stochastic finite element modelling in linear transient heat transfer a stochastic heat transfer variational principle is suggested for transient and steady state heat problems the non statistical formulation is based on the combination of the second order perturbation technique and second moment analysis the principle allows incorporation of system uncertainties into the conventional finite element equations which are solved for the first two probabilistic moments of the nodal random temperature field computational aspects of the problem are discussed numerical algorithms have been worked out and easily adapted to an existing finite element code the formalism presented may be directly employed for a wide class of field problems

long time behavior of a cooperative periodic parabolic system in a spatiotemporally degenerate environment this paper is the continuation of our work 1 41 on the study of the cooperative periodic parabolic system tu u u x t v a x t up tv v v x t u b x t vqin 0 u v 0 0 on 0 u x 0 v x 0 u0 x v0 x 0 0 in where p q 1 rn n 2 is a bounded smooth domain 0 and a b 0 are smooth functions that are t periodic in t and is a varying parameter the unknown functions u x t and v x t stand for the densities of two cooperative species at location x and time t the aim of our work is to establish the long time behavior of u v when the species are exposed to a spatiotemporally degenerate environment in 1 and 41 we dealt with the three cases that a and b have simultaneous spatiotemporal degeneracy simultaneous spatial degeneracy and simultaneous temporal degeneracy in this paper we consider some other natural situations of degeneracies our results reveal further interesting effects of spatial and temporal degeneracies on the dynamics of such a cooperative system in addition we provide a sharp improvement of the results in 41 when simultaneous temporal degeneracy occurs

a multigrid solver for two dimensional stochastic diffusion equations steady and unsteady diffusion equations with stochastic diffusivity coefficient and forcing term are modeled in two dimensions by means of stochastic spectral representations problem data and solution variables are expanded using the polynomial chaos system the approach leads to a set of coupled problems for the stochastic modes spatial finite difference discretization of these coupled problems results in a large system of equations whose dimension necessitates the use of iterative approaches in order to obtain the solution within a reasonable computational time to accelerate the convergence of the iterative technique a multigrid method based on spatial coarsening is implemented numerical experiments show good scaling properties of the method both with respect to the number of spatial grid points and the stochastic resolution level

superlinear indefinite systems beyond lotka volterra models abstract this paper analyzes the dynamics of a superlinear indefinite parabolic system as a byproduct a number of new results related to population dynamics and economy are obtained among them it is shown that the presence of refuge areas in competitive environments is an optimal mechanism to avoid extinction and that incorporating local symbiosis in competitive environments increases productivity and allows avoiding extinction of the weaker species undoubtedly a paradigm of global markets and possibly of earth biodiversity our analysis combines a series of well known results for systems with some very recent pioneering findings within the context of superlinear indefinite equations

a modified stochastic perturbation method for stochastic hyperbolic heat conduction problems abstract the stochastic hyperbolic heat conduction problem is addressed the random field is approximated by using the karhunen loeve expansion truncated after a finite numbers of terms and a modified stochastic perturbation method mspm is proposed for the stochastic hyperbolic heat conduction problems the mspm is based on the stochastic perturbation theory and can provide the mean and covariance of the random temperature including some third and forth order terms compared with the original stochastic perturbation method the mspm is more accurate and is more convenient for the numerical implementation and hence is more applicable for the stochastic hyperbolic heat conduction problem two numerical examples demonstrate that the proposed method can provide very accurate results and can be used for the stochastic hyperbolic heat conduction problems

first variations of principal eigenvalues with respect to the domain and point wise growth of positive solutions for problems where bifurcation from infinity occurs abstract in this paper the first variation of the principal eigenvalue of in 0 with respect to a general family of holomorphic perturbations of 0 is analyzed then the results from this analysis are used to ascertain the point wise growth to infinity of the positive solutions of a class of sublinear elliptic boundary value problems with vanishing coefficients at the value of the parameter where bifurcation from infinity occurs

reduction of dimensions in random elastic soil medium abstract the paper deals with an application of the plane strain analysis in a stochastic three dimensional soil medium in a framework of random elasticity theory the geostatical state of stresses and the problem of a unit force acting in a statistically homogeneous half space are considered only the modulus of elasticity is considered to be random and is modelled as a three dimensional 3 d homogeneous random field as the result of imposed constrains due to the plane strain assumption the additional body and surface forces are induced in order to determine them additional equations must be introduced the equations in a form of constrain relations are proposed in this paper these equations are also valid for a case of uniformly distributed external loading first the two dimensional 2 d problem and its reduction to the uni axial strain state for the gravity forces and uniform unlimited surface loading is considered then it is generalised into a 2 d schematization of the 3 d state next the problem of a unit force acting in a statistically homogeneous half space is considered for a 3 d state of stress and strain the resulting stresses are compared with those for a 2 d state these stresses for the multidimensional state of strain and stress are presented as a sum of two components the first one reflects plane strain state stresses and is given in a form of a 3 d random field this term allows for incorporating a spatial 3 d soil variability into a two dimensional analysis the second component can be treated as a correction term and it represents the longitudinal influence of a 3 d analysis some numerical results are presented in this paper the proposed method can be regarded as a framework for further research aiming at application to a variety of geotechnical problems for which the plane strain state is assumed

stochastic boundary elements for two dimensional potential flow in homogeneous domains abstract a stochastic boundary element formulation is presented for the analysis of two dimensional steady state potential flow through homogeneous domains the operator of the governing differential equation is assumed to be random and is described by a set of correlated random variables the perturbation method in conjunction with the boundary element method is employed to derive the systems of equations for the unknown boundary variables and their respective first and second order derivatives with respect to the random variables these quantities are then used to calculate the desired response statistics a general procedure is developed which is next applied for the specific cases of random geometric configuration and random material parameter the random geometric configuration is modeled using a finite set of correlated random variables the random material parameter is modeled as a homogeneous random field which allows the use of deterministic fundamental solutions and integral representations for homogeneous domains the random field is first discretized into a set of correlated random variables and then the general procedure is applied a transformation of the correlated random variables into an uncorrelated set is performed to reduce the number of numerical operations the results for the boundary variables are used to calculate the response statistics of internal potentials these calculations require the modeling of the interior of the domain under consideration several models for representing the interior of the domain are presented for both random configuration and random material parameter and their influence on the response statistics is analysed distributed sources are considered in the present study using the particular integral approach a number of numerical examples are presented to demonstrate the validity of the present formulations the results obtained from the present analyses are compared with those obtained from monte carlo simulations with 5000 samples and a good agreement of results is observed

uncertainty propagation using wiener haar expansions an uncertainty quantification scheme is constructed based on generalized polynomial chaos pc representations two such representations are considered based on the orthogonal projection of uncertain data and solution variables using either a haar or a legendre basis governing equations for the unknown coefficients in the resulting representations are derived using a galerkin procedure and then integrated in order to determine the behavior of the stochastic process the schemes are applied to a model problem involving a simplified dynamical system and to the classical problem of rayleigh benard instability for situations involving random parameters close to a critical point the computational implementations show that the wiener haar wha representation provides more robust predictions that those based on a wiener legendre wle decomposition however when the solution depends smoothly on the random data the wle scheme exhibits superior convergence suggestions regarding future extensions are finally drawn based on these experiences

blow up rates of radially symmetric large solutions abstract this paper adapts a technical device going back to j lopez gomez optimal uniqueness theorems and exact blow up rates of large solutions j differential equations 224 2006 385 439 to ascertain the blow up rate of the unique radially symmetric large solution given through the main theorem of j lopez gomez uniqueness of radially symmetric large solutions discrete contin dyn syst supplement dedicated to the 6th aims conference poitiers france 2007 pp 677 686 the requested underlying estimates are based upon the main theorem of s cano casanova j lopez gomez existence uniqueness and blow up rate of large solutions for a canonical class of one dimensional problems on the half line j differential equations 244 2008 3180 3203 precisely we show that if is a ball or an annulus f c 0 is positive and non decreasing v c 0 c 2 0 satisfies v 0 0 v u 0 v u 0 for every u 0 and v u h u p 1 as u for some h 0 and p 1 then for each 0 u u f dist x v u u possesses a unique positive large solution in l which must be radially symmetric by uniqueness and we can estimate the exact blow up rate of l x at in terms of p h and f see theorem 1 1

computation of heat conduction in materials with random variable thermophysical properties a method for the direct computation of mean values and variances of the temperature in conduction heated objects with random variable thermophysical properties is presented this method is based on a taylor expansion of the finite element formulation of the heat conduction equation and offers a powerful alternative to the computationally expensive monte carlo method both steady state and transient problems are considered some example problems are solved and the results discussed the simulations indicate that the variability of the thermophysical properties may cause a considerable variability of the temperature within the heated object this may have important consequences on the design of heating operations in food process engineering

uniqueness and blow up rate of large solutions for elliptic equation δu λu b x h u abstract in this paper we establish the blow up rate of the large positive solution of the singular boundary value problem u u b x h u in u on where is a smooth bounded domain in r n the weight function b x is a non negative continuous function in the domain h u is locally lipschitz continuous and h u u is increasing on 0 and h u h u p for sufficiently large u with h 0 and p 1 naturally the blow up rate of the problem equals its blow up rate for the very special but important case when h u h u p we distinguish two cases i is a ball domain and b is a radially symmetric function on the domain in theorem 1 1 ii is a smooth bounded domain and b satisfies some local condition on each boundary normal section assumed in theorem 1 2 the blow up rate is explicitly determined by functions b and h in case i the singular boundary value problem has a unique solution u satisfying lim d x 0 u x k h b x x 0 1 where d x dist x b r and k are defined by b r r r s r b t d t d s k 1 c 0 1 1 p 1 1 p 1 in case ii the blow up rates of the solutions to the boundary value problem are established and the uniqueness is proved

existence and boundary blow up rates of solutions for boundary blow up elliptic systems abstract in this paper we study some elliptic systems with boundary blow up conditions in a smooth bounded domain by constructing the suitable upper and lower solutions we discuss the existence and global estimate of the positive solution furthermore the boundary blow up rates of the positive solution are also partly discussed

pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs in this paper we analyze the uniqueness and the pointwise growth of the positive solutions of a nonlinear elliptic boundary value problem of general sublinear type with a weight function multiplying the nonlinearity when this function vanishes on some subdomain the problem exhibits a bifurcation from infinity in this case almost nothing is known about the pointwise growth of the positive solutions as the parameter approaches the critical value where the bifurcation from infinity occurs in this work we show that the positive solutions grow to infinity in the region where the weight function vanishes and that on its support they stabilize to the minimal positive solution of the original equation subject to infinite dirichlet boundary conditions this behavior provides us with the uniqueness of the positive solution near the value of the parameter where the bifurcation from infinity occurs also we solve the problem using spectral collocation methods coupled with path following techniques to show how the main uniqueness result is optimal throughout the paper the mathematical analysis aids the numerical study and the numerical study confirms and illuminates the analysis

multi resolution analysis of wiener type uncertainty propagation schemes a multi resolution analysis mra is applied to an uncertainty propagation scheme based on a generalized polynomial chaos pc representation the mra relies on an orthogonal projection of uncertain data and solution variables onto a multi wavelet basis consisting of compact piecewise smooth polynomial functions the coefficients of the expansion are computed through a galerkin procedure the mra scheme is applied to the simulation of the lorenz system having a single random parameter the convergence of the solution with respect to the resolution level and expansion order is investigated in particular results are compared to two monte carlo sampling strategies demonstrating the superiority of the mra for more complex problems however the mra approach may require excessive cpu times adaptive methods are consequently developed in order to overcome this drawback two approaches are explored the first is based on adaptive refinement of the multi wavelet basis while the second is based on adaptive block partitioning of the space of random variables computational tests indicate that the latter approach is better suited for large problems leading to a more efficient flexible and parallelizable scheme

a stochastic particle mesh scheme for uncertainty propagation in vortical flows abstract a new mesh particle scheme is constructed for uncertainty propagation in vortical flow the scheme is based on the incorporation of polynomial chaos pc expansions into a lagrangian particle approximation of the navier stokes equations the main idea of the method is to use a unique set of particles to transport the stochastic modes of the solution the particles are transported by the mean velocity field while their stochastic strengths are updated to account for diffusive and convective effects induced by the coupling between stochastic modes an integral treatment is used for the evaluation of the coupled stochastic terms following the framework of the particle strength exchange pse methods which yields a conservative algorithm it is also shown that it is possible to apply solution algorithms used in deterministic setting including particle mesh techniques and particle remeshing thus the method combines the advantages of particles discretizations with the efficiency of pc representations validation of the method on uncertain diffusion and convection problems is first performed an example is then presented of natural convection of a hot patch of fluid in infinite domain and the computations are used to illustrate the effectiveness of the approach for both large number of particles and high order pc expansions

fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters summary this paper proposes a fuzzy interval perturbation method fipm and a modified fuzzy interval perturbation method mfipm for the hybrid uncertain temperature field prediction involving both interval and fuzzy parameters in material properties and boundary conditions interval variables are used to quantify the non probabilistic uncertainty with limited information whereas fuzzy variables are used to represent the uncertainty associated with the expert opinions the level cut method is introduced to decompose the fuzzy parameters into interval variables fipm approximates the interval matrix inverse by the first order neumann series while mfipm improves the accuracy by considering higher order terms of the neumann series the membership functions of the interval temperature field are eventually derived using the fuzzy decomposition theorem three numerical examples are provided to demonstrate the feasibility and effectiveness of the proposed methods for solving heat conduction problems with hybrid uncertain parameters pure interval parameters and pure fuzzy parameters respectively copyright 2015 john wiley sons ltd

random field finite elements the probabilistic finite element method pfem is formulated for linear and non linear continua with inhomogeneous random fields analogous to the discretization of the displacement field in finite element methods the random field is also discretized the formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization furthermore it is shown that a reduced set of the uncorrelated variables is sufficient for the second moment analysis based on the linear formulation of the pfem the method is then extended to transient analysis in non linear continua the accuracy and efficiency of the method is demonstrated by application to a one dimensional elastic plastic wave propagation problem and a two dimensional plane stress beam bending problem the moments calculated compare favourably with those obtained by monte carlo simulation also the procedure is amenable to implementation in deterministic fem based computer programs

elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equation abstract we derive a result on the limit of certain sequences of principal eigenvalues associated with some elliptic eigenvalue problems this result is then used to give a complete description of the global structure of the curves of positive steady states of a parameter dependent diffusive version of the classical logistic equation in particular we characterize the bifurcation values from infinity to positive steady states the stability of the positive steady states as well as the asymptotic behaviour of positive solutions is also discussed

finite dimensional approximation of non linear problems 3 simple bifurcation points note univ pavia cnr ist analisi numer i 27100 pavia italy ecole polytech f 91128 palaiseau france ecole polytech ctr math appl cnrs era 747 f 91128 palaiseau france brezzi f univ pavia ist mat appl i 27100 pavia italy isi document delivery no mn015times cited 75cited reference count 20 reference asn article 1981 001 record created on 2006 08 24 modified on 2017 05 12

optimal uniqueness theorems and exact blow up rates of large solutions in this paper we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non linearity and combine these results with the localization method introduced in lopez gomez the boundary blow up rate of large solutions j differential equations 195 2003 25 45 to prove that any large solution l of u a x up p 1 a 0 must satisfy limx x0l x fx0 dist x i0 pp 1p 1p 1p 1p 1foreachx0 where fx0 t t 0sfx01p 1 p 1p 1ds i0 limt 0fx0 t fx0 t fx0 t 2 and fx0 is any smooth extension of the boundary normal section of a at x0 i e fx0 t a x0 tnx0 t 0 t 0 subsequently nx0 stands for the outward unit normal at x0 therefore the theory can be extended to cover the general case when fx0 l1p 1

three dimensional stochastic finite element method for elasto plastic bodies a new stochastic finite element method sfem is formulated for three dimensional softening elasto plastic bodies with random material properties the method is based on the karhunen loeve and polynomial chaos expansions and able to efficiently estimate complete probabilistic characteristics of the response such as moments or pdfs to reduce the computational complexity in the three dimensional setting two alterations are made with respect to the two dimensional sfem proposed earlier by the authors first a variability preserving modification of the karhunen loeve expansion is rigorously derived and applied in the stochastic discretization of random fields representing material properties second an efficient algorithm for parallel processing is developed with time consumption being the same order as for an ordinary fem rendering the proposed sfem an effective alternative to monte carlo simulation the applicability of the proposed method to stochastic analysis of strain localization is examined using monte carlo simulation then it is applied to a fault formation problem which is a recent concern of earthquake engineering ground surface layers are modelled by a softening elasto plastic body and the evolution of probabilistic characteristics of the rupture process is analysed in detail some practical observations are made regarding the nature of the fault formation from the stochastic viewpoint copyright 2001 john wiley sons ltd

on determinant preserver problems abstract let m n and t n be the vector spaces of n n matrices and upper triangular matrices over a field f with some cardinality and characteristic restrictions respectively we characterise transformations on these two spaces separately which satisfy one of the following conditions 1 det a b det a b for all a b and 2 is surjective and det a b det a b for all a b and two specific 3 is additive and preserves determinant

basis random variables in finite element analysis galerkin s method is applied to random operator equations appropriate hilbert spaces are defined for random functions and solutions are projected into these spaces allowing the first and second moment properties of the solution to be calculated an equivalent energy based approach similar to the rayleigh ritz method is developed from which a stochastic finite element technique is derived several one and two dimensional example problems are solved and the results discussed

finite dimensional approximation of nonlinear problems part ii limit points note univ paris 6 f 75230 paris 05 france ecole polytech ctr math appl cnrs equipe rech 747 f 91128 palaiseau france univ pavia cnr ist anal numer i 27100 pavia italy brezzi f univ pavia cnr ist math appl i 27100 pavia italy isi document delivery no lr761times cited 54cited reference count 13 reference asn article 1981 002doi 10 1007 bf01396184 record created on 2006 08 24 modified on 2017 05 12

determinant preserving maps on matrix algebras abstract let m n be the algebra of all n n complex matrices if m n m n is a surjective mapping satisfying det a b det a b a b m n c then either is of the form a man a m n or is of the form a ma t n a m n where m n m n are nonsingular matrices with det mn 1

multiple spatial and temporal scales method for numerical simulation of non classical heat conduction problems one dimensional case abstract a multiple spatial and temporal scales method is studied to simulate numerically the phenomenon of non fourier heat conduction in periodic heterogeneous materials the model developed is based on the higher order homogenization theory with multiple spatial and temporal scales in one dimensional case the amplified spatial scale and the reduced temporal scale are introduced respectively to account for the fluctuations of non fourier heat conduction due to material heterogeneity and non local effect of the homogenized solution by separating the governing equations into various scales the different orders of homogenized non fourier heat conduction equations are obtained the reduced time dependence is thus eliminated and the fourth order governing differential equations are derived to avoid the necessity of c1 continuous finite element implementation a c0 continuous mixed finite element approximation scheme is put forward numerical results are shown to demonstrate the efficiency and validity of the proposed method

nonstationary flow and nonergodic transport in random porous media 1 transport processes taking place in natural formations are often characterized by the spatial nonstationarity of flow field and the nonergodic condition of solute spreading the former may originate from statistical inhomogeneity of porous media properties or from the influence of boundary conditions as well as from conditioning procedures on measured data while the latter is generally due to the finite size of the solute source in real world applications these aspects sometimes dominate the transport phenomena and known literature results based on statistical homogeneity and ergodicity assumptions cannot be properly applied in this paper a method is proposed to handle different and concurrent causes of the flow field nonstationarity and to describe nonergodic transport of inert solutes by spatial moments in a domain of finite size the goal is reached by expanding the steady state flow equation in taylor series limited to the first order and by the recursive application of finite element fe method the unknowns are the piezometric head mean values and its derivatives in respect to the fluctuating porous media hydraulic conductivity from the latter the velocity statistics are derived on the basis of darcy s law according to the first order approximation by neglecting the pore scale dispersion the spatial moments of a solute plume are a posteriori obtained by a consistent lagrangian analysis starting from the knowledge of the velocity field covariance matrices without any restriction regarding the statistical homogeneity of flow and or ergodicity conditions the proposed method is here applied to investigate the influence of boundary conditions on the solute transport developing in a limited domain the results obtained from different test cases give a velocity field behavior in agreement with literature findings and allow us to define the nonergodic transport in bounded domains the comparison of the results with some ad hoc developed monte carlo simulations ensures the applicability of the proposed approach at least to the small heterogeneity cases here considered

on solving nonlinear transient heat transfer problems with random parameters abstract a variational methodology is proposed for nonlinear transient heat transfer systems with random parameters defined by their first two probabilistic moments the finite element formalism is based on the combination of the second order perturbation and mean based second moment analysis a hierarchical system of first order partial differential equations is obtained and solved for the first two probabilistic moments of the random temperature field numerical aspects of the problem are discussed and illustrative results are given the approach presented may be employed for a wide class of field problems

multiplicity of large solutions for quasi monotone pulse type nonlinearities abstract this paper discusses the keller osserman condition from a dynamical perspective in order to obtain a rather astonishing multiplicity result of large solutions it turns out that for any given increasing positive function f u that satisfies the keller osserman condition destroying the monotonicity of f u on a compact set with arbitrarily small measure can originate an arbitrarily large number of explosive solutions moreover some counterexamples to an important result of 6 are given

refuge versus dispersion in the logistic equation abstract in this paper we consider a logistic equation with nonlinear diffusion arising in population dynamics in this model there exists a refuge where the species grows following a malthusian law and in addition there exists also a non linear diffusion representing a repulsive dispersion of the species we prove existence and uniqueness of positive solution and study the behavior of this solution with respect to the parameter the growth rate of the species mainly we use bifurcation techniques the sub supersolution method and a construction of appropriate large solutions

finite dimensional approximation of nonlinear problems in the first two papers of this series 4 5 we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a banach space we derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point the abstract theory is applied to the galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von karman equations

existence uniqueness and blow up rate of large solutions for a canonical class of one dimensional problems on the half line this paper shows the existence and the uniqueness of the positive solution l t of the singular boundary value problem u t f t h u t t 0 u 0 u 0 where f is a continuous non decreasing function such that f 0 0 and h is a non negative function satisfying the keller osserman condition moreover it also ascertains the exact blow up rate of l t at t 0 in the special case when there exist h 0 and p 1 such that h u hup for sufficiently large u naturally the blow up rate of the problem in such a case equals its blow up rate for the very special but important case when h u hup for all u 0 so our results are substantial improvements of some previous findings of j lopez gomez uniqueness of large solutions for a class of radially symmetric elliptic equations in s cano casanova j lopez gomez c mora corral eds spectral theory and nonlinear analysis with applications to spatial ecology world scientific 2005 pp 75 110 and j lopez gomez optimal uniqueness theorems and exact blow up rates of large solutions j differential equations 224 2006 385 439

nonlinear determinant preserving maps on matrix algebras abstract let f be a field having at least n 2 1 distinct elements and denote by m n the space of all n n matrices over f we prove that if and are maps from m n into itself one of them being surjective such that det x y det x y for all x y m n there exist then x 0 m n and u v m n satisfying det u v 1 such that either x u x x 0 v and x u x x 0 v for all x m n or x u x x 0 t v and x u x x 0 t v for all x m n

comparative study of projection schemes for stochastic finite element analysis we present a comparison of subspace projection schemes for stochastic finite element analysis in terms of accuracy and computational efficiency more specifically we compare the polynomial chaos projection scheme with reduced basis projection schemes based on the preconditioned stochastic krylov subspace numerical studies are presented for two problems 1 static analysis of a plate with random young s modulus and 2 settlement of a foundation supported on a randomly heterogeneous soil monte carlo simulation results based on exact structural analysis are used to generate benchmark results against which the projection schemes are compared we show that stochastic reduced basis methods require significantly less computer memory and execution time compared to the polynomial chaos approach particularly for large scale problems with many random variables for the class of problems considered we find that stochastic reduced basis methods can be up to orders of magnitude faster while providing results of comparable or better accuracy

numerical approximation of poroelasticity with random coefficients using polynomial chaos and hybrid high order methods abstract in this work we consider the biot problem with uncertain poroelastic coefficients the uncertainty is modeled using a finite set of parameters with prescribed probability distribution we present the variational formulation of the stochastic partial differential system and establish its well posedness we then discuss the approximation of the parameter dependent problem by non intrusive techniques based on polynomial chaos decompositions we specifically focus on sparse spectral projection methods which essentially amount to performing an ensemble of deterministic model simulations to estimate the expansion coefficients the deterministic solver is based on a hybrid high order discretization supporting general polyhedral meshes and arbitrary approximation orders we numerically investigate the convergence of the probability error of the polynomial chaos approximation with respect to the level of the sparse grid finally we assess the propagation of the input uncertainty onto the solution considering an injection extraction problem

permanent polya problem for additive surjective maps abstract let m n f denote the set of square matrices of size n over a field f with characteristics different from two we say that the map f m n f m n f is additive if f a b f a f b for all a b m n f the main goal of this paper is to prove that for n 2 there are no additive surjective maps t m n f m n f such that per t a det a for all a m n f also we show that an arbitrary additive surjective map t m n f m n f which preserves permanent is linear and thus can be completely characterized

the maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems abstract in this work we deal with the problem of the existence and uniqueness of principal eigenvalues for some linear weighted boundary value problems associated to a general second order uniformly elliptic operator for a large class of sign definited weights we characterize whether the boundary value problem admits a principal eigenvalue or not

explicit solution to the stochastic system of linear algebraic equations α1a1 α2a2 αmam x b abstract this paper presents a novel solution strategy to the stochastic system of linear algebraic equations 1 a 1 2 a 2 m a m x b arising from stochastic finite element modelling in computational mechanics in which i i 1 m denote random variables a i i 1 m real symmetric deterministic matrices b a deterministic random vector and x the unknown random vector to be solved the system is first decoupled by simultaneously diagonalizing all the matrices a i via a similarity transformation and then it is trivial to invert the sum of the diagonalized stochastic matrices to obtain the explicit solution of the stochastic equation system unless all the matrices a i share exactly the same eigen structure the joint diagonalization can only be approximately achieved hence the solution is approximate and corresponds to a particular average eigen structure of the matrix family specifically the classical jacobi algorithm for the computation of eigenvalues of a single matrix is modified to accommodate multiple matrices and the resulting jacobi like joint diagonalization algorithm preserves the fundamental properties of the original version including its convergence and an explicit solution for the optimal givens rotation angle three numerical examples are provided to illustrate the performance of the method

a fourier karhunen loeve discretization scheme for stationary random material properties in sfem in order to overcome the computational difficulties in karhunen loeve k l expansions of stationary random material properties in stochastic finite element method sfem analysis a fourier karhunen loeve f k l discretization scheme is developed in this paper by following the harmonic essence of stationary random material properties and solving a series of specific technical challenges encountered in its development three numerical examples are employed to investigate the overall performance of the new discretization scheme and to demonstrate its use in practical sfem simulations the proposed f k l discretization scheme exhibits a number of advantages over the widely used k l expansion scheme based on fe meshes including better computational efficiency in terms of memory and cpu time convenient a priori error control mechanism better approximation accuracy of random material properties explicit methods for predicting the associated eigenvalue decay speed and geometrical compatibility for random medium bodies of different shapes copyright 2007 john wiley sons ltd

hua s fundamental theorems of the geometry of matrices and related results abstract we briefly survey some recent improvements of hua s fundamental theorem of the geometry of rectangular matrices then we discuss possible further generalizations as well as some related open problems in the theory of preservers we solve one such open problem using ovchinnikov s characterization of automorphisms of the poset of idempotent matrices using ovchinnikov s result we obtain a short proof of the fundamental theorem of the geometry of square matrices

the boundary blow up rate of large solutions abstract in this paper we ascertain the blow up rate of the large solutions of a class of sublinear elliptic boundary value problems with a weight function in front of the nonlinearity that vanishes on the boundary of the underlying domain at different rates according to the point of the boundary x all previous results in the literature assumed the decay rate of the underlying weight function to be the same at any point of this hypothesis substantially simplified the mathematical analysis of the problem as it allowed constructing global sub and supersolutions in an open neighborhood of obtaining general results requires localizing at each particular point of the boundary making particularly involved the mathematical analysis of the problem

a formulation for stochastic finite element analysis of plate structures with uncertain poisson s ratio up to now the young s modulus is mainly dealt within the analysis of response variability however since the poisson s ratio is the other material constant which influences the behavior of structures the independent evaluation of the effects of this parameter on the response variability is of importance in this paper a formulation to determine the response variability in plate structure due to the randomness of poisson s ratio is given to filter out the independent contributions of randomness in poisson s ratio to the response variability the constitutive matrix has to be decomposed into several sub matrices in order to include the poisson s ratio in the constitutive relation as a non linear parameter a polynomial expansion of poisson s ratio is introduced to demonstrate the validity of the proposed formulation an example is chosen and the results are compared with those obtained by means of monte carlo simulation through the formulation proposed in this paper it becomes possible for the non statistical weighted integral stochastic approach to deal with all the uncertain material parameters in its application

on the positive solutions of semilinear equations δ ℎ 0 on the compact manifolds in this paper we study the existence nonexistence and uniqueness of positive solutions of semilinear equations u u hu p 0 on compact riemannian manifolds as well as on bounded smooth domains in r n with homogeneous dirichlet or neumann boundary conditions

boundary blow up rates of large solutions for elliptic equations with convection terms abstract by karamata regular variation theory a perturbation method and constructing comparison functions we show the exact asymptotic behavior of large solutions to the semilinear elliptic equations with convection terms u u q b x f u x u x x where is a smooth bounded domain in r n the weight function b x is a non negative continuous function in the domain which may be vanishing on the boundary or be singular on the boundary f u c 2 0 is increasing on 0 satisfying the keller osserman condition and regularly varying at infinity with index 1

asymptotic behavior of degenerate logistic equations abstract we analyze the asymptotic behavior of positive solutions of parabolic equations with a class of degenerate logistic nonlinearities of the type u n x u an important characteristic of this work is that the region where the logistic term n vanishes that is k 0 x n x 0 may be non smooth we analyze conditions on n and k 0 guaranteeing that the solution starting at a positive initial condition remains bounded or blows up as time goes to infinity the asymptotic behavior may not be the same in different parts of k 0

iterative solution of the random eigenvalue problem with application to spectral stochastic finite element systems a new algorithm for the computation of the spectral expansion of the eigenvalues and eigenvectors of a random non symmetric matrix is proposed the algorithm extends the deterministic inverse power method using a spectral discretization approach the convergence and accuracy of the algorithm is studied for both symmetric and non symmetric matrices the method turns out to be efficient and robust compared to existing methods for the computation of the spectral expansion of random eigenvalues and eigenvectors

the structure of the set of 1 node solutions of a class of degenerate bvp s abstract a recent study 12 13 of a class of degenerate bvp s showed that there were two possibilities for the structure of the set of 1 node solutions left open was the question of whether each one was possible using some elementary phase plane techniques combined with some comparison arguments obtained from the maximum principle this paper constructs examples showing that indeed each can occur

trace and determinant preserving maps of matrices abstract we show that if a map on the set of positive definite matrices satisfies det a b det a b or tr a b 1 tr a b 1 with det i 1 then is of the form a m a m or a m a t m for some invertible matrix m with det m m 1 we also characterize the map s s preserving the similar trace equality or the determinant equality det t a 1 t b det t a 1 t b t 0 1 in s where s denotes the set of complex matrices symmetric matrices or upper triangular matrices respectively