steady infiltration from large shallow ponds exact quasi linear solutions are obtained for steady infiltration from a shallow half plane pond on the surface of an isotropic semi infinite porous medium three particular boundary value problems are considered namely constant dirichlet boundary conditions in relative permeability and vertical flux and a mixed boundary value problem the boundary conditions on the surface of the porous media for these problems correspond physically first to fully saturated conditions under the pond and fully unsaturated conditions elsewhere second to a constant vertical flux under the pond and zero vertical flux elsewhere and third to fully saturated conditions under the pond and zero vertical flux elsewhere each problem has essentially the same diffusive boundary layer or capillary fringe connecting the fully saturated and unsaturated regions the total flux per unit length of boundary due to capillarity in the first problem is infinite and for the latter two problems finite constants strong analogies between our results for a surface source and the corresponding results of waechter and philip for buried spherical and cylindrical sources are established finally the exact results for the half plane pond are used in an approximate description of steady infiltration from a large shallow pond of arbitrary shape subject to the minimum radius of curvature of the pond s perimeter being large relative to 2 where is the inverse length scale introduced in quasi linear models a boundary layer develops from capillarity at the pond s edge away from which the solution is adequately described by a diffusion equation representing a balance between the vertical flow from gravity and the horizontal flow from capillarity an approximate expression is obtained analytically for the total flow from large shallow ponds

a distributed observer for a time invariant linear system a time invariant linear distributed observer is described for estimating the state of an m 0 channel n dimensional continuous time linear system of the form dot x ax y i c ix i in lbrace 1 2 ldots m rbrace the state x is simultaneously estimated by m agents assuming each agent i senses y i and receives the state z j of each of its neighbors estimators neighbor relations are characterized by a constant directed graph mathbb n whose vertices correspond to agents and whose arcs depict neighbor relations for the case when the neighbor graph is strongly connected the overall distributed observer consists of m linear estimators one for each agent m 1 of the estimators are of dimension n and one estimator is of dimension n m 1 using results from the classical decentralized control theory it is shown that subject to the assumptions that none of the c i are zero the neighbor graph mathbb n is strongly connected the system whose state to be estimated is jointly observable and nothing more it is possible to freely assign the spectrum of the overall distributed observer for the more general case when mathbb n has q 1 strongly connected components it is explained how to construct a family of q distributed observers one for each component which can estimate x at a preassigned convergence rate

on mass response functions field transport of reactive solute species is investigated through a class of stochastic models here termed mass response functions mrfs which incorporate simplified concepts of chemical physical nonequilibrium kinetics in the formulation of transport by travel time distributions mrfs are probability density functions pdfs associated with solute particles travel time within transport volumes the theory hinges on recent advances in modeling transport of solutes in groundwater and in basin scale transport volumes and links the approaches of surface hydrologists with recent subsurface transport models the relationship between mrfs and the theory of solute transport by continuous motions is investigated it is found that mrfs extend the basic formulation of transport of inert solutes to a particular case of sorption process the relationship between mrfs and the basic differential convection dispersion equation incorporating linear sorption is also investigated it is found here that not only are transfer functions of solutes consistent with any mechanistic three dimensional 3 d model of convection dispersion but also that they are under limit conditions the product of the travel time distribution of the carrier flow with a bounded continuous function the latter is the solution to an initial value problem which results from solving the general 3 d differential equations of convection dispersion with sorption under some simplifying assumptions and formally coincides with the resident concentration included as an assumption in the original mrf formulation travel time distributions and mrfs underlain by statistical constraints rather than by dynamical models are proposed non gaussian distributions are studied by statistical mechanical tools and are found to represent the norm rather than the exception in this formulation of transport of reactive solutes the concepts are applied to a field study and are shown to yield reliable models of solute migration in nonpoint pollution problems

temporal moments revisited why there is no better way for physically based model reduction in time 1 many hydro geo logical problems are highly complex in space and time coupled with scale issues variability and uncertainty especially time dependent models often consume enormous computational resources but model reduction techniques can alleviate this problem temporal moments tm offer an approach to reduce the time demands of transient hydro geo logical simulations tm reduce transient governing equations to steady state and directly simulate the temporal characteristics of the system if the equations are linear and coefficients are time independent this is achieved by an integral transform projecting the dynamic system response onto monomials in time in comparison to classical approaches of model reduction that involve orthogonal base functions however the monomials for tm are nonorthogonal which might impair the quality and efficiency of model reduction thus we raise the question of whether there are more suitable temporal base functions than the monomials that lead to tm in this work we will derive theoretically that there is only a limited class of temporal base functions that can reduce hydro geo logical models by comparing those to tm we conclude that in terms of gained efficiency versus maintained accuracy tm are the best possible choice while our theoretical results hold for all systems of linear partial or ordinary differential equations pdes odes with any order of space and time derivatives we illustrate our study with an example of pumping tests in a confined aquifer for that case we demonstrate that two four tm are sufficient to represent more than 80 90 of the dynamic behavior and that the information content strictly increases with increasing tm order

consensus based overlapping decentralized estimator in this technical note a new algorithm for state estimation is proposed in the form of a multi agent network based on a synergy between local kalman filters and a dynamic consensus strategy between the agents it is shown that it is possible under general conditions concerning local resources and the network topology to achieve asymptotic stability of the whole estimation algorithm by a proper choice of the consensus gains it is demonstrated that the consensus gains can be obtained by minimizing the total mean square estimation error capabilities of the network to achieve reduction of the measurement noise influence are also discussed

consensus based linear distributed filtering we address the consensus based distributed linear filtering problem where a discrete time linear stochastic process is observed by a network of sensors we assume that the consensus weights are known and we first provide sufficient conditions under which the stochastic process is detectable i e for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors without noise is asymptotically stable next we develop a distributed sub optimal filtering scheme based on minimizing an upper bound on a quadratic filtering cost in the stationary case we provide sufficient conditions under which this scheme converges conditions expressed in terms of the convergence properties of a set of coupled riccati equations

application of the finite difference heterogeneous multiscale method to the richards equation 1 this paper extends the finite difference heterogeneous multiscale method fdhmm to simulate transient unsaturated water flow problems in random porous media the numerical method is based on the use of two different schemes for the original equation at different grid levels which allows numerical results at a lower cost than solving the original equations the main feature of fdhmm is that the necessary data for the macroscopic model are supplied by solving the microscopic model on a sparse spatial domain the generated code is verified by applying the linearization model of the richards equation considering two different constitutive relationships this method is applied to several test examples with different soil textures and boundary conditions both the dirichlet and the periodic boundary conditions are considered for solving the local microscopic model when the water flow in heterogeneous unsaturated soils is simulated by fdhmm the numerical experiments demonstrate that fdhmm can effectively simulate the transient unsaturated water flow in the specific soils the numerical experiments also demonstrate that fdhmm can achieve accurate global mass balance and is a globally convergent algorithm and the spatial correlation length of random coefficients under the specific standard deviation has relatively little influence on the accuracy of the method

conditions for synchronizability in arrays of coupled linear systems synchronization in arrays of coupled continuous time linear systems is studied sufficiency of certain conditions for the existence of a synchronizing feedback law are analyzed it is shown that for neutrally stable systems that are detectable from their outputs a linear feedback law exists under which any number of coupled systems synchronize provided that the directed weighted graph describing the interconnection is fixed and connected an algorithm generating one such feedback law as well as the trajectory that the solutions converge to are presented it is also shown that for critically unstable systems detectability is not sufficient whereas full state coupling is for the existence of a linear feedback law that is synchronizing for all coupling configurations described by a connected graph

diffusion strategies for distributed kalman filtering and smoothing we study the problem of distributed kalman filtering and smoothing where a set of nodes is required to estimate the state of a linear dynamic system from in a collaborative manner our focus is on diffusion strategies where nodes communicate with their direct neighbors only and the information is diffused across the network through a sequence of kalman iterations and data aggregation we study the problems of kalman filtering fixed lag smoothing and fixed point smoothing and propose diffusion algorithms to solve each one of these problems we analyze the mean and mean square performance of the proposed algorithms provide expressions for their steady state mean square performance and analyze the convergence of the diffusion kalman filter recursions finally we apply the proposed algorithms to the problem of estimating and tracking the position of a projectile we compare our simulation results with the theoretical expressions and note that the proposed approach outperforms existing techniques

on the probabilistic structure of water age the age distribution of water in hydrologic systems has received renewed interest recently especially in relation to watershed response to rainfall inputs the purpose of this contribution is first to draw attention to existing theories of age distributions in population dynamics fluid mechanics and stochastic groundwater and in particular to the mckendrick von foerster equation and its generalizations and solutions a second and more important goal is to clarify that when hydrologic fluxes are modeled by means of time varying stochastic processes the age distributions must themselves be treated as random functions once their probabilistic structure is obtained it can be used to characterize the variability of age distributions in real systems and thus help quantify the inherent uncertainty in the field determination of water age we illustrate these concepts with reference to a stochastic storage model which has been used as a minimalist model of soil moisture and streamflow dynamics

burgers equation a general nonlinear solution of infiltration and redistribution 1 the general one dimensional solution of burgers equation is developed using a series of transformations and the green s function method the solution gives the distribution of the reduced water content in a semi infinite and in a finite domain for arbitrary initial moisture distributions the boundary condition at the soil surface can be either a time dependent flux or constant water content while the bottom boundary condition for the finite case is a constant water content value explicit results for a uniform discrete hydrostatic and steady state initial moisture profiles are derived an analytical solution that spans the preponding to the postponding period of rainfall is also obtained expressions for the time to ponding and infiltration equations are presented for the various cases of initial moisture profiles and a shallow water table these results allowed the quantification of the error in the various approximations to the time to ponding and the cumulative infiltration in the postponding period

simulation of groundwater age distributions the objective of our work is to examine how to simulate the age of groundwater in such a way that it can be compared to actual measurements we start by showing that computation of kinematic age the one obtained by tracking water along streamlines is ill posed in heterogeneous aquifers this together with its inability to account for mixing processes makes it inadequate for comparison with age measurements which are the result of some averaging of the age distribution in the water sample the type of averaging depends on the measurement procedure therefore we go on to write the equations for the cumulative distribution function of residence time under transient flow conditions this allows us to derive transient equations for the mean age as well as for the higher order moments of its distribution which generalize previous results by others these moments can be used for approximating age measurements which need not be equal to the mean age of the water sample using both a synthetic and a real example we show that mean age is an acceptable estimate of radiometric age measurements in many cases including a second order correction variance of residence time distribution always improves results on the other hand higher order approximations converge slowly for old compared to half life waters to the point that third order approximations often worsen the results

statistical properties of a class of nonlinear systems driven by colored multiplicative gaussian noise we derive the time dependent univariate and bivariate probability distribution function for an overdamped system with a quadratic potential driven by colored gaussian noise whose amplitude depends on the system state x as x alpha particular attention is paid to the effect of the correlation function of the noise on the statistical properties of the system we obtain exact expressions for the fractional moments as well as the correlation function of the system and calculate the fractal dimension we also consider the special case of a constant potential and determine the criteria for anomalous diffusion and stochastic localization of free particles

cauchy data requirement of the inverse problem of the mean age equation a classical theoretical inverse problem in groundwater hydraulics is the calibration of a heterogeneous isotropic hydraulic conductivity field using known hydraulic head data at each point in the domain it has been long known that a necessary condition for the uniqueness of the solution to this theoretical inverse problem is the cauchy data i e the hydraulic conductivity values or equivalently flux along a line crossing all streamtubes in the entire domain this result has been cited in identifying the value of boundary flux data in practical inverse problems although in general such data are generally not available in this work we show that groundwater mean age data replace this cauchy data requirement

transport behavior of a passive solute in continuous time random walks and multirate mass transfer 1 we consider the transport behavior of a passive solute in a heterogeneous medium modeled by continuous time random walks ctrw and linear multirate mass transfer mrmt within the ctrw framework we formulate a transport model which is formally equivalent to mrmt in both approaches the total concentration is divided into mobile and immobile parts the immobile concentration is given by the convolution in time of the mobile concentration and a memory function the memory function is a functional of the distribution of transition and trapping times for the ctrw and the mrmt approach respectively and determines the transport behavior of the solute based on different expressions for the memory function in the two frameworks we derive conditions for which both approaches describe the same transport behavior we focus on anomalous transport behavior that can arise if the transition and trapping time distributions behave algebraically in a given time regime using an expansion of the laplace transform of the memory function we develop explicit expressions for the time behavior of the flux concentration as well as for the center of mass velocity and the macro dispersion coefficients of the solute distribution we observe anomalous power law as well as normal fickian transport behavior depending on the exponents that dominate the trapping and transition time distributions respectively the results show that the character of the anomalous transport does not depend on the details of the transport model but only on the exponents dominating the transition or trapping time distributions the unified transport framework presented here comprising ctrw and mrmt shows new aspects and opens new perspectives for the modeling of transport in heterogeneous media

water dynamics in a gradually nonhomogeneous soil described by the linearized richards equation 1 in order to investigate the influence of the soil vertical nonhomogeneity on the dynamics of the water in the upper soil layer an analytical solution of the linearized richards equation was derived here the hydraulic conductivity ks at saturation is assumed to decrease exponentially with depth in accordance with field data reported in the literature and collected during our surveys in mountain catchments gardner s constitutive laws were assumed for the hydraulic conductivity and water retention characteristics k s and s the resulting one dimensional richards equation is linear and its coefficients decrease exponentially with depth an analytical solution was found by using the method of laplace transform and compared with some test cases both analytically and numerically the soil water content profile exhibits a maximum at one point in the domain moreover it accounts for a different behavior in the water dynamics depending on the prevailing role of diffusive effects related to the soil water retention or of the transport effects related to the hydraulic conductivity profile

decentralized stabilization and pole assignment for general proper systems considered is the problem of finding existence conditions and a controller synthesis procedure using decentralized control for assigning the poles of a linear time invariant proper system described by a state space model c a b d where no assumption is made regarding the structure of d this problem has direct application to the decentralized stabilization problem decentralized robust servomechanism problem etc and is a nontrivial extension to the standard decentralized problem where it is assumed that the direct feedthrough terms either are absent or have a block diagonal structure

survey generic properties and control of linear structured systems a survey in this survey paper we consider linear structured systems in state space form where a linear system is structured when each entry of its matrices like a b c and d is either a fixed zero or a free parameter the location of the fixed zeros in these matrices constitutes the structure of the system indeed a lot of man made physical systems which admit a linear model are structured a structured system is representative of a class of linear systems in the usual sense it is of interest to investigate properties of structured systems which are true for almost any value of the free parameters therefore also called generic properties interestingly a lot of classical properties of linear systems can be studied in terms of genericity moreover these generic properties can in general be checked by means of directed graphs that can be associated to a structured system in a natural way we review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms by properties we mean here system specific properties like controllability the finite and infinite zero structure and so on as well as solvability issues of certain classical control problems like disturbance rejection input output decoupling and so on in this paper we do not try to be exhaustive but instead by a selection of results we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool we emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only moreover the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well known polynomially bounded combinatorial techniques for larger systems

a note on distributed finite time observers the robust distributed estimation for a class of time invariant plants is achieved via a finite time observer its error reaching zero after a finite time in the absence of perturbation two types of robustness are also shown first input to state stability with respect to measurement noises and additive perturbations is proven second we demonstrate that the estimation error stays bounded in the presence of known transmission delays

correlation anti correlation transition by state dependent poisson noise noise may induce some degrees of order in many biological and complex systems we present an example of a noise dependent transition from correlation to anti correlation of the states of a bivariate system coupled by state dependent poisson noises by varying the degree of dependence of the rate of jumps on the other variable the system undergoes different degrees of correlation from independence to perfect correlation which in this case coincides with perfect synchronization in the limit of the deterministic periodic case

optimal design for synchronization of cooperative systems state feedback observer and output feedback this technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree a leader node or command generator is considered which generates the desired tracking trajectory a framework for cooperative tracking control is proposed including full state feedback control observer design and dynamic output feedback control the classical system theory notion of duality is extended to networked systems it is shown that unbounded synchronization regions that achieve synchronization on arbitrary digraphs containing a spanning tree can be guaranteed by using linear quadratic regulator based optimal control and observer design methods at each node

continuous groundwater velocity fields and path lines in linear bilinear and trilinear finite elements darcy velocity fields obtained from finite element solutions of heads in groundwater flow exhibit discontinuities at element boundaries thus giving rise to inaccuracies in path line construction several methods have been developed to resolve those inaccuracies including global postprocessing of velocity fields mixed hybrid finite element formulations and stream function formulations all of these techniques either lead to a considerable increase in the computational effort or are not general enough for all purposes the point of view taken here is that standard finite element flow models yield exact water balances which in the usual approach to path line computation are not fully used by starting out from patches with flux conserving boundaries a new postprocessing procedure is derived that allows construction of a continuous flux distribution over the whole model domain in this procedure only the head gradients of adjacent elements are used thus avoiding the solution of another global system of equations furthermore application of a stream function interpolation inside each patch allows the fast computation of path lines without any time stepping the path lines computed with the proposed procedure are compared to path lines computed by usual particle tracking and examples are presented showing that the new method is vastly superior to traditional particle tracking

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

infiltration models for semi infinite soil profiles 1 infiltration models for hydrological applications are developed for rational forms of the soil hydraulic conductivity and moisture retention functions the models are based on the traveling and kinematic wave solutions of the governing equation that proved to be highly accurate in specific flow conditions the approximate solutions describe the one dimensional infiltration into a semi infinite medium for uniform initial conditions under either a time dependent flux or a constant head boundary condition they capture the profile development from early to late time accurately due to the proper derivation of the wetting front speed in terms of the time varying surface boundary potential and flux rate algebraic expressions of theoretical and practical importance are derived in terms of well defined soil water parameters and include the effect of the antecedent moisture content in a specific fashion practical results include simple expressions for the surface moisture variation for variable rainfall patterns time to ponding expressions and infiltration equations that account explicitly for the initial condition formulas for the depth of the wetting zone and algebraic equations for parameter estimation of the soil hydraulic parameters by inverse analysis

multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface the present work explores a class of analytical solutions of moisture movement in unsaturated porous media characterized by an exponential dependence of the hydraulic conductivity and the moisture content on water pressure the green s function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration in a semi infinite flow domain with arbitrary initial conditions boundary conditions and root uptake forcing functions and for various simple source geometry the general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation evaporation root uptake and moisture redistribution can be easily deduced from the general analytical model the model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest new explicit solutions have been obtained for one dimensional infiltration under various prescribed time dependent flux boundary conditions and for two and three dimensional moisture redistribution for constant initial or boundary conditions the multidimensional solution is essentially the product of two or three time dependent terms with each term being a function of only one space variable

estimation of aquifer parameters under transient and steady state conditions 1 maximum likelihood method incorporating prior information in this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions the parameters include values and directions of principal hydraulic conductivities or transmissivities in anisotropic media specific storage or storativity interior and boundary recharge or leakage rates coefficients of head dependent interior and boundary sources and boundary heads in transient situations the initial head distribution can also be estimated if the system is originally at a steady state paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters the inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters since not all the factors which contribute to the prior errors can be quantified statistically at the outset the covariance matrices of these errors are expressed in terms of several parameters which if unknown can be estimated jointly with the hydraulic parameters by a stagewise optimization process when transient head data are separated by a fixed time interval the temporal structure of these data is approximated by a lag one autoregressive model with a correlation coefficient that can be treated as another unknown parameter estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature all of which are based on the maximum likelihood concept might be useful for selecting the best groundwater model or the best method of parameterizing a particular model among a number of given alternatives

integrate and fire neurons with threshold noise a tractable model of how interspike interval correlations affect neuronal signal transmission many neurons exhibit interval correlations in the absence of input signals we study the influence of these intrinsic interval correlations of model neurons on their signal transmission properties for this purpose we employ two simple firing models one of which generates a renewal process while the other leads to a nonrenewal process with negative interval correlations different methods to solve for spectral statistics in the presence of a weak stimulus spike train power spectra cross spectra and coherence functions are presented and their range of validity is discussed using these analytical results we explore a lower bound on the mutual information rate between output spike train and input stimulus as a function of the system s parameters we demonstrate that negative correlations in the baseline activity can lead to enhanced information transfer of a weak signal by means of noise shaping of the background noise spectrum we also show that an enhancement is not compulsory char22 for a stimulus with power exclusively at high frequencies the renewal model can transfer more information than the nonrenewal model does we discuss the application of our analytical results to other problems in neuroscience our results are also relevant to the general problem of how a signal affects the power spectrum of a nonlinear stochastic system

kinematics of age mixing in advection dispersion models this paper investigates age mixing processes arising in advection dispersion models where large scale travel and residence time distributions can be explicitly calculated based on the underlying velocity field in particular we analyze spatially integrated age mixing dynamics by comparing the age distributions of the storage and of the outflow s the relevance of the work lies in the impact of age mixing dynamics on the shape of travel time distributions ttds which ultimately control the long term memory of catchment transport processes we set up a theoretical framework that bridges previous lagrangian and eulerian water age theories in heterogeneous media the framework allows for the analysis of the dynamical connection between water age distributions in large scale volume and flux samples theoretical advances are then illustrated through the application to a finite one dimensional domain with constant advection and dispersion coefficient therein we analyze the type of mixing emerging for different peclet numbers and diverse spatiotemporal patterns of solute input we find that in spite of the enhanced nonstationarity of ttds the type of mixing is markedly invariant moreover for relatively low peclet numbers the different ages available in the control volume are systematically removed from the domain at a rate nearly proportional to their relative abundance random sampling emerging large scale patterns of age mixing yield theoretical and practical implications for watershed hydrology where ttds can be used to infer general patterns of catchment response across scales

on the construction of a functional solution method for the infiltration in porous media problems abstract in this paper we consider a transient vertical one dimensional flow problem of water in unsaturated porous media modelled by the non linear richards equation constitutive relations of van genuchten will be employed and pade approximants are used to represent the hydraulic capacity and conduction in a simplified fashion from the proposed methodology a construction of a functional solution is presented with the objective to define an initialisation of a recursive scheme in the spirit of adomian decomposition this solution is optimised and evaluated using the governing equation for a self consistency test the results are presented for some soil types and its related soil parameters that are reported in the literature

numerical evaluation of a set of analytical infiltration equations in this paper a set of analytical infiltration equations that are commonly used to evaluate one and three dimensional water infiltration from a surface disc source is studied both the quasi exact analytical formulation and the related approximations for short and long times are assessed the analytical properties of the quasi exact formulation are evaluated using a proposed scaling procedure in order to define the validity domains of related approximations both quasi exact and approximate analytical equations are then studied with respect to their ability to reproduce numerically generated cumulative infiltrations from a 10 cm radius disc source for four soils sand loam silt and silty clay at several initial saturations the quasi exact formulation is suitable for sand loam and silt when their soil dependent and saturation independent shape parameters and are properly chosen between 0 75 and 1 and 0 3 and 1 7 respectively approximations derived for the same shape parameters can also be used provided that their use is restricted to proposed validity intervals however none of these equations applies for silty clay since its hydraulic properties do not fulfill the conditions required for the use of the quasi exact formulation

temporal moments for transport with mass transfer described by an arbitrary memory function in heterogeneous media 1 temporal moment equations are generalized for transport under linear mass transfer which has been used to model a broad range of small scale processes kinetic sorption diffusion into immobile regions and transport through heterogeneous aquifers solving the moment equations which are formally identical to steady state transport equations is computationally more efficient than evaluating the temporal moments by integrating the transient flux concentrations we derive recursive relations for the moments of the flux concentration which involve the moments of the memory function but do not dependent on its shape it turns out that two mass transfer models have the same kth temporal moment if the moments of order lower than k are equal particularly the mean retention time i e the first moment of the retention probability density function pdf in the immobile domain decides the second temporal moment of concentration a mass transfer model with two first order rate coefficients can match up to the fourth temporal moment described by a multirate model with a predescribed pdf of the mass transfer rate coefficient the kth temporal moment is finite when the k 1 th moment of the memory function exists

state dependent fire models and related renewal processes we introduce a general class of stochastic processes forced by instantaneous random fires i e jumps that reset the state variable x to a given value since in many physical systems the fire activity is often dependent on the actual value of the state variable as in the case of natural fires in ecosystems and firing dynamics in neuronal activity the frequency of fire occurrence is assumed to be state dependent such dynamics leads to independent interfire statistics i e to renewal point processes various functions relating the frequency of fire occurrence to x t are analyzed and compared the relation between the probabilistic dynamics of x t and the interfire statistics is derived and some exact probability distribution of both x t and the interfire times are obtained for systems with different degrees of complexity after studying processes in which the fire activity is coupled only to a deterministic drift we also analyze processes forced by either additive or multiplicative gaussian white noise

age distribution dynamics with stochastic jumps in mortality while deterministic age distribution models have been extensively studied and applied in various disciplines little work has been devoted to understanding the role of stochasticity in birth and mortality terms in this paper we analyse a stochastic m kendrick von foerster equation in which jumps in mortality represent intense losses of population due to external events we present explicit solutions for the probability density functions of the age distribution and the total population and for the temporal dynamics of their moments we also derive the dynamics of the mean age of the population and its harmonic mean the framework is then used to calculate the age distribution of salt in the soil root zone where the accumulation of salt by atmospheric deposition is counteracted by plant uptake and by jump losses due to percolation events

stochastic recession rates and the probabilistic structure of stream flows 1 this paper investigates the impact of interevent variability of streamflow recession rates on two key streamflow statistics namely the equilibrium probability density function pdf and the autocorrelation the relevance of the problem lies in the need to quantify and predict streamflow availability on the basis of measurable rainfall and landscape attributes by explicitly incorporating the stochasticity of the underlying climate and transport processes novel expressions for the seasonal pdf and the autocorrelation of the daily streamflows are derived by incorporating the randomness of the recession rates into a probabilistic framework where the streamflow fluctuations are explicitly related to the intermittency of the rainfall forcing the presence of stochastic recession time constants is shown to impact only the third and higher order moments of the probability density function of the daily streamflows without altering the mean and the variance of the pdf a remarkable effect is instead produced on the correlation structure which may exhibit long term persistence even in the presence of a weak randomness of the recession rate a relevant case study is then discussed to show that incorporating the stochasticity of the recession time constant leads to an improvement of the model ability to capture the behavior of the equilibrium streamflow pdf and of the underlying correlation function

distributed moving horizon estimation for linear constrained systems this paper presents a novel distributed estimation algorithm based on the concept of moving horizon estimation under weak observability conditions we prove convergence of the state estimates computed by any sensors to the correct state even when constraints on noise and state variables are taken into account in the estimation process simulation examples are provided in order to show the main features of the proposed method

ito versus stratonovich a survey is given of the facts and fancies concerning the nonlinear langevin or ito equation actually it is merely a pre equation which becomes an equation when an interpretation rule is added the rules of ito and stratonovich differ but both are mathematically consistent and therefore equally admissible conventions the reason why they seem to lead to physical differences is that the langevin approach used to arrive at the equation involves a tacit assumption for systems with external noise this assumption can be justified and it is then clear that the stratonovich rule applies systems with internal noise however can only be properly described by a master equation and the ito stratonovich controversy never enters afterward one is free to model the resulting fluctuations either with an ito or a stratonovich scheme but that does not lead to any new information

salient views and view dependent dictionaries for object recognition a sparse representation based approach is proposed to determine the salient views of 3d objects the salient views are categorized into two groups the first are boundary representative views that have several visible sides and object surfaces that may be attractive to humans the second are side representative views that best represent views from sides of an approximating convex shape the side representative views are class specific and possess the most representative power compared to other within class views using the concept of characteristic view class we first present a sparse representation based approach for estimating the boundary representative views with the estimated boundaries we determine the side representative views based on a minimum reconstruction error criterion furthermore to evaluate our method we introduce the notion of view dependent dictionaries built from salient views for applications in 3d object recognition and retrieval the proposed view dependent dictionaries encode information on geometry across views and representation of the object through a series of experiments on four publicly available 3d object datasets we demonstrate the effectiveness of our approach compared to two existing state of the art algorithms and one baseline method highlightsa sparse representation based approach is proposed to determine the salient views of 3d objects the salient views are categorized into boundary representative and side representative views we present a sparse representation based approach for estimating the boundary representative views we determine the side representative views based on a minimum reconstruction error criterion we introduce view dependent dictionaries for applications in 3d object recognition and retrieval

network topology and communication data rate for consensusability of discrete time multi agent systems this paper investigates the joint effect of agent dynamic network topology and communication data rate on consensusability of linear discrete time multi agent systems neglecting the finite communication data rate constraint and under undirected graphs a necessary and sufficient condition for consensusability under a common control protocol is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability the result is established by solving a discrete time simultaneous stabilization problem a lower bound of the optimal convergence rate to consensus which is shown to be tight for some special cases is provided as well moreover a necessary and sufficient condition for formationability of multi agent systems is obtained as a special case the discrete time second order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence the effects of undirected graphs on consensability formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph laplacian matrix an extension to directed graphs is also made the consensus problem under a finite communication data rate is finally investigated

in plane rotation and scale invariant clustering using dictionaries in this paper we present an approach that simultaneously clusters images and learns dictionaries from the clusters the method learns dictionaries and clusters images in the radon transform domain the main feature of the proposed approach is that it provides both in plane rotation and scale invariant clustering which is useful in numerous applications including content based image retrieval cbir we demonstrate the effectiveness of our rotation and scale invariant clustering method on a series of cbir experiments experiments are performed on the smithsonian isolated leaf kimia shape and brodatz texture datasets our method provides both good retrieval performance and greater robustness compared to standard gabor based and three state of the art shape based methods that have similar objectives

non fickian dispersion of groundwater age 1 we expand the governing equation of groundwater age to account for non fickian dispersive fluxes using continuous random walks groundwater age is included as an additional fifth dimension on which the volumetric mass density of water is distributed and we follow the classical random walk derivation now in five dimensions the general solution of the random walk recovers the previous conventional model of age when the low order moments of the transition density functions remain finite at their limits and describes non fickian age distributions when the transition densities diverge previously published transition densities are then used to show how the added dimension in age affects the governing differential equations depending on which transition densities diverge the resulting models may be nonlocal in time space or age and can describe asymptotic or preasymptotic dispersion a joint distribution function of time and age transitions is developed as a conditional probability and a natural result of this is that time and age must always have identical transition densities this implies that a transition density defined for age can substitute for a density in time and this has implications for transport model parameter estimation we present examples of simulated age distributions from a geologically based heterogeneous domain that exhibit non fickian behavior and show that the non fickian model provides better descriptions of the distributions than the fickian model

noise induced transitions in state dependent dichotomous processes in a number of stochastic systems the random forcing is represented as a dichotomous markov noise a common characteristic of these models is that the noise is usually supposed to be independent of the state of the forced dynamical system however there are several situations in which positive or negative feedback exist between the system and the random driver this paper investigates a class of systems characterized by feedback between dichotomous markov noise and the system s dynamics the effect of the feedback is accounted for through a state dependency in the transition rates of the dichotomous noise we study noise induced transitions in these systems with special attention to the delicate problem of correctly defining the deterministic counterpart of the stochastic system we find that i if in the absence of any feedback the dynamical system has a single deterministic stable point the deterministic dynamics remain monostable when a negative feedback is introduced while they may become bistable in the presence of a positive feedback ii noise may induce bistability in the presence of a null or negative feedback iii bistable deterministic dynamics induced by the positive feedback may be destroyed by the noise which tends to stabilize the system around a new intermediate stable state between those of the deterministic dynamics

can one gauge the shape of a basin this paper investigates the effects of geometrical factors characterizing the shape of a river basin on the features of its hydrologic response in particular we wonder if by measuring the hydrologic response i e gauging the salient geomorphic features of the basin can be recovered we argue that the basic structure of the channel network tends in ideal conditions to yield some universal characters of the width function w x defining the relative proportion of a contributing area at a distance x from the outlet w x exhibits low frequency features which are geometry dominated and high frequency features determined by recurrent aggregation patterns it is suggested that given the shape of the basin one can indeed forecast in a rational manner the main characters of the hydrologic response which are imprinted in reproducible width functions however the inverse problem i e the determination of the shape from the measure of the hydrologic response is less solidly defined because of the possible loss of irretrievable information induced by the dynamics of runoff processes therefore the question posed in the title cannot be solved in general although many elements for a general theory are seemingly established

the quasilinear approximation for unsaturated porous media flow this paper gives a review of the quasilinear approximation an exponential relationship between hydraulic conductivity and moisture potential and the uses this has been put to since the time of its creation one of the major attractions of this approximation is that under steady regimes the highly nonlinear richards equation governing unsaturated flow can be linearized this simplification has enabled analytic and semianalytic solutions to be found for many unsaturated flow problems these are reviewed and the current research areas in which the quasilinear approximation is being used are discussed

coupled estimation of flow and solute transport parameters a methodology for solving the coupled linear flow and transport inverse problem is presented it allows the estimation of aquifer parameters transmissivity storativity recharge boundary heads and flows leakage dispersivity molecular diffusion porosity retardation linear decay boundary concentrations using their prior estimates as well as head and concentration measurements as basic information transient flow and transport equations are solved using the finite element method in space and a weighted finite difference scheme in time flow and transport domains can be one two or quasi three dimensional applying linear one dimensional elements linear two dimensional triangles or bilinear two dimensional rectangles mixed at will time regimes can be transient or steady state in any equation flow or transport parameters are estimated on the basis of maximum likelihood theory which allows us to obtain information about parameters uncertainty minimization of the negative log likelihood is performed using marquardt s method the applicability of the method is shown by means of two real examples they illustrate that the proposed approach can successfully address model selection parameter uncertainty and nontrivial identifiability problems estimation of time dependent sources and the role of prior estimates are also addressed in the examples while the formulation of the problem leaves room for both stochastic and deterministic treatment of hydraulic parameters the latter has been adopted in both examples limitations of the approach are also apparent

infiltration models for soil profiles bounded by a water table 1 approximate solutions of richards equation are developed for rational forms of the soil hydraulic conductivity and moisture retention functions using a perturbation expansion method a novel approach is devised in the perturbation technique whereby a priori introduced parameters are estimated in an optimal context to ensure the accuracy of the perturbation solution at all times and for all flow conditions the perturbation model describes the one dimensional nonlinear nonsteady infiltration for arbitrary initial conditions under either a time dependent surface flux or a constant head boundary condition into either a semi infinite or a finite medium bounded from below by a shallow water table the optimal perturbation approach proved to be an effective method by which closed form linear solutions can be adapted to nonlinear soils through proper scaling factors the results show that the first order linear term of the optimal perturbation solution is sufficiently accurate for practical applications especially for shallow water table conditions they offer the means to analyze the effect of nonuniform initial conditions and the influence of the water table on the infiltration process practical results in terms of well defined soil water parameters and the antecedent moisture content include algebraic expressions for the surface moisture content variation under variable rainfall conditions time to ponding expressions and infiltration equations for deep and shallow water table conditions and a prediction formula for the water table recharge rate

distributing the kalman filter for large scale systems this paper presents a distributed kalman filter to estimate the state of a sparsely connected large scale n dimensional dynamical system monitored by a network of n sensors local kalman filters are implemented on nl dimensional subsystems nl lt n obtained by spatially decomposing the large scale system the distributed kalman filter is optimal under an lth order gauss markov approximation to the centralized filter we quantify the information loss due to this lth order approximation by the divergence which decreases as l increases the order of the approximation l leads to a bound on the dimension of the subsystems hence providing a criterion for subsystem selection the approximated centralized riccati and lyapunov equations are computed iteratively with only local communication and low order computation by a distributed iterate collapse inversion dici algorithm we fuse the observations that are common among the local kalman filters using bipartite fusion graphs and consensus averaging algorithms the proposed algorithm achieves full distribution of the kalman filter nowhere in the network storage communication or computation of n dimensional vectors and matrices is required only nl lt n dimensional vectors and matrices are communicated or used in the local computations at the sensors in other words knowledge of the state is itself distributed

exactly solvable model with an absorbing state and multiplicative colored gaussian noise we study the temporal evolution of a system that has an absorbing state and that is driven by colored gaussian noise whose amplitude depends on the system state x as x alpha exact analytical expressions for the probability density functions of the system and of the absorption time are derived we also calculate numerical characteristics of the probability density functions namely the fractional moments of the system and the mean absorption time and analyze the role of the functional form of the noise correlation function

transit time and age distributions for nonlinear time dependent compartmental systems many processes in nature are modeled using compartmental systems reservoir pool box systems usually they are expressed as a set of first order differential equations describing the transfer of matter across a network of compartments the concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions until now explicit formulas for transit time and age distributions of nonlinear time dependent compartmental systems were not available we compute densities for these types of systems under the assumption of well mixed compartments assuming that a solution of the nonlinear system is available at least numerically we show how to construct a linear time dependent system with the same solution trajectory we demonstrate how to exploit this solution to compute transit time and age distributions in dependence on given start values and initial age distributions furthermore we derive equations for the time evolution of quantiles and moments of the age distributions our results generalize available density formulas for the linear time independent case and mean age formulas for the linear time dependent case as an example we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time dependent input signal which represents fossil fuel additions we derive time dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business as usual scenario

time dependent linearized two dimensional infiltration and evaporation from nonuniform and nonperiodic strip sources using a linearized equation describing unsaturated homogeneous and isotropic porous media flow a general two dimensional time dependent mathematical model is presented for infiltration and or infiltration evaporation from nonuniform and nonperiodic strip sources located at the soil surface the analysis is based on an exponential relationship between the unsaturated hydraulic conductivity and the soil water pressure head and also assumes a constant value for the derivative of unsaturated hydraulic conductivity with respect to water content in the mathematical analysis laplace transform and fourier analysis techniques are used simultaneously and a general equation in an integral form for the distribution of matric flux potential has been obtained the result of warrick and lomen 1976 for a single strip source is shown to be a special case of this general model the solution for infiltration from two strip sources is presented as another special case also a third special case is presented for infiltration from two strip sources and evaporation from another strip located in the middle part the horizontal and vertical flux components for these cases are presented all results are expressed in integral forms and calculated with a computer using a numerical integration method the solutions predict the matric flux potential and flux components as functions of space and time examples that illustrate the applicability of some of the solutions are presented these solutions are of interest in the design of both sprinkler and furrow irrigation systems the results may also be used for different purposes in civil and agricultural engineering applications

probabilistic dynamics of some jump diffusion systems some exact solutions to the forward chapman kolmogorov equation are derived for processes driven by both gaussian and compound poisson shot noise the combined action of these two forms of white noise is analyzed in transient and equilibrium conditions for different jump distributions and additive gaussian noise steady state distributions with power law tails are obtained for exponentially distributed jumps and multiplicative linear gaussian noise two applications are discussed namely the virtual waiting time or takacs process including gaussian oscillations and a simplified model of soil moisture dynamics in which rainfall is modeled as a compound poisson process and fluctuations in potential evapotranspiration are gaussian

a solute flux approach to transport in heterogeneous formations 1 the general framework it is common to represent solute tranport in heterogeneous formations in terms of the resident concentration c x t regarded as a random space function the present study investigates the alternative representation by q the solute mass flux at a point of a control plane normal to the mean flow this representation is appropriate for many field applications in which the variable of interest is the mass of solute discharged through a control surface a general framework to compute the statistical moments of q and of the associated total solute discharge q and mass m is established with x the direction of the mean flow a solute particle is crossing the control plane at y z and at the travel arrival time the associated expected solute flux value is proportional to the joint probability density function pdf g1 of and whereas the variance of q is shown to depend on the joint pdf g2 of the same variables for two particles in turn the statistical moments of and depend on those of the velocity components through a system of stochastic ordinary differential equations for a steady velocity field and neglecting the effect of pore scale dispersion a major simplification of the problem results in the independence of the random variables and as a consequence the pdf of and can be derived independently of a few approximate approaches to derive the statistical moments of and are outlined these methods will be explored in paper 2 in order to effectively derive the variances of the total solute discharge and mass while paper 3 will deal with the nonlinear effect of the velocity variance upon the moments of and

multidimensional steady infiltration with prescribed boundary conditions at the soil surface the present work explores a class of analytical solutions of steady moisture movement in unsaturated porous media characterized by an exponential dependence of the hydraulic conductivity the green s function method is used to derive a general analytical model which can handle multidimensional steady infiltration problems in a semi infinite medium with arbitrary boundary conditions and root uptake forcing functions and for various simple source geometries the power of the green s function method is such that a number of new problems were amenable to analysis and solutions to problems already solved were obtained in a form better suited for numerical computation of special importance is the capability of the analytical model to handle the difficult problem of mixed boundary conditions in an approximative fashion the general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation root uptake and isothermal evaporation can be easily deduced new solutions include the case of surface sources under a prescribed exponential head and flux distribution an inverse power flux distribution and periodic root uptake the inverse power flux distribution allows the approximate modeling of constant potential sources with evaporation at the nonwetted surfaces it is shown that all two and three dimensional infiltration solutions are essentially integrals of two functions one dependent on the geometry and distribution of the source and the other dependent on the boundary condition at the land surface near field and far field approximations have also been obtained and simple algebraic equations have been derived for the flux and potential beneath the centerline of the source the proposed model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest in civil and agricultural engineering

robust distributed estimation for linear systems under intermittent information we provide a comprehensive solution to the estimation problem of the state for a linear time invariant system in a distributed fashion over networks that allow only intermittent information transmission by attaching to each node an observer that employs information received from its neighbors triggered by asynchronous communication events we propose a distributed state observer that guarantees global exponential stability of the zero estimation error set the design of parameters is formulated as linear matrix inequalities a thorough robustness analysis of the proposed observer to unmodeled dynamics unknown communication times as well as measurement and communication noise characterized in terms of input to state stability is presented these properties of the proposed observer are shown analytically and validated numerically

prescription induced jump distributions in multiplicative poisson processes generalized langevin equations gle with multiplicative white poisson noise pose the usual prescription dilemma leading to different evolution equations master equations for the probability distribution contrary to the case of multiplicative gaussian white noise the stratonovich prescription does not correspond to the well known mid point or any other intermediate prescription by introducing an inertial term in the gle we show that the ito and stratonovich prescriptions naturally arise depending on two time scales the one induced by the inertial term and the other determined by the jump event we also show that when the multiplicative noise is linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution we apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white poisson noise whose features are tailored to the characters of the daily precipitation a method is finally suggested to infer the most appropriate prescription from the data

multidimensional linearized nonsteady infiltration toward a shallow water table the green s function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration toward a shallow water table with arbitrary initial conditions boundary conditions and root uptake forcing functions and for various simple source geometries the general green s function solution allows the derivation of particular analytical solutions pertaining to cases of surface and subsurface irrigation evaporation root uptake and moisture redistribution the model assumes that the hydraulic conductivity function is an exponential function of the water pressure and a linear function of the moisture content one dimensional solutions are obtained for time dependent distributions of the flux at the land surface and of root uptake in the subsurface two and three dimensional solutions are also derived for point and line sources in the domain for a strip a rectangle and a disc source at the land surface and for two and three dimensional moisture redistribution and root uptake most of the solutions are a product of two terms one term is a function of depth while the other term is a function of time and the lateral coordinates numerical results show the effect of the water table and soil type on the two dimensional moisture movement from a strip source

linking age survival and transit time distributions although the concepts of age survival and transit time have been widely used in many fields including population dynamics chemical engineering and hydrology a comprehensive mathematical framework is still missing here we discuss several relationships among these quantities by starting from the evolution equation for the joint distribution of age and survival from which the equations for age and survival time readily follow it also becomes apparent how the statistical dependence between age and survival is directly related to either the age dependence of the loss function or the survival time dependence of the input function the solution of the joint distribution equation also allows us to obtain the relationships between the age at exit or death and the survival time at input or birth as well as to stress the symmetries of the various distributions under time reversal the transit time is then obtained as a sum of the age and survival time and its properties are discussed along with the general relationships between their mean values the special case of steady state case is analyzed in detail some examples inspired by hydrologic applications are presented to illustrate the theory with the specific results

stochastic mckendrick von foerster models with applications abstract a newly presented mckendrick von foerster model with a stochastically perturbed mortality rate is examined a transformation method converting the model with non local boundary conditions into a system of stochastic functional differential equations is offered the method could be viewed as analogous to the one which is widely used for such type of deterministic problems the derived stochastic functional differential equations yield multiple classic population models with naturally born stochasticity including delayed nicholson s blowflies general recruitment and models with cannibalism which by itself could be objects of future analysis and applications

gossip and distributed kalman filtering weak consensus under weak detectability the paper presents the gossip interactive kalman filter gikf for distributed kalman filtering for networked systems and sensor networks where intersensor communication and observations occur at the same time scale the communication among sensors is random each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link we show that under a weak distributed detectability condition 1 the gikf error process remains stochastically bounded irrespective of the instability of the random process dynamics and 2 the network achieves weak consensus i e the conditional estimation error covariance at a uniformly randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semidefinite matrices independent of the initial state to prove these results we interpret the filtering states estimates and error covariances at each node in the gikf as stochastic particles with local interactions we analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched random riccati equation the switching being dictated by a nonstationary markov chain on the network graph

towards a minimal order distributed observer for linear systems abstract in this paper we consider the distributed estimation problem for continuous time linear time invariant lti systems a single linear plant is observed by a network of local observers each local observer in the network has access to only part of the output of the observed system but also receives information on the state estimates of its neighbors each local observer should in this way generate an estimate of the plant state in this paper we study the problem of existence of a reduced order distributed observer we show that if the observed system is observable and the network graph is a strongly connected directed graph then a distributed observer exists with state space dimension equal to n n i 1 n p i where n is the number of network nodes n is the state space dimension of the observed plant and p i is the rank of the output matrix of the observed output received by the i th local observer in the case of a single observer this result specializes to the well known minimal order observer in classical observer design

multiple outflows spatial components and nonlinearities in age theory water age has become an important variable for the characterization of hydrologic systems the goal of this paper is to analyze the role of multiple outflows spatial components and nonlinearities in age theory we first extend the theory to linear systems with multiple outflows including the relationship between age distribution at death and survival time distribution at birth we further show that for each outflow there is a survival time distribution at birth which normalized corresponds to the impulse response function for the specific outflow we also analyze how the impulse response function affects both the amplitude gain and time delay of the outflow and the long term average partitioning with regard to linear spatially extended systems we link the impulse response function to the green s function this allows us to easily compute the loss function and the age distribution for the system finally we focus on nonlinear systems to analyze the effects of storage dependent and age distribution dependent loss functions by considering the burgers equation we show how the relationships between spatial dynamics and the age distribution are complicated by nonlinearities this article is protected by copyright all rights reserved

comparative study of ecohydrological streamflow probability distributions we run a comparative study of ecohydrological models of streamflow probability distributions pdfs p q derived by botter et al 2007a 2009 against field data gathered in different hydrological contexts streamflows measured in several catchments across various climatic regions of northeastern italy and the united states are employed the relevance of the work stems from the implied analytical predictive ability of hydrologic variability whose role on stream and riparian ecological processes and large scale management schemes is fundamental the tools employed are analytical models of p q and of the related flow duration curve d q derived by coupling suitable storage discharge relations with a stochastic description of streamflow production through soil moisture dynamics and are expressed as a function of few macroscopic rainfall soil vegetation and geomorphological parameters in this work we compare the performances of a recent version of the model which includes the effects of nonlinear subsurface storage discharge relations to those provided by the linear version through the application of the models to 13 test catchments belonging to various climatic and geomorphic contexts a general agreement between predicted and observed daily streamflows pdfs is shown though differences emerge between the linear and the nonlinear approaches in particular by including the effects of a nonlinear storage discharge relation the model accuracy is shown to increase with respect to the linear scheme in most examined cases we show that this is not simply attributable to the added parameter but corresponds to a proper likelihood increase the nonlinear model is shown to exhibit three basic forms for p q monotonically decreasing with an atom of probability in q 0 bell shaped with the mode close to zero bell shaped with the mode close to the mean corresponding to different hydrologic regimes which are clearly detectable in field data inferences on the nonlinear character of the relation between subsurface storage and discharge from observed p q are finally drawn

intertime jump statistics of state dependent poisson processes a method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state dependent poisson noise is proposed such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis a model for the timing of human activities shows the capability of state dependent poisson noise to generate power law distributions the application of the method to a model for neuron dynamics and to a hydrological model accounting for land atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state dependent poisson models

design of distributed lti observers for state omniscience consider that an autonomous linear time invariant lti plant is given and that each member of a network of lti observers accesses a portion of the output of the plant the dissemination of information within the network is dictated by a pre specified directed graph in which each vertex represents an observer this paper proposes a distributed estimation scheme that is a natural generalization of consensus in which each observer computes its own state estimate of the plant using only the portion of the output vector accessible to it and the state estimates of other observers that according to the graph are available to it unlike straightforward high order solutions in which each observer broadcasts its measurements throughout the network the average dimension of the state of each observer in the proposed scheme does not exceed the order of the plant plus one we determine necessary and sufficient conditions for the existence of a parameter choice for which the proposed scheme attains asymptotic omniscience of the state of the plant at all observers the conditions reduce to certain detectability requirements that imply that if omniscience is not possible under the proposed scheme then it is not viable under any other scheme including higher order lti nonlinear and time varying ones subject to the same graph

linearized unsteady multidimensional infiltration the parameters in the linearized multidimensional unsteady equation for unsaturated flow in homogeneous soils can be chosen so that small time flow rates are given correctly with the quasi linear steady solution as the large time limit matched in this way the linearized equation offers insight into the time course of multidimensional infiltration the laplace transform reduces the equation and its governing conditions into forms similar to those for quasi linear steady flows the problems of unsteady infiltration from buried spherical and cylindrical cavities are solved in many cases the solutions are approximately reducible to the product of the steady solution and a function only of time and radial coordinate theorems show that approximate product solutions apply not only to these configurations but generally to multidimensional cavities of arbitrary shape multidimensional infiltration from finite supply surfaces involves two characteristic lengths and two characteristic times one set deriving from the capillarity gravity interaction and the other from the capillarity geometry interaction we explore the influence of the two characteristic times on the time scales of approach to steady moisture distribution near the supply surface and to steady discharge the analysis provides explanation of the relatively rapid approach to the steady state observed in three dimensional infiltration from small supply surfaces

a perturbative view on the subsurface water pressure response at hillslope scale 1 this work deals with a rearrangement of richards equation to obtain a better understanding of the components of the subsurface water and pressure flows and their interactions in a hillslope the basic idea proposed in this paper is the normalization of the spatial and temporal coordinates according to the physical knowledge of the processes and the geometry of a hillslope the pressure head and all the other quantities contained in richards equation are rescaled to obtain a dimensionless equation the pressure head is also split into an equilibrium component and a transient component and expanded in a perturbation series subsequently richards equation itself is conveniently split into two equations connected by a source sink term results of these manipulations show that for the first order approximation the water and pressure flow is slope normal while slope parallel effects only occur at successive orders integrating the perturbed equation obtained for the long term pressure head component results in the well known boussinesq equation for the water table level further integrations then lead to the hillslope storage boussinesq model and finally to a generalization of the o loughlin formula for the slope parallel long term subsurface flow the introduced source sink term is estimated at the first order of approximation to be proportional to the temporal variation of water pressure head at the bottom of the integration domain the treatment of the equations clarifies some of the mechanisms acting in water pressure redistribution at hillslope scale even without solving the equation