on the convergence of the series expansion analysis for self avoiding walks attached to a surface extensions of exact enumeration data for self avoiding walks attached to the surfaces of face centered cubic and triangular lattices are reported the convergence of the estimates for the critical points pc and exponent gamma 1 obtained by the baker hunter 1973 confluent singularity analysis is discussed and comparison made with estimates of pc from the corresponding bulk series

a numerical adaptation of self avoiding walk identities from the honeycomb to other 2d lattices recently duminil copin and smirnov proved a long standing conjecture of nienhuis that the connective constant of self avoiding walks saws on the honeycomb lattice is

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

parametric representation of 3d grain ensembles in polycrystalline microstructures as a straightforward generalization of the well known voronoi construction laguerre tessellations have long found application in the modelling analysis and simulation of polycrystalline microstructures the application of laguerre tessellations to real as opposed to computed microstructures such as those obtained by modern 3d characterization techniques like x ray microtomography or focused ion beam serial sectioning is hindered by the mathematical difficulty of determining the correct seed location and weighting factor for each of the grains in the measured volume in this paper we propose an alternative to the laguerre approach representing grain ensembles with convex cells parametrized by orthogonal regression with respect to 3d image data applying our algorithm to artificial microstructures and to microtomographic data sets of an al 5 wt cu alloy we demonstrate that the new approach represents statistical features of the underlying data like distributions of grain sizes and coordination numbers as well as or better than a recently introduced approximation method based on the laguerre tessellation furthermore our method reproduces the local arrangement of grains i e grain shapes and connectivities much more accurately the additional computational cost associated with orthogonal regression is marginal

branched polymers attached in a wedge geometry the authors use exact enumeration and monte carlo techniques to test some recent predictions by duplantier and saleur 1986 of the values of the critical exponent gamma for uniform star branched polymers in a wedge geometry in two dimensions results support their predictions the authors have also estimated the exponent v and amplitude governing the n dependence of the mean square radius of gyration and the mean square end to end branch length in some cases the branches are distinguished and have different mean lengths but the exponent v is equal to the bulk self avoiding walk value in every case

critical exponents for numbers of differently anchored polymer chains on fractal lattices with adsorbing boundaries we study the problem of polymer adsorption in a good solvent when the container of the polymer solvent system is taken to be a member of the sierpinski gasket sg family of fractals members of the sg family are enumerated by an integerb 2 b and it is assumed that one side of each sg fractal is an impenetrable adsorbing boundary we calculate the critical exponents 1 11 and s which within the self avoiding walk model saw of the polymer chain are associated with the numbers of all possible saws with one both and no ends anchored to the adsorbing impenetrable boundary respectively by applying the exact renormalization group rg method for 2 b 8 and the monte carlo renormalization group mcrg method for a sequence of fractals with 2 b 80 we obtain specific values for these exponents the obtained results show that all three critical exponents 1 11 and s in both the bulk phase and crossover region are monotonically increasing functions withb we discuss their mutual relations their relations with other critical exponents pertinent to saws on the sg fractals and their possible asymptotic behavior in the limitb when the fractal dimension of the sg fractals approaches the euclidean value 2

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

reversible simulation of irreversible computation abstract computer computations are generally irreversible while the laws of physics are reversible this mismatch is penalized by among other things generating excess thermic entropy in the computation computing performance has improved to the extent that efficiency degrades unless all algorithms are executed reversibly for example by a universal reversible simulation of irreversible computations all known reversible simulations are either space hungry or time hungry the leanest method was proposed by bennett and can be analyzed using a simple reversible pebble game the reachable reversible simulation instantaneous descriptions pebble configurations of such pebble games are characterized completely as a corollary we obtain the reversible simulation by bennett and moreover show that it is a space optimal pebble game we also introduce irreversible steps and give a theorem on the tradeoff between the number of allowed irreversible steps and the memory gain in the pebble game in this resource bounded setting the limited erasing needs to be performed at precise instants during the simulation the reversible simulation can be modified so that it is applicable also when the simulated computation time is unknown

physics like models of computation abstract reversible cellular automata are computer models that embody discrete analogues of the classical physics notions of space time locality and microscopic reversibility they are offered as a step towards models of computation that are closer to fundamental physics

crossover exponent for piecewise directed walk adsorption on sierpinski fractals we study the problem of critical adsorption of piecewise directed random walks on a boundary of fractal lattices that belong to the sierpinski gasket family by applying the exact real space renormalization group method we calculate the crossover exponent associated with the number of adsorbed steps for the complete fractal family we demonstrate that our results are very close to the results obtained for ordinary self avoiding walk and discuss the asymptotic behaviour of at the fractal to euclidean lattice crossover

fluctuation driven computing on number conserving cellular automata a number conserving cellular automaton ncca is a cellular automaton in which the states of cells are denoted by integers and the sum of all of the numbers in a configuration is conserved throughout its evolution nccas have been widely used to model physical systems that are ruled by conservation laws of mass or energy imai et al 13 showed that the local transition function of ncca can be effectively translated into the sum of a binary flow function over pairs of neighboring cells in this paper we explore the computability of nccas in which the pairwise number flows are performed at fully asynchronous timings despite the randomness that is associated with asynchronous transitions useful computation still can be accomplished efficiently in the cellular automata through the active exploitation of fluctuations 18 specifically certain numbers may flow randomly fluctuating between forward and backward directions in the cellular space as if they were subject to brownian motion because random fluctuations promise a powerful resource for searching through a computational state space the brownian like flow of the numbers allows for efficient embedding of logic circuits into our novel asynchronous ncca

emergence of universal global behavior from reversible local transitions in asynchronous systems reversible computing usually focuses on how to establish a valid equivalence between the global reversibility and local reversibility in computational systems hitherto the equivalence has been precisely developed in cellular automata combinational circuits and quantum computers but it implicitly assumes that the underlying systems are synchronously timed alternative systems include the delay insensitive di circuits and asynchronous cellular automata acas where the local operations of each component cell may be executed independently at random times despite the randomness associated with asynchronous timings equivalence between the global and local reversibility can be simply achieved in both di circuits morita 2001 and acas lee et al 2003 provided that their local operations transitions are thoroughly serialized the complete exclusion of concurrency in local behavior however will profoundly depress the parallel processing efficiency of di circuits as well as the intrinsic massive parallelism of acas this paper aims at exploring what kind of complex global behavior may arise from the concurrent operations that are invertible at local level to this end we show that di circuits composed of reversible elements can actually exhibit universal input and output behavior with the universality emerging from the concurrency in reversible local operations likewise by further embedding all circuits into the cellular space the emergence of universal global transitions from reversible local transitions can be exactly identified in an aca which due to the bijectivity of its local function has significantly lower complexity as compared to other models

two dimensional anisotropic spiral self avoiding walks two models of anisotropic spiral self avoiding random walks recently proposed by manna 1984 have been investigated by the method of exact series expansions the number of such n step walks cn appears to behave like cn approximately constant mu nnbeta exp alpha square root n where both mu which is known exactly and the constant factor are model dependent but alpha approximately 0 14 and beta approximately 0 9 appear to be model independent the mean square end to end distance exponent nu 0 855 or 0 02 for both models

critical exponents of the self avoiding walks on a family of finitely ramified fractals the authors have studied the self avoiding walks saw on a family of finitely ramified fractals the first member b 2 of the family is the two dimensional sierpinski gasket while the last member b infinity appears to be a wedge of the homogeneous triangular lattice by means of the exact renormalisation group transformations they have calculated the critical exponents alpha nu and gamma and the connectivity constant mu of saw on each member of a sequence 2 or b or 8 of the studied fractal family the obtained exact results are compared with the recent phenomenological proposals and with the results believed to be exact in the case of a homogeneous two dimensional lattice

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

general design of reversible sequential machines based on reversible logic elements this paper proposes a scheme for decomposing reversible sequential machines rsms into simple reversible logic elements rles this scheme is generalized from the previous constructions of reversible turing machines rtms using various rles lee et al 2012 in which each rtm is composed by a uniform circuit of identical rsms associated with two states each rsm s operation in the circuit however is subject to strict conditions that prevent direct extension of their constructions to more general rsms our novel scheme to the contrary imposes no condition on the operations of an rsm which may take any arbitrary number of states moreover each rsm s construction can work asynchronously without a clock signal to synchronize all rles comprising the construction

design of 1 tape 2 symbol reversible turing machines based on reversible logic elements this paper proposes a novel scheme for constructing reversible turing machines rtms via various reversible logic elements a reversible logic element is similar to a conventional reversible logic gate except that the element also carries a 1 bit memory that can store binary states the usage of internal states allows much more efficient and straightforward constructions of rtms based on reversible elements than based on reversible logic gates in particular a remarkable feature of our constructions is that they can operate asynchronously whereby the clock signal which is indispensable for synchronizing all elements as in a reversible logic circuit can possibly be removed from the construction

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

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

statistical mechanics of polymer chains grafted to adsorbing boundaries of fractal lattices embedded in three dimensional space abstract we study the adsorption problem of linear polymers immersed in a good solvent when the container of the polymer solvent system is taken to be a member of the sierpinski gasket sg family of fractals embedded in the three dimensional euclidean space members of the sg family are enumerated by an integer b 2 b and it is assumed that one side of each sg fractal is impenetrable adsorbing boundary we calculate the surface critical exponents 11 1 and s which within the self avoiding walk model saw of polymer chain are associated with the numbers of all possible saws with both one and no ends grafted to the adsorbing surface adsorbing boundary respectively by applying the exact renormalization group method for 2 b 4 we have obtained specific values for these exponents for various types of polymer conformations to extend the obtained sequences of exact values for surface critical exponents we have applied the monte carlo renormalization group method for fractals with 2 b 40 the obtained results show that all studied exponents are monotonically increasing functions of the parameter b for all possible polymer states we discuss mutual relations between the studied critical exponents and compare their values with those found for other types of lattices in order to attain a unified picture of the attacked problem

time and space bounds for reversible simulation we prove a general upper bound on the trade off between time and space that suffices for the reversible simulation of irreversible computation previously only simulations using exponential time or quadratic space were known the trade off shows for the first time that we can simultaneously achieve subexponential time and subquadratic space the boundary values are the exponential time with hardly any extra space required by the lange mckenzie tapp method and the log 3 th power time with square space required by the bennett method we also give the first general lower bound on the extra storage space required by general reversible simulation this lower bound is optimal in that it is achieved by some reversible simulations

fast methods for computing centroidal laguerre tessellations for prescribed volume fractions with applications to microstructure generation of polycrystalline materials abstract ideas from the mathematical theory of optimal transport have recently been transferred to the micromechanics of polycrystalline materials leading to fast methods for generating polycrystalline microstructures with grains of prescribed volume fraction in terms of centroidal laguerre tessellations in this work we improve the state of the art solvers for a given set of seeds and corresponding volume fractions summing to unity there is a set of laguerre weights such that the corresponding laguerre tessellation realizes the prescribed volume fractions exactly furthermore the laguerre weights are unique up to a constant and can be determined by solving a convex optimization problem however whenever the optimization algorithm encounters a weight vector leading to an empty cell the optimization problem is no longer locally strictly convex to account for the latter backtracking strategies are typically employed we show that modern gradient based optimization algorithms devoid of backtracking like the malitsky mishchenko method and the barzilai borwein scheme easily overcome the described difficulty leading to a significant speed up compared to more traditional solvers furthermore for computing centroidal laguerre tessellations of prescribed volume fraction we propose an anderson accelerated version of lloyd s algorithm and show by numerical experiments that it consistently reduces the run time we demonstrate the capabilities of our proposed methods for generating microstructures of polycrystalline materials with prescribed grain size distribution

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

asymptotic behaviour of the number of self avoiding walks on finitely ramified fractals we study self avoiding walks saws on the checkerboard cb family of fractals each member of which can be labelled by an odd integer b 3 or b infinity so that the fractal dimension df tends to the euclidean value 2 when b to infinity by applying the exact renormalization group method for b 3 5 and 7 and the monte carlo renormalization group method for a sequence of fractals with 5 or b or 81 we have calculated the critical exponent gamma associated with the total number of distinct saws it turns out that gamma being always larger than the corresponding euclidean value 43 32 increases monotonically with b in order to learn the asymptotic behaviour of gamma for large b we have applied the finite size scaling fss method based on previous exact results for wedges of the two dimensional euclidean lattices and thereby we have shown that applying the same method fss we have also demonstrated that the critical exponent nu associated with the mean squared end to end distance of saws tends to the euclidean value 3 4 from below when b to infinity the obtained results extend and in a way weld together the previous studies of saws various families of finitely ramified fractals

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

self avoiding walks attached to triangular and face centred cubic lattice surfaces extended exact enumeration data the analysis of exact enumeration data of self avoiding walks attached to the surfaces of triangular and face centred cubic lattices is consistent with gamma 1 0 718 or 0 008 136 delta pc where delta pc pc 0 0995 in three dimensions and 0 9530 or gamma 1 or 0 9548 in two dimensions where pc for the triangular lattice is assumed to lie in the range 0 240 915 or pc or 0 240 93

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

self interacting polymer chains terminally anchored to adsorbing surfaces of three dimensional fractal lattices abstract we have studied the adsorption problem of self attracting linear polymers modeled by self avoiding walks saws situated on three dimensional fractal structures exemplified by 3d sierpinski gasket sg family of fractals as containers of a poor solvent members of sg family are enumerated by an integer b b 2 and it is assumed that one side of each sg fractal is an impenetrable adsorbing surface we calculate the critical exponents 1 11 and s which are related to the numbers of all possible saws with one both and no ends anchored to the adsorbing boundary respectively by applying the exact renormalization group rg method for the first three members of the sg fractal family b 2 3 and 4 we have obtained specific values of these exponents for chain and globular polymer phase we discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase

phenomenological renormalisation of the self avoiding walk in two dimensions phenomenological renormalisation is used to calculate the exponent v and the connective constant of the self avoiding walk problem on a square lattice a transfer matrix technique is developed for the polymer problem the results indicate that flory s value v 0 75 is true in two dimensions to extremely high accuracy

tests of hyperuniversality for self avoiding walks a universal combination of amplitudes for the end to end distance of n step self avoiding walks and for the number of n step self avoiding polygons is estimated numerically for various lattices in d 2 universality of this amplitude combination is confirmed to good accuracy while in d 3 the data are consistent with universality but the error limits are rather large for finite width square lattice strips the authors calculate universal critical point correlation amplitudes by fixed fugacity monte carlo simulations in addition these amplitudes are calculated analytically either exactly or approximately by cardy s conformal mapping approach numerical values agree well with the theoretical predictions

exact enumeration results for self avoiding walks on the honeycomb lattice attached to a surface we consider self avoiding walks on the honeycomb lattice interacting with a surface with different energies associated between sites in contact with a linear boundary to the left of the origin and those in contact with the right of the boundary we numerically confirm recent exact results for the polymer adsorption transition and corresponding critical exponents with mixed ordinary and special boundary conditions the phase diagram is elucidated with the aid of some rigorous arguments

optimal polyhedral description of 3d polycrystals method and application to statistical and synchrotron x ray diffraction data a methodology is presented for optimal polyhedral description of 3d polycrystals from experimental properties this is achieved by determining by optimization appropriate attributes of the seeds of laguerre tessellations the resulting tessellations are optimal in the sense that no further improvements are possible using convex geometries the optimization of laguerre tessellation combines a new computationally efficient algorithm for updating tessellations between iterations to a generic optimization algorithm the method is applied to different types of experimental data either statistical such as grain size distributions or grain based as provided by synchrotron x ray diffraction experiments it is then shown how the tessellations can be meshed for finite element simulations the new method opens the way to more systematic and quantitative analyses of microstructural effects on properties the presented algorithms are implemented and distributed in the free open source software package neper

on two dimensional self avoiding random walks following nienhuis 1982 exact evaluation of the connective constant of the honeycomb lattice self avoiding walk model and the exact exponent values he has conjectured the author has re examined the available data on all three regular two dimensional lattices in the case of the triangular lattice the author has additionally corrected and extended the extant series the author finds support for nienhuis value gamma 111 32 for all three lattices and further finds that alpha 1 2 for all three lattices as given by nienhuis result nu 3 4 and the hyperscaling relation d nu 2 alpha the author is unable to find any consistent evidence of a correction to scaling exponent delta 1 1 cannot be ruled out

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