w stability and local input output stability results a new type of input output stability is defined based on the use of a sobolev space w w is well suited like the lebesgue space l sub 2 to obtain stability characterizations in the time and frequency domains moreover if compared with l sub 2 w has additional properties which enable one to establish local stability results a local version of the small gain theorem is established in this framework as well as some consequences of this result in particular local versions of the passivity theorem and of the circle criterion the relationship between w stability and asymptotic stability is studied

pseudo random number generators and the square site percolation threshold selected pseudo random number generators are applied to a monte carlo study of the two dimensional square lattice site percolation model a generator suitable for high precision calculations is identified from an application specific test of randomness after extended computation and analysis an ostensibly reliable value of p c 0 592 phantom rule 0 2em 0ex 745 phantom rule 0 2em 0ex 98 4 is obtained for the percolation threshold

effects of random and deterministic discrete scale invariance on the critical behavior of the potts model the effects of disorder on the critical behavior of the q state potts model in noninteger dimensions are studied by comparison of deterministic and random fractals sharing the same dimensions in the framework of a discrete scale invariance we carried out intensive monte carlo simulations in the case of a fractal dimension slightly smaller than two d f 1 974636 we give evidence that the disorder structured by discrete scale invariance does not change the first order transition associated with the deterministic case when q 7 furthermore the study of the high value q 14 shows that the transition is a second order one both for deterministic and random scale invariance but that their behavior belongs to different university classes

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

regularity properties of the solutions to the 3d maxwell landau lifshitz system in weighted sobolev spaces this paper is concerned with special regularity properties of the solutions to the maxwell landau lifshitz mll system describing ferromagnetic medium besides the classical results on the boundedness of tm te and th in the spaces l i l 2 w and l 2 i w 1 2 w we derive also estimates in weighted sobolev spaces this kind of estimates can be used to control the taylor remainder when estimating the error of a numerical scheme

iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics abstract the tangent plane scheme is a time marching scheme for the numerical solution of the nonlinear parabolic landau lifshitz gilbert equation which describes the time evolution of ferromagnetic configurations exploiting the geometric structure of the equation the tangent plane scheme requires only the solution of one linear variational form per time step which is posed in the discrete tangent space determined by the nodal values of the current magnetization we develop an effective solution strategy for the arising constrained linear systems which is based on appropriate householder reflections we derive possible preconditioners which are essentially independent of the time step and prove linear convergence of the preconditioned gmres algorithm numerical experiments underpin the theoretical findings

current induced magnetization dynamics global existence of weak solutions abstract we consider a model of current induced magnetization dynamics described by the landau lifshitz gilbert llg equations of the magnetization in which an additional current dependent term is added two methods namely faedo galerkin penalty fgp method and hyperbolic regularization method are used to show the existence of finite energy global weak solutions

finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii we prove the existence of weak solutions to the harmonic map heat flow and wave maps into spheres of nonconstant radii weak solutions are constructed as proper limits of iterates from a fully practical scheme based on lowest order conforming finite elements where discrete lagrange multipliers are employed to exactly meet the sphere constraint at mesh points computational studies are included to motivate interesting dynamics in two and three spatial dimensions

analysis of a coupled spin drift diffusion maxwell landau lifshitz system abstract the existence of global weak solutions to a coupled spin drift diffusion and maxwell landau lifshitz system is proved the equations are considered in a two dimensional magnetic layer structure and are supplemented with dirichlet neumann boundary conditions the spin drift diffusion model for the charge density and spin density vector is the diffusion limit of a spinorial boltzmann equation for a vanishing spin polarization constant the maxwell landau lifshitz system consists of the time dependent maxwell equations for the electric and magnetic fields and of the landau lifshitz gilbert equation for the local magnetization involving the interaction between magnetization and spin density vector the existence proof is based on a regularization procedure l 2 type estimates and moser type iterations which yield the boundedness of the charge and spin densities furthermore the free energy is shown to be nonincreasing in time if the magnetization spin interaction constant in the landau lifshitz equation is sufficiently small

convergence of an implicit explicit midpoint scheme for computational micromagnetics abstract based on lowest order finite elements in space we consider the numerical integration of the landau lifschitz gilbert equation llg the dynamics of llg is driven by the so called effective field which usually consists of the exchange field the external field and lower order contributions such as the stray field the latter requires the solution of an additional partial differential equation in full space following bartels and prohl 2006 we employ the implicit midpoint rule to treat the exchange field however in order to treat the lower order terms effectively we combine the midpoint rule with an explicit adams bashforth scheme the resulting integrator is formally of second order in time and we prove unconditional convergence towards a weak solution of llg numerical experiments underpin the theoretical findings

a landau lifshitz type equation in studying thin film micromagnetics the paper is concerned with a landau lifshitz type equation which was first raised by desimone and otto etc when studying thin film micromagnetics we get the existence of a continuous solution using penalty approximation compensated compactness and commutator estimate

convergence result for the constraint preserving mid point scheme for micromagnetism an important progress was recently done in numerical approximation of weak solutions to a micromagnetic model equation the problem with the nonconvex side constraint of preserving the length of the magnetization was tackled by using reduced integration several schemes were proposed and their convergence to weak solutions was proved all schemes were derived from the landau lifshitz gilbert form of the micromagnetic equation however when the precessional term in the original landau lifshitz ll form of the micromagnetic equation tends to zero the above schemes become unusable we propose a scheme derived from the mid point rule for the ll form of the micromagnetic equation combined with the reduced integration we show convergence to a weak solution of the ll equation and demonstrate the usefulness of the proposed scheme to study the limit process when the precessional parameter of the micromagnetic equation goes to zero

partial regularity to the landau lifshitz equation with spin accumulation abstract in this paper we consider a model for the spin magnetization system that takes into account the diffusion process of the spin accumulation this model consists of the landau lifshitz equation describing the precession of the magnetization coupled with a quasi linear parabolic equation describing the diffusion of the spin accumulation this paper establishes the global existence and uniqueness of weak solutions for large initial data in r 2 moreover partial regularity is shown in particular the solution is regular on r 2 0 with the exception of at most finite singular points

higher order regularity results in 3d for the landau lifshitz equation with an exchange field abstract we derive and prove higher order regularity results for the landau lifshitz ll equation describing the evolution of spin fields in continuum ferromagnets these results are based on the weight s min 1 s which helps to get nonlinear parts under control

robust nonlinear control associating robust feedback linearization and h sub spl infin control in this note a robust nonlinear controller for a nonlinear system subject to model uncertainties is proposed such a controller associates a robust feedback linearization with a robust linear h sub spl infin controller the robust feedback linearization exactly transforms the nonlinear system into a linear system equal to the linear approximation of the original nonlinear system around a nominal operating point the robustness of the resulting overall nonlinear controller is proved by theoretical arguments and illustrated through an application example the control of a magnetic bearing system

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

on a hyperbolic parabolic system arising in magnetoelasticity the evolution of a magnetoelastic material is described by a nonlinear hyperbolic parabolic system we introduce a simplified but nontrivial model and prove the existence of a unique solution to the corresponding initial boundary value problem

critical behavior of the susceptible infected recovered model on a square lattice by means of numerical simulations and epidemic analysis the transition point of the stochastic asynchronous susceptible infected recovered model on a square lattice is found to be c0 0 176 500 510 where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor this point corresponds to an infection recovery rate of c 1 c0 c0 4 665 713 and a net transmissibility of 1 c0 1 3 c0 0 538 4102 which falls between the rigorous bounds of the site and bond thresholds the critical behavior of the model is consistent with the two dimensional percolation universality class but local growth probabilities differ from those of dynamic percolation cluster growth as is demonstrated explicitly

hausdorff measure of the singular set of landau lifshitz equations with a nonlocal term this paper is concerned with the partial regularity of the stationary solutions to the landau lifshitz system of ferromagnetic spin chain with gilbert damping and a nonlocal term in 3 dimensions the hausdorff measure of the singular set is discussed

the gilbert equation with dry friction type damping a modified gilbert equation for micromagnetics is considered obtained by augmenting the standard viscous like dissipation with a rate independent term we prove existence of a weak solution both with and without viscous dissipation by scaling time we show that if the applied field varies very slowly then gyromagnetic effects and viscous dissipation become negligible in the infinitesimally slow loading limit the system thus becomes fully rate independent

the effective conductivity of arrays of squares large random unit cells and extreme contrast ratios an integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two component checkerboard like composites with complicated unit cells at very high contrast ratios the scheme extends recent work on multi component checkerboards at medium contrast ratios general improvement include the simplification of a long range preconditioner the use of a banded solver and a more efficient placement of quadrature points this together with a reduction in the number of unknowns allows for a substantial increase in achievable accuracy as well as in tractable system size results accurate to at least nine digits are obtained for random checkerboards with over a million squares in the unit cell at contrast ratio 106 furthermore the scheme is flexible enough to handle complex valued conductivities and using a homotopy method purely negative contrast ratios examples of the accurate computation of resonant spectra are given

percolation of dimers on square lattices abstract a theoretical approach based on exact calculations of configurations on finite rectangular cells is applied to study the percolation of homonuclear dimers on square lattices an efficient algorithm allows us to calculate the detailed structure of the configuration space for m l x l y cells with m varying from 16 to 36 the percolation process has been monitored by following the percolation function defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied sites the percolation threshold has been calculated by means of two complementary methods one based on well known renormalization techniques and the other based on determining the inflection point of the percolation function curves a comparison of the results obtained by these two methods has been performed the study includes the use of finite size scaling theory to extrapolate numerical results towards the thermodynamic limit the effect of jamming due to dimers is also established finally the critical exponents and have been obtained and values compared with numerical results and expected theoretical estimations the present results show agreement and even improvement in the case of with respect to some numeric values available in the literature

wong zakai approximation for the stochastic landau lifshitz gilbert equations abstract in this work we study stochastic landau lifshitz gilbert equations sllges in one dimension with non zero exchange energy only firstly by introducing a suitable transformation we convert the sllges to a highly nonlinear time dependent partial differential equation with random coefficients which is not fully parabolic we then prove that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity property following regular approximation of the brownian motion and using reverse transformation we show existence of strong solution of sllges taking values in a two dimensional unit sphere s 2 in r 3 the construction of the solution and its corresponding convergence results are based on wong zakai approximation

newman ziff algorithm for the bootstrap percolation application to the archimedean lattices abstract we propose very efficient algorithms for the bootstrap percolation and the diffusion percolation models by extending the newman ziff algorithm of the classical percolation m e j newman and r m ziff 2000 27 using these algorithms and the finite size scaling we calculated with high precision the percolation threshold and critical exponents in the eleven two dimensional archimedean lattices we present the condition for the continuous percolation transition in the bootstrap percolation and the diffusion percolation and show that they have the same critical exponents as the classical percolation within error bars in two dimensions we conclude that the bootstrap percolation and the diffusion percolation almost certainly belong to the same universality class as the classical percolation

homogenization of the demagnetization field operator in periodically perforated domains in this paper we study the homogenization of the demagnetization field operator in periodically perforated domains using the two scale convergence method as an application we homogenize the landau lifshitz equation in such domains we consider regular homothetic holes

site trimer percolation on square lattices percolation of site trimers k mers with k 3 is investigated in a detailed way making use of an analytical model based on renormalization techniques in this problem results are compared to those obtained here by means of extensive computer simulations five different deposition possibilities for site trimers are included according to shape and orientation of the depositing objects analytical results for the percolation threshold p c are all close to 0 55 while numerical results show a slight dispersion around this value a comparison with p c values previously reported for monomers and dimers establishes the tendency of p c to decrease as k increases critical exponent was also obtained both by analytical and numerical methods results for the latter give values very close to the expected value 4 3 showing that this percolation case corresponds to the universality class of random percolation

maxwell s equations with vector hysteresis electromagnetic processes in magnetic materials are described by maxwell s equations in ferrimagnetic insulators assuming that d e e we have the equation

numerical scheme for augmented landau lifshitz equation in heat assisted recording the motivation of heat assisted recording is to improve the thermal stability of recorded data bits by increasing the strength of the uniaxial anisotropy during the recording process the medium is heated by a laser reducing the coercivity and allowing the head to write data bits we present a micromagnetic model based on the augmented landau lifshitz equation taking into account a phenomenological power law describing the dependence of the saturation magnetization on the temperature a full discrete numerical scheme is presented and the convergence of approximate solutions to a weak one is shown

transfer matrix computation of generalized critical polynomials in percolation percolation thresholds have recently been studied by means of a graph polynomial pb p henceforth referred to as the critical polynomial that may be defined on any periodic lattice the polynomial depends on a finite subgraph b called the basis and the way in which the basis is tiled to form the lattice the unique root of pb p in 0 1 either gives the exact percolation threshold for the lattice or provides an approximation that becomes more accurate with appropriately increasing size of b initially pb p was defined by a contraction deletion identity similar to that satisfied by the tutte polynomial here we give an alternative probabilistic definition of pb p which allows for much more efficient computations by using the transfer matrix than was previously possible with contraction deletion we present bond percolation polynomials for the 4 82 kagome and 3 122 lattices for bases of up to respectively 96 162 and 243 edges much larger than the previous limit of 36 edges using contraction deletion we discuss in detail the role of the symmetries and the embedding of b for the largest bases we obtain the thresholds pc 4 82 0 676 803 329 pc kagome 0 524 404 998 pc 3 122 0 740 420 798 comparable to the best simulation results we also show that the alternative definition of pb p can be applied to study site percolation problems this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

symplectic flow for the square root of the negative laplacian abstract the paper is concerned with symplectic flow for the square root of the negative laplacian which is motivated when studying a one dimensional model about ferromagnetic thin film without gilbert damping term only gyromagnetic term remained derived from the stationary model of a desimone r v kohn s muller and f otto existence of weak solution to the model is proved by viscosity approximation and commutator estimate

the weak solutions to the evolution problems of harmonic maps on demontre l existence de solutions faibles globales a des problemes d evolution des applications harmoniques de varietes de riemann compactes sans bord dans des spheres

global solutions of a dynamical equation in ferrimagnet abstract we consider global solutions of a dynamical equation in ferrimagnet we show that it admits a global weak solution by using the penalty method by the energy estimates method we show there exists a unique global smooth solution finally we establish the relationship between this equation and wave maps

a convergent finite element approximation for the quasi static maxwell landau lifshitz gilbert equations we propose a q linear scheme for the numerical solution of the quasi static maxwell landau lifshitz gilbert mllg equations despite the strong nonlinearity of the landau lifshitz gilbert equation the proposed method results in a linear system at each time step we prove that as the time and space steps tend to zero with no further conditions when email protected 12 1 the finite element solutions converge weakly to a weak solution of the mllg equations numerical results are presented to show the applicability of the method

optimal error estimates of a linearized backward euler fem for the landau lifshitz equation we present a fully discrete linearized backward euler finite element method for the landau lifshitz equation in which a new linearization is proposed for the gyromagnetic term optimal almost unconditional error estimates of the scheme in l 2 and h 1 norms are proved i e when the stepsizes h and tau are smaller than given constants the analysis relies on the new linearization and an error splitting argument proposed by li and sun int j numer anal model 10 2013 pp 622 633 and siam j numer anal 51 2013 pp 1959 1977 numerical results in both two and three dimensional spaces are provided to confirm our theoretical analysis and show the unconditional stability convergence of the scheme

initial boundary value problems for anisotropic landau lifshitz equations in three or four space dimensions abstract in this paper we will show the existence of partially regular solutions to the initial boundary value problem for landau lifshitz equations with nonpositive anisotropy constants in three or four space dimensions the partial regularity is proved up to the boundary both for the dirichlet problem and for the neumann problem in addition for the neumann case a generalized stability condition which ensures the partial regularity is given for equations with positive or negative anisotropy coefficients we will give two results of existence and uniqueness for the solutions corresponding to ground states

global weak solutions of the fractional landau lifshitz maxwell equation abstract the fractional landau lifshitz maxwell equation is considered in this paper we show the global existence of suitable weak solutions by galerkin method and the vanishing viscosity method the main difficulties in this study are due to the loss of compactness of this system and the fact that the nonlinear term is nonlocal and of the same order of the equation to overcome these difficulties we introduce the commutator estimates and some cancellation properties to this equation which prove to be proper tools in the study of landau lifshitz type equations

normalized coprime factorizations and balancing for unstable nonlinear systems in this paper we first study the normalized right and left coprime factorizations of a nonlinear system from a state space point of view in order to do so we introduce the notion of inner and co inner nonlinear systems secondly we deal with balancing for unstable nonlinear systems for linear systems there are several ways to approach this problem and we generalize the ideas of balancing the normalized coprime factorization and of lqg balancing to the nonlinear case lqg balancing can be seen as measuring the influence of a state component on a certain future and past energy function we extend this interpretation to the nonlinear case furthermore we use the normalized coprime factorization to give another way of balancing the unstable nonlinear system we give the relation between these two methods of balancing which is similar to the relation in the linear case

a convergent implicit finite element discretization of the maxwell landau lifshitz gilbert equation we propose an implicit fully discrete scheme for the numerical solution of the maxwell landau lifshitz gilbert equation which is based on linear finite elements and satisfies a discrete sphere constraint as well as a discrete energy law as numerical parameters tend to zero solutions weakly accumulate at weak solutions of the maxwell landau lifshitz gilbert equation a practical linearization of the nonlinear scheme is proposed and shown to converge for certain scalings of numerical parameters computational studies are presented to indicate finite time blow up behavior and to study combined electromagnetic phenomena in ferromagnets for benchmark problems

robust stabilization of normalized coprime factor plant descriptions with h sub infinity bounded uncertainty the problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by h sub infinity bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system this problem can be reduced to a nehari extension problem directly and gives an optimal stability margin all controllers satisfying a suboptimal stability margin are characterized and explicit state space formulas are given

existence of partially regular weak solutions to landau lifshitz maxwell equations abstract in this paper the authors establish the existence of partially regular weak solutions to the landau lifshitz equations coupling with static maxwell systems in 3 dimensions by ginzburg landau approximation it is proved that the hausdorff measure of the singular set is locally finite this extends the similar results of ding and guo s ding b guo hausdorff measure of the singular set of landau lifshitz equations with a nonlocal term comm math phys 250 1 2004 95 117 from the stationary solutions to weak solutions and the results of wang c wang on landau lifshitz equations in dimensions at most four indiana univ math j 55 5 2006 1615 1644 from landau lifshitz equations to landau lifshitz maxwell equations

existence regularity and local uniqueness of the solutions to the maxwell landau lifshitz system in three dimensions abstract we study a model of ferromagnetism governed by maxwell s equations coupled with the non linear landau lifshitz equation of micromagnetism we are interested in the cases of space periodic solutions for 3d domains obtaining the regularity of the solution m in w per 2 2 space and of the solutions e h in w per 1 2 space we state the existence theorem finally we prove the local uniqueness of the solutions