continuum percolation in two dimensions monte carlo tests of scaling and universality for non interacting discs detailed results are reported for the connectivity properties of a system of discs of unit radius free to be situated anywhere within a square of area 2l2 ordinary lattke percolation would correspond to the discs being situated on the vertices of a j2l x j2l lattice computer simulations are carried out for a sequence of increasing system sizes ranging from l 20 to l 1000 for each value of l a large number of realisations are generated for 25 values of the disc concentration x we calculate a variety of estimates for the threshold parameter x as well as the critical exponents p y t and v our exponent estimates are in close agreement with accepted values for ordinary lattice percolation therefore this continuum system appears to be in the same universality class as lattice percolation

variations on mobile processes the paper investigates a concurrent computation model chi calculus in which communications resemble cut eliminations for classical proofs two bisimilarities local bisimilarity and barbed bisimilarity on chi processes are studied and are shown to be congruence relations the former equivalence turns out to be strictly stronger than the latter it is shown that chi calculus is capable of modeling sequential computation in that it captures the operational semantics of call by name lambda calculus a translation from pi calculus to chi calculus is given demonstrating that practically speaking pi is a sublanguage of chi a higher order version of chi calculus is proposed and examined it combines the communication mechanism of chi calculus and the recursion mechanism of full lambda calculus and therefore extends both

structure and perimeters of percolation clusters site percolation clusters are simulated at the percolation threshold on the square lattice an algorithm for walks around each cluster is used to obtain information on its fractal geometry the fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it if the vacant perimeter sites have only nearest neighbour connectivity then the perimeter has dimension de 1 37 or 0 03 instead of that of the hull dh 1 75 the authors also measured the mass of internal dangling sites surrounded by the backbone s blobs singly and doubly connected sites the number of blobs and the average linear distance between entry into the exit from a blob

a separable kernel decomposition method for approximating the dsr continuation operator we develop a separable kernel decomposition method for approximating the double square root dsr continuation operator in one way migrations in this paper this new approach is a further development of separable approximations of the single square root ssr operator the separable approximation of the dsr operator generally involves solving a complicated nonlinear system of integral equations instead of solving this nonlinear system directly our new method consists of repeatedly applying the separable kernel technique developed for the two variable ssr operator to the multivariable dsr operator numerical experiments demonstrate the efficiency of the proposed method we illustrate the fast convergence of the obtained separable approximation we also demonstrate the capability of this novel approximation for imaging an area with geologic complexities through synthetic data

algebraic theories for name passing calculi in a theory of processes the names are atomic data items which can be exchanged and tested for identify a well known example of a calculus for name passing is the calculus where names are additionally used as communication ports we provide complete axiomatisations of late and early bisimulation equivalences in such calculi since neither of the equivalences is a congruence we also axiomatise the corresponding largest congruences we consider a few variations of the signature of the language among these a calculus of deterministic processes which is reminiscent of sequential functional programs with a conditional construct most of our axioms are shown to be independent the axiom systems differ only by a few simple axioms and reveal the similarities and the symmetries of the calculi and the equivalences

the fractal dimension of percolation cluster hulls large simulations of 2d site percolation on a square lattice provide several estimates of the fractal dimension dh of the hull or outer boundary of percolation clusters close to criticality statistical estimates based on an ensemble of more than 106 clusters with varying sizes yield dh 1 74 or 0 02 geometrical measurements of the hull two point correlation for individual clusters with more than 105 sites give dh 1 76 or 0 01 the observed scaling behaviour is the same both slightly above and below pc

the optimized expansion based low rank method for wavefield extrapolation abstractspectral methods are fast becoming an indispensable tool for wavefield extrapolation especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation however for inhomogeneous media we face difficulties in dealing with the mixed space wavenumber domain extrapolation operator efficiently to solve this problem we evaluated an optimized expansion method that can approximate this operator with a low rank variable separation representation the rank defines the number of inverse fourier transforms for each time extrapolation step and thus the lower the rank the faster the extrapolation the method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low rank representation as a result we obtain lower rank representations compared with the standard low rank method within reasonable accuracy and thus cheaper extrapola

fourier finite difference migration many existing migration schemes cannot simultaneously handle the two most important problems of migration imaging of steep dips and imaging in media with arbitrary velocity variations in all directions for example phase shift k migration is accurate for nearly all dips but it is limited to very simple velocity functions on the other hand finite difference schemes based on one way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events we propose a new hybrid migration method named fourier finite difference migration wherein the downward continuation operator is split into two downward continuation operators one operator is a phase shift operator for a chosen constant background velocity and the other operator is an optimized finite difference operator for the varying component of the velocity function if there is no variation of velocity then only a phase shift operator will be applied automatically on the other hand if there is a strong variatio

series study of random percolation in three dimensions new high density series data for the mean number percolation probability and susceptibility of finite clusters are presented for bond and site percolation on four standard three dimensional lattices a pade approximant analysis of both high and low density series makes particular use of the rather precise unbiased estimates of the percolation threshold pc obtained recently by heermann and stauffer 1981 for the simple cubic lattice for this lattice the authors obtain the biased estimate gamma 1 73 or 0 03 for the site problem and a similar estimate but with larger uncertainties for the bond problem such a value is significantly larger than earlier series estimates assuming gamma to be universal they obtain precise although biased estimates of pc for both bond and site percolation on all four lattices using the bond estimates of pc they find an overall biased estimate of beta 0 454 or 0 008 for bond percolation on all three dimensional lattices the corresponding site problem requires further study scaling estimates of other critical exponents are alpha 0 64 or 0 05 delta 4 81 or 0 14 delta 2 18 or 0 04 nu 0 88 or 0 02 and nu 0 03 or 0 03

two kinds of separable approximations for the one way wave operator le rousseau and de hoop 2001 developed a generalized screen method that generalizes the phase screen and the split step fourier methods to increase their accuracies with large and rapid lateral variations using two taylor approximations and a perturbation hypothesis this approach approximates the one way wave operator by products of functions in space variables and functions in wavenumber variables this approximation enables the inverse fourier transform with respect to wavenumbers to be independent of the space variables thus resulting in significant improvement of the computational efficiency in spite of its great success this method has low convergence and it suffers from the presence of branch points resulting from the choice of the background medium

testing equivalence for mobile processes the impact of applying the testing approach to a calculus of processes with dynamic communication topology is investigated a proof system is introduced that consists of two groups of laws those for strong observational equivalence and those needed to deal with invisible actions soundness and completeness of this proof system w r t a testing preorder are shown a fully abstract denotational model for the language is presented that takes advantage of reductions of processes to normal forms

theory of interaction abstract theory of interaction aims to provide a foundational framework for computation and interaction it proposes four fundamental principles that characterize the common features of all models of computation and interaction these principles suffice to support a model independent treatment of the two most important relationships in computer science the equality between processes and the relative expressiveness between models based on the two relationships the theory of equality the theory of expressiveness and the theory of completeness are developed

asynchronous process calculi the first and higher order paradigms we compare the first and the higher order paradigms for the representation of mobility in process calculi the prototypical calculus in the first order paradigm is the calculus here we focus on an asynchronous calculus l that may be regarded as the basis of some experimental programming languages or proposal of programming languages like pict join blue we extend l so to allow the communication of higher order values that is values that may contain processes and show that the extension does not add expressiveness the resulting higher order calculus can be compiled down into l this paper is mostly a tutorial it also contains original contributions the main one is the full abstraction proof which with respect to previous proofs is simpler and does not rely on certain non finitary features of the languages such as infinite summation another contribution is the study of optimisations of the compilation with which we are able to handle recursive types and to prove full abstraction also for strong behavioural equivalences

the efficient determination of the percolation threshold by a frontier generating walk in a gradient the frontier in gradient percolation is generated directly by a type of self avoiding random walk the existence of the gradient permits one to generate an infinite walk on a computer of finite memory from this walk the percolation threshold pc for a two dimensional lattice can be determined with apparently maximum efficiency for a naive monte carlo calculation or n 12 for a square lattice the value pc 0 592745 or 0 000002 is found for a simulation of n 2 6 1011 total steps occupied and blocked perimeter sites the power of the method is verified on the kagome site percolation case

a theory of communicating processes with value passing a semantic theory of process algebras which allows processes to communicate values is described a behavioural theory of testing is given for such processes and is modelled by an extension of acceptance trees a proof system is also given for this model and is shown to be both sound and complete finally the model is shown to be fully abstract with respect to the behavioural theory

varieties of if then else four classes of algebras are considered the algebras in each class contain functions whose behavior models a version of the if then else instruction in one version for example the algebras contain a function kappa of four arguments such that kappa x y u v u if x y and kappa x y u v v if x ne y none of the considered classes is an equational class but equational axioms are found for each class such that an equation is valid in the class if it is derivable in standard equational logic from the axioms

a symbolic semantics for the π calculus we use symbolic transition systems as a basis for providing the calculus with an alternative semantics the latter is more amenable to automatic manipulation and sheds light on the logical differences among different forms of bisimulation over algebras of name passing processes symbolic transitions have the formformula where is a boolean combination of equalities on names that has to hold for the transition to take place and is standard a calculus action on top of the symbolic transition system a symbolic bisimulation is defined that captures the standard ones finally a sound and complete proof system is introduced for symbolic bisimulation

deciding bisimulation equivalences for a class of non finite state programs traditionally many automatic program verification techniques have been applicable only to finite state programs in this paper we extend some of these techniques to a class of infinite state programs that in addition to having a finite state control component may read store and write but not perform any other computations on data such programs are data independent in the sense that their behavior does not depend on the actual data values supplied we consider the problems of deciding strong equivalence and observation equivalence defined by bisimulations as in ccs between such programs these equivalences have major applications in verification of communication protocols we present reductions of these problems to the problem of deciding strong equivalence and observation equivalence between finite state programs for which polynomial time algorithms exist the equivalence problems on data independent programs are shown to be np hard in the size of the programs

new heuristic percolation criterion for continuum systems a heuristic criterion is introduced and applied for derivation of percolation thresholds in continuum systems the criterion is comprehensive in the sense that it applies to systems with diverse bonding criteria as well as to systems with a correlated distribution of sites its usefulness is manifested by the excellent quantitative agreement between the values obtained and available monte carlo data

prestack migration by split step dsr the double square root dsr prestack migration equation though defined for depth variable velocity can be used to image media with strong velocity variations using a phase shift plus interpolation pspi or split step correction the split step method is based on applying a phase shift correction to the extrapolated wavefield a correction that attempts to compensate for the lateral velocity variations i show how to extend dsr prestack migration to lateral velocity media and exemplify the method by applying the new algorithm to the marmousi data set the split step dsr migration is very fast and offers excellent imaging results

a complexity analysis of bisimilarity for value passing processes abstract we study the complexity of deciding bisimilarity between non deterministic processes with explicit primitives for manipulating data values in particular we consider a language with value passing input output of data and parametric definitions of processes we distinguish the case in which data cannot be tested and the case in which a simple equality test over data is permitted in the first case our main result shows that the problem is pspace hard for the full calculus in the second case we first show that the problem is conp complete in the fragment with value passing and no parametric definitions we then define a compositional polynomial time translation of the full calculus to the fragment with parametric definitions but no value passing the translation preserves bisimilarity this fact establishes the decidability of the full calculus and shows that the fragment without value passing is computationally equivalent to the full calculus for the latter bisimilarity is then proved to be exp complete finally we add to our language a parallel composition operator and show that for a certain restricted syntactic format the bisimilarity problem is still decidable and exp complete

illumination a new method for studying 3d percolation fronts in a concentration gradient a new method of studying percolation fronts is introduced in situations where the concentration is not constant gradient percolation approach it consists in an efficient way of determining subsets of the percolation cluster which are exactly at the percolation threshold the method is applied to both lattice and continuum percolation in order to determine the percolation threshold in 3d more accurately two variations of this method illumination and projection seem to give a similar scaling behaviour at low gradients for the cubic lattice case leading to a new estimate for the percolation threshold pc 0 31173 or 0 00007 for continuum percolation of overlapping spheres the new estimate for the critical volume fraction is 0 291 or 0 002 and the value of the critical exponent alpha sigma for the width of the front scaled with the concentration gradient is very close to the one for the lattice case

simplified model for fractal dimension of clouds abstract projections of three dimensional random percolation clusters onto a two dimensional plane give roughly the same fractal dimension 1 3 for the perimeter versus area relation as lovejoy s observation of real clouds and cellular automata simulations of nagel and raschke

concentration gradient approach to continuum percolation in two dimensions the author has investigated percolation properties of a system of overlapping discs randomly distributed with a gradient of concentration fractal properties and critical exponents of this system appear to be identical to their counterparts on a lattice this is in agreement with the universality of critical exponents of percolation the concentration gradient approach permits a precise calculation of the percolation threshold corresponding to a critical area fraction of 0 6766 or 0 0005 he has investigated the part of the external perimeter of the percolation cluster which is accessible to discs of various sizes the fractal dimension of this accessible perimeter is found to decrease abruptly as a function of the radius of invading discs from 1 75 or 0 02 to 1 35 or 0 02

monte carlo study of invasion percolation clusters in two and three dimensions the authors consider the process of growing invasion percolation clusters from a point into an infinite medium the form considered is the simplest one in which the cluster is permitted to grow into regions it has previously surrounded it is shown that this process can yield extremely good monte carlo estimates of the percolation threshold pc for the square triangular and match square lattices they obtain pc values of 0 5925 or 0 0003 0 5000 or 0 0003 and 0 4072 or 0 0002 and for the simple cubic lattice 0 31158 or 0 00006 the errors quoted are purely statistical and represent one standard deviation two critical exponents are obtained which they suggest should be identified in terms of the fractal dimension d and gap exponent delta of ordinary percolation based on these identifications they obtain values for 1 d and 1 delta of 0 527 or 0 002 and 0 393 or 0 004 in two dimensions and 0 402 or 0 003 and 0 454 or 0 005 in three dimensions these results are consistent with known exact results and best series and monte carlo estimates suggesting that the form of invasion percolation considered is probably in the same universality class as ordinary percolation