existence and uniqueness of solution in sobolev space for an unsteady crystal growth problem with zero surface tension abstract we study an initial value problem for a two dimensional dendritic crystal growth model with zero surface tension if the initial data is in sobolev space h 2 r it is proved that an unique local solution exists in proper sobolev space

analyticity and nonexistence of classical steady hele shaw fingers this paper concerns analyticity of a classical steadily translating nger in a hele shaw cell and nonexistence of solutions when the relative nger width is smaller than 1 it is proven that any classical solution to the nger problem if it exists for sufciently small but nonzero surface tension is close to some saffman taylor zero surface tension solution and satises some algebraic decay conditions at 1 must belong to the analytic function space a0 as dened in section 1 and chosen in a previous study 34 of the existence of nger solutions further it is proven that for any x ed 2 0 1 there can be no classical steadynger solution when surface tension is sufciently small which contradicts a previous conclusion based on numerical simulation c 2002 wiley periodicals inc

perturbation theory for the effective diffusion constant in a medium of random scatterers we develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random medium the random medium contains point scatterers of density uniformly distributed throughout the material the tracer is a langevin particle subjected to the quenched random force generated by the scatterers via our perturbative analysis we determine when the random potential can be approximated by a gaussian random potential we also develop a self similar renormalization group approach based on thinning out the scatterers this scheme is similar to that used with success for diffusion in gaussian random potentials and agrees with known exact results to assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation

sampled data state estimation for markovian jumping fuzzy cellular neural networks with mode dependent probabilistic time varying delays in this paper the problem of state estimation for markovian jumping fuzzy cellular neural networks fcnns using sampled data with mode dependent probabilistic time varying delays is investigated by developing a delay decomposition approach the information of the delayed states can be taken into full consideration by introducing a stochastic variable with a bernoulli distribution the information of probability distribution of the time varying delay is considered and transformed into one with deterministic time varying delay the main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally asymptotically stable in the mean square based on the lyapunov krasovskii functional including triple integral terms and decomposed integral intervals delay distribution dependent stability criteria are obtained in terms of linear matrix inequalities lmis finally two numerical examples are given to illustrate the effectiveness of the proposed theoretical results

closed form solutions for the effective conductivity of two phase periodic composites with spherical inclusions in this paper we use approximate solutions of the nemat nasser et al to estimate the effective conductivity of two phase composites with non overlapping spherical inclusions systems with different inclusion distributions are considered cubic lattice distributions simple cubic body centered cubic and face centered cubic and random distributions the effective conductivities of the former are obtained in closed form and compared with exact solutions from the fast fourier transform based methods for systems containing randomly distributed spherical inclusions the solutions are shown to be directly related to the static structure factor and we obtain its analytical expression in the infinite volume limit

improved bounds on the conductivity of composites by interpolation different bounds on the conductivity of a composite material may improve on each other in different conductivity regimes if so the question arises of how to efficiently interpolate between the bounds in this paper i show how to do an interpolation with a two point pade approximation method for bounds on two component composites the interpolation method is shown to be in a sense the best possible the method is discussed in the context of equiaxed polycrystals where the classic hashin shtrikman bounds and the more recent null lagrangian bounds partly improve on each other denoting the principal conductivities of the crystallite sigma 1 leq sigma 2 leq sigma 3 the method gives improved lower bounds for equiaxed polycrystals which have sigma 2 0 77 sigma 1 0 23 sigma 3 geq sigma 1 sigma 3 the method also gives improved upper bounds

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

delay slope dependent stability results of recurrent neural networks by using the fact that the neuron activation functions are sector bounded and nondecreasing this brief presents a new method named the delay slope dependent method for stability analysis of a class of recurrent neural networks with time varying delays this method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed lyapunov krasovskii functional then some improved delay dependent stability criteria with less computational burden and conservatism are obtained numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

analyticity of classical steady needle crystals abstract this paper is a continuation of our previous work rigorous results in selection of steady needle crystals j differential equations 197 2004 349 426 it concerns analyticity of a classical steadily translating needle crystal it is proved that any classical solution to the needle crystal problem with sufficiently small but nonzero surface tension if its slope deviation is close to some ivantsov zero surface tension solution and if its curvature satisfies some algebraic decay conditions at must belong to the analytic function space a 0 defined in 1 and chosen in the previous study mentioned above the analyticity result implies that there can be no classical steady needle crystal solution when anisotropy is zero

periodic conduction problems the fast multipole method and convergence of integral equations and lattice sums this paper presents a version of the fast multipole method fmm for integral equations describing conduction through three dimensional periodic heterogeneous media the proposed method is based on the standard rather than periodic fundamental solution and therefore it is very close to the original fmm in deriving the method particular attention is paid to convergence of arising integral equations and lattice sums it is shown that convergence can be achieved without introducing artificial compensatory sources or boundary conditions

further results on exponential stability for impulsive switched nonlinear time delay systems with delayed impulse effects this paper is concerned with the problem of exponential stability for a class of impulsive switched nonlinear time delay systems with delayed impulse effects by using the multiple lyapunov krasovskii functionals technique some exponential stability criteria are obtained respectively for two kinds of impulsive signals destabilizing impulsive signal and stabilizing impulsive signal the derived results not only characterise the effects of delayed impulse time delay and switching on nonlinear systems but also remove some restriction conditions furthermore a more precise bound of system state is given compared with existing results on related problems the obtained results are less conservative three examples are provided to illustrate the effectiveness and the generality of the proposed results

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

the effective conductivity of a periodic array of spheres we consider the problem of determining the effective conductivity k of a composite material consisting of equal sized spheres of conductivity alpha arranged in a cubic array within a homogeneous matrix of unit conductivity we modify zuzovski brenner9s 1977 method and thereby obtain a set of infinite linear equations for the coefficients of the formal solution equivalent to that derived by mckenzie et al 1978 using a method originally devised by rayleigh 1892 on solving these equations we derive expressions for k ast to o c 9 c being the volume fraction of the spheres for simple body centred and face centred cubic arrays and also obtain numerical values for k over the whole range of alpha and c we show that these results for cubic arrays can be used to estimate ast for random arrays of identical spheres for arrays of highly conducting and nearly touching spheres batchelor o9brien 1977 showed that begin equation k ast sim begin cases k 1 ln 1 chi k 2 alpha infty chi c c max frac 1 3 rightarrow 1 2k 1 ln alpha k9 2 quad chi 1 alpha rightarrow infty end cases end equation where c max corresponds to the volume fraction when the spheres are actually touching each other and determined k 1 for the three cubic arrays our numerical results are consistent with the above asymptotic expressions except for the fact that the numerical values for the constants k 2 and k9 2 thereby obtained do not quite satisfy the relation k9 2 k 1 3 9 ln 2 k 2 given by batchelor o9brien we have been unable to find the reason for this slight discrepancy

state estimation for markovian jump linear systems with bounded disturbances in this paper we investigate the state estimation problem for a class of markovian jump linear systems mjlss in the presence of bounded polyhedral disturbances a set membership estimation algorithm is first proposed to find the smallest consistent set of all possible states which is shown to be expressed by a union of multiple polytopes the posterior probabilities of the system jumping modes are then estimated by introducing the lebesgue measure based on which the optimal point estimate is further provided moreover a similarity relationship for polytopes is defined and an approximate method is presented to calculate the minkowski sum of polytopes which can help reduce the computational complexity of the overall estimation algorithm

rigorous results in selection of steady needle crystals abstract this paper concerns the existence of solutions to a steady needle crystal growth problem in a one sided model we rigorously prove that for small nonzero anisotropy analytic symmetric needle crystal solutions exist in the limit of surface tension e 2 if only if the stokes constant s for a relatively simple nonlinear differential equation is zero this stokes constant s depends on the parameter 2 9 7 e 8 7 and earlier numerical calculations by a number of investigators have shown this to be zero for a discrete set of values of it is also proven that for 0 there can be no symmetric needle crystal solution in the considered space the methodology consists of two steps first the original problem is reduced to a weak half strip problem for any in a compact set of 0 1 by relaxation of the symmetry condition the weak problem is shown to have a unique solution in the function space considered for any 0 m for some m 0 when a symmetry is invoked the weak problem is shown equivalent to the original needle crystal problem next by considering the behavior of the solution in neighborhood of an appropriate complex turning point for 0 m we extract an exponentially small term in e as e 0 that generally violates the symmetric condition we prove that the symmetry condition is satisfied for small e when the parameter is constrained appropriately

the effective conductivity of random suspensions of spherical particles the effective conductivity of an infinite random mono disperse hard sphere suspension is reported for particle to matrix conductivity ratios of 10 and 0 01 for sphere volume fractions c up to 0 6 the conductivities are computed with a method previously described by the authors which includes both far and near field interactions and the particle configurations are generated via a monte carlo method the results are consistent with the previous theoretical work of d j jeffrey to o c 2 and the bounds computed by s torquato and f lado it is also found that the clausius mosotti equation is reasonably accurate for conductivity ratios of 10 or less all the way up to 60 by volume the calculated conductivities compare very well with those of experiments in addition percolation like numerical experiments are performed on periodically replicated cubic lattices of n nearly touching spheres with an infinite particle to matrix conductivity ratio where the conductivity is computed as spheres are removed one by one from the lattice under suitable normalization of the conductivity and volume fraction it is found that the initial volume fraction must be extremely close to maximum packing in order to observe a percolation transition indicating that the near field effects must be very large relative to far field effects these percolation transitions occur at the accepted values for simple sc bodycentred bcc and face centred fcc cubic lattices also the vulnerability of the lattices computed here are exactly those of previous investigators due to limited data above the percolation threshold we could not correlate the conductivity with a power law near the threshold however it can be correlated with a power law for large normalized volume fractions in this case the exponents are found to be 1 70 1 75 and 1 79 for sc bcc and fcc lattices respectively

existence and uniqueness of analytic solution for unsteady crystals with zero surface tension abstract we study the initial value problem for two dimensional dendritic crystal growth with zero surface tension if the initial data is analytic and close to ivantsov steady solution it is proved that unique analytic solution exists locally in time the analysis is based on a nirenberg theorem on abstract cauchy kovalevsky problem in properly chosen banach spaces

existence and selection of steady bubbles in a hele shaw cell abstract this paper concerns the existence of a steadily translating bubble in a hele shaw cell for small but non zero surface tension 2 we rigorously conclude that for bubble velocity u relative to the fluid velocity at infinity in the interval 1 2 analytic symmetric solutions exist in the asymptotic limit of surface tension 2 0 if and only if the stokes constant for a relatively simple nonlinear differential equation is zero this stokes constant s depends on the parameter 0 1 corresponding to bubble size and a u 1 2 2 u 1 2 2 2 1 2 4 3 earlier calculations have shown s to be zero for a discrete set of values of a

rigorous results in steady finger selection in viscous fingering this paper concerns the existence of a steadily translating finger solution in a hele shaw cell for small but non zero surface tension 2 though there are numerous numerical and formal asymptotic results for this problem we know of no mathematically rigorous results that address the selection problem we rigorously conclude that for relative finger width in the range with small analytic symmetric finger solutions exist in the asymptotic limit of surface tension if and only if the stokes constant for a relatively simple nonlinear differential equation is zero this stokes constant s depends on the parameter and earlier calculations by a number of authors have shown it to be zero for a discrete set of values of a the methodology consists of proving the existence and uniqueness of analytic solutions for a weak half strip problem for any in a compact subset of 0 1 the weak problem is shown to be equivalent to the original finger problem in the function space considered provided we invoke a symmetry condition next we consider the behavior of the solution in a neighborhood of an appropriate complex turning point for the restricted case for some this turning point accounts for exponentially small terms in as 0 that generally violate the symmetry condition we prove that the symmetry condition is satisfied for small when the parameter a is constrained appropriately

event triggered state estimation for markovian jumping impulsive neural networks with interval time varying delays abstractthis paper investigates the event triggered state estimation problem of markovian jumping impulsive neural networks with interval time varying delays the purpose is to design a state estimator to estimate system states through available output measurements in the neural networks there are a set of modes which are determined by markov chain a markovian jumping time delay impulsive neural networks model is employed to describe the event triggered scheme and the network related behaviour such as transmission delay data package dropout and disorder the proposed event triggered scheme is used to determine whether the sampled state information should be transmitted the discrete delays are assumed to be time varying and belong to a given interval which means that the lower and upper bounds of interval time varying delays are available first we design a state observer to estimate the neuron states second based on a novel lyapunov krasovskii functional lkf with triple integral terms and us