absence of singular continuous spectrum for certain self adjoint operators we give a sufficient condition for a self adjoint operator to have the following properties in a neighborhood of a pointe of its spectrum a its point spectrum is finite b its singular continuous spectrum is empty c its resolvent satisfies a class of a priori estimates

analysis of a model for imaging in photolithography abstract the governing equation of a model for imaging in photolithography is studied the density p of the photoactive component of the resist which is a function of time and position decreases at a rate assumed proportional to the local light intensity it satisfies a nonlinear differential equation d dt t f t of which an evaluation of the right hand side requires solving maxwell s equations in a periodic 2d configuration of dielectrics consisting of the resist and the substrate the electric permittivity of the resist is a function of position which depends on the maxwell problem is studied by applying the limiting absorption principle it is proved using the contraction mapping theorem that for every exposure time and every initial density has a unique solution which is a smooth function of time and position when all data are smooth

multiple invasion percolation we generalize the standard site invasion percolation model to permit simultaneous invasion of several sites we propose two kinds of generalizations one in which the invasion flux is controlled by the perimeter size and another where the growth process is commanded by the scaling properties the acceptance profile as well as the fractal dimensions df are carefully studied for the model based on scaling relations df can be treated as a mere real parameter in the range 0 in the intervals 0 91 and 2 the system is frustrated for df 2 the model exhibits also an interesting burst phenomenon which is explained in the text in the 91 region 2 the clusters obey exactly and in any scale the relation m rg df between the mass m and the gyration radius rg these stabilized random fractals may be very useful in the study of dilute systems

spectral theory for symmetric systems in an exterior domain ii abstract our work is devoted to the investigation of spectral theory for symmetric systems with certain coercive boundary conditions in an exterior domain we verify the discreteness of non zero eigenvalues and the principle of limiting absorption

the n steps invasion percolation model abstract a new kind of invasion percolation is introduced in order to take into account the inertia of the invader fluid the inertia strength is controlled by the number n of pores or steps invaded after the perimeter rupture the new model belongs to a different class of universality with the fractal dimensions of the percolating clusters depending on n a blocking phenomenon takes place in two dimensions it imposes an upper bound value on n for pore sizes larger than the critical threshold the acceptance profile exhibits a permanent tail

spectral analysis of strongly propagative systems on considere la theorie spectrale et la theorie de diffusion pour des systemes symetriques d ordre 1 du type a x t x t l 1 n b t t x x l 0 ou t x est une fonction a valeurs c m sur r n 1 be 1 l n sont des matrices symetriques m m et a x une fonction sur r m avec des valeurs sur les matrices m m symetriques

weak solutions of the landau lifshitz bloch equation abstract the landau lifshitz bloch llb equation is a formulation of dynamic micromagnetics valid at all temperatures treating both the transverse and longitudinal relaxation components important for high temperature applications we study llb equation in case the temperature raised higher than the curie temperature the existence of weak solution is showed and its regularity properties are also discussed in this way we lay foundations for the rigorous theory of llb equation that is currently not available

convergence of the galerkin method two dimensional electromagnetic problems the application of the galerkin method to a class of two dimensional time harmonic electromagnetic scattering and radiation problems in exterior domains is studied the scatterers and sources consist of a periodic grating on the one hand and of bounded objects on the other in both cases maxwell s equations reduce to an elliptic system of two coupled partial differential equations for two components of the electromagnetic field a region is chosen which encloses all scatterers and sources and outside of which there is homogeneous material then on this region a boundary value problem and its variational formulation are derived which are equivalent to the original problem on the unbounded domain the boundary operator which represents the influence of outer space leads to a perturbation of the sesquilinear form of the variational problem which is not weakly continuous on the canonical hilbert space using a theorem of michlin the convergence of the galerkin method is proved this provides at the same tim

computational studies for the stochastic landau lifshitz gilbert equation the stochastic landau lifshitz gilbert equation describes the thermally induced dynamics of magnetic moments in ferromagnetic materials solutions of this highly nonlinear stochastic pde are unit vector fields and satisfy an energy estimate these are crucial properties to construct a convergent discretization in space and time we propose a convergent finite element approximation of the problem based on the midpoint rule the numerical scheme preserves the underlying properties of the continuous problem further we construct a robust and efficient newton multigrid solver for the solution of the nonlinear systems associated with the discretized problems at each time level computational studies show the optimal convergence behavior of the scheme in the case of smooth solutions long time dynamics for finite ensembles of spins evidence the ergodicity of an invariant measure of the continuum model numerical experiments in two dimensions demonstrate pathwise finite time blow up behavior of the solution w

a finite element approximation for the stochastic landau lifshitz gilbert equation abstract the stochastic landau lifshitz gilbert llg equation describes the behaviour of the magnetisation under the influence of the effective field containing random fluctuations we first transform the stochastic llg equation into a partial differential equation with random coefficients without the ito term the resulting equation has time differentiable solutions we then propose a convergent linear scheme for the numerical solution of the reformulated equation as a consequence we show the existence of weak martingale solutions to the stochastic llg equation a salient feature of this scheme is that it does not involve solving a system of nonlinear algebraic equations and that no condition on time and space steps is required when 1 2 1 numerical results are presented to show the applicability of the method

martingale weak solutions of the stochastic landau lifshitz bloch equation abstract the present paper studies the stochastic landau lifshitz bloch equation which is recommended as the only valid model at temperature around the curie temperature and is especially important for the simulation of heat assisted magnetic recording we study the stochastic landau lifshitz bloch equation in the case that the temperature is raised higher than the curie temperature the global existence of martingale weak solutions is proved by using a new argument and regularity properties of the weak solutions are discussed

topology dynamics and finite size effects of a kinetic growth model ramified polymerization is studied through computational simulations on the square lattice of a kinetic growth model generalized to incorporate branching and impurities the polymer configuration is identified with a bond tree in order to examine its topology the fractal dimensions of clusters are obtained at criticality simulations also allow the study of time evolution of clusters as well as the determination of time autocorrelations and dynamical critical exponents in regard to finite size effects a fourth order cumulant technique is employed to estimate the critical branching probability bc and the critical exponents and finally for the case when impurities are not present the surface roughness is described in terms of the hurst exponents

limiting amplitude principle for acoustic propagators in perturbed stratified fluids abstract by use of the commutator method we study the resolvent estimate at low frequencies of acoustic operators c x 2 in perturbed stratified fluids and prove the principle of limiting amplitude for such operators

existence of a unique solution and invariant measures for the stochastic landau lifshitz bloch equation abstract the landau lifshitz bloch equation perturbed by a space dependent noise was proposed in 10 as a model for evolution of spins in ferromagnetic materials at the full range of temperatures including the temperatures higher than the curie temperature in the case of a ferromagnet filling a bounded domain d r d d 1 2 3 we show the existence of strong in the sense of pdes martingale solutions furthermore in cases d 1 2 we prove uniqueness of pathwise solutions and the existence of invariant measures 1

global weak solutions to a spatio temporal fractional landau lifshitz bloch equation abstract the present paper deals with global existence of weak solutions of a time space fractional landau lifshitz bloch equation involving the weak caputo derivative and a fractional laplacian we use faedo galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model the uniqueness is also discussed in a special one dimensional case

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness

invasion percolation a new form of percolation theory a new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system the model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance the name invasion percolation is proposed for this new process similarities to and differences from ordinary percolation theory are discussed