statistical analysis of the music algorithm in the presence of modeling errors taking into account the resolution probability this paper considers the statistical performance of the music method under the condition that two closely spaced sources impinging on an array of sensors are effectively resolved i e the spectrum exhibits two peaks in the neighborhood of the true directions of arrival doa the music algorithm is known to have an infinite resolution power in theory however in the presence of modeling errors sources can not be resolved with certainty even if the array correlation matrix is perfectly known the focus of this paper is to predict the bias and variance of the doa estimates taking into account the possible resolution failure of music this performance prediction based on our recent mathematical investigation is new to the best of our knowledge a general mathematical framework to derive closed form expressions of the bias and variance versus the model mismatch conditioned on a general statistical resolution test is proposed in order to illustrate our mathematical approach statistical tests with one and two conditions respectively are investigated the accuracy of the performance prediction is illustrated in a simulation study it is found that the proposed approach outperforms the classical technique which ignores the possible resolution failure of the music algorithm therefore our results provide better tools for determining the necessary antenna calibration accuracy to achieve some targeted specifications on the estimator performance

low density series expansions for directed percolation on square and triangular lattices greatly extended series have been derived for moments of the pair connectedness for bond and site percolation on the directed square and triangular lattices the length of the various series has been at least doubled to more than 110 100 terms for the square lattice bond site problem and more than 55 terms for the bond and site problems on the triangular lattice analysis of the series leads to very accurate estimates for the critical parameters and generally seems to rule out simple rational values for the critical exponents the values of the critical exponents for the average cluster size parallel and perpendicular connectedness lengths are estimated by d 2 277 69 4 k d 1 733 825 25 and d 1 096 844 14 respectively an improved estimate for the percolation probability exponent is obtained from the scaling relation d k c 2 d 0 276 49 4 in all cases the leading correction to scaling term is analytic

operator approach to performance analysis of root music and root min norm the authors carry out a performance analysis of two eigenstructure based direction of arrival estimation algorithms using a series expansion of projection operators or projectors on the signal and noise subspaces in the interest of algebraic simplicity an operator formalism is utilized a perturbation analysis is performed on the projectors the results of which are used to determine the effect on the estimated parameters the approach makes it possible to carry out the analysis to any chosen order of expansion of the projectors by using an original recurrence formula developed for the higher order terms in the series expansion of the projectors this method is used to study the root music and root min norm algorithms and establish the superiority of root music in all cases the analysis has also resulted in insightful asymptotic expressions that describe the statistical behavior of the estimated angles and radii of the signal zeros

conformal invariance and self avoiding walks in restricted geometries the prediction of conformal invariance for the statistics of self avoiding random walks restricted to both semi infinite and wedge shaped geometries are tested by extrapolating exact enumerations close agreement is found both for the angular distribution of the end to end vector and for the dependence of the critical exponent gamma 2 on the opening angle of the wedge

direction finding with partly calibrated uniform linear arrays a new method for direction finding with partly calibrated uniform linear arrays ulas is presented it is based on the conventional estimation of signal parameters via rotational invariance techniques esprit by modeling the imperfections of the ulas as gain and phase uncertainties for a fully calibrated array it reduces to the conventional esprit algorithm moreover the direction of arrivals doas unknown gains and phases of the uncalibrated sensors can be estimated in closed form without performing a spectral search hence it is computationally very attractive the cramer rao bounds crbs of the partly calibrated ulas are also given simulation results show that the root mean squared error rmse performance of the proposed algorithm is better than the conventional methods when the number of uncalibrated sensors is large it also achieves satisfactory performance even at low signal to noise ratios snrs

non universal critical behaviour in mean field theory of inhomogeneous systems abstract we consider the layered magnetic systems with inhomogeneous inter layer couplings and study their critical properties within the framework of mean field theory we consider two kinds of distribution of the couplings i quasi periodic according to the fibonacci sequence and ii smoothly inhomogeneous in which the couplings deviate from the bulk couplings by an amount of al 2 where l measures the distance from a free surface according to analytical and accurate numerical results the critical behaviour of both the problems is non universal and the corresponding critical exponents are coupling dependent

the three dimensional ising model revisited numerically several basic universal amplitude ratios are studied afresh for three dimensional nearest neighbor ising models in revising earlier work modern estimates of the critical temperature and exponents are used in conjunction with biased inhomogeneous differential approximants to extrapolate the longest available series expansions to find the critical amplitudes c for the susceptibility 1 for the correlation length 1 a for the specific heat c t and b for the spontaneous magnetization m0 we find c c 4 95 0 15 1 1 1 960 0 01 a a 0 523 0 009 a c b 0 0581 0 0010 while a 1 3 verifies hyperuniversality to within 0 8 a method for calculating amplitude ratios which allows for corrections to scaling yields estimates for c c and 1 1 in excellent agreement with those derived from the individual amplitudes finally explicit formulae are given for the numerical evaluation of t 1 t c t and m0 t over the full temperature range from criticality to t 0 and corresponding plots and convenient near critical representations are also presented

directed percolation with a wall or edge we examine the effects of introducing a wall or edge into a directed percolation process scaling ansatze are presented for the density and survival probability of a cluster in these geometries and we make the connection to surface critical phenomena and field theory the results of previous numerical work for a wall can thus be interpreted in terms of surface exponents satisfying scaling relations generalizing those for ordinary directed percolation new exponents for edge directed percolation are also introduced they are calculated in mean field theory and measured numerically in 2c 1 dimensions

critical behaviour of the two dimensional potts model with a continuous number of states a finite size scaling analysis we investigate the critical behaviour of the two dimensional q state potts model using finite size scaling and transfer matrix methods for the continuous transition range 0 these results for continuous q were obtained from a transfer matrix constructed for a generalized whitney polynomial representing the potts models an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed

effects of surface wedge corner and mixed boundary conditions on the local critical behaviour critical exponents for the o n spin model local field near a surface an edge and a corner are calculated by means of the renormalisation group method for the special geometry where the wedge or comer is formed by mutually perpendicular d 1 dimensional walls each having von neumann special transition or dirichlet ordinary transitions boundary conditions the combined effect of two or more interacting surfaces leads to new local susceptibility exponents which are calculated to order e e 4 d the case of two or more von neumann surfaces presents some difficulty in that a double divergence arises in the first order perturbation calculation of the local susceptibilities

critical exponents near a random fractal boundary the critical behaviour of correlation functions near a boundary is modified from that in the bulk when the boundary is smooth this is known to be characterized by the surface scaling dimension we consider the case when the boundary is a random fractal specifically a self avoiding walk or the frontier of a brownian walk in two dimensions and show that the boundary scaling behaviour of the correlation function is characterized by a set of multifractal boundary exponents given exactly by conformal invariance arguments to be this result may be interpreted in terms of a scale dependent distribution of opening angles of the fractal boundary on short distance scales these are sharply peaked around similar arguments give the multifractal exponents for the case of coupling to a quenched random bulk geometry

percolation and conduction in restricted geometries the finite size scaling behaviour for percolation and conduction is studied in two dimensional triangular shaped random resistor networks at the percolation threshold the numerical simulations are performed using an efficient star triangle algorithm the percolation exponents linked to the critical behaviour at corners are in good agreement with the conformal results the conductivity exponent t is found to be independent of the shape of the system its value is very close to recent estimates for the surface and bulk conductivity exponents

multiresolution schemes for the reactive euler equations we present multiresolution mr schemes for the efficient numerical solution of the one dimensional system of the reactive euler equations which has possibly stiff source terms the original version of the method was developed by a harten 1995 comm pure appl math 48 12 1305 for homogeneous hyperbolic conservation laws by computing the cell average mr representation of the solution we obtain much information about the solution s regularity this description of smoothness is then used to reduce the number of direct flux computations as well as the expensive high order eno essentially nonoscillatory reconstruction both of which are now performed only near discontinuities thereby the numerical solution procedure becomes considerably more efficient in the present case of the reactive euler equations the average efficiency factor measured by counting the number of actual flux computations ranges from about 5 to 12 this is on the same order of and in some cases comes reasonably close to actual speed up factors obtained by code timings which were between 3 to 5 the mr overhead rate was about 10 for the eno and 36 for tvd schemes respectively the quality of the solution is shown to be the same as that of the finest grid detailed numerical and performance results are shown for up to fourth order accuracy for source terms ranging from moderate to extremely stiff

calibrating nested sensor arrays with model errors we consider the problem of direction of arrival doa estimation based on a nonuniform linear nested array which is known to provide o n 2 degrees of freedom dofs using only n sensors both subspace based and sparsity based algorithms require certain modeling assumptions e g exactly known array geometry including sensor gain and phase in practice however the actual sensor gain and phase are often perturbed from their nominal values which disrupts the existing doa estimation algorithms in this paper we investigate the self calibration problem for perturbed nested arrays proposing corresponding robust algorithms to estimate both the model errors and the doas the partial toeplitz structure of the covariance matrix is employed to estimate the gain errors and the sparse total least squares stls is used to deal with the phase error issue in addition we provide the cramer rao bound crb to analyze the robustness of the estimation performance of the proposed approaches furthermore we extend the calibration strategies to general nonuniform linear arrays numerical examples are provided to verify the effectiveness of the proposed strategies

bias analysis of the music location estimator the authors present a rigorous bias analysis of the music location estimator and they derive an accurate and concise bias expression the analysis is based on the second order taylor series expansion of the derivative of the null spectrum properties of the null spectrum and statistics of the estimated signal eigenvectors it is proven that in the derivation the remainder term in the second order taylor series can be dropped but the second order terms cannot be simulations verify that the bias expression is valid over a wide range of signal to noise ratios snrs extending down into the resolution threshold region of music although asymptotic this expression can be accurately applied to a limited number of snapshot cases the utility of the expression is shown by using it in a study of music location estimator characteristics estimate bias and standard deviation are compared for variations in snr numbers of sensors and snapshots and source correlation music resolvability and estimator performance bounds are addressed accounting for bias

the random projection method for stiff detonation capturing in this paper we present a simple and robust random projection method for underresolved numerical simulation of stiff detonation waves in chemically reacting flows this method is based on the random projection method proposed by the authors for general hyperbolic systems with stiff reaction terms w bao and s jin j comput phys 163 2000 pp 216 248 where the ignition temperature is randomized in a suitable domain it is simplified using the equations of instantaneous reaction and then extended to handle the interactions of detonations extensive numerical experiments including interaction of detonation waves and in two dimensions demonstrate the reliability and robustness of this novel method

directed percolation near a wall series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction the percolation threshold is found to be the same as that for the bulk however the values of the critical exponents for the percolation probability and mean cluster size are quite different from those for the bulk and are estimated by and respectively on the other hand the exponent characterizing the scale of the cluster size distribution is found to be unchanged by the presence of the wall the parallel connectedness length which is the scale for the cluster length distribution has an exponent which we estimate to be and is also unchanged the exponent of the mean cluster length is related to and by the scaling relation and using the above estimates yields to within the accuracy of our results we conjecture that this value of is exact and further support for the conjecture is provided by the direct series expansion estimate

critical behaviour at an edge the critical behaviour of a magnetic system with o n spin symmetry bounded by two d 1 dimensional hyperplanes meeting at an angle alpha is studied within mean field theory and in d 4 epsilon dimensions new exponents emerge for correlation functions and magnetisation and susceptibilities for spins close to the edge they can be expressed in terms of known bulk and surface exponents together with a single new edge exponent which depends however on the angle alpha this exponent is computed to first order in epsilon

on the asymptotic performance analysis of subspace doa estimation in the presence of modeling errors case of music this paper provides a new analytic expression of the bias and rms error root mean square error of the estimated direction of arrival doa in the presence of modeling errors in first order approximations of the rms error are derived which are accurate for small enough perturbations however the previously available expressions are not able to capture the behavior of the estimation algorithm into the threshold region in order to fill this gap we provide a second order performance analysis which is valid in a larger interval of modeling errors to this end it is shown that the doa estimation error for each signal source can be expressed as a ratio of hermitian forms with a stochastic vector containing the modeling error then an analytic expression for the moments of such a hermitian forms ratio is provided finally a closed form expression for the performance bias and rms error is derived simulation results indicate that the new result is accurate into the region where the algorithm breaks down

a sensitivity analysis of the music algorithm a first order analysis of the sensitivity of the music algorithm to system errors which cause differences between the array manifold used by music and the true array manifold is presented the effect of such errors on the direction of arrival estimates is investigated the ability of the music algorithm to resolve two closely spaced sources in the presence of phase and gain errors in the array elements or the receivers or errors in the element locations is analyzed a formula for computing the failure threshold of music as a function of source separation and other system parameters is derived and tested by simulation the analysis assumes that the exact covariance matrix of array element outputs is known the infinite data case

the equilibrium state method for hyperbolic conservation laws with stiff reaction terms a new fractional step method is proposed for numerical simulations of hyperbolic conservation laws with stiff source terms arising from chemically reactive flows in stiff reaction problems a well known spurious numerical phenomenon the incorrect propagation speed of discontinuities may occur in general fractional step algorithm due to the underresolved numerical solution in both space and time the basic idea of the present proposed scheme is to replace the cell average representation with a two equilibrium states reconstruction during the reaction step which allows us to obtain the correct propagation of discontinuities for stiff reaction problems in an underresolved mesh because the definition of these two equilibrium states for each transition cell is independent of its neighboring cells the proposed method can be extended to multi dimensional problems directly in addition this method is promising to deal with more complicated real world problems after being extended to multi species multi reactions system extensive numerical examples for one and two dimensional scalar and euler system demonstrate the reliability and robustness of this novel method

magnetization at corners in two dimensional ising models we investigate the corner spin magnetization of two dimensional ferromagnetic ising models in various wedge geometries results are obtained for triangular and square lattices by numerical studies on finite wedges using the star triangle transformation as well as analytic calculations using corner transfer matrices and a fermionic representation of the row to row transfer matrix the corner magnetizations vanish at the bulk critical temperature tc with an exponent c differing from the bulk exponent for isotropic systems with free edges we find that c is given simply by c 2 where is the angle at the corner for apex magnetizations of conical lattices we obtain the strikingly similar result a 4 these formulas apply equally well to anisotropic lattices if the angle is interpreted as an effective angle eff determined by the relative strengths of the interactions

performance analysis of time reversal music in this paper we study the performance of multiple signal classification music in computational time reversal tr applications the analysis builds upon classical results on first order perturbation of singular value decomposition the closed form of mean squared error mse matrix of tr music is derived for the single frequency case in both multistatic co located and non co located scenarios the proposed analysis is compared with cramer rao lower bound crlb and it is exploited for comparison of tr music when linear and nonlinear multiple scattering is present finally a numerical analysis is provided to confirm the theoretical findings

consistency and mse performance of music based doa of a single source in white noise with randomly missing data music is a popular algorithm for estimating the direction of arrival doa in array signal processing applications in this paper we analyze the performance of the music algorithm for a single source system in the presence of noisy and missing data when only a random subset of the entries in the data matrix are observed we prove consistency of the doa estimate when signal from a single source is impinging on low coherence arrays and derive an analytic expression for the mean squared error mse performance of music for the case of uniform linear arrays in the large array and relatively large sample setting our analysis is mathematically justified in both the sample rich and deficient regimes the expression for the mse is a simple function of array geometry signal to noise ratio snr the fraction of entries observed and the ratio of the number of sensors to number of snapshots we derive a phase transition threshold which separates a regime where music is consistent from a regime where music is inconsistent this threshold depends upon the snr the probability of observing entries in the data matrix and number of sensors and snapshots in a simple manner which we make explicit

critical behaviour at an edge for the saw and ising model the authors have studied the behaviour of two and three dimensional self avoiding walks confined to a wedge of wedge angle alpha series have been obtained and analysed for the angular dependent critical exponents characterising various edge susceptibilities in terms of a general scaling form for the edge free energy fe approximately t d 2 nu psi e ht y0 nu h1t y1 nu h2t y2 nu they find for the two dimensional case the following scaling indices y0 91 48 y1 3 8 y2 alpha 5 pi 8 alpha they argue that these results are exact from which follow all exponents for the bulk surface and edge problem in three dimensions the authors obtain y0 approximately 2 488 y1 0 65 or 0 02 y2 alpha alpha b pi alpha where a 0 51 or 0 04 b 0 847 or 0 017 which for y2 is precisely of the functional form given by mean field theory y2 alpha 1 2 pi 2 they argue that a 1 2 for all three dimensional o n models this simple angular dependence of y2 is different from that suggested by cardy s one loop epsilon expansion 1983 for the square lattice they have also studied the case in which the wedge is rotated through an angle of pi 4 and find that the various exponents are unchanged for the three dimensional ising model in a wedge analogy with the saw results plus mean field results in conjunction with rg and series work yield y0 approximately 2 485 y1 0 71 or 0 02 and y2 a b pi alpha with a 1 2 and b 0 79 or 0 02

critical behaviour in parabolic geometries the authors study two dimensional systems with boundary curves described by power laws using conformal mappings they obtain the correlations at the bulk critical point three different classes of behaviour are found and explained by scaling arguments which also apply to higher dimensions for an ising system of parabolic shape the behaviour of the order at the tip is also found

percolation in an edge percolation in a three dimensional lattice bounded by two free plane surfaces meeting at an angle chi is studied within a real space renormalisation scheme the edge critical behaviour at various surface and bulk transitions is analysed the author does not find evidence for a first order edge transition at higher values of alpha as has recently been observed for an ising model at an edge dependence of the edge scaling power ye on the opening angle alpha has been confirmed

branched polymers in a wedge geometry in three dimensions we investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and we show that the growth constant is equal to f where is the self avoiding walk limit thef and dependences of the corresponding critical exponent f are studied using monte carlo techniques in the casef 1 our results are compared with existing predictions obtained from series expansion and renormalization group methods we have also estimated the amplitudes for the mean square radius of gyration and the mean square end to end branch length our results for the ratio of the mean square radius of gyration of anf star to that of a linear polymer of the same degree of polymerization attached in a similar wedge and the analogous ratio for the mean square end to end branch length are consistent with these ratios being lattice independent quantities

gradient critical phenomena in the ising quantum chain we consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings in the direction of the gradient an interface region separates the ordered phase from the disordered one we develop a scaling theory for the density profiles induced by the gradient perturbation which involves a characteristic length given by the width of the interface region the scaling predictions are tested in the framework of the mean field ginzburg landau theory then we consider the ising quantum chain in a linearly varying transverse field which corresponds to the extreme anisotropic limit of a classical two dimensional ising model the quantum hamiltonian can be diagonalized exactly in the scaling limit where the eigenvalue problem is the same as for the quantum harmonic oscillator the energy density the magnetization profile and the two point correlation function are studied either analytically or by exact numerical calculations their scaling behaviour is in agreement with the predictions of the scaling theory

corner transfer matrices and corner magnetization for the ising model the authors consider the corner magnetization of an ising square lattice with free edges along a diagonal direction using some remarkable properties of the corner transfer matrix they give a unified treatment for various opening angles the calculation of the magnetization is reduced to the solution of a matrix equation in the thermodynamic limit they construct an explicit form of this equation and discuss its numerical and asymptotic solution and the results obtained thereby

fractal dimensions of confined clusters in two dimensional directed percolation the fractal structure of directed permlation clusters grown at the percolation threshold inside parabolic l e systems is shrdied in two dimensions via monte carlo simulations with a fe surface at y fcx and a dynamical exponent e surface shape is a relevant permrbation when k ilz and the fractal dimensions of the isompic clusters vary mntin nuously with k analytic expressions for these variations are obtained using a blob picture approach

single antenna power measurements based direction finding in this paper the problem of estimating direction of arrival doa of multiple uncorrelated sources from single antenna power measurements is addressed utilizing the fact that the antenna pattern is bandlimited and can be modeled as a finite sum of complex exponentials we first show that the problem can be transformed into a frequency estimation problem then we explain how the annihilating filter method can be used to solve for the doa in the noiseless case in the presence of noise we propose to use cadzow denoising that is formulated as an iterative algorithm derived from exploiting the matrix rank and linear structure properties furthermore we have also derived the cramer rao bound crb and reviewed several alternative approaches that can be used as a comparison to the proposed approach from the simulation and experimental results we demonstrate that the proposed approach significantly outperforms other approaches it is also evident from the monte carlo analysis that the proposed approach converges to the crb

performance prediction of maximum likelihood direction of arrival estimation in the presence of modeling errors this paper provides new analytic expressions for the root mean square rms error and bias of the maximum likelihood ml direction of arrival doa estimator in the presence of steering vector modeling errors previous work has provided a first order approximation of these performance measures which is valid for small modeling errors in order to take into account larger errors and provide tools for designing an experimental setup a more accurate but still easy to use performance analysis is necessary for such an investigation the doa estimation errors are expressed as a hermitian form with a stochastic vector composed of the modeling errors closed form expressions relating the bias and rms errors to the statistical moments of the modeling error are then deduced from the statistics of this hermitian form simulations are provided to illustrate the usefulness of the theoretical results

repulsion of random and self avoiding walks from excluded points and lines the authors investigate the repulsion of random walks rws and self avoiding walks saws induced by a excluding a single lattice point or b excluding all points on a half line from infinity to the origin for saws they use exact enumeration and monte carlo methods to study the asymptotic behaviour of the displacement away from the excluded set on three four and five dimensional hypercubic lattices when the saw begins one lattice site away from an excluded point along the x direction the mean displacement after n steps xn approaches a finite limit at a power law rate as n to infinity however the distribution of projected displacements exhibits a residual asymmetry in the asymptotic limit reflective of a long range influence of the excluded point this general pattern of behaviour also occurs for a purely random walk for a saw which starts one lattice spacing away from the axis of the excluded half line enumeration data suggest that the mean displacement along the axis diverges as n nu with v 3 4 in two dimensions but as nz with z approximately 0 35 in three dimensions this unexpected behaviour appears to be corroborated by constant fugacity monte carlo data however for the corresponding rw model both the solution to the diffusion equation and a heuristic argument indicate that xn diverges as n1 2 in two dimensions and as n1 2 ln n in three dimensions

finite lattice extrapolation algorithms two algorithms for sequence extrapolation due to van den broeck and schwartz 1979 and bulirsch and stoer 1964 are reviewed and critically compared applications to three state and six state quantum chains and to the 2 1 d ising model show that the algorithm of bulirsch and stoer is superior in particular if only very few finite lattice data are available

scaling dimensions and conformal anomaly in anisotropic lattice spin models the effect of anisotropic interactions on the eigenvalue spectrum of the row to row transfer matrix of critical lattice spin models is investigated it is verified that the predictions of conformal theory apply to anisotropic systems if one allows for spatial rescaling by incorporating an anisotropy factor zeta ay ax sin theta where ay and ax are lattice spacings and theta is an angle describing the anisotropy for exactly solvable models these anisotropy angles can be calculated analytically using corner transfer matrices this is done for the eight vertex model hard hexagons and interacting hard squares and it is found that theta pi u lambda 10u 3 and 5u respectively where u is the spectral parameter and lambda is the crossing parameter for each of these models the amplitude of the finite size corrections to the free energy at criticality is found to be of the form pi zeta c 6n2 where zeta is the anisotropy factor and the central charge or conformal anomaly is given by c 1 4 5 and 7 10 respectively this is an analytic result for the eight vertex model for the hard hexagon and square models the largest eigenvalues are found accurately by numerically solving their inversion identities for various anisotropies and strip widths up to n 48 finally the authors argue that the anisotropy angle for magnetic hard squares and the q state potts models is also given by theta pi u lambda so this result is quite general

numerical studies of critical percolation in three dimensions presents results of high statistics simulations of the spreading of 3d percolation close to the critical point the main results are i a more precise estimate of the spreading resp chemical distance dimension ii a novel heuristic scaling theory for percolation near surfaces and iii more precise values for critical surface and edge exponents in addition the author verifies the very precise results of ziff and stell 1988 for the percolation thresholds and studies in detail corrections to scaling the latter is made possible by simulating bond and site percolation in a number of different geometries in addition in most cases one could measure more than one observable during each simulation which provided quite severe internal consistency constraints in some cases the author found quite important deviations from scaling which are not easily described by a single power or logarithmic correction term

a short note on the counter intuitive spurious behaviors in stiff reacting flow a well known spurious numerical phenomenon may occur in solving stiff detonation problems due to the under resolved numerical solution in both space and time most people believe that decreasing numerical dissipation or stiffness will delay or eliminate the onset of spurious numerical phenomenon however several counter intuitive spurious behaviors were observed by h c yee et al 2013 10 recently and the mechanism of the generation of these strange phenomena remains an open question the goal of this short note is to give a reasonable explanation for these counter intuitive spurious behaviors existing in the detonation problems the simplified 2 i 2 system and the reactive euler equations with stiff reacting source terms and discontinuities in developing the mechanism of spurious numerical phenomenon in detonation problems we find the parameters of the intermediate state are very important because they determine whether the spurious phenomenon will happen or not furthermore these counter intuitive spurious behaviors are mainly due to the oscillation of those intermediate state parameters as the time step or grid is refined gradually these findings may help us to get a further understanding of some of the difficulties in numerical combustion and problems with stiff nonlinear source terms and discontinuities in general

self avoiding walks near an excluded line the problem of a saw starting next to an excluded line say the negative x axis is studied in two dimensions using arguments based on conformal invariance and scaling it is shown that the moments of the displacement along the x axis after n steps xn grow like x2k 1n approximately n 2k 1 v the argument can however be simplified and extended also to the case of three dimensions

critical points and intermediate phases on wedges of zd the authors examine the phase structure of self avoiding walks the ising magnet and bond percolation defined on subsets of zd d or 2 which have the geometry of wedges they prove that if the cross sectional area of the wedge diverges with its width then the high temperature critical point of any of these models defined on the wedge coincides with that of the corresponding model on the full lattice for the ising magnet and bond percolation they show that there is a non trivial low temperature critical point if the cross sectional area of the wedge diverges logarithmically with its width moreover for bond percolation they show that the low temperature critical point of a logarithmic wedge may be made arbitrarily close to that of the full lattice by taking the coefficient of the logarithm large enough corollaries to these theorems include the existence of an intermediate phase for the ising magnet and bond percolation on logarithmic wedges and the existence of a first order transition for percolation models on a subclass of these wedges

a performance analysis of subspace based methods in the presence of model errors i the music algorithm application of subspace based algorithms to narrowband direction of arrival doa estimation requires that both the array response in all directions of interest and the spatial covariance of the noise must be known in practice however neither of these quantities is known precisely depending on the degree to which they deviate from their nominal values serious performance degradation can result the performance of the music algorithm is examined for situations in which the noise covariance and array response are perturbed from their assumed values theoretical expressions for the error in the music doa estimates are derived and compared with simulations performed for several representative cases and with the appropriate cramer rao bound an optimally weighted version of music is proposed for a particular class of array errors

the random projection method for stiff multispecies detonation capturing in this paper we extend the random projection method proposed for general hyperbolic systems with stiff reaction terms for underresolved numerical simulation of stiff inviscid multispecies detonation waves the key idea in this method is to randomize the ignition temperatures in suitable domains several numerical experiments in both one and two dimensions demonstrate the reliability and robustness of this novel method

a modified fractional step method for the accurate approximation of detonation waves the numerical approximation of combustion processes may lead to numerical difficulties which are caused by different time scales of the transport part and the reactive part of the model equations here we consider a modified fractional step method that overcomes this difficulty on standard test problems and allows the use of a mesh width and time step determined by the nonreactive part without precisely resolving the very small reaction zone high resolution godunov methods are employed and the structure of the riemann solution is used to determine where burning should occur in each time step the modification is implemented in the software package clawpack numerical results for 1d and 2d detonation waves are shown including a detonation wave diffracting around a corner

self avoiding walks in wedges the authors consider the number of self avoiding walks confined to a subset zd f of the d dimensional hypercubic lattice zd such that the coordinates x1 x2 xd of each vertex in the walk satisfy x1 or 0 and 0 or xk or fk x1 for k 2 3 d they show that if fk x to infinity as x to infinity the connective constant of walks in zd f is identical to the convective constant of walks in zd they also explore conditions on fk which lead to a smaller connective constant for walks in zd f and in particular consider walks between two parallel d 1 dimensional hyperplanes finally they contrast some of these results with recent work by grimmett on percolation on subsets of the square lattice

universality of neighbour avoiding and self avoiding walks on the square lattice it is shown that within position space renormalisation group psrg theory neighbour avoiding walks naws and self avoiding walks saws on the square lattice obey the same end to end distance critical exponent nu this universality is shown by applying a recent finite lattice renormalisation transformation to ordinary and oriented naw and saw problems and then using an exact equivalence between saws on an oriented lattice and naws on its covering lattice the universality class includes several oriented walk problems

corner critical exponents from the mean field renormalisation group the previously introduced method of mean field renormalisation has provided a unified approach to bulk and surface critical behaviour the method is used for the computation of the critical exponent associated with the order parameter at corners applications to the square and triangular ising model are presented the angle dependence of the corner critical exponent is qualitatively reproduced the results for the bulk critical exponents are more accurate than in previously employed mean field renormalisation schemes

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

critical phenomena at perfect and non perfect surfaces the effect of imperfections on surface critical properties is studied for ising models with nearest neighbour ferromagnetic couplings on simple cubic lattices in particular results of monte carlo simulations for flat perfect surfaces are compared to those for flat surfaces with random weak or strong interactions between neighbouring spins in the surface layer and for surfaces with steps of monoatomic height surface critical exponents at the ordinary transition in particular are found to be robust against these perturbations

directed compact percolation near a wall ii cluster length and size for paper i see ibid vol 27 p 3743 50 1994 the mean cluster size and length for the unbiassed growth of compact clusters near a dry wall are considered in the case of the cluster size below pc an exact expression is obtained for a seed of arbitrary width and distance from the surface it is found that the critical exponent gamma 1 for any finite distance from the surface crossover to the bulk value gamma 2 as the distance from the surface tends to infinity is observed this extends an existing result for the exponent beta of the percolation probability which changes from a value of 2 in the presence of a surface to 1 in the bulk limit the value delta 3 of the scaling size exponent is unchanged by the introduction of the surface the cluster size above pc and the mean cluster length are investigated using differential approximants from which we conjecture that these functions satisfy second order differential equations accepting this conjecture gives a mean size exponent the same as below pc and a logarithmic divergence of the mean length from both sides of the critical point the latter result together with scaling theory predicts that the exponent v sub has the value 2 the same as for the bulk problem

doa estimation via manifold separation for arbitrary array structures in this paper we consider the manifold separation technique mst which stems from the wavefield modeling formalism developed for array processing mst is a method for modeling the steering vector of antenna arrays of practical interest with arbitrary 2 d or 3 d geometry it is the product of a sampling matrix dependent on the antenna array only and a vandermonde structured coefficients vector depending on the wavefield only this allows fast direction of arrival doa algorithms designed for linear arrays to be used on arrays with arbitrary configuration in real world applications the calibration measurements used to determine the sampling matrix are corrupted by noise this impairs the performance of mst based algorithms in particular we study the effect of noisy calibration measurements on subspace based doa algorithms using mst expressions describing the error in the doa estimates due to calibration noise and truncation are derived this allows predicting the performance of mst based algorithms in real world applications the analysis is verified by simulations we established a link between the optimal number of selected modes and the statistics of calibration noise we analyze the modeling error when mst is used for 1 d azimuth doa estimation

monte carlo estimates of the corner critical exponents of the three dimensional ising model the authors use monte carlo simulations to estimate for the first time the corner critical exponents for the three dimensional ising model with a free boundary condition at bulk criticality finite size dependences of the spin spin correlation functions are used to obtain bulk corner 1 75 0 2

mixed order phase transition of the contact process near multiple junctions we have studied the phase transition of the contact process near a multiple junction of m semi infinite chains by monte carlo simulations as opposed to the continuous transitions of the translationally invariant m 2 and semi infinite m 1 system the local order parameter is found to be discontinuous for m 2 furthermore the temporal correlation length diverges algebraically as the critical point is approached but with different exponents on the two sides of the transition in the active phase the estimate is compatible with the bulk value while in the inactive phase it exceeds the bulk value and increases with m the unusual local critical behavior is explained by a scaling theory with an irrelevant variable which becomes dangerous in the inactive phase quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results

ising model at an edge a position space renormalisation group approach the critical behaviour of a three dimensional ising model bounded by two plane surfaces meeting at an angle alpha is studied using the migdal kadanoff and two terminal cluster renormalisation methods the authors obtain expressions for the edge fixed point and for the independent edge exponent yhe at the various transitions they find that yhe is not completely universal but depends on the angle alpha and that it shows some unexpected features

thermal percolation for interacting monomers adsorbed on square lattices in this paper the percolation of monomers on a square lattice is studied as the particles interact with either repulsive or attractive energies by means of a finite size scaling analysis the critical exponents and the scaling collapsing of the fraction of percolating lattice are found a phase diagram separating a percolating from a non percolating region is determined the main features of the phase diagram are discussed in terms of simple considerations related to the interactions present in the problem the influence of the phase transitions occurring in the system is reflected by the phase diagram in addition a scaling treatment maintaining constant the surface coverage and varying the temperature of the system is performed in all the considered cases the universality class of the model is found to be the same as for the random percolation model

a new flux splitting scheme a new flux splitting scheme is proposed the scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of roe s solver in the euler and navier stokes solutions carried out in this study the scheme is robust and converges as fast as the roe splitting we propose an appropriately defined cell face advection mach number using values from the two straddling cells via associated characteristic speeds this interface mach number is then used to determine the upwind extrapolation for the convective quantities accordingly the name of the scheme is coined as the advection upstream splitting method ausm we also introduce a new pressure splitting which is shown to behave successfully yielding much smoother results than other existing pressure splittings of particular interest is the supersonic blunt body problem in which the roe scheme gives anomalous solutions the ausm produces correct solutions without difficulty for a wide range of flow conditions as well as grids

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones

on the expectation of the product of four matrix valued gaussian random variables the formula for the expectation of the product of four scalar real gaussian random variables is generalized to matrix valued real or complex gaussian random variables as an application of the extended formula a simple derivation is presented of the covariance matrix of instrumental variable estimates of parameters in multivariable regression models

theoretical and numerical structure for unstable one dimensional detonations the spatio temporal structure of unstable detonations in a single space dimension is studied through a combination of numerical and asymptotic methods a new high resolution numerical method for computing unstable detonations is developed this method combines the piecewise parabolic method ppm with conservative shock tracking and adaptive mesh refinement a new nonlinear asymptotic theory for the spatio temporal growth of instabilities is also developed this asymptotic theory involves a nonclassical hopf bifurcation because resonant acoustic scattering states with exponential growth in space cross the imaginary axis and become nonlinear eigenmodes in a complex free boundary problem for a nonlinear hyperbolic equation an interplay between the asymptotic theory and numerical simulation is used to elucidate the spatio temporal mechanisms of nonlinear stability near the transition boundary in particular a quantitative qualitative explanation is developed for the experimentally observed instabilities

self organized formulation of standard percolation phenomena abstract we consider standard percolation processes such as epidemic processes with or without immunization we show that their dynamics can be formulated so that they mimic self organized critical phenomena the wetting probability p needs not to be fine tuned to its critical value p c in order to arrive at criticality but it rather emerges as a singularity in some time dependent distribution on the one hand this casts doubts on the significance of self organized as opposed to ordinary criticality on the other hand it suggests very efficient algorithms where percolation problems are studied at several values of p in a single run as an example we apply such an algorithm to directed percolation in 2 1 dimensions where it allows a very precise determination of critical behavior

the random projection method for hyperbolic conservation laws with stiff reaction terms we propose a random projection method for numerical simulations of hyperbolic conservation laws with stiff source terms arising from chemically reactive flows ut f u x g u y 1 u in this problem the chemical time scales may be orders of magnitude faster than the fluid dynamical time scales making the problem numerically stiff a classic spurious numerical phenomenon the incorrect propagation speeds of discontinuities occurs in underresolved numerical solutions we introduce a random projection method for the reaction term by replacing the ignition temperature with a uniformly distributed random variable the statistical average of this method corrects the spurious shock speed as will be proved with a scalar model problem and demonstrated by a wide range of numerical examples in inviscid detonation waves in both one and two space dimensions

corner exponents in the two dimensional potts model the critical behavior at a corner in two dimensional ising and three state potts models is studied numerically on the square lattice using transfer operator techniques the local critical exponents for the magnetization and the energy density for various opening angles are deduced from finite size scaling results at the critical point for isotropic or anisotropic couplings the scaling dimensions compare quite well with the values expected from conformal invariance provided the opening angle is replaced by an effective one in anisotropic systems

anisotropic critical phenomena in parabolic geometries the directed self avoiding walk the critical behaviour of directed self avoiding walks is studied on parabolic like systems with a free boundary at x or ctalpha using a scaling argument 1 c is shown to be a marginal variable when alpha vperpendicular to v 1 2 i e on a parabola as a consequence the directed walk may display varying local exponents such a behaviour is indeed observed for restricted walks this generalizes a result of cardy 1983 showing that non universal behaviour occurs at corners for isotropic systems

on the resolution probability of music in presence of modeling errors the problem of resolving closely spaced signal sources using an antenna array remains a difficult one although several estimation methods are available in the literature when the array correlation matrix is known the resolution capability of subspace algorithms is infinitely high however in the presence of modeling errors the resolution deteriorates even for a known correlation matrix in this paper we analyze the music method by way of three different definitions of the resolution assuming gaussian circular random modeling errors we determine the corresponding expressions of the probability of source resolution versus the model mismatch a first series of simulations validates the mathematical expression of the three resolution probabilities a second series of simulations is used to select among them the tightest one to the empirical one the results are useful e g for determining the necessary antenna calibration accuracy to achieve a target performance