a new class of volterra differential equations for which the solutions are globally asymptotically stable on etudie le systeme de lotka volterra i u i e i j 1 m p ij u j u i 0 0 0 t ou p p ij est une matrice reelle mxm et ou i 1 2 m les constantes e i sont choisies de telle maniere qu un point stationnaire q q i existe dans le premier quadrant

the geostatistical characteristics of the borden aquifer a complete reexamination of sudicky s 1986 field experiment for the geostatistical characterization of hydraulic conductivity at the borden aquifer in ontario canada is performed the sampled data reveal that a number of outliers low ln k values are present in the data base these low values cause difficulties in both variogram estimation and determining population statistics the analysis shows that assuming either a normal distribution or exponential distribution for log conductivity is appropriate the classical cressie hawkins and squared median of the absolute deviations smad estimators are used to compute experimental variograms none of these estimators provides completely satisfactory variograms for the borden data with the exception of the classical estimator with outliers removed from the data set theoretical exponential variogram parameters are determined from nonlinear nl estimation differences are obtained between nl fits and those of sudicky 1986 for the classical screened estimated variogram nl fits produce an ln k variance of 0 24 nugget of 0 07 and integral scales of 5 1 m horizontal and 0 21 m vertical along a a for b b these values are 0 37 0 11 8 3 and 0 34 the fitted parameter set for b b data horizontal and vertical is statistically different than the parameter set determined for a a we also evaluate a probabilistic form of dagan s 1982 1987 equations relating geostatistical parameters to a tracer cloud s spreading moments the equations are evaluated using the parameter estimates and covariances determined from line a a as input with a velocity equal to 9 0 cm day the results are compared with actual values determined from the field test but evaluated by both freyberg 1986 and rajaram and gelhar 1988 the geostatistical parameters developed from this study produce an excellent fit to both sets of calculated plume moments when combined with dagan s stochastic theory for predicting the spread of a tracer cloud

friction induced vibration in periodic linear elastic media for a one dimensional finite elastic continuum with distributed contacts and periodic boundary conditions the presence of unstable waves is investigated the stability of the waves is evaluated and explanations for instabilities under a constant coefficient of friction are provided a negative slope in the coefficient of friction as a function of sliding speed is not a necessary condition for the occurrence of dynamic instability dynamic instability occurs in the form of self excited unstable travelling waves the stabilizing effects of external and internal damping were studied low and high frequency terms of the travelling waves are stabilized by adding external and internal damping respectively responses corresponding to unstable eigenvalues can dominate the system response it is presumed that this can lead to squeaking or squealing noise in applications

dynamic stability of shallow shells subjected to follower forces dynamic stability of cylindrically curved shallow shells subjected to follower forces is presented the shell analysis uses a two field variable variational principle with the transverse displacement and airy stress function as field variables starting from the variational equation of the problem the euler lagrange equations governing the problem and the boundary conditions on the transverse displacement and the airy stress function are obtained a finite element formulation that preserves c 1 continuity is used for the solution of the problem numerical results are given and the results obtained are discussed it is shown that the use of the two field variable variational principle permits through static condensation a reduction in the effort needed for the solution of the stability problem to that of flat plate similarity between the response of a flexible structure to a follower force and the aerodynamic supersonic panel flutter is discussed practical applications of the problem are large space structures such as solar power stations which can undergo flutter or divergence instabilities due to their low rigidity when thrusted by follower forces

divergence and flutter instability of elastic specially orthotropic plates subject to follower forces abstract divergence and flutter instabilities of a rectangular specially orthotropic plate simply supported on a pair of opposite sides subject to follower forces are computationally analyzed the effects of the tangential follower parameter aspect ratio boundary condition on the side opposite the loaded edge and material orthotropy on the magnitude of the critical load and the mode divergence or flutter of instability are detailed for the three boundary conditions considered built in simply supported and free free for the side opposite the loaded edge and given material orthotropy the plane is divided into regions corresponding to different governing instabilities both the number and size of these regions depend strongly upon the boundary condition considered as does the governing instability for a given boundary condition the configuration of the stability regions is independent of material orthotropy material orthotropy affects only the buckling loads corresponding to the instabilities and the size of the regions

spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields 2 numerical simulations two models for horizontally averaged unsaturated flow have been developed from two different approaches in the first chen et al this issue of these companion papers in this paper the results from both the spatially horizontally averaged richards equation share model and the averaged green ampt model are compared with the results from a three dimensional finite difference model of unsaturated flow which is perceived as the reference solution the results of the averaged green ampt model show very good agreement with the averaged results from the three dimensional model while share model results are applicable only when fluctuations in soil parameters are small with respect to their mean values it is also shown that methods of simple parameter averaging arithmetic or geometric averages with the local richards equation does not yield meaningful results in heterogeneous soils this study suggests that spatially horizontally averaged simplified models such as the averaged green ampt model are attractive alternatives to perturbation models such as the share model in heterogeneous fields due to their simplicity in formulation accuracy in predicting average behaviors and minimal requirement of computer effort the spatially horizontally averaged simplified models can be easily implemented in large scale models such as atmospheric mesoscale models boundary and initial conditions the average saturation at each depth was obtained by areal integration of the local scale water saturation over the specified area under the assumption of independent vertical soil columns at field scales relative occurrence frequency curves of the spatially varying parameters were required for the solution of the average quantities the second model developed was the spatially horizontally averaged richards equation share model this model was developed by using spatial averaging and regular perturbation techniques under the assumption of no source or sink in the study area the share model was expressed as a system of two coupled one dimensional partial differential equations in terms of the mean saturation and the cross covariance of saturation and saturated hydrau

on the discretization of an elastic rod with distributed sliding friction a one dimensional elastic system with distributed contact under fixed boundary conditions is investigated in order to study dynamic behavior under sliding friction a partial differential equation of motion is established and its exact solution is presented due to the friction the eigenvalue problem is non self adjoint mathematical methods for handling the non self adjoint system such as the non self adjoint eigenvalue problem and the eigenvalue problem with a proper inner product are reviewed and applied the exact solution showed that the undamped elastic system under fixed boundary conditions is neutrally stable when the coefficient of friction is a constant the assumed mode approximation and the lumped parameter discretization method are evaluated and their solutions are compared with the exact solution as a cautionary example the assumed modes approximation leads to false conclusions about stability the lumped parameter discretization algorithm generates reliable results

stochastic analysis of unsaturated flow in heterogeneous soils 1 statistically isotropic media steady unsaturated flow with vertical mean infiltration through unbounded heterogeneous porous media is analyzed using a perturbation approximation of the stochastic flow equation which is solved by spectral representation techniques the hydraulic conductivity k is related to the capillary pressure head by k ks exp where ks is the saturated conductivity and is a soil parameter a general formulation is presented for the case with ks and represented as statistically homogeneous spatial random fields in part 1 solutions are developed assuming is constant and representing ks variability by one dimensional and three dimensional isotropic random fields results are obtained for head variances and covariance functions effective hydraulic conductivities variances of the unsaturated hydraulic conductivity flux variances and variance of pressure gradient when the parameter is relatively large corresponding to coarse textured soils the head variance decreases and all of the results demonstrate a trend toward gravitationally dominated one dimensional vertical flow the effective conductivity is dependent on the correlation scale of ln ks and the mean hydraulic gradient

dynamic stability of a rectangular plate with four free edges subjected to a follower force one of the four free edges of the plate is subjected to a tangential follower force the flutter load and divergence load are obtained for various slenderness ratios of the rectangular plate by means of modal analysis in the calculation many weak instabilities were found

stochastic analysis of field measured unsaturated hydraulic conductivity unsaturated hydraulic conductivity k values as a function of soil water pressure head h were measured in the soil at 75 cm depth at 70 different sites separated from one another by a distance of l m along a horizontal transect k field was viewed as a random function of spatial location x field data were analyzed 1 to examine the isotropy and stationarity of k 2 to check the ergodicity of k in the mean and covariance functions and 3 to characterize the distribution properties of k by estimating the higher order correlations that is third and fourth cumulants the mean functions were estimated by averaging over h and x the covariance function was studied to investigate its spatial origin dependency logs and square roots of k were used for estimating the third and fourth cumulants results showed that spatial covariance functions are anisotropic and both lag and origin dependent that is spatially nonhomogeneous because the stationarity statistical homogeneity of k is scale dependent which was indicated by the identification of locally stationary covariance regions the ergodic properties of k are also scale dependent at smaller spatial scales results related to the distribution characteristics of k indicated that although ln k is marginally gaussian distributed in the context of spatial stochastic processes the random field of ln k is not gaussian because the third and fourth cumulants of the field are still significantly different from zero and have the same order of magnitude as the first and second cumulants the square root transformation however resulted in a random field that is approximately gaussian although marginal distributions of k remained skewed analyses of ln k and k indicated that better transformations which would result in both marginal and joint gaussian behavior for the random field of k are needed

an iterative geostatistical inverse method for steady flow in the vadose zone an iterative geostatistical inverse approach is developed to estimate conditional effective unsaturated hydraulic conductivity parameters soil water pressure head and degree of saturation in heterogeneous vadose zones this approach is similar to the classical cokriging technique and it uses a linear estimator that depends on covariances and cross covariances of unsaturated hydraulic parameters soil water pressure head and degree of saturation the linear estimator is however improved successively by solving the governing flow equation and by updating the residual covariance and cross covariance functions in an iterative manner as a result the nonlinear relationship between unsaturated hydraulic conductivity parameters and head is incorporated in the estimation and the estimated fields are approximate conditional means the ability of the iterative approach is demonstrated through some numerical examples

a geostatistical approach to the trickle irrigation design in heterogeneous soil 1 theory a geostatistical approach was used to investigate the spatial variability of two measured soil hydraulic parameters the saturated hydraulic conductivity ks and d log k h d h where k is the hydraulic conductivity and h is the soil water pressure head using a linearized solution to steady infiltration from a circular shallow pond the spatial distribution of the midway soil water pressure head between emitters hc for a given trickle discharge rate q and spacing between emitters d was calculated using the spatially variable soil parameters ks and the spatial distribution of the crop yield y was calculated from the spatially variable hc by using a quadratic expression for the y hc relationships it was found that the spatial variability of each of the measured input parameters ks and or the calculated output variables hc and y is expressed through the variogram and can be characterized in terms of the coefficient of variation cv and the integral scale j in the case of log ks for which the sill is reached at relatively small range two different were tested results showed that the kriged values of log ks as well as the resultant values of hc hc ks d q were relatively insensitive to the selected the spatial variability of hc reduced the average over the field crop yield that would have been obtained when hc was uniform throughout the field the spatially variable soil parameters ks and were used to calculate the spatial distribution of the spacing between emitters d required to achieve for a given trickle discharge a prespecified value of hc uniform throughout the field it was found that the use of a spatially variable d increased the field crop yield by 3 relative to the yield that was obtained when a single valued d uniform throughout the field was used the spatial distribution of d was combined with hydraulic principles to derive the spatial distribution of lateral diameter and length for engineering design requirements

stability of a rectangular plate under nonconservative and conservative forces abstract a study is made of the flutter and divergence instabilities of a rectangular plate with two independent loading parameters the plate is subjected to the combined action of a tangential follower force and a unidirectional axial force along one edge two opposite sides of the plate are simply supported one side being clamped and the other being a free edge where the in plane forces act depending on the relative magnitudes of the follower and axial forces the plate may lose its stability by flutter or divergence the flutter problem is solved by maximizing the flutter load over the frequency and thereby obtaining the maximum point of an eigencurve the stability boundaries are given for plates with different aspect ratios the two dimensional nature of the problem reveals some interesting results not observed in the one dimensional counterpart of the problem which is a cantilevered column under vertical and follower forces the effect of an elastic foundation on the stability boundaries are determined the influence of poisson s ratio on the flutter load and frequency is investigated it is shown that no general rule can be formulated as to the effect of poisson s ratio on the flutter load and that this effect will vary according to the aspect ratio and axial load

recent directions in matrix stability abstract matrix stability has been intensively investigated in the past two centuries we review work that has been done in this topic focusing on the great progress that has been achieved in the last decade or two we start with classical stability criteria of lyapunov routh and hurwitz and lienard and chipart we then study recently proven sufficient conditions for stability with particular emphasis on p matrices we investigate conditions for the existence of a stable scaling for a given matrix we review results on other types of matrix stability such as d stability additive d stability and lyapunov diagonal stability we discuss the weak principal submatrix rank property shared by lyapunov diagonally semistable matrices we also discuss the uniqueness of lyapunov scaling factors maximal lyapunov scaling factors cones of real positive semidefinite matrices and their applications to matrix stability and inertia preserving matrices

dynamic stability of a free free cylindrical shell under a follower force the dynamic stability of a completely free isotropic circular cylindrical shell under a follower force is investigated the first order shear deformation and rotary inertia are included in the kinetic energy and the strain energy a finite element model of the shell is formulated using the trigonometric ring element in the circumferential direction and the lagrangian element in the longitudinal direction using the eigenvalue curves and the method of multiple scales the dynamic stability is studied for the case of the follower force with a pulsating part as well as the constant follower force the effect of the thickness ratio and the length ratio is presented in both cases the numerical results for the shells are compared with those of a beam model having equivalent dimensions the numerical results show that the shell under a constant follower force behaves like a beam in a certain range the analysis of the shell under a pulsating follower force shows that the beamlike modes of the shell have larger unstable regions than the other modes however for the case of a pulsating load the modes of higher circumferential wave number are of importance in that the combination resonance of difference type takes place frequently

flutter analysis of periodically supported curved panels abstract this paper presents the one dimensional axial wave propagation in an infinitely long periodically supported cylindrically curved panel subjected to supersonic airflow the aerodynamic forces are based on piston theory for this study the structure is considered as an assemblage of a number of identical cylindrically curved panels each of which will be referred to as a periodic element a high precision triangular finite element with certain wave boundary conditions floquet s principle is introduced in flutter problems of the proposed structure for the first time the airflow is assumed in the direction of the straight edges of the panel it is assumed that the deflection function accounts for a phase lag term only and does not consider any attenuation terms aerodynamic damping has been neglected for brevity for a given geometry a three dimensional plot related to the phase constant flutter frequency and pressure parameter has been obtained corresponding to the optimum periodic angle the flutter line line of instability has been identified the limiting values of flutter frequencies and pressure parameters of the flutter line are compared with the critical flutter condition of a single curved panel using two methods an exact approach and a finite element method the critical flutter results for multi supported 1 span 2 span and 3 span curved panels are obtained using the band discretization principle

dynamic stability of rectangular plates subjected to pulsating follower forces the dynamic stability of isotropic and nonsymmetric laminated plates with four free edges subjected to pulsating follower forces is discussed the results are obtained using the first order shear deformation theory the discretized equation of motion is obtained by the finite element method and then the method of multiple scales is adopted to investigate the dynamic instability regions the effects of poisson ratio as well as aspect and thickness ratios on the dynamic instability region for isotropic plates are investigated the influences of aspect ratio lamination angle and the number of layers for nonsymmetric cross ply and angle ply laminated plates are also studied

conditional stochastic averaging of steady state unsaturated flow by means of kirchhoff transformation we consider the effect of measuring randomly varying soil hydraulic properties on one s ability to predict steady state unsaturated flow subject to random sources and or initial and boundary conditions our aim is to allow optimum unbiased prediction of system states pressure head water content and fluxes deterministically without upscaling and without linearizing the constitutive characteristics of the soil it has been shown by neuman et al 1999 that such prediction is possible by means of first ensemble moments of system states and fluxes conditioned on measured values of soil properties when the latter scale in a linearly separable fashion as proposed by vogel et al 1991 the uncertainty associated with such predictions can be quantified by means of the corresponding conditional second moments the derivation of moment equations for soils whose properties do not scale in the above manner requires linearizing the corresponding constitutive relations which may lead to major inaccuracies when these relations are highly nonlinear as is often the case in nature when the scaling parameter of pressure head is a random variable independent of location the steady state unsaturated flow equation can be linearized by means of the kirchhoff transformation for gravity free flow linearization is also possible in the presence of gravity when hydraulic conductivity varies exponentially with pressure head for the latter case we develop exact conditional first and second moment equations which are nonlocal and therefore non darcian we solve these equations analytically by perturbation for unconditional vertical infiltration and compare our solution with the results of numerical monte carlo simulations our analytical solution demonstrates in a rigorous manner that the concept of effective hydraulic conductivity does not apply to ensemble averaged unsaturated flow except when gravity is the sole driving force

statistical analysis of spatial variability in unsaturated flow parameters core scale estimates of soil parameters of the gardner russo and van gemachten models of the hydraulic conductivity and water retention functions were obtained for 417 undisturbed soil cores taken from a wall of a trench 20 m long 2 5 m deep using a procedure based on inverse problem methodology these estimates were used to evaluate the first two statistical moments of the underlying random space functions rsfs using the restricted maximum likelihood estimation procedure coupled with the weighted least squares procedure to estimate parameters of models of the covariance and the drift functions of the pertinent rsfs the fitted models were used to evaluate the mean and covariance functions of the hydraulic conductivity and water rentention functions for given water saturations covariance functions of log saturated conductivity log ks and the shape parameters of the gardner russo and van genuchten models exhibited statistical anisotropy characterized by aspect ratios that vary between 3 to 4 correlation scales of log ks were larger than those of the shape parameters consequently the product of the variance of log unsaturated conductivity and its correlation scale remained essentially invariant for a considerable range of water saturation the implications of these results regarding stochastic modeling of transport in heterogeneous porous formations and possible applications of the results of this study are discussed briefly

stochastic analysis of unsaturated flow one dimensional monte carlo simulations and comparisons with spectral perturbation analysis and field observations a numerical experiment was designed to study the stochastic behavior of one dimensional transient unsaturated flow in a monte carlo setting soil hydraulic properties log saturated hydraulic conductivity ln ks pore size distribution parameter and the specific water capacity c are assumed to be statistically homogeneous random fields described by exponential correlation functions with identical correlation lengths fifty realizations of each soil hydraulic property with statistical properties obtained from a field experiment are generated by using a nearest neighbor model numerical solutions of the one dimensional flow equation are used repeatedly to obtain realizations of soil water pressure head and flux q corresponding to the realizations of in ks and c the dependence of and q on the statistical properties of ln ks and c and the magnitude of the hydraulic head gradient g prevailing at the lower boundary are investigated in addition results of monte carlo analysis and spectral perturbation analyses are compared with field observations the greatest variability of and q are observed when soil hydraulic properties are uncorrelated and have large variances and integral scales and when g at the lower boundary is unity the monte carlo and spectral perturbation analyses tend to agree reasonably well for the flow domains in which ergodicity of local soil hydraulic properties is assured results of the monte carlo and spectral perturbation analyses are also supported by field observations

on the unique solvability of the runge kutta equations we consider the existence of a unique solution to the systems of equations that arise when we apply a runge kutta method to a stiff nonlinear system of differential equationsu f t u withf satisfying a one sided lipschitz condition with constant for any given product h whereh denotes the step size we present algebraic conditions on the runge kutta matrixa which are necessary and sufficient for unique solvability of the equations as a second topic we consider the question whether the solution to the system of equations is stable with respect to perturbations known as bsi stability for this property also necessary and sufficient algebraic conditions ona are presented

block diagonal semistability factors and lyapunov semistability of block triangular matrices abstract the concept of lyapunov diagonal semi stability is generalized to the block diagonal case unifying the theory of lyapunov diagonal stability and lyapunov stability the corresponding generalizations of the concepts of maximal lyapunov scaling factors are applied to study the lyapunov semistability of block triangular matrices

effective soil water characteristics and ensemble soil water profiles in heterogeneous soils one dimensional vertical flows through spatially heterogeneous areas are studied with numerical solutions for a variety of soil types to ascertain the behavior of the ensemble soil heterogeneity is treated using the distributions of parameters describing the characteristic relations of conductivity water content and pressure head values of the critical parameters taken from a modified brooks corey or van genuchten model have previously 7lsqb smith and diekkruger 1992 been shown in two extensive data sets to exhibit little interdependence the static ensemble characteristics except for saturated and residual water content parameters are shown to have regular bias compared to a soil with the mean characteristic parameters the measured data also are shown not to support the popular similar media heterogeneity model using both analytic approximate flow models and an ensemble solution of richards equation the effective dynamic ensemble characteristics in three example soils are studied as suggested in previous studies such effective characteristics are conditional to flow conditions and are here shown to be quite different from ensemble static characteristics this indicates that irrespective of the sample size effective soil dynamic characteristics are not measurable for samples possessing significant heterogeneity

maximal lyapunov scaling factors and their applications in the study of lyapunov diagonal semistability of block triangular matrices abstract for a lyapunov diagonally semistable matrix a we introduce the concept of maximal lyapunov scaling factor that is a lyapunov scaling factor d of a such that the range of ad da t is of maximal dimension we investigate properties of maximal lyapunov scaling factors and apply them in proving a characterization for block triangular lyapunov diagonally semistable matrices in terms of lyapunov diagonal semistability of the diagonal blocks the latter result is used to prove that a block triangular matrix is lyapunov diagonally semistable if and only if every 2 2 block principal submatrix of it is lyapunov diagonally semistable

infiltration in stratified heterogeneous soils relative importance of parameters and model variations 1 this study presents a framework that accounts for the uncertainty relative importance and relative contribution of uncertain and spatially variable parameters and the influence of statistical model assumptions in problems of infiltration in unsaturated heterogeneous formations the relative importance of the saturated hydraulic conductivity k s the van genuchten and 3 parameters was quantified toward the mean pressure head profile and the fluctuations about it the broad implications of our study for site characterizations efforts are the following statistical moments were seen not to be sufficient for producing reliable modeling estimates significant information on the detailed shape of the probability distribution is required in order to produce meaningful predictions when limited data are available optimum allocation of resources is accomplished by concentrating on k s when more extensive sampling can be done both k s and appear to be critical total system performance analyses may not provide the most appropriate modeling estimates the results of the relative importance of the parameters for a specific layer did not coincide with the conclusions drawn from an analysis of the system as a whole

lyapunov diagonal semistability of real h matrices we characterize lyapunov diagonally stable real h matrices and those real h matrices which are lyapunov diagonally semistable but not lyapunov diagonally stable called lyapunov diagonally near stable the latter characterization is given in terms of the principal submatrix rank property defined here we apply our results to the numerical abscissas of real matrices one of our main tools is a slight strengthening of classical results of ostrowski which we derive from a fundamental theorem of wielandt

conditional stochastic analysis of solute transport in heterogeneous variably saturated soils a method is developed for the conditional monte carlo simulation of steady stateflow and transient transport from point sources in variably saturated porous media it combines the geostatistical method a linearized approximation of the soil water tension perturbation solution and afinite element numerical model the method is used to investigate the usefulness of conditional simulation for predicting solute transport under a variety of sampling network designs applied to a number of hypothetical soils saturated hydraulic conductivity data yield the largest reduction of conditional uncertainty in relatively wet soils with mild heterogeneities in highly heterogeneous soils or under dry conditions soil water tension data by themselves taken at a sampling density of one to two correlation scales along the expected mean travel path can greatly reduce prediction uncertainty about solute concentration parameter uncertainty about statistical properties of the independent random variables becomes less important as the number of conditioning data increases however even with a very high number of sampling data uncertainty of predicted concentration levels remains significant