effect of local dispersion on solute transport in randomly heterogeneous media recently an exact eulerian lagrangian theory of advective transport in space time random velocity fields was developed by one of us we present a formal extension of this theory that accounts for anisotropic local dispersion the resultant conditional mean transport equation is generally nonlocal in space time to assess the impact of local dispersion on the prediction of transport under uncertainty we adopt a first order pseudo fickian approximation for this equation we then solve it numerically by galerkin finite elements for two dimensional transport from an instantaneous square source in a uniform unconditional mean flow field subject to isotropic local dispersion we use a higher order approximation to compute explicitly the standard deviation and coefficient of variation of the predicted concentrations our theory shows in an exact manner and our numerical results demonstrate under the above closure approximations that the effect of local dispersion on first and second concentration moments varies monotonically with the magnitude of the local dispersion coefficient when this coefficient is small relative to macrodispersion its effect on the prediction of nonreactive transport under uncertainty can for all practical purposes be disregarded this is contrary to some recent assertions in the literature that local dispersion must always be taken into account no matter how small

laplacian growth on a random lattice abstract several properties of dla and dbm clusters grown with infinite noise reduction on a recently proposed vectorizable random lattice are described the purpose of this work is twofold to see how the cluster shapes are affected when these random lattices are continuously changed into regular lattices and on the other side to study the properties of these lattices themselves for dbm growth the shapes of the clusters are continuously changed into the ordered shapes that one finds on a regular lattice dla rules on the other hand present a sharp transition at zero disorder even on infinitesimally disordered lattices will dla models give rise to random looking clusters and only for zero disorder lattices one recovers the usual needle type structures the origin of this behavior is discussed for full disorder in the lattices we analyze the statistical properties of the mass distribution of four possible growth models finding that a mild anisotropy is still present in these lattices dla with counters on sites sdla is the model which most strongly reflects this anisotropy

laplacian growth with infinite noise reduction abstract four models of laplacian growth with infinite noise reduction on a square lattice are investigated these are the four possible combinations of dla and dbm with counters on bonds or sites which we call sdla bdla sdbm and bdbm all four give rise to compact patterns with nontrivial scaling exponents which we roughly estimate while bdla and bdbm are nearly identical and sdla is very similar to both sdbm produces a different pattern resembling the effect of a finite surface tension also the scaling exponent for this case could be different from the rest

improving the accuracy of risk prediction from particle based breakthrough curves reconstructed with kernel density estimators an edited version of this paper was published by agu copyright 2015 american geophysical union

impact of sampling volume on the probability density function of steady state concentration 1 in recent years statistical theory has been used to compute the ensemble mean and variance of solute concentration in aquifer formations with second order stationary velocity fields the merit of accurately estimating the mean and variance of concentration however remains unclear without knowing the shape of the probability density function pdf in a setup where a conservative solute is continuously injected into a domain the concentration is bounded between zero and the concentration value in the injected solution at small travel distances close to the fringe of the plume an observation point may fall into the plume or outside so that the statistical concentration distribution clusters at the two limiting values obviously this results in non gaussian pdf s of concentration with increasing travel distance the lateral plume boundaries are smoothed resulting in increased probability of intermediate concentrations likewise averaging the concentration in a larger sampling volume as typically done in field measurements leads to higher probabilities of intermediate concentrations we present semianalytical results of concentration pdf s for measurements with point like or larger support volumes based on stochastic theory applied to stationary media to this end we employ a reversed auxiliary transport problem in which we use analytical expressions for first and second central spatial lateral moments with an assumed gaussian pdf for the uncertainty of the first lateral moment and gauss like shapes in individual cross sections the resulting concentration pdf can be reasonably fitted by beta distributions the results are compared to monte carlo simulations of flow and steady state transport in 3 d heterogeneous domains in both methods the shape of the concentration pdf changes with distance to the contaminant source near the source the distribution is multimodal whereas it becomes a unimodal beta distribution far away from the contaminant source the semianalytical and empirical pdf s differ slightly which we contribute to the numerical artifacts in the monte carlo simulations but also to hard assumptions made in the semianalytical approach our results imply that geostatistical techniques for interpolation and other statistical inferences based on gaussian distributions such as kriging and cokriging may be feasible only far away from the contaminant source for calculations near the source the beta like distribution of concentration should be accounted for

remarks on scaling a model of witten sander type we try to prove rigorously that the perimeter of the large witten sander cluster does not scale as the square root of its area by making a forced comparison with the ill posed hele shaw problem of fluid dynamics the attempt is not completely successful nevertheless some interesting consequences of the comparison are derived

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

the method of distributions for dispersive transport in porous media with uncertain hydraulic properties predictions of solute transport in subsurface environments are notoriously unreliable due to aquifer heterogeneity and uncertainty about the values of hydraulic parameters probabilistic framework which treats the relevant parameters and solute concentrations as random fields allows for quantification of this predictive uncertainty by providing deterministic equations for either probability density function or cumulative distribution function cdf of predicted concentrations the method of distributions enables one to estimate e g the probability of a contaminant s concentration exceeding a safe dose we derive a deterministic equation for the cdf of solute concentration which accounts for uncertainty in flow velocity and initial conditions the coefficients in this equation are expressed in terms of the mean and variance of concentration the accuracy and robustness of the cdf equations are analyzed by comparing their predictions with those obtained with monte carlo simulations and an assumed beta cdf

a review of statistical data association for motion correspondence motion correspondence is a fundamental problem in computer vision and many other disciplines this article describes statistical data association techniques originally developed in the context of target tracking and surveillance and now beginning to be used in dynamic motion analysis by the computer vision community the mahalanobis distance measure is first introduced before discussing the limitations of nearest neighbor algorithms then the track splitting joint likelihood multiple hypothesis algorithms are described each method solving an increasingly more complicated optimization real time constraints may prohibit the application of these optimal methods the suboptimal joint probabilistic data association algorithm is therefore described the advantages limitations and relationships between the approaches are discussed

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

tracking multiple particles in fluorescence time lapse microscopy images via probabilistic data association tracking subcellular structures as well as viral structures displayed as particles in fluorescence microscopy images yields quantitative information on the underlying dynamical processes we have developed an approach for tracking multiple fluorescent particles based on probabilistic data association the approach combines a localization scheme that uses a bottom up strategy based on the spot enhancing filter as well as a top down strategy based on an ellipsoidal sampling scheme that uses the gaussian probability distributions computed by a kalman filter the localization scheme yields multiple measurements that are incorporated into the kalman filter via a combined innovation where the association probabilities are interpreted as weights calculated using an image likelihood to track objects in close proximity we compute the support of each image position relative to the neighboring objects of a tracked object and use this support to recalculate the weights to cope with multiple motion models we integrated the interacting multiple model algorithm the approach has been successfully applied to synthetic 2 d and 3 d images as well as to real 2 d and 3 d microscopy images and the performance has been quantified in addition the approach was successfully applied to the 2 d and 3 d image data of the recent particle tracking challenge at the ieee international symposium on biomedical imaging isbi 2012

the coherent state method of evaluating the density matrix for an oscillator in a constant magnetic field the coherent state method is proposed for evaluating the bloch density matrix for a charged isotropic oscillator placed in a constant magnetic field the method first reduces the bloch equation satisfied by the density matrix e beta h to a partial differential equation by means of the coherent state representation and then calculates the density matrix a generalised problem in which a uniform electric field coexists is also discussed

phase transition of binary component dla diffusion limited aggregation sql square lattice system contacted with thermal bath in the perimeter to make the dla model associate with more realistic processes of crystal growth the authors construct and study a new model including the experimental variables required diffusion particles of multicomponents diffuse on the square lattice as in the dla model the aggregation perimeter contacts with a thermal bath of temperature t and the sticking probability p consists of a constant probability pc and the thermal one pt at a neighbouring site of the perimeter as p 1 alpha pc alpha pt alpha is a parameter which includes the non equilibrium equilibrium tendency of the system pt is evaluated by the thermodynamic distribution of the ising system including up to next nearest neighbour interactions and chemical potentials the system has the possibility of phase transitions they show the phase transitions aggregation patterns correlation functions fractal dimensions and so on

simple analytical results for harmonically trapped quantum gases by making use of the generating function for the associated laguerre polynomials we derive new analytical results for harmonically trapped quantum gases in arbitrary dimensions these exact expressions prove to be very numerically efficient and possess a much simpler mathematical form than those previously reported in the literature as a direct consequence of our work new summation relations for laguerre polynomials are also established

comment on reflecting and absorbing boundary conditions on the tail of the laplacian random walk in a recent letter lyklema and evertsz see ibid vol 19 p 895 900 1986 found a value of nu for the eta 1 laplacian random walk which differs from the value the authors obtained for the diffusion limited self avoiding walk dlsaw they show that this results from different boundary conditions at the ends of these chains and not from a failing in our monte carlo studies of the dlsaw

dirac equation with position dependent effective mass and solvable potentials in the schrodinger equation we study the one dimensional non hermitian imaginary potential with a real energy spectrum in the framework of the position dependent effective mass dirac equation the dirac equation is mapped into the exactly solvable schrodinger like equation endowed with position dependent effective mass that we present a new procedure to solve it the point canonical transformation in non relativistic quantum mechanics is applied as an algebraic method to obtain the mass function and then by using the obtained mass function the imaginary potential can be obtained the spinor wavefunctions for some of the obtained electrostatic potentials are given in terms of orthogonal polynomials we also obtain the relativistic bound state spectrum for each case in terms of the bound state spectrum of the solvable potentials

diffusion on a quasiperiodic chain an exact solution to the problem of diffusion on a quasiperiodic chain is provided by a decimation method involving scaling by an irrational length factor

needle crystal formation in two dimensions a simple model based on conformal mapping is constructed to simulate the two dimensional growth of needle crystals growing out regularly from a common point the resulting patterns are very similar to those which were obtained by other methods the radius of gyration exponent beta is measured and found to be in the range 0 58 0 65 independent of the number of needles n it is shown that for large patterns beta asymptotically approaches a value of 2 3 to compare the patterns with the dla aggregates the average slope alpha was measured for the density density correlation function plotted logarithmically log r to log c r the relation between alpha and beta which is characteristic of dla fractal aggregates is satisfied only in the case n 8

conditional estimation of solute travel time in heterogeneous formations impact of transmissivity measurements solute transport through heterogeneous formations is modeled by the travel time approach i e the time it takes a solute particle to travel from the source to a control plane due to uncertainty is a random variable characterized by its cumulative probability density function g this function is used by regulatory agencies in pollution site assessment the main aim of the present study is to examine the impact of data namely measured transmissivities upon g and reduction of uncertainty this is achieved for two dimensional steady flow of average uniform head gradient by using a lagrangian approach developed in the past dagan 1982 1984 1989 rubin 1990 1991 the impact of data is seen in conditioning on measured values and in estimation of parameters characterizing flow and formation properties the approach is illustrated by a simulation based on synthetic data the results show how uncertainty is reduced by increasing the density of measurements for a control plane sufficiently far from the source

supersymmetry and potentials with bound states at arbitrary energies ii for pt i see ibid vol 19 p 2297 1986 it has been shown previously that a potential v0 chi in one dimension which supports no bound states may be used as a reference potential from which by successive applications of the concept of a supersymmetric partner to a given hamiltonian it is possible to find a potential vn chi which supports any specified number n of bound states at any chosen energies ej j 1 n the reflection coefficient of vn is related to the reflection coefficient of v0 various alternative representations of the potentials constructed by this procedure are presented an illustrative example in which vn is constructed by using a sech2 chi barrier as the reference potential is discussed

laplacian growth with separately controlled noise and anisotropy conformal mapping models are used to study the competition of noise and anisotropy in laplacian growth for this purpose a family of models is introduced with the noise level and directional anisotropy controlled independently fractalization is observed in both anisotropic growth and growth with varying noise the fractal dimension is determined from the cluster size scaling with cluster area for isotropic growth d 1 7 at both high and low noise for anisotropic growth with reduced noise the dimension can be as low as d 1 5 and apparently is not universal also we study the fluctuations of particle areas and observe in agreement with previous studies that exceptionally large particles may appear during growth leading to pathologically irregular clusters this difficulty is circumvented by using an acceptance window for particle areas

piecewise stationary motion modeling and iterative smoothing to track heterogeneous particle motions in dense environments one of the major challenges in multiple particle tracking is the capture of extremely heterogeneous movements of objects in crowded scenes the presence of numerous assignment candidates in the expected range of particle motion makes the tracking ambiguous and induces false positives lowering the ambiguity by reducing the search range on the other hand is not an option as this would increase the rate of false negatives we propose here a piecewise stationary motion model pmm for the particle transport along an iterative smoother that exploits recursive tracking in multiple rounds in forward and backward temporal directions by fusing past and future information our method termed pmms can recover fast transitions from freely or confined diffusive to directed motions with linear time complexity to avoid false positives we complemented recursive tracking with a robust inline estimator of the search radius for assignment a k a gating where past and future information are exploited using only two frames at each optimization step we demonstrate the improvement of our technique on simulated data especially the impact of density variation in frame to frame displacements and motion switching probability we evaluated our technique on the 2d particle tracking challenge dataset published by chenouard et al in 2014 using high snr to focus on motion modeling challenges we show superior performance at high particle density on biological applications our algorithm allows us to quantify the extremely small percentage of motor driven movements of fluorescent particles along microtubules in a dense field of unbound diffusing particles we also show with virus imaging that our algorithm can cope with a strong reduction in recording frame rate while keeping the same performance relative to methods relying on fast sampling

matrix representation of the generators of symplectic algebras i the case of sp 4 r because of their many physical applications there has been considerable interest lately in the basis for irreducible representations irreps of symplectic groups and in the matrix elements of the generators of these groups with respect to this basis in the present paper the authors carry out this programme for the irreps in the positive discrete series of sp 4 r by building up this basis from powers of the raising generators applied to the lowest weight state by using the dyson boson realisation of the generators their matrix representation can be obtained by direct differentiation while the overlap of the states of the basis can be determined with the help of coherent states the extension of the analysis to symplectic groups of arbitrary dimension is straightforward and will be implemented explicitly for sp 6 r in a later paper

a re examination of diffusion limited aggregation with finite lifetime the authors study generalized diffusion limited aggregation with a lifetime tau a model introduced by miyazima et al 1988 their monte carlo simulations for tau 1 and for tau 2 indicate that the asymptotic behaviour is most likely to be identical for all finite values of tau their estimate for the exponent v characterizing the asymptotic regime is in strong disagreement with that found by miyazima et al

spectral and thermodynamic properties of a fibonacci quasicrystal the authors present calculations leading to the phonon density of states in a fibonacci quasicrystal with fixed end points the method is based on a selective elimination process and the results show that the system at low frequencies has the behaviour of a periodic lattice the high frequency end of the spectrum is found to have large forbidden bands and in the limit of longer chains the higher frequency modes are seen to be suppressed the density of state function has further been used to calculate the heat capacity which is found to be lower than its periodic counterpart the electronic energy has been calculated from the associated transmission coefficient and the results show that the spectrum is largely band like in contrast to the uniform scaling structure which has been reported it is also shown that in the limit the quasicrystal reduces to a periodic structure the calculations reproduce the usual results

noise reduction in eden models ii surface structure and intrinsic width for pt i see ibid vol 20 p 257 1987 the authors suggest a picture of the intrinsic surface width in eden models and show that it is a major source of corrections to scaling of the surface roughness using the multiple hit noise reduction method they can control the intrinsic width and thereby improve the scaling behaviour systematically as is demonstrated in detailed calculations on the square lattice they calculate the number of excess perimeter sites as a function of time and find that its asymptotic value decays with a power law as a function of increasing hitting number substrate effects and anisotropy become more apparent if noise reduction is applied

regular versus irregular laplacian growth multifractal spectroscopy the authors analyse the effect of tip stability on the multifractality of interfacial patterns by applying the method of noise reduction to a random laplacian growth on the square lattice while the distribution of perimeter sites over the harmonic measure is smooth in the case of random fractal objects with tip splitting separate peaks appear if the tips are stable these peaks can be identified with the subset of growth sites corresponding to the tips they demonstrate the consequences of such behaviour in the multifractal spectrum

quasiperiodicity and magnetic phase transition of a class of one dimensional aperiodic systems it has been proven that the quasiperiodicity and magnetic phase transition of a one dimensional aperiodic system depend on the characteristic values of the corresponding substitution rule by means of the principle of the argument we have developed a general method to study the properties of the characteristic equations of any substitutional sequences which relates to the study of one dimensional quasiperiodic lattices particularly a class of typical sequences which consist of k letters and is given by the substitution rule a1 a2 a2 a3 a k 1 a k a k ma k na1 k 2 3 4 and m n 1 2 3 are systematically studied

noise reduced diffusion limited deposition to investigate the role of fluctuations in diffusion limited growth the authors apply the noise reduction algorithm to the problem of two dimensional deposition on a substrate consisting of a straight line the authors consider the scaling of the height and the width of trees growing on the square lattice for the sizes studied they find two length scales characterised by different exponents depending on the noise reduction parameter m using these exponents the effective fractal dimension deff of trees is calculated and for m 1 they obtain deff approximately 1 57 the density profile in the direction of growth and the scaling properties of the lateral correlation function are also determined

multiple particle tracking in 3 d t microscopy method and application to the tracking of endocytosed quantum dots we propose a method to detect and track multiple moving biological spot like particles showing different kinds of dynamics in image sequences acquired through multidimensional fluorescence microscopy it enables the extraction and analysis of information such as number position speed movement and diffusion phases of e g endosomal particles the method consists of several stages after a detection stage performed by a three dimensional 3 d undecimated wavelet transform we compute for each detected spot several predictions of its future state in the next frame this is accomplished thanks to an interacting multiple model imm algorithm which includes several models corresponding to different biologically realistic movement types tracks are constructed thereafter by a data association algorithm based on the maximization of the likelihood of each imm the last stage consists of updating the imm filters in order to compute final estimations for the present image and to improve predictions for the next image the performances of the method are validated on synthetic image data and used to characterize the 3 d movement of endocytic vesicles containing quantum dots

noise reduction in eden models i the authors adapt the multiple hit method of noise reduction introduced earlier for diffusion limited growth to eden models a and c on the square lattice the dynamic scaling is improved considerably they obtain 0 33 or 0 015 model a for the dynamic exponent beta of surface roughening with relatively small computing effort results for model c support universality

extended supersymmetry for the bound states of the generalized hulthen potential hierarchy using the associated hypergeometric differential equation we analytically solve the bound states corresponding to a hierarchy of the radial potential v0 e r 1 e r c e r 1 e r 2 as a generalization of the hulth n potential then an analytic solution corresponding to a special case for which the parameter c is expected to be in terms of l l 1 is also derived meanwhile without introducing a superpotential and in the framework of supersymmetric quantum mechanics it is shown that these bound states can be calculated by two different algebraic methods based on these two approaches it is noted that the bound states realize an extended supersymmetry structure

concentration variance and spatial covariance in second order stationary heterogeneous conductivity fields the concentration variance and spatial covariance resulting from convective dispersive transport driven by a uniform mean flow in second order stationary conductivity fields was derived in a lagrangian framework based on a first order approximation of solute particle trajectories the approximation of the concentration co variances for large injection volumes is considerably simplified by defining the concentration at a certain location x and time t in terms of the backward solute trajectory probability distribution this is the probability that the trajectory of a fictitious microscopic and indivisible solute particle which is in a volume x centered around x at time t was at the time of solute injection t0 in the injection volume v0 the approximated concentration co variances were validated against concentration covariances derived from transport simulations in generated second order stationary conductivity fields the approximate solutions reproduced fairly well the effects of local scale dispersion and of the spatial variability of the hydraulic conductivity on the concentration co variance the effect of the spatial structure of the hydraulic conductivity field on the spatial covariance of the concentrations was investigated in order to identify parameters that can be unequivocally determined from the structure of the concentration field for a given spreading of the solute plume in the mean flow direction x11 t a given spatial correlation length of the loge transformed hydraulic conductivity in the transverse to flow direction i 2 and a given local scale dispersion dd the concentration covariance was nearly invariant and hardly influenced by the anisotropy of the covariance function e and the variance f2 of the loge transformed conductivity as a result e and f2 cannot be unequivocally determined from the spatial structure of the concentration field the concentration variance and spatial covariance in the transverse to mean flow direction are predominantly determined by the lateral component of the local scale dispersion dd22 and by the spatial correlation length of the loge transformed conductivity in the transverse to flow direction i 2 these two parameters might be unequivocally derived from the concentration co variance

monte carlo approach to dendritic growth the connection between diffusion limited aggregation and the equations of dendritic growth is critically examined a different type of monte carlo simulation is proposed and used to construct two dimensional dendrite like patterns the wavelength occurring for short times is in good agreement with the linear stability analysis the time dependence of the characteristic wavelengths is also determined

large time behavior of concentration variance and dilution in heterogeneous formations consider the advection and dispersion of a conservative nonsorbing solute in a spatially variable but statistically homogeneous velocity field a lagrangian approach leads to expressions for the large time mean and variance of concentration the expressions require only the macroscopic velocity vector um the macrodispersion tensor dm and an additional tensor the macroscopic velocities and macrodispersivities are well known from numerous previous studies but is introduced here for the first time the tensor is needed to describe the kinetics of dilution of a plume two cases with the same um anddm have different dilution characteristics depending on the characteristic times of dilution are given by tensor d 1m it is demonstrated for the first time through a lagrangian approach that the coefficient of variation of concentration at the center of the plume becomes proportionate to 1 t as was previously shown in the eulerian theory ofkapoor and gelhar 1994a b expressions for the geometric mean of the dilution index and the reactor ratio are derived numerical simulations support the validity of the approach

impact of aquifer heterogeneity structure and local scale dispersion on solute concentration uncertainty in this paper we study the influence of high log conductivity variance sigma 2 y and local scale dispersion on the first two concentration moments as well as on higher order moments skewness

path integral evaluation of the bloch density matrix for an oscillator in an electric and magnetic field the bloch density matrix for an electron in a three dimensional oscillator potential in the presence of parallel electric and magnetic fields is presented in cylindrical coordinates

monte carlo study of linear diffusion limited aggregation linear diffusion limited aggregation is studied on the square lattice the radius of gyration exponent nu 0 79 or 0 01 is estimated using the monte carlo method and a scaling analysis

reflecting and absorbing boundary conditions on the tail of the laplacian random walk the authors introduce a new version of the laplacian random walk lrw for which the tail of the trajectory acts like a hard wall for incoming diffusing particles they show how to implement these reflecting boundary conditions through the use of a modified discrete laplace equation from an exact enumeration on the square lattice they find that reflecting boundary conditions on the tail of the trajectory give rise to a denser fractal compared with the recently studied laplacian random walk with absorbing boundary conditions

equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings the two main techniques for the generation of quasiperiodic tilings de bruijn s grid method 1981 and the projection formalism are generalised a very broad class of quasiperiodic tilings is obtained in this way the two generalised methods are shown to be equivalent the standard calculation of fourier spectra is extended to the whole general class of tilings various applications are discussed

stochastic modeling of groundwater flow by unconditional and conditional probabilities 2 the solute transport the problem of solute transport in a heterogeneous formation whose transmissivity or hydraulic conductivity are subject to uncertainty is studied for two and three dimensional flows approximate closed form solutions are derived for the case of a solute pulse in an average uniform flow through a formation of unconditional stationary random transmissivity the solute concentration regarded as a random variable is determined in terms of its expectation and variance and is found to be subject to a high degree of uncertainty the uncertainty is greatly reduced if the solute input zone is large compared to the transmissivity integral scale in any case the concentration expectation does not obey a diffusion type equation in the case of two dimensional flows unless the solute body has traveled a distance larger than a few tens transmissivity integral scales this distance may be exceedingly large in many conceivable applications

dynamical systems for quasiperiodic chains and new self similar polynomials dynamical systems in sl 2 r or sl 2 c naturally appear in the transfer matrix method for quasiperiodic chains characterized by arbitrary irrational numbers we show new subdynamical systems and invariants that are related to full diagonal and off diagonal components of the transfer matrices they are analogous to formulae of chebyshev polynomials of the first and second kinds applying them to an electronic problem on the fibonacci chain we obtain sets of self similar polynomials quasiperiodic extension of the chebyshev polynomials of the first and second kinds with self similar properties two scaling factors of the self similarities coincide with ones obtained by the perturbative decimation renormalization group method

single quantum dot tracking based on perceptual grouping using minimal paths in a spatiotemporal volume semiconductor quantum dots qds are new fluorescent probes with great promise for ultrasensitive biological imaging when detected at the single molecule level qd tagged molecules can be observed and tracked in the membrane of live cells over unprecedented durations the motion of these individual molecules recorded in sequences of fluorescence images can reveal aspects of the dynamics of cellular processes that remain hidden in conventional ensemble imaging due to qd complex optical properties such as fluorescence intermittency the quantitative analysis of these sequences is however challenging and requires advanced algorithms we present here a novel approach which instead of a frame by frame analysis is based on perceptual grouping in a spatiotemporal volume by applying a detection process based on an image fluorescence model we first obtain an unstructured set of points individual molecular trajectories are then considered as minimal paths in a riemannian metric derived from the fluorescence image stack these paths are computed with a variant of the fast marching method and few parameters are required we demonstrate the ability of our algorithm to track intermittent objects both in sequences of synthetic data and in experimental measurements obtained with individual qd tagged receptors in the membrane of live neurons while developed for tracking qds this method can however be used with any fluorescent probes

eulerian lagrangian approach for modeling of flow and transport in heterogeneous geological formations this paper presents a new eulerian lagrangian method for modeling flow and transport of passive solutes in heterogeneous porous formations the physically plausible random velocity fields are generated by a geostatistical based model the ability of the method to correctly reproduce the velocity field statistics and to satisfy mass balance is tested and demonstrated for the case of two dimensional flow the method is found particularly useful in dealing with large fields where numerical fixed grid methods such as finite difference or finite elements become very demanding from a computational point of view the transport problem is solved in a lagrangian framework by the particle tracking approach which uses a suitable grid refinement to correctly handle the velocity fluctuation at any a priori defined resolution the new method is employed to compute the probability distribution functions of the concentration and travel times and to investigate the limitations of existing methods for predicting concentrations

hamiltonian structure of real monge ampere equations the variational principle for the real homogeneous monge ampere equation in two dimensions is shown to contain three arbitrary functions of four variables there exist two different specializations of this variational principle where the lagrangian is degenerate and furthermore contains an arbitrary function of two variables the hamiltonian formulation of these degenerate lagrangian systems requires the use of dirac s theory of constraints as in the case of most completely integrable systems the constraints are second class and dirac brackets directly yield the hamiltonian operators thus the real homogeneous monge ampere equation in two dimensions admits two classes of infinitely many hamiltonian operators namely a family of local as well as another family non local hamiltonian operators and symplectic 2 forms which depend on arbitrary functions of two variables the simplest non local hamiltonian operator corresponds to the kac moody algebra of vector fields and functions on the unit circle hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair in the case of real monge ampere equations with constant right hand side this compatible pair is the only pair of hamiltonian operators that survives then the complete integrability of all these real monge ampere equations follows by magri s theorem some of the remarkable properties we have obtained for the hamiltonian structure of the real homogeneous monge ampere equation in two dimensions turn out to be generic to the real homogeneous monge ampere equation and the geodesic flow for the complex homogeneous monge ampere equation in arbitrary number of dimensions hence among all integrable nonlinear evolution equations in one space and one time dimension the real homogeneous monge ampere equation is distinguished as one that retains its character as an integrable system in multiple dimensions

fractal deterministic cracks abstract cracks are grown in an elastic medium submitted to external shear by solving the full equations of motion on a two dimensional lattice one finds that deterministic fracture patterns are in general branched and can be fractal this effect is due to the competition between the direction of global stress and the local growth direction imposed by the lattice anisotropy viscoelastic effects are also discussed

fracture patterns and scaling laws abstract fracture is determined by the growth of cracks and can be described as a moving boundary problem similar to dielectric breakdown or viscous fingering the vectorial nature of the elastic medium allows however for a much larger variety of boundary conditions and growth rules than in the scalar electrostatic analogue giving rise to a number of new effects one can model this problem on a square lattice and it is found that the patterns of cracks can be fractal even without including noise due only to the interplay of anisotropy and memory the shapes of the cracks can be compared to the ones found experimentally for stress corrosion an effect that can be mimicked by a damage memory on the surface of the crack a quantity of experimental interest in the breaking characteristics force vs displacement in a model with quenched disorder and the possibility that several cracks be present in the system one finds scaling laws in the system size for the breaking characteristics just before the system breaks fully apart the distribution of local strain is multifractal this means that the volume fraction responsible for the final cracking goes to zero in the thermodynamic limit the scaling and multiscaling laws seem to be quite universal

first order based cumulative distribution function for solute concentration in heterogeneous aquifers theoretical analysis and implications for human health risk assessment quantifying the uncertainty of solute concentration in heterogeneous aquifers is an important step in both human health and ecological risk analysis the need for a probabilistic representation of transport is justified by the incomplete characterization of the subsurface we derive the one point concentration cumulative distribution function cdf while taking into account the spatial statistical structure of the hydraulic conductivity space dimensionality the injection source size the peclet number and the sampling volume at the monitoring location the cdf is application oriented and derived at first order in the log conductivity variance we illustrate how several key parameters control the shape of the concentration cdf the cdf shape is important since it reflects both uncertainty and the dilution state of the plume the transition from a bimodal to a unimodal cdf is examined and results are further supported by analyzing the concentration coefficient of variation results indicate the significance of the statistical anisotropy ratio i e the ratio between the hydraulic conductivity correlation scales in determining the cdf shape the importance of the sampling volume in the tails of the concentration cdf and a comparison between the proposed model with the cdf approach i e beta distribution are also shown finally we illustrate how the framework could be used in applications by evaluating the human health risk cdf our results are formally valid for low to moderate heterogeneous aquifers and source sizes small as compared to the hydraulic conductivity correlation length the proposed approach can serve as a benchmark tool for other methods

path integrals for potential problems with δ function perturbation the author presents several examples of potential problems with a function perturbation by means of path integrals the idea is to sum a perturbation series expansion resulting in an energy dependent green function g e the energy levels en of the perturbed problem are determined by the equation one dimensional case ig v a a en gamma where g v is the green function of the unperturbed problem gamma is the strength of the potential and a its location in r in d dimensional radial problems with a spherically shaped delta function located at r a this equation changes into ig v l a a en ad 1 where l denotes the angular momentum number

structure factor of 1d systems superlattices based on two letter substitution rules i delta bragg peaks the recent generalization to the case of arbitrary tile lengths and arbitrary scattering factors of the calculation of the structure factor of 1d substitutional systems is studied in detail this method makes a easy to find all the peaks in the diffraction spectrum of a system the well known periodic and quasiperiodic spectra with delta peaks at integer multiples of a single number and integer linear combinations of two incommensurate frequencies respectively were found to be the l 0 subsets of two more general types of spectra infinite periodic or limit periodic and infinite quasiperiodic or limit quasiperiodic characterized by rational numbers of the type m nl l 0 infinity in place of the above integers substitution rules that produce quasicrystalline quasiperiodic and infinite quasiperiodic spectra give the same type of spectrum for all values of the ratio rho rho a rho b of the two tile lengths rho a and rho b this is not the case for the other rules thus the same substitution rule such as the copper mean rule can give an infinite periodic spectrum for a single rational ratio rho rho a rho b of the two tile lengths rho a and rho b a periodic like spectrum for other rational rho and a spectrum in some aspects similar to that of a random system when rho is an irrational number on the other hand a thue morse system diffracts as a periodic crystal when p not 1 but has no non trivial delta peaks when rho 1 other thue morse like systems can have infinite periodic spectra for all rho