoidal functions numerical simulations indicated that the periodic solutions and soliton solutions are quite stable against finite perturbations

multigrid one shot method for state constrained aerodynamic shape optimization this paper presents applications of an optimization based multigrid method to state constrained aerodynamic shape optimization problems the one shot simultaneous pseudo time stepping method has been applied successfully to such problems reducing the cost of computation up to 70 from that of a traditional gradient method however the number of optimization iterations is comparatively large in this method since we update the design parameters in each time step of state and costate runs in this paper we use an optimization based multigrid strategy to reduce the total number of optimization iterations while keeping the idea of the one shot pseudo time stepping method design examples of drag reduction with constant lift together with geometrical constraints for an rae2822 airfoil are included the total effort required for convergence of the optimization problem is between four and six times that of forward simulation runs depending on computational grid size

multistable pulselike solutions in a parametrically driven ginzburg landau equation department of interdisciplinary studies faculty of engineering tel aviv university tel aviv 69978 israel dated february 8 2008 it is well known that pulse like solutions of the cubic complex ginzburg landau equation are un stable but can be stabilised by the addition of quintic terms in this paper we explore an alternativemechanism where the role of the stabilising agent is played by the parametric driver our analysis isbased on the numerical continuation of solutions in one of the parameters of the ginzburg landauequation the di usion coe cient c starting from the nonlinear schr odinger limit for which c 0 the continuation generates recursively a sequence of coexisting stable solutions with increasingnumber of humps the sequence converges to a long pulse which can be interpreted as a boundstate of two fronts with opposite polarities i introduction

boundary regularity and the dirichlet problem for harmonic maps in a previous paper 10 we developed an interior regularity theory for energy minimizing harmonic maps into riemannian manifolds in the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed dirichlet boundary condition we show that such maps are regular in a full neighborhood of the boundary assuming appropriate regularity on the manifolds the boundary and the data the reader may refer to theorem 2 7 for a statement of the precise result it is not surprising that the boundary regularity is actually stronger than the partial regularity we obtained for the interior this is due to the fact that there are no nontrivial smooth harmonic maps from hemispheres s which map the boundary s 9s to a point i j n 2 and is analogous to the fact that in certain cases we were able to obtain complete regularity in the interior many authors have worked on boundary regularity for this general type of problem we mention hildebrandt and widman 5 and hamilton 4 as having obtained important results specifically for harmonic maps morrey had obtained the boundary regularity for domain dimension n 2 in conjunction with his investigation of the plateau problem in riemannian manifolds 8 in 3 of this paper we observe that the direct method gives solvability of the dirichlet problem under reasonable hypotheses on the manifolds we give as an application an amusing proof of a theorem of sacks and uhlenbeck 9 on the existence of minimal 2 spheres representing the second homotopy group of a manifold the same method gives smooth harmonic representations for k n for a certain class of manifolds n these are characterized by the nonexistence of lower dimensional harmonic spheres whose homogeneous extensions are minimal see proposition 3 4 in the last section of the paper we discuss approximation of l maps by smooth maps we give a simple example of an l map from the three dimensional ball to the two sphere which is not an l limit of continuous maps we