renormalization and scaling methods for quasi static interface problems we study the temporal evolution of an interface separating two phases for its large time behavior by adapting renormalization group methods and scaling theory we consider a full two phase model in the quasi static regime and implement a renormalization procedure in order to calculate the characteristic length of a self similar system r t that is the time dependent length scale characterizing the pattern growth when the dynamical undercooling is non zero 0 we find that r t increases as t 1 where can take on values in the continuous spectrum 3 2 f or 0 the spectrum is 3 0 so that the single value of 1 is selected by the plane wave imposed by jasnow and vinals it is also shown that in almost all of these cases the capillarity length d0 arising from the surface tension 0 is not relevant for the large time behavior even though it has a crucial role at the early stage evolution of an interface the exception is 3 i e r t t 1 3 for which d0 is invariant

prefix free regular languages and pattern matching we explore the regular expression matching problem with respect to prefix freeness of the pattern we prove that a prefix free regular expression gives only a linear number of matching substrings in the size of a given text based on this observation we propose an efficient algorithm for the prefix free regular expression matching problem furthermore we suggest an algorithm to determine whether or not a given regular language is prefix free

dynamical renormalization group calculation of a two phase sharp interface model the temporal evolution of an interface separating two phases is studied using renormalization group and scaling theory and exact calculation of a sharp interface model incorporating surface tension and kinetic undercooling under conditions favoring rapid solidification the characteristic length r t varies as t 1 2 while the total surface area of the interface s t varies as t d 1 2 this complements the results of jasnow and vinals who found r t approximately t in the quasistatic regime the transition in exponents from r t approximately t to r t approximately t 1 2 as solidification proceeds from the quasistatic to the rapid solidification regime suggests a complex evolution toward a self similar late stage growth

non parametric test of ordered alternatives in incomplete blocks often in medical studies study subjects become a natural block of observations repeated over a time period some subjects miss observations thus becoming incomplete blocks of observations we are interested in testing an ordered alternative or time trend and propose a non parametric method to detect a trend in incomplete blocks our approach is to estimate the trend by the linear regression method within each block and apply the one sample wilcoxon test to the estimated linear trends the one sample wilcoxon test will be sensitive to the trend if it exists the proposed test statistic is asymptotically normal and consistent we can also estimate the overall magnitude of the linear trend and its confidence interval by a proper non parametric method by monte carlo studies we compare the performance of the proposed test against extended page and jonckheere tests published in 2000 by john wiley sons ltd

mean field diffusion limited aggregation a density model for viscous fingering phenomena we explore a universal density formalism to describe nonequilibrium growth processes specifically the immiscible viscous fingering in hele shaw cells usually referred to as the saffman taylor problem for that we develop an alternative approach to the viscous fingering phenomena whose basic concepts have been recently published in a rapid communication phys rev e 63 045305 r 2001 this approach uses the diffusion limited aggregation dla paradigm as a core we introduce a mean field dla generalization in stochastic and deterministic formulations the stochastic model a quasicontinuum dla simulates monte carlo patterns which demonstrate a striking resemblance to natural hele shaw fingers and for steady state growth regimes follow precisely the saffman taylor analytical solutions in channel and sector configurations the relevant deterministic theory a complete set of differential equations for a time development of density fields is derived from that stochastic model as a principal conclusion we prove an asymptotic equivalency of both the stochastic and deterministic mean field dla formulations to the classic saffman taylor hydrodynamics in terms of an interface evolution

the transition between quasi static and fully dynamic for interfaces abstract renormalization group and scaling theory have been used to determine the large time growth exponent for the characteristic length r t of an interface in the form r t t the exponent is different in the two cases quasi static in which the time derivative in the heat equation is suppressed and the fully dynamic system this paper examines the transition between the two regimes through an examination of the green s function for elliptic equations as a limit of the fundamental solution for parabolic equations the key interface equation can be written as a sum of two terms the elliptic c 0 and parabolic for c 0 the exponent can take on values in a continuous spectrum as c takes on finite values a unique exponent is selected from this spectrum

non deterministic approach to anisotropic growth patterns with continuously tunable morphology the fractal properties of some real snowflakes the authors demonstrate that a tunable family of patterns resembling a range of experimentally observed snowflakes is obtained from a simple but somewhat ad hoc non deterministic growth model an extension of the niemeyer pietronero wiesmann eta model in which they i use noise reduction to enable the asymptotic behaviour to become more readily apparent from simulations of reasonable size ii replace the eta model boundary conditions by the boundary conditions of the diffusion limited aggregation dla model and iii include a surface tension parameter they measure the fractal dimension of some real snowflakes and obtain quantitative agreement with certain cases of the model they conclude that the model although somewhat ad hoc gives patterns that are in both qualitative and quantitative agreement with a range of real snowflake patterns

diffusion limited aggregation near the percolation threshold abstract diffusion limited aggregation dla and dielectric breakdown db models have been used to simulate growth controlled by a laplacian field on a square lattice network a fraction near the percolation threshold c of the bonds had a high conductivity equal to 1 while the others had a low conductivity equal to r we used 10 5 r r 10 8 for db we find crossover from growth on an incipient percolation cluster with fractal dimensionality d 1 3 for small length scales to that on a uniform substrate d 1 7 for a large length scales the crossover length behaves as l r a with the crossover exponent a 0 25 the results were using a scaling theory

decidability of involution hypercodes given a finite set x of strings x is a hypercode if a string in x is not a subsequence of any other string in x we consider hypercodes for involution codes which are useful for dna strand design and define an involution hypercode we then tackle the involution hypercode decidability problem that is to determine whether or not a given language is an involution hypercode based on the hypercode properties we design a polynomial runtime algorithm for regular languages we also prove that it is decidable whether or not a context free language is an involution hypercode note that it is undecidable for some other involution codes such as involution prefix codes suffix codes and k intercodes

a distribution free rank test for ordered alternatives in randomized complete block designs abstract a distribution free rank test for detecting ordered alternatives in randomized complete block designs and repeated measures designs is proposed for four or fewer treatments the null hypothesis distribution of the statistic is well known and readily available to the user the article establishes the asymptotic normality of an appropriately standardized form of the statistic and the consistency of the test asymptotic relative efficiency comparisons are made with jonckheere s test page s l hollander s test and a normal theory competitor the authors illustrate the good intermediate sample size characteristics of the test via a monte carlo study

surface tension and dynamics of fingering patterns we study the minimal class of exact solutions of the saffman taylor problem with zero surface tension which contains the physical fixed points of the regularized nonzero surface tension problem new fixed points are found and the basin of attraction of the saffman taylor finger is determined within that class specific features of the physics of finger competition are identified and quantitatively defined which are absent in the zero surface tension case this has dramatic consequences for the long time asymptotics revealing a fundamental role of surface tension in the dynamics of the problem a multifinger extension of microscopic solvability theory is proposed to elucidate the interplay between finger widths screening and surface tension s1063 651x 98 51204 4 the displacement of a viscous fluid by a nonviscous one within the gap of a hele shaw cell 1 has been one of the most studied problems in interfacial pattern formation for several decades 2 the relative simplicity of the problem has made possible an analytical understanding of the subtle role of surface tension s in the selection of the saffmantaylor finger 3 as a prototype of the so called microscopic solvability ms scenario of pattern selection 2 more recently the increasingly interesting and controversial issue of the role of surface tension in the dynamics of fingering patterns has been raised it is known that the zero surface tension saffman taylor st problem is ill posed as an initial value problem and is plagued of finite time singularities 4 5 studies of laplacian growth with zero surface tension however have proven insightful for instance in cases with needlelike growth 6 in the case of smooth interfaces which concerns us here a rich variety of physically relevant morphologies has been found among solutions of the s50 problem which remain smooth all the time free of finite time singularities 4 7 8 given the difficulty to get analytical information from the sfi0 problem this has raised the question of what part of the physics of fingering dynamics if any is captured by those solutions within this spirit dai kadanoff and zhou explored via numerical simulation the qualitative differences of distinct classes of initial conditions 9 for the so called polelike class and for finite time the problem was concluded to be qualitatively similar with and without surface tension more recently siegel and tanveer 10 have shown that the regularized problem i e vanishingly small s may differ significantly from the idealized problem s50 in order one time and therefore smooth time evolving solutions of the s50 problem do not coincide in general with the limit of solutions of the regularized problem since evidence of this is found only for the particular case of single finger configurations the conclusion may not apply to other situations 11 furthermore from a less stringent standpoint one could seek for situations where the evolution with and without surface tension are at least qualitatively equivalent in the sense that a small quantitative difference between the two remains bounded for all time 12 further physical insight is thus still necessary to clarify the phenomenology which may be appropriately captured by the idealized problem particularly

renormalization group calculation of late stage interface dynamics the temporal evolution of an interface separating two phases is studied for its large time behavior the calculation involves adaptation of methodology known in the physics literature as renormalization group and scaling theory we consider the fully dynamic set of equations i e the sharp interface model incorporating surface tension and kinetic undercooling this extends earlier results and those of jasnow and vinals that were obtained for the quasi static regime the characteristic length r t governing the morphology of late stage growth is found to vary as t1 2 while the total surface area of the interface s t varies as t d 1 2 thus the growth exponents in this fully dynamic analysis differ from the r t sim t found for the quasi static regime by jasnow and vinals in both cases however the capillarity length arising from surface tension is irrelevant for large time behavior even though it is a crucial factor for the initial growth velocity and the linear stability of the interface

growth and form in the zero noise limit of discrete laplacian growth processes with inherent surface tension ii the triangular lattice abstract laplacian growth models that include surface tension in a lowest approximation are simulated on the triangular lattice in the deterministic zero noise limit in the absence of surface tension the zero noise clusters are needle star shaped objects with the star tips directed along the lattice axes the star tips are characterized by a needle staircase with constant step lengths independent of cluster size further back from the tip the star arms can develop side branch whiskers as an effective surface tension is introduced and increased in these models the step lengths in the staircases become shorter and the needle arms become wider depending on the details of the model tip splitting may occur as the surface tension is increased still further typically in the limit where surface tension dominates the growth becomes regular and compact the essential properties of the laplacian growth models considered here are derived algebraically by combining a stationary contour approximation with conformal mapping methods comparisons are drawn between the growth and form arising from these laplacian models on the square paper i and triangular lattices

deterministic generalized automata a generalized automaton ga is a finite automaton where the single transitions are defined on words rather than on single letters generalized automata were considered by k hashiguchi who proved that the problem of calculating the size of a minimal ga is decidable

testing ordered alternatives in the presence of incomplete data abstract in testing the null hypothesis of no treatment effects in a randomized block experiment a researcher may restrict attention to an ordered alternative and thereby increase the power of his test jonckheere and later page proposed such test statistics based on the kendall and spearman correlation coefficients motivated by notions of distance between permutations we generalize jonckheere s and page s tests to the situation in which one or more observations are missing from one or more blocks conditional on the pattern of missing observations the resulting statistics are shown to be asymptotically normal for a particular pattern of missing observations the asymptotic efficiency of the extended page test is found in many cases to be not much lower than for the standard page test

simulating hydrodynamics a pedestrian model a hele shaw cell contains two fluids seperated by an interface because the fluids are held in a narrow regions between two plates the cell can be described by a set of two dimensional hydrodynamic equations which determine the velocity fields in the fluids as well as the motion of the interface between them a discretized version of these equations can be implemented in terms of the motion of random walkers the walkers have the effect of carrying pieces of the fluid from one place to another they simulate a discrete version of the laplace equation and obey the appropriate boundary conditions for the fluid the walker hydrodynamic connection is explored in the limiting situation in which the viscosity of one of the fluids vanishes an algorithm is constructed and a few exemplary simulations are shown

flory approximant for the fractal dimension of the viscous finger pattern transient and asymptotic behaviors we present a flory type mean field theory to calculate the fractal dimension d of the radial viscous finger pattern formed by the less viscous fluid in a hele shaw cell we predict a the relation between the interfacial tension s between the two fluids and the onset of the asymptotic behavior and b the variation of the effective fractal dimension with time in the transient regime for a fixed

asymptotic behavior of viscous fingering patterns in circular geometry an examination of the scaling structure along with some extensive simulations on viscous fingering in circular geometry strongly suggest that the asymptotic patterns are compact experiments and simulations are in a transient regime that may exhibit a reasonable range where apparent fractal growth may be found arguments to connect the case of viscous fingering with that of vanishing surface tension are made

structural five fold symmetry in the fractal morphology of diffusion limited aggregates abstract the statistical self similarity of the geometry of diffusion limited aggregates and the multifractal nature of the growth probability distribution on the surface of the growing clusters are investigated using the wavelet transform this study reveals the existence of a predominant structural five fold symmetry in the internal frozen region as well as in the active outer region of the interface this observation is corroborated by a statistical analysis of the screening effects that govern diffusion limited aggregation dla growth in linear and sector shaped cells the existence of this symmetry is likely to be a clue to a hierarchichal fractal ordering we report on the discovery of fibonacci sequences in the inner extinct region of large mass off lattice dla clusters with a branching ratio which converges asymptotically to the golden mean we suggest an interpretation of the dla morphology as a quasifractal counterpart of the well ordered snowflake fractal architecture