critical exponents for branching annihilating random walks with an even number of offspring recently takayasu and tretyakov phys rev lett 68 3060 1992 studied branching annihilating random walks baws with n 1 char21 5 offspring these models exhibit a continuous phase transition to an absorbing state for odd n the models belong to the universality class of directed percolation for even n the particle number is conserved modulo 2 and the critical behavior is not compatible with directed percolation in this article i study the baw with n 4 using time dependent simulations and finite size scaling obtaining precise estimates for various critical exponents the results are consistent with the conjecture ensuremath beta ensuremath nu mathrm ensuremath perp 1 2 ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp 7 4 ensuremath gamma 0 ensuremath delta 2 7 ensuremath eta 0 and mathrm ensuremath delta mathit h 9 2 these critical exponents characterize respectively the dependence of the order parameter ensuremath beta ensuremath nu mathrm ensuremath perp and relaxation time ensuremath nu mathrm ensuremath parallel ensuremath nu mathrm ensuremath perp on system size the growth of fluctuations ensuremath gamma close to the critical point the long time behavior of the probability of survival ensuremath delta and average number of particles ensuremath eta when starting at time zero with just two particles and finally the decay of the order parameter mathrm ensuremath delta mathit h at the critical point in the presence of an external source

exact determinants and inverses of generalized lucas skew circulant type matrices in this paper we consider generalized lucas skew circulant type matrices including the skew circulant and skew left circulant firstly we discuss the invertibility of generalized lucas skew circulant matrix and present the determinant and the inverse matrix by constructing the transformation matrices furthermore the invertibility of generalized lucas skew left circulant matrix is also discussed the determinant and the inverse matrix of generalized lucas skew left circulant matrix are obtained respectively

spatial three dimensional secondary instability of compressible boundary layer flows three dimensional linear secondary instability theory is extended for compressible and high mach number boundary layer flows the effect of a small but finite amplitude compressible tollmien schlichting wave on the growth of dimensional perturbations is investigated the focus is on principal parametric resonance responsible for the strong growth of subharmonics in a low disturbance environnement the effect of increasing number on the onset growth and shape of eigenfunctions of the subharmonics is assessed and the resulting vortical structure is examined

determinants and inverses of circulant matrices with jacobsthal and jacobsthal lucas numbers abstract let n 3 and let j n circ j 1 j 2 j n and j n circ j 0 j 1 j n 1 be the n n circulant matrices associated with the jacobsthal numbers j 1 j n and the jacobsthal lucas numbers j 0 j n 1 respectively the determinants and the inverses of j n and j n are obtained in terms of j 1 j n and j 1 j n 1 respectively

on the norms of circulant matrices with the fibonacci and lucas numbers let us define a a i j and b b i j as nxn matrices where a i j f m o d j i n and b i j l m o d j i n we find out some bounds for the a and b matrices concerned with the spectral and euclidean norms

a recursive algorithm for the inversion of matrices with circulant blocks we investigate the recursive inversion of matrices with circulant blocks matrices of this type appear in several applications of computational electromagnetics and in the numerical solution of integral equations with the boundary element method the inversion is based on the diagonalization of each circulant block by means of the discrete fourier transform and the application of a recursive algorithm for the inversion of the matrix with diagonal blocks determined by the eigenvalues of each block the efficiency of the recursive inversion is exhibited by determining its computational complexity an implementation of the algorithm in matlab is given and numerical results are presented to demonstrate the efficiency in terms of cpu time of our approach

on the inverse of circulant matrix via generalized k horadam numbers in this paper by considering the circulant matrix c n h circ h k 1 h k 2 h k n whose entries are the generalized k horadam numbers we present a new generalization to compute determinants and inverses of c n h in fact the results in here are the most general statements to obtain the inverses and determinants in such matrices having the elements of all second order sequences

on the bounds for the norms of r circulant matrices with the fibonacci and lucas numbers abstract in this paper we have found upper and lower bounds for the spectral norms of r circulant matrices in the forms a c r f 0 f 1 f n 1 b c r l 0 l 1 l n 1 and we have obtained some bounds for the spectral norms of kronecker and hadamard products of a and b matrices

asymptotics of the transition probabilities of the simple random walk on self similar graphs it is shown explicitly how self similar graphs can be obtained as blow up constructions of finite cell graphs c this yields a larger family of graphs than the graphs obtained by discretising continuous self similar fractals for a class of symmetrically self similar graphs we study the simple random walk on a cell graph c starting at a vertex v of the boundary of c it is proved that the expected number of returns to v before hitting another vertex in the boundary coincides with the resistance scaling factor using techniques from complex rational iteration and singularity analysis for green functions we compute the asymptotic behaviour of the n step transition probabilities of the simple random walk on the whole graph the results of grabner and woess for the sierpinski graph are generalised to the class of symmetrically self similar graphs and at the same time the error term of the asymptotic expression is improved finally we present a criterion for the occurrence of oscillating phenomena of the n step transition probabilities

secondary instability mechanisms in compressible axisymmetric boundary layers secondary instability mechanisms in compressible axisymmetric boundary layers are analyzed using spectrally accurate mean flow and stability codes results show that subharmonic disturbances are the most dangerous secondary disturbances in an environment with a low to moderate intensity of the primary disturbance the relation between spatial and temporal analyses of the secondary disturbance is explored at mach 1 6 along a flat plate and mach 6 8 along a cone spatial direct numerical simulations are utilized to confirm the quantitative predictions from spatial secondary instability theory

critical and oscillatory behavior of a system of smart preys and predators it is shown that a system of smart preys and predators exhibits irreversible phase transitions between a regime of prey predator coexistence and an state where predator extinction is observed within the coexistence regime the system exhibits a transition between a regime where the densities of species remain constant and another with self sustained oscillations respectively this transition is located by means of a combined treatment involving finite size scaling and fourier transforms furthermore it is shown that the transition can be rationalized in terms of the standard percolation theory the existence of an oscillatory regime in the thermodynamic limit which is in contrast to previous findings of boccara et al phys rev e 50 4531 1994 may be due to subtle differences between the studied models

random walks in fractal media a theoretical evaluation of the periodicity of the oscillations in dynamic observables in this work we address the time evolution of random walks on a special type of sierpinski carpets which we call walk similar ws by considering highly symmetric fractals symmetrically self similar graphs ssg very recently kr n and teufl 2003 trans am math soc 356 393 have developed a technique based on the fact that the random walk gives rise to an equivalent process in a similar subset the method is used in order to obtain the time scaling factor as the average passing time apt of the walker from a site in the subset to any different site in the subset for ssg the apt is independent of the starting point in the present work we generalize this technique under the less stringent symmetry conditions of the ws carpets such that the apt depends on the starting point therefore we calculate exactly the weighted apt by performing monte carlo simulations on several ws carpets we verify that plays the role of by setting the logarithmic period of the oscillatory asymptotic behaviour of dynamic observables

brownian motion on the sierpinski gasket we construct a brownian motion taking values in the sierpinski gasket a fractal subset of 2 and study its properties this is a diffusion process characterized by local isotropy and homogeneity properties we show for example that the process has a continuous symmetric transition density p t x y with respect to an appropriate hausdorff measure and obtain estimates on p t x y

non equilibrium critical behaviour on fractal lattices a simple one component surface reaction model exhibiting a critical point has been studied on deterministic fractal lattices with fractal dimension 1 df 2 results from time dependent simulations show a change in the value of the critical exponents with df two of the exponents interpolate very nicely between the values in one and two dimensions

a fast algorithm for computing the determinants of banded circulant matrices let c n be a k 1 diagonal complex circulant matrix of order n k 1 and let detc n be the determinant of c n an algorithm for computing detc n is presented with the cost of oklog 2k log 2n k 4 multiplication and an asymptotic formula for detc n is obtained moreover a result on symmetric circulant matrices with integer entries is also given using mathematica in a personal computer we give some numerical examples which illustrate that the algorithm is very efficient and the asymptotic formula is accurate enough when the order n of the circulant matrix is sufficiently large

on the determinants and inverses of circulant matrices with fibonacci and lucas numbers abstract let a n circ f 1 f 2 f n and b n circ l 1 l 2 l n be circulant matrices where f n is the fibonacci number and l n is the lucas number we prove that a n is invertible for n 2 and b n is invertible for any positive integer n afterwards the values of the determinants of matrices a n and b n can be expressed by utilizing only the fibonacci and lucas numbers in addition the inverses of matrices a n and b n are derived

extinction survival and dynamical phase transition of branching annihilating random walk we analyze statistical properties of random walkers which disappear when they meet and make offsprings by a controllable rate numerical results for one two and three dimensions and for the sierpinski gasket are assessed in view of the mean field theory predictions universality classes are found to depend on the number of offsprings in space dimension less than 3

on the oscillatory dynamical behaviour of epidemic spreading in fractal media we present numerical evidence that dynamical physical processes that develop a time dependent characteristic length and take place in fractal media exhibiting spatial discrete scale invariance dsi with fundamental scaling ratio b may become coupled to the topology of the fractal leading to the observation of time dsi the hallmark of time dsi is the observation of a log periodic modulation of the dynamic or kinetic observables which is characterized by a well defined fundamental time scaling ratio both fundamental scaling ratios are linked according to b 1 z where z is the dynamic exponent characteristic of the physical process specifically we have studied the epidemic behaviour of the contact process cp in sierpinski carpets the cp exhibits second order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility we observed that relevant dynamic observables such as the number of active sites the survival probability of the epidemics and the mean square displacement of the epidemic from the origin r2 t exhibit log periodic modulations by fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents since at criticality one has that r2 t t2 z an independent estimation of the dynamic exponent can be performed in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and

numerical investigation of the three dimensional development in boundary layer transition a numerical method for solving the complete navier stokes equations for incompressible flows is introduced that is applicable for investigating three dimensional transition phenomena in a spatially growing boundary layer results are discussed for a test case with small three dimensional disturbances for which detailed comparison to linear stability theory is possible the validity of our numerical model for investigating nonlinear transition phenomena is demonstrated by realistic spatial simulations of the experiments by kachanov and levchenko1 for a subharmonic resonance breakdown and of the experiments of klebanoff et al 2 for a fundamental resonance breakdown

series analysis of the generalized contact process abstract we study critical behavior in a one parameter family of generalized contact processes using series expansions our results show that the entire family belongs to a single universality class and permit a more accurate assessment of exponent uncertainties

critical behaviour of the irreversible phase transitions of a dimer monomer process on fractal media the dynamic critical behaviour of a dimer monomer surface reaction process the zgb model of the type 1 2 a2 b to ab is studied on two different fractals namely a sierpinski carpet and percolating clusters which have almost the same fractal dimension df equivalent to 1 89 in both surfaces the model exhibits two continuous irreversible phase transitions for the sierpinski carpet the values of the critical exponents interpolate between those of directed percolation in 1 1 and 1 2 dimensions results corresponding to percolating clusters are not conclusive enough to assign the universality class of the model

pure point spectrum of the laplacians on fractal graphs abstract we establish the pure point spectrum of the laplacians on two point self similar fractal graphs all eigenvalues have infinite multiplicity and a countable system of orthonormal eigenfunctions with compact support is complete in the corresponding hilbert space

a note on a fast breakdown free algorithm for computing the determinants and the permanents of k tridiagonal matrices k tridiagonal matrices have attracted much attention in recent years which are a generalization of tridiagonal matrices in this note a breakdown free numerical algorithm of o n is presented for computing the determinants and the permanents of k tridiagonal matrices even though the algorithm is not a symbolic algorithm it never suffers from breakdown furthermore it produces exact values when all entries of the k tridiagonal matrices are given in integer in addition the algorithm can be simplified for a general symmetric toeplitz case and it generates the kth powers of fibonacci pell and jacobsthal numbers for a certain symmetric toeplitz case

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

random walk statistics on fractal structures we consider some statistical properties of simple random walks on fractal structures viewed as networks of sites and bonds range renewal theory mean first passage time etc asymptotic behaviors are shown to be controlled by the fractal d and spectral d dimensionalities of the considered structure a simple decimation procedure giving the value of d is outlined and illustrated in the case of the sierpinski gaskets recent results for the trapping problem the self avoiding walk and the true self avoiding walk are briefly reviewed new numerical results for diffusion on percolation clusters are also presented

explicit inverse matrices of tribonacci skew circulant type matrices the determinants and inverses of tribonacci skew circulant type matrices are discussed in the paper firstly tribonacci skew circulant type matrices are defined in addition we show the invertibility of the tribonacci skew circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices by utilizing the relation between circulant and left circulant the invertibility of the tribonacci skew left circulant are also discussed finally the determinants and the inverse matrices of these matrices are given respectively

weyl s problem for the spectral distribution of laplacians on p c f self similar fractals we establish an analogue of weyl s classical theorem for the asymptotics of eigenvalues of laplacians on a finitely ramified i e p c f self similar fractalk such as for example the sierpinski gasket we consider both dirichlet and neumann boundary conditions as well as laplacians associated with bernoulli type multifractal measures onk from a physical point of view we study the density of states for diffusions or for wave propagation in fractal media more precisely let x be the number of eigenvalues less thanx then we show that x is of the order ofxds 2 asx where the spectral exponent ds is computed in terms of the geometric as well as analytic structures ofk further we give an effective condition that guarantees the existence of the limit ofx ds 2 x asx this condition is in some sense generic in addition we define in terms of the above spectral exponents and calculate explicitly the spectral dimension ofk