multivariable self tuning control a model following approach abstract a multivariable self tuning control algorithm based on the model following approach is proposed in this paper reference is made to systems described by arm ax models with an a apriori known interactor matrix the cost function is defined in terms of variance of the norm of a suitably defined generalized error a detuned version of the model following procedure is also given so as to cope with non minimum phase systems the proposed algorithm is finally applied to the self tuning control problem of a simulated binary distillation column

limited range multilinear extrapolation with applications to the bilinear hilbert transform we prove a limited range off diagonal extrapolation theorem that generalizes a number of results in the theory of rubio de francia extrapolation and use this to prove a limited range multilinear extrapolation theorem we give two applications of this result to the bilinear hilbert transform first we give sufficient conditions on a pair of weights w 1 w 2 for the bilinear hilbert transform to satisfy weighted norm inequalities of the form begin aligned bh l p 1 left w 1 p 1 right times l p 2 left w 2 p 2 right longrightarrow l p w p end aligned where w w 1w 2 and frac 1 p frac 1 p 1 frac 1 p 2 frac 3 2 this improves the recent results of culiuc et al by increasing the families of weights for which this inequality holds and by pushing the lower bound on p from 1 down to frac 2 3 the critical index from the unweighted theory of the bilinear hilbert transform second as an easy consequence of our method we obtain that the bilinear hilbert transform satisfies some vector valued inequalities with muckenhoupt weights this reproves and generalizes some of the vector valued estimates obtained by benea and muscalu in the unweighted case we also generalize recent results of carando et al on marcinkiewicz zygmund estimates for multilinear calderon zygmund operators

new maximal functions and multiple weights for the multilinear calderon zygmund theory a multi sub linear maximal operator that acts on the product of m lebesgue spaces and is smaller than the m fold product of the hardy littlewood maximal function is studied the operator is used to obtain a precise control on multilinear singular integral operators of calderon zygmund type and to build a theory of weights adapted to the multilinear setting a natural variant of the operator which is useful to control certain commutators of multilinear calderon zygmund operators with bmo functions is then considered the optimal range of strong type estimates a sharp end point estimate and weighted norm inequalities involving both the classical muckenhoupt weights and the new multilinear ones are also obtained for the commutators

the design of a precompensator for multivariable adaptive control a network theoretic approach a network theoretic approach to the design of a dynamic precompensator c s for a multiinput multioutput plant t s is considered the design is based on the relative degree of each element of t s specifically an efficient algorithm is presented for determining whether a given plant t s has a diagonal precompensator c s such that for almost all cases t s c s has a diagonal interactor the algorithm also finds any optimal precompensator in the sense that the total relative degree is minimal the algorithm can be easily modified to work even when a t s represented by a nonsquare matrix is given

flow rule of dense granular flows down a rough incline we present experimental findings on the flow rule for granular flows on a rough inclined plane using various materials including sand and glass beads of various sizes and four types of copper particles with different shapes we characterize the materials by measuring h s the thickness at which the flow subsides as a function of the plane inclination ensuremath theta on various surfaces measuring the surface velocity u of the flow as a function of flow thickness h we find that for sand and glass beads the pouliquen flow rule u sqrt gh ensuremath sim ensuremath beta h h s provides reasonable but not perfect collapse of the u h curves measured for various ensuremath theta and mean particle diameter d improved collapse is obtained for sand and glass beads by using a recently proposed scaling of the form u sqrt gh ensuremath beta h phantom rule 0 2em 0ex mathrm tan 2 phantom rule 0 2em 0ex ensuremath theta h s phantom rule 0 2em 0ex mathrm tan 2 phantom rule 0 2em 0ex ensuremath theta 1 where ensuremath theta 1 is the angle at which the h s ensuremath theta curves diverge measuring the slope ensuremath beta for ten different sizes of sand and glass beads we find a systematic strong increase of ensuremath beta with the divergence angle ensuremath theta 1 of h s copper materials with different shapes are not well described by either flow rule with u ensuremath sim h 3 2

thermodynamically consistent phase field models of fracture variational principles and multi field fe implementations the computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies this can be overcome by a diffusive crack modeling based on the introduction of a crack phase field in this paper we outline a thermodynamically consistent framework for phase field models of crack propagation in elastic solids develop incremental variational principles and consider their numerical implementations by multi field finite element methods we start our investigation with an intuitive and descriptive derivation of a regularized crack surface functional that converges for vanishing length scale parameter to a sharp crack topology functional this functional provides the basis for the definition of suitable convex dissipation functions that govern the evolution of the crack phase field here we propose alternative rate independent and viscous over force models that ensure the local growth of the phase field next we define an energy storage function whose positive tensile part degrades with increasing phase field with these constitutive functionals at hand we derive the coupled balances of quasi static stress equilibrium and gradient type phase field evolution in the solid from the argument of virtual power here we consider a canonical two field setting for rate independent response and a time regularized three field formulation with viscous over force response it is then shown that these balances follow as the euler equations of incremental variational principles that govern the multi field problems these principles make the proposed formulation extremely compact and provide a perfect base for the finite element implementation including features such as the symmetry of the monolithic tangent matrices we demonstrate the performance of the proposed phase field formulations of fracture by means of representative numerical examples copyright 2010 john wiley sons ltd

pointwise convergence of vector valued fourier series we prove a vector valued version of carleson s theorem let y x h theta be a complex interpolation space between an unconditionality of martingale differences umd space x and a hilbert space h for p in 1 infty and f in l p mathbb t y the partial sums of the fourier series of f converge to f pointwise almost everywhere apparently all known examples of umd spaces are of this intermediate form y x h theta in particular we answer affirmatively a question of rubio de francia on the pointwise convergence of fourier series of schatten class valued functions

design of simple low order finite elements for large strain analysis of nearly incompressible solids a simple four node quadrilateral and an eight node hexahedron for large strain analysis of nearly incompressible solids are proposed based on the concept of deviatoric volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart the formulation developed is applicable to arbitrary material models the closed form of the corresponding exact tangent stiffnesses which have a particularly simple structure is derived it ensures asymptotically quadratic rates of convergence of the newton raphson scheme employed in the solution of the implicit finite element equilibrium equations from a practical point of view the incorporation of the proposed elements into existing codes is straightforward it requires only small changes in the routines of the standard displacement based 4 node quadrilateral and 8 node brick a comprehensive set of numerical examples involving hyperelasticity as well as multiplicative elasto plasticity is provided it illustrates the performance of the proposed elements over a wide range of applications including strain localisation problems metal forming simulation and adaptive analysis

nonlocal rheological properties of granular flows near a jamming limit we study the rheology of sheared granular flows close to a jamming transition we use the approach of partially fluidized theory pft with a full set of equations extending the thin layer approximation derived previously for the description of the granular avalanches phenomenology this theory provides a picture compatible with a local rheology at large shear rates g d r midi eur phys j e 14 341 2004 and it works in the vicinity of the jamming transition where a description in terms of a simple local rheology comes short we investigate two situations displaying important deviations from local rheology the first one is based on a set of numerical simulations of sheared soft two dimensional circular grains the next case describes previous experimental results obtained on avalanches of sandy material flowing down an incline both cases display close to jamming significant deviations from the now standard pouliquen s flow rule o pouliquen phys fluids 11 542 1999 11 1956 1999 this discrepancy is the hallmark of a strongly nonlocal rheology and in both cases we relate the empirical results and the outcomes of pft the numerical simulations show a characteristic constitutive structure for the fluid part of the stress involving the confining pressure and the material stiffness that appear in the form of an additional dimensionless parameter this constitutive relation is then used to describe the case of sandy flows we show a quantitative agreement as far as the effective flow rules are concerned a fundamental feature is identified in pft as the existence of a jammed layer developing in the vicinity of the flow arrest that corroborates the experimental findings finally we study the case of solitary erosive granular avalanches and relate the outcome with the pft analysis

weighted norm inequalities off diagonal estimates and elliptic operators part i general operator theory and weights this is the first part of a series of four articles in this work we are interested in weighted norm estimates we put the emphasis on two results of different nature one is based on a good inequality with two parameters and the other uses calderon zygmund decomposition these results apply well to singular non integral operators and their commutators with bounded mean oscillation functions singular means that they are of order 0 non integral that they do not have an integral representation by a kernel with size estimates even rough so that they may not be bounded on all lp spaces for 1 p 8 pointwise estimates are then replaced by appropriate localized lp lq estimates we obtain weighted lp estimates for a range of p that is different from 1 8 and isolate the right class of weights in particular we prove an extrapolation theorem a la rubio de francia for such a class and thus vector valued estimates

on calderon s conjecture with constants cfi p1 p2 depending only on fi p1 p2 and p p1p2 p1 p2 hold the flrst result of this type is proved in 4 and the purpose of the current paper is to extend the range of exponents p1 and p2 for which 2 is known in particular the case p1 2 p2 1 is solved to the a rmative this was

extrapolation from a weights and applications abstract we generalize the a p extrapolation theorem of rubio de francia to a weights in the context of muckenhoupt bases our result has several important features first it can be used to prove weak endpoint inequalities starting from strong type inequalities something which is impossible using the classical result second it provides an alternative to the technique of good inequalities for proving l p norm inequalities relating operators third it yields vector valued inequalities without having to use the theory of banach space valued operators we give a number of applications to maximal functions singular integrals potential operators commutators multilinear calderon zygmund operators and multiparameter fractional integrals in particular we give new proofs which completely avoid the good inequalities of coifman s inequality relating singular integrals and the maximal operator of the fefferman stein inequality relating the maximal operator and the sharp maximal operator and the muckenhoupt wheeden inequality relating the fractional integral operator and the fractional maximal operator

uncertainty principle estimates for vector fields abstract we derive weighted norm estimates for integral operators of potential type and for their related maximal operators these operators are generalizations of the classical fractional integrals and fractional maximal functions the norm estimates are derived in the context of a space of homogeneous type the conditions required of the weight functions involve generalizations of the fefferman phong r bump condition the results improve some earlier ones of the same kind and they also extend to homogeneous spaces some estimates that were previously known to hold only in the classical euclidean setting

an algorithm for the calculation of a nilpotent interactor matrix for linear multivariable systems a new algorithm for the calculation of the delay structure for a linear multivariable system is presented the algorithm evaluates a nilpotent interactor matrix from the matrix of coefficients of the numerator of a right matrix fraction description of the system the resulting nilpotent interactor is a product of first degree nilpotent polynomial matrices

lack of natural weighted estimates for some singular integral operators we show that the classical hormander condition or analogously the l r hormander condition for singular integral operators t is not sufficient to derive coifman s inequality rn tf x p w x dx c rn mf x p w x dx where 0 p m is the hardy littlewood maximal operator w is any a weight and c is a constant depending upon p and the a constant of w this estimate is well known to hold when t is a calderon zygmlmd operator as a consequence we deduce that the following estimate does not hold rn t f x p w x dx c rn mf x p mw x dx where 0 p 1 and where w is an arbitrary weight however by a recent result due to a lerner this inequality is satisfied whenever t is a calderon zygmund operator one of the main ingredients of the proof is a very general extrapolation theorem for a weights

on the role of the interactor matrix in multiinput multioutput adaptive control recent papers have shown that the system interactor matrix plays an important role in the multiinput multioutput adaptive control in these papers however the impression may have been inadvertently conveyed that the interactor matrix can be taken to be diagonal in almost all cases this note shows that this impression is false and that in general a nondiagonal interactor matrix should be considered

the bilinear hilbert transform in umd spaces we prove l p bounds for the bilinear hilbert transform acting on functions valued in intermediate umd spaces such bounds were previously unknown for umd spaces that are not banach lattices our proof relies on bounds on embeddings from bochner spaces l p mathbb r x into outer lebesgue spaces on the time frequency scale space mathbb r 3

extrapolation of weights revisited new proofs and sharp bounds abstract we use an appropriate factorization of the a p weights to give another proof of the extrapolation theorem of rubio de francia it provides sharp bounds in terms of the a p constant of the weights then we extend the result to more general settings including off diagonal and partial range extrapolation among the applications we prove by iteration a multivariable extrapolation theorem and give a sharp bound for calderon zygmund operators on l p w for weights in a q q p

multivariable adaptive control as a natural extension of siso adaptive control the concepts of a potentially structural non singularity and a structural non singularity are introduced in this paper using these concepts we derive the result that for almost all cases the plant to be controlled has a diagonal interactor by using an appropriate diagonal proper precompensator furthermore both the precom pensator and the interactor can be determined only from the structural information of t s the relative degrees of each element of t s without requiring any parametric information about t s therefore by assuming that the a priori knowledge of the plant consists of the relative degrees of each element of t s as well as the observability index of t s we can make mi mo adaptive control be quite a natural extension of siso adaptive control

global convergence for adaptive one step ahead optimal controllers based on input matching this paper establishes global convergence for adaptive one step ahead optimal controllers applied to a class of linear discrete time single input single output systems the class of systems includes all stable systems whether they are minimum phase or not all minimum phase systems whether they are stable or not and some unstable nonminimum phase systems the key substantive assumption is that the one step ahead optimal controller designed using the true system parameters leads to a stable closed loop system subject to this natural restriction it is shown that a simple adaptive control algorithm based on input matching is globally convergent in the sense that the system inputs and outputs remain bounded for all time and the input converges to the one step ahead optimal input both deterministic and stochastic cases are treated

numerical modelling of non linear electroelasticity the numerical modelling of non linear electroelasticity is presented in this work based on well established basic equations of non linear electroelasticity a variational formulation is built and the finite element method is employed to solve the non linear electro mechanical coupling problem numerical examples are presented to show the accuracy of the implemented formulation copyright 2006 john wiley sons ltd

the structure of the reverse holder classes in this paper we study the structure of the class of functions rhs which satisfy the reverse holder inequality with exponent s i to do so we introduce a new operator the minimal operator which is analogous to the hardy littlewood maximal operator and a new class of functions rhcc which plays the same role for rhs that the class ax does for the ap classes

quantitative estimates and extrapolation for multilinear weight classes in this paper we prove a quantitative multilinear limited range extrapolation theorem which allows us to extrapolate from weighted estimates that include the cases where some of the exponents are infinite this extends the recent extrapolation result of li martell and ombrosi we also obtain vector valued estimates including ell infty spaces and in particular we are able to reprove all the vector valued bounds for the bilinear hilbert transform obtained through the helicoidal method of benea and muscalu moreover our result is quantitative and in particular allows us to extend quantitative estimates obtained from sparse domination in the banach space setting to the quasi banach space setting our proof does not rely on any off diagonal extrapolation results and we develop a multilinear version of the rubio de francia algorithm adapted to the multisublinear hardy littlewood maximal operator as a corollary we obtain multilinear extrapolation results for some upper and lower endpoints estimates in weak type and mathrm bmo spaces

a phase field description of dynamic brittle fracture abstract in contrast to discrete descriptions of fracture phase field descriptions do not require numerical tracking of discontinuities in the displacement field this greatly reduces implementation complexity in this work we extend a phase field model for quasi static brittle fracture to the dynamic case we introduce a phase field approximation to the lagrangian for discrete fracture problems and derive the coupled system of equations that govern the motion of the body and evolution of the phase field we study the behavior of the model in one dimension and show how it influences material properties for the temporal discretization of the equations of motion we present both a monolithic and staggered time integration scheme we study the behavior of the dynamic model by performing a number of two and three dimensional numerical experiments we also introduce a local adaptive refinement strategy and study its performance in the context of locally refined t splines we show that the combination of the phase field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions

quasi banach valued inequalities via the helicoidal method abstract we extend the helicoidal method from 1 to the quasi banach context proving in this way multiple banach and quasi banach vector valued inequalities for paraproducts and for the bilinear hilbert transform bht as an immediate application we obtain mixed norm estimates for in the whole range of lebesgue exponents one of the novelties in the quasi banach framework that is when 0 r 1 which we expect to be useful in other contexts as well is the linearization of the operator k t f k g k r 1 r achieved by dualizing its weak l p quasinorms through l r see proposition 8 another important role is played by the sharp evaluation of the operatorial norm t i 0 f 1 f g 1 g 1 h r which is obtained by dualizing the weak l p quasinorms through l with r in the banach case the linearization of the operator and the sharp estimates for the localized operatorial norm can be both achieved through the classical generalized restricted type l 1 dualization

the bilinear maximal functions map into l p for 2 3 p 1 the bilinear maximal operator defined below maps lp x lq into lr provided 1 0 2t t in particular mfg is integrableif f and g are square integrable answering a conjecture posed by alberto calder6n

a finite element implementation of the nonlocal granular rheology summary inhomogeneous flows involving dense particulate media display clear size effects in which the particle length scale has an important effect on flow fields hence nonlocal constitutive relations must be used in order to predict these flows recently a class of nonlocal fluidity models has been developed for emulsions and subsequently adapted to granular materials these models have successfully provided a quantitative description of experimental flows in many different flow configurations in this work we present a finite element based numerical approach for solving the nonlocal constitutive equations for granular materials which involve an additional non standard nodal degree of freedom the granular fluidity which is a scalar state parameter describing the susceptibility of a granular element to flow our implementation is applied to three canonical inhomogeneous flow configurations 1 linear shear with gravity 2 annular shear flow without gravity and 3 annular shear flow with gravity we verify our implementation demonstrate convergence and show that our results are mesh independent copyright 2016 john wiley sons ltd

design of g interactor and its application to direct multivariable adaptive control in the design of multi input multi output mimo adaptive control systems an interactor plays an important role the derivation of the interactor requires system parameter values unless the interactor is in diagonal form this is a considerable restriction when the interactor is applied to the adaptive control system design in mimo adaptive control many parameters must be estimated to achieve good tracking over parametrization causes many problems e g bad tracking performance and long calculation time of control input a design of interactor called a g interactor for unknown mimo plants is given it is applied to mimo adaptive control systems the g interactor requires minimum information on the plant such as the relative degree of each element of the plant transfer matrix for this design a canonical form called the g canonical form of a matrix a is investigated the canonical form is also used to eliminate redundant parameters of mimo adaptive control systems numerical examples show the effect

continuum theory of partially fluidized granular flows a continuum theory of partially fluidized granular flows is developed the theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order parameter equation which describes the transition between the flowing and static components of the granular system we apply this theory to several important granular problems avalanche flow in deep and shallow inclined layers rotating drums and shear granular flows between two plates we carry out quantitative comparisons between the theory and experiment

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

plug flow and the breakdown of bagnold scaling in cohesive granular flows cohesive granular media flowing down an inclined plane are studied by discrete element simulations previous work on cohesionless granular media demonstrated that within the steady flow regime where gravitational energy is balanced by dissipation arising from intergrain forces the velocity profile in the flow direction scales with depth in a manner consistent with the predictions of bagnold here we demonstrate that this bagnold scaling does not hold for the analogous steady flows in cohesive granular media we develop a generalization of the bagnold constitutive relation to account for our observation and speculate as to the underlying physical mechanisms responsible for the different constitutive laws for cohesive and noncohesive granular media

multivariable adaptive control without a prior knowledge of the delay matrix this paper is concerned with the structure and role of the time delay matrix in discrete time multivariable processes interpretations and properties of this matrix as a multivariable generalization of the siso delay term are discussed it is formally shown that a finite time horizon or multi step cost function for the multivariable case can be minimized subject to a suitable choice of output and control horizons and without prior knowledge of the system delay matrix

extrapolation for multilinear muckenhoupt classes and applications abstract in this paper we solve a long standing problem about the multivariable rubio de francia extrapolation theorem for the multilinear muckenhoupt classes a p which were extensively studied by lerner et al and which are the natural ones for the class of multilinear calderon zygmund operators as well as for some bilinear rough singular integral operators furthermore we go beyond the classes a p and extrapolate within the classes a p r which appear naturally associated to the weighted norm inequalities for multilinear sparse forms which control fundamental operators such as the bilinear hilbert transform we give several applications which can be easily obtained using extrapolation first weighted norm inequalities scalar and vector valued for the bilinear rough singular integral operators are established second for the bilinear hilbert transform one can extrapolate from the recent result of culiuc et al who considered the banach range extend the estimates to the quasi banach range and furthermore prove trivially vector valued inequalities we also extend recent results of carando et al on marcinkiewicz zygmund estimates for multilinear calderon zygmund operators finally our last application gives new weighted estimates scalar and vector valued for the commutators of multilinear calderon zygmund operators bilinear rough singular integral operators and for the bilinear hilbert transform with bmo functions using ideas from benyi et al

boundedness results for commutators with bmo functions via weighted estimates a comprehensive approach we present a unified method to obtain unweighted and weighted estimates of linear and multilinear commutators with bmo functions that is amenable to a plethora of operators and functional settings our approach elaborates on a commonly used cauchy integral trick recovering many known results but yielding also numerous new ones in particular we solve a problem about the boundedness of the commutators of the bilinear hilbert transform with functions in bmo

stochastic flow rule for granular materials there have been many attempts to derive continuum models for dense granular flow but a general theory is still lacking here we start with mohr coulomb plasticity for quasi two dimensional granular materials to calculate average stresses and slip planes but we propose a stochastic flow rule sfr to replace the principle of coaxiality in classical plasticity the sfr takes into account two crucial features of granular materials discreteness and randomness via diffusing spots of local fluidization which act as carriers of plasticity we postulate that spots perform random walks biased along slip lines with a drift direction determined by the stress imbalance upon a local switch from static to dynamic friction in the continuum limit based on a fokker planck equation for the spot concentration this simple model is able to predict a variety of granular flow profiles in flat bottom silos annular couette cells flowing heaps and plate dragging experiments with essentially no fitting parameters although it is only expected to function where material is at incipient failure and slip lines are inadmissible for special cases of admissible slip lines such as plate dragging under a heavy load or flow down an inclined plane we postulate a transition to rate dependent bagnold rheology where flow occurs by sliding shear planes with different yield criteria the sfr provides a general framework for multiscale modeling of plasticity in amorphous materials cycling between continuum limit state stress calculations mesoscale spot random walks and microscopic particle relaxation

formulation and finite element implementation of a multiplicative model of coupled poro plasticity at finite strains under fully saturated conditions in this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro plasticity fully saturated conditions are assumed the model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts together with an additive elastoplastic decomposition of the fluid content the final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation the particular case of an associated drucker prager model in effective stresses is considered as a model example a complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate we describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem finally we present representative numerical simulations to illustrate the features of the proposed models in particular the case of strain localization in globally undrained conditions is studied in the proposed framework