three dimensional free vibration of pretwisted beams a method for analyzing the free vibration of pretwisted structural members of arbitrary but uniform cross section is presented this method is based on three dimensional elasticity theory and three dimensional finite element formulation the equations of elasticity and the governing equations of motion are obtained using a rotating coordinate system that rotates along with the cross section the relationship between the fixed cartesian coordinate system and the rotating coordinate system is based on the pretwist angle rate this method can capture warping poisson effects and shear effects hamilton s principle is used to derive the equations of motion that in turn are used to obtain the natural frequencies and mode shapes results showing the relationship between the rate of pretwist and the natural frequencies of prismatic members with rectangular cross sections and different lengths are presented the results also show coupling between the two bending modes and coupling between the axial and torsional modes if the axis of rotation and the centroid of the cross section are not coincident coupling among all four basic modes and higher modes may occur this behavior is difficult or sometimes impossible to capture with simpler technical theories because the method is based on three dimensional elasticity theory it can accurately capture the behavior of long or short beams thin or thick sections arbitrary geometry and inhomogeneous laminated anisotropic materials

length of optimal path in random networks with strong disorder abstract we study the optimal distance l opt in random networks in the presence of disorder implemented by assigning random weights to the links the optimal distance between two nodes is the length of the path for which the sum of weights along the path cost is a minimum we study the case of strong disorder for which the distribution of weights is so broad that its sum along any path is dominated by the largest link weight in the path we find that in random graphs l opt scales as n 1 3 where n is the number of nodes in the network thus l opt increases dramatically compared to the known small world result for the minimum distance l min which scales as log n we also study theoretically and by simulations scale free networks characterized by a power law distribution for the number of links p k k and find that l opt scales as n 1 3 for 4 and as n 3 1 for 3 opt scales logarithmically with n

percolation critical exponents in scale free networks we study the behavior of scale free networks having connectivity distribution p k k 2l close to the percolation threshold we show that for networks with 3 l 4 known to undergo a transition at a finite threshold of dilution the critical exponents are different than the expected mean field values of regular percolation in infinite dimensions networks with 2 l 3 possess only a percolative phase nevertheless we show that in this case percolation critical exponents are well defined near the limit of extreme dilution where all sites are removed and that also then the exponents bear a strong l dependence the regular mean field values are recovered only for l 4

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

pose estimation using line based dynamic vision and inertial sensors an observer problem from a computer vision application is studied rigid body pose estimation using inertial sensors and a monocular camera is considered and it is shown how rotation estimation can be decoupled from position estimation orientation estimation is formulated as an observer problem with implicit output where the states evolve on so 3 a careful observability study reveals interesting group theoretic structures tied to the underlying system structure a locally convergent observer where the states evolve on so 3 is proposed and numerical estimates of the domain of attraction is given further it is shown that given convergent orientation estimates position estimation can be formulated as a linear implicit output problem from an applications perspective it is outlined how delayed low bandwidth visual observations and high bandwidth rate gyro measurements can provide high bandwidth estimates this is consistent with real time constraints due to the complementary characteristics of the sensors which are fused in a multirate way

equation of state for directed percolation using field theoretic renormalization group methods we calculate the equation of state for non equilibrium systems belonging to the universality class of directed percolation to second order in by introducing a parametric representation the result can be written to this order in a very simple form we use our result to obtain a universal amplitude ratio to second order in

universality classes for self avoiding walks in a strongly disordered system we study the behavior of self avoiding walks saws on square and cubic lattices in the presence of strong disorder we simulate the disorder by assigning random energy e taken from a probability distribution p e t o each site or bond of the lattice we study the strong disorder limit for an extremely broad range of energies with p e 1 e for each configuration of disorder we find by exact enumeration the optimal saw of fixed length n and fixed origin that minimizes the sum of the energies of the visited sites or bonds we find the fractal dimension of the optimal path to be d opt51 5260 10 in two dimensions 2d and d opt51 8260 08 in 3d our results imply that saws in strong disorder with fixed n are much more compact than saws in disordered media with a uniform distribution of energies optimal paths in strong disorder with fixed end toend distance r and saws on a percolation cluster our results are also consistent with the possibility that saws in strong disorder belong to the same universality class as the maximal saw on a percolation cluster at criticality for which we calculate the fractal dimension d max51 6460 02 for 2d and d max51 8760 05 for 3d values very close to the fractal dimensions of the percolation backbone in 2d and 3d

water propagation in two dimensional petroleum reservoirs abstract in the present paper we investigate the problem of water propagation in 2 dimensional 2d petroleum reservoir in which each site has the probability p of being occupied we first analyze this propagation pattern described by darcy equations by focusing on its geometrical features we find that the domain walls of this model at p p c 0 59 are schramm loewner evolution sle curves with 3 05 0 1 consistent with the ising universality class we also numerically show that the fractal dimension of these domain walls at p p c is d f 1 38 consistent with sle 3 along with this analysis we introduce a self organized critical soc model in which the water movement is modeled by a chain of topplings taking place when the water saturation exceeds the critical value we present strong indications that it coincides with the reservoir simulation described by darcy equation we further analyze the soc model and show numerically that for this model the spanning cluster probability has a maximum around p 0 65

theory of minimum spanning trees i mean field theory and strongly disordered spin glass model the minimum spanning tree mst is a combinatorial optimization problem given a connected graph with a real weight cost on each edge find the spanning tree that minimizes the sum of the total cost of the occupied edges we consider the random mst in which the edge costs are quenched independent random variables there is a strongly disordered spin glass model due to newman and stein phys rev lett 72 2286 1994 which maps precisely onto the random mst we study scaling properties of random msts using a relation between kruskal s greedy algorithm for finding the mst and bond percolation we solve the random mst problem on the bethe lattice bl with appropriate wired boundary conditions and calculate the fractal dimension d 6 of the connected components viewed as a mean field theory the result implies that on a lattice in euclidean space of dimension d there are of order w d ensuremath d large connected components of the random mst inside a window of size w and that d d c d 6 is a critical dimension this differs from the value 8 suggested by newman and stein we also critique the original argument for 8 and provide an improved scaling argument that again yields d c 6 the result implies that the strongly disordered spin glass model has many ground states for dg6 and only of order one below six the results for msts also apply on the poisson weighted infinite tree which is a mean field approach to the continuum model of msts in euclidean space and is a limit of the bl in a companion paper we develop an ensuremath epsilon 6 ensuremath d expansion for the random mst on critical percolation clusters

universal scaling behavior of directed percolation around the upper critical dimension in this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension in particular we determine numerically the order parameter its fluctuations as well as the susceptibility as a function of the control parameter and the conjugated field additionally to the universal scaling functions several universal amplitude combinations are considered we compare our results with those of a renormalization group approach

theory of minimum spanning trees ii exact graphical methods and perturbation expansion at the percolation threshold continuing the program begun by the authors in a previous paper we develop an exact low density expansion for the random minimum spanning tree mst on a finite graph and use it to develop a continuum perturbation expansion for the mst on critical percolation clusters in space dimension d the perturbation expansion is proved to be renormalizable in d 6 dimensions we consider the fractal dimension d sub p of paths on the latter mst our previous results lead us to predict that d sub p 2 for d d sub c 6 using a renormalization group approach we confirm the result for d 6 and calculate d sub p to first order in epsilon 6 d for d 6 using the connection with critical percolation with the result d sub p 2 epsilon 7 o epsilon sup 2

soc in a population model with global control abstract we study a plant population model introduced recently by wallinga oikos 74 1995 377 it is similar to the contact process simple epidemic directed percolation but instead of using an infection or recovery rate as control parameter the population size is controlled directly and globally by removing excess plants we show that the model is very closely related to directed percolation dp anomalous scaling laws appear in the limit of large populations small densities and long times these laws associated critical exponents and even some non universal parameters can be related to those of dp as in invasion percolation and in other models where the roles of control and order parameters are interchanged the critical value pc of the wetting probability p is obtained in the scaling limit as singular point in the distribution of removal rates we show that a mean field type approximation leads to a model studied by zhang et al j stat phys 58 1990 849 finally we verify the claim of wallinga that family extinction in a marginally surviving population is governed by dp scaling laws and speculate on applications to human mitochondrial dna

critical behavior of the two and three dimensional contact replication processes the two and three dimensional contact replication processes crp for monoclonal reproduction were analyzed through intensive monte carlo simulations in these models the occupation rates are equally divided among the empty nearest neighbor sites of an occupied site as the one dimensional case the two dimensional version of the model belongs to the directed percolation universality class and the critical rate defining the absorbing state transition is lambdac 1 083 20 7 however the critical exponents of the three dimensional crp are those of the four dimensional original contact process and consequently the data suggest that the crp model has a distinct upper critical dimension dc 3

transition between strong and weak disorder regimes for the optimal path abstract we study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path l opt in a disordered erd s renyi er random network and scale free sf network each link i is associated with a weight i exp ar i where r i is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder we find that for any finite a there is a crossover network size n a such that for n n a the scaling behavior of l opt is in the strong disorder regime while for n n a the scaling behavior is in the weak disorder regime we derive the scaling relation between n a and a with the help of simulations and also present an analytic derivation of the relation

optimal path in random networks with disorder a mini review abstract we review the analysis of the length of the optimal path l opt in random networks with disorder i e random weights on the links in the case of strong disorder in which the maximal weight along the path dominates the sum we find that l opt increases dramatically compared to the known small world result for the minimum distance l min for erd s renyi er networks l opt n 1 3 while for scale free sf networks with degree distribution p k k we find that l opt scales as n 3 1 for 3 4 and as n 1 3 for 4 thus for these networks the small world nature is destroyed for 2 3 our numerical results suggest that l opt scales as ln 1 n we also find numerically that for weak disorder l opt ln n for er models as well as for sf networks we also study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path l opt in er and sf networks

invasion percolation a new form of percolation theory a new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system the model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance the name invasion percolation is proposed for this new process similarities to and differences from ordinary percolation theory are discussed

technical communique observability analysis of rotation estimation by fusing inertial and line based visual information a revisit this note presents a simple approach to the observability analysis of the rotation estimation using line based dynamic vision and inertial sensors the problem was originally raised and formulated in rehbinder and ghosh 2003 pose estimation using line based dynamic vision and inertial sensors ieee transactions on automatic control 48 2 186 199 where the unobservable subgroup was derived using complex matrix manipulations by solving linear quaternion equations and using set operations we not only successfully obtain the same result but also naturally extend it for the case with linearly dependent lines the development in this note is more straightforward and gives rise to a clearer picture of the problem

optimal paths in disordered media scaling of the crossover from self similar to self affine behavior we study optimal paths in disordered energy landscapes using energy distributions of the type p mathrm log 10 e mathrm const that lead to the strong disorder limit if we truncate the distribution so that p mathrm log 10 e mathrm const only for e mathrm min l el e mathrm max and p mathrm log 10 e 0 otherwise we obtain a crossover from self similar strong disorder to self affine moderate disorder behavior at a path length mathcal l ifmmode times else texttimes fi we find that mathcal l ifmmode times else texttimes fi ensuremath propto mathrm log 10 e mathrm max e mathrm min ensuremath kappa where the exponent ensuremath kappa has the value ensuremath kappa 1 60 ifmmode pm else textpm fi 0 03 both in d 2 and d 3 we show how the crossover can be understood from the distribution of local energies on the optimal paths

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

approximation for directed percolation in d 1 1 we introduce an approximation specific to a continuous variable formulation of directed percolation which is strictly equivalent to 1 1 dimensional directed bond percolation we find that the critical exponent associated with the order parameter percolation probability is beta 1 1 square root 5 2 0 276 393 202 em leader in remarkable agreement with the best current numerical estimate beta 0 276 486 8

transport in weighted networks partition into superhighways and roads transport in weighted networks is dominated by the minimum spanning tree mst the tree connecting all nodes with the minimum total weight we find that the mst can be partitioned into two distinct components having significantly different transport properties characterized by centrality the number of times a node or link is used by transport paths one component superhighways is the infinite incipient percolation cluster for which we find that nodes or links with high centrality dominate for the other component roads which includes the remaining nodes low centrality nodes dominate we find also that the distribution of the centrality for the infinite incipient percolation cluster satisfies a power law with an exponent smaller than that for the entire mst the significance of this finding is that one can improve significantly the global transport by improving a tiny fraction of the network the superhighways

on two dimensional directed percolation extended series expansions for the mean size and the first and second moments of the pair connectedness for both bond and site percolation on the directed square and triangular lattices have been obtained analysis based on differential approximants allows the critical percolation probabilities and exponents to be estimated and as a result the critical exponents are conjectured to be gamma 41 18 nu perpendicular to 79 72 and nu sub 26 15 scaling then gives beta 199 720 alpha 299 360 and delta 1839 199

transport and percolation theory in weighted networks we study the distribution p of the equivalent conductance for erdos renyi er and scale free sf weighted resistor networks with n nodes each link has conductance geax where x is a random number taken from a uniform distribution between 0 and 1 and the parameter a represents the strength of the disorder we provide an iterative fast algorithm to obtain p and compare it with the traditional algorithm of solving kirchhoff equations we find both analytically and numerically that p for er networks exhibits two regimes i a low conductance regime for eapc where pc 1 k is the critical percolation threshold of the network and k is the average degree of the network in this regime p is independent of n and follows the power law p where 1 k a ii a high conductance regime for eapc in which we find that p has strong n dependence and scales as pf apc n 1 3 for sf networks with degree distribution pkk kminkkmax we find numerically also two regimes similar to those found for er networks

the threshold of coexistence and critical behaviour of a predator prey cellular automaton we study a probabilistic cellular automaton to describe two population biology problems the threshold of species coexistence in a predator prey system and the spreading of an epidemic in a population by carrying out mean field approximations and numerical simulations we obtain the phase boundaries thresholds related to the transition between an active state where prey and predators present a stable coexistence and a prey absorbing state the numerical estimates for the critical exponents show that the transition belongs to the directed percolation universality class in the limit where the cellular automaton maps into a model for the spreading of an epidemic with immunization we observe a crossover from directed percolation class to the dynamic percolation class patterns of growing clusters related to species coexistence and spreading of epidemic are shown and discussed

directed percolation with an absorbing boundary abstract we consider directed percolation with an absorbing boundary in 1 1 and 2 1 dimensions the distribution of cluster lifetimes and sizes depend on the boundary the new scaling exponents can be related to the exponents characterizing standard directed percolation 1 1 dimension in addition we investigate the backbone cluster and red bonds and calculate the distribution of living sites along the absorbing boundary

propagating waves and end modes in pretwisted beams abstract a method is presented for studying propagating waves and end modes in a uniformly pretwisted beam the variationally derived equations of motion are based on three dimensional elasticity and finite element modelling of the cross section this discretization procedure accommodates arbitrarily shaped cross sections of inhomogeneous anisotropic material properties that follow the pretwist rotation rate an harmonic solution form in both timetand axial co ordinate is introduced i e exp i k t resulting in a two parameter algebraic eigensystem by specifying the axial wavenumberk the eigenproblem permits real frequencies of propagating modes to be determined by specifying real frequency both real and complex axial wavenumbers can be extracted where real values pertain to propagating modes and the complex ones to edge vibrations or end modes due to pretwist the effect of extension torsion and flexural are coupled examples of homogeneous isotropic beams with rectangular and square cross sections are given to illustrate the method of analysis and the physical behavior

scaling laws and topological exponents in voronoi tessellations of intermittent point distributions voronoi tessellations of scale invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures as an example we analyse voronoi diagrams of intermittent particle distributions generated by a directed percolation process in 2 1 dimensions we observe that the average area of a cell increases much faster with the number of its neighbours than in natural cellular structures where lewis law predicts a linear behaviour we propose and numerically verify a universal scaling law that relates shape and size of the cells in scale invariant tessellations an exponent related to the topological properties of the tessellation is introduced and estimated numerically

geometry of minimum spanning trees on scale free networks abstract the minimum spanning trees on scale free graphs are shown to be scale free as well in the presence of random edge weights the probability distribution of the weights on the tree differs from regular lattices reflecting the typically short distances small world property we consider also the trees in the absence of such randomness and the ensuing massive degeneracy which is analyzed with graph theoretical arguments

scaling of optimal path lengths distribution in complex networks we study the distribution of optimal path lengths in random graphs with random weights associated with each link disorder with each link i we associate a weight i expari where ri is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder we suggest in an analogy with the average length of the optimal path that the distribution of optimal path lengths has a universal form that is controlled by the expression 1 pc a where is the optimal path length in strong disorder a and pc is the percolation threshold this relation is supported by numerical simulations for erd s renyi and scale free graphs we explain this phenomenon by showing explicitly the transition between strong disorder and weak disorder at different length scales in a single network

cluster structure near the percolation threshold derives exact relations that allow one to describe unambiguously and quantitatively the structure of clusters near the percolation threshold pc in particular the author proves the relations p dpij dp lambda ij where p is the bond density pij is the pair connectedness function and lambda ij is the average number of cutting bonds between i and j from this relation it follows that the average number of cutting bonds between two points separated by a distance of the order of the connectedness length xi diverges as mod p pc mod 1 the remaining multiply connected bonds in the percolating backbone which lump together in blobs diverge with a dimensionality dependent exponent he also shows that in the cell renormalisation group of reynolds et al 1978 1980 the thermal eigenvalue is simply related to the average number of cutting bonds in the spanning cluster he discusses a percolation model in which the blobs can be controlled by varying a parameter and study the influence on the critical exponents

absorbing state phase transitions with extremal dynamics extremal dynamics represents a path to self organized criticality in which the order parameter is tuned to a value of zero the order parameter is associated with a phase transition to an absorbing state given a process that exhibits a phase transition to an absorbing state we define an extremal absorbing process providing the link to the associated extremal nonabsorbing process stationary properties of the latter correspond to those at the absorbing state phase transition in the former studying the absorbing version of an extremal dynamics model allows to determine certain critical exponents that are not otherwise accessible in the case of the bak sneppen bs model the absorbing version is closely related to the f avalanche introduced by paczuski maslov and bak phys rev e 53 414 1996 or in spreading simulations to the bs branching process also studied by these authors the corresponding nonextremal process belongs to the directed percolation universality class we revisit the absorbing bs model obtaining refined estimates for the threshold and critical exponents in one dimension we also study an extremal version of the usual contact process using mean field theory and simulation the extremal condition slows the spread of activity and modifies the critical behavior radically defining an extremal directed percolation universality class of absorbing state phase transitions asymmetric updating is a relevant perturbation for this class even though it is irrelevant for the corresponding nonextremal class

tricritical directed percolation we consider a modification of the contact process incorporating higher order reaction terms the original contact process exhibits a non equilibrium phase transition belonging to the universality class of directed percolation the incorporated higher order reaction terms lead to a non trivial phase diagram in particular a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions the corresponding tricritical scaling behavior is analyzed in detail i e we determine the critical exponents various universal scaling functions as well as universal amplitude combinations

directed percolation series expansion for some three dimensional lattices low density series expansions have been obtained for the directed cubic lattice bond problem and the directed cubic and body centred cubic lattice site problems estimates of the critical probabilities and critical exponents gamma gamma 0 nu nu perpendicular to for these problems are obtained the exponent values are found to be consistent with the universality of directed percolation and reggeon field theory and the hyperscaling relation beta d nu perpendicular to nu gamma 2

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

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

effect of disorder strength on optimal paths in complex networks we study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path opt in a disordered erd s renyi er random network and scale free sf network each link i is associated with a weight ti expsarid where ri is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder we find that for any finitea there is a crossover network size n sad at which the transition occurs for n n sad the scaling behavior of opt is in the strong disorder regime with opt n 1 3 for er networks and for sf networks with lo 4 and opt n sl 3d sl 1d for sf networks with 3 l 4 for n n sad the scaling behavior is in the weak disorder regime with opt ln n for er networks and sf networks with l 3 in order to study the transition we propose a measure which indicates how close or far the disordered network is from the limit of strong disorder we propose a scaling ansatz for this measure and demonstrate its validity we proceed to derive the scaling relation between n sad and a we find thatn sa d a 3 for er networks and for sf networks with lo 4 and n sa d a sl 1d sl 3d for sf networks with 3 l 4

optimal paths in complex networks with correlated weights the worldwide airport network we study complex networks with weights wij associated with each link connecting node i and j the weights are chosen to be correlated with the network topology in the form found in two real world examples a the worldwide airport network and b the e coli metabolic network here wijxijkikj where ki and kj are the degrees of nodes i and j xij is a random number and represents the strength of the correlations the case 0 represents correlation between weights and degree while 0 represents anticorrelation and the case 0 reduces to the case of no correlations we study the scaling of the lengths of the optimal paths opt with the system size n in strong disorder for scale free networks for different we find two different universality classes for opt in strong disorder depending on i if 0 then for 2 the scaling law optn 1 3 where is the power law exponent of the degree distribution of scale free networks and ii if 0 then opt nopt with opt identical to its value for the uncorrelated case 0 we calculate the robustness of correlated scale free networks with different and find the networks with 0 to be the most robust networks when compared to the other values of we propose an analytical method to study percolation phenomena on networks with this kind of correlation and our numerical results suggest that for scale free networks with 0 the percolation threshold pc is finite for 3 which belongs to the same universality class as 0 we compare our simulation results with the real worldwide airport network and we find good agreement

quaternions further contributions to a matrix oriented approach abstract by representing quaternions as four dimensional vectors and the multiplication of quaternions as matrix by vector product we employ a matrix oriented approach to the topic we investigate properties of the fundamental real matrix associated with a quaternion and examine a frequently considered quaternion equation from which the n th power of a quaternion can be determined

dynamic exponents of a probabilistic three state cellular automaton abstract in this work a three state cellular automaton proposed to describe part of a biological immune system is revisited we obtain the dynamic critical exponent z of the model by means of a recent technique that mixes different initial conditions moreover by using two distinct approaches we have also calculated the global persistence exponent g related to the probability that the order parameter of the model does not change its sign up to time t p t t g

input power to waveguides calculated by a finite element method this paper considers the power injected into waveguide structures from forces that are concentrated along the waveguide but are otherwise arbitrary the motion of the structure is described by a set of coupled linear one dimensional wave equations these equations are in this work devised by the waveguide finite element method which is a versatile tool for describing wave motion in general structures that have uniform properties along one direction two separate procedures are derived the first is based on spatial and frequency averaging of a modal solution the second procedure is based on a spatial fourier transform which by nature assumes the waveguide to be infinite it is shown that in the limit of zero damping the two methods are identical subsequently input power to a stiffener in a railway car structure is calculated and compared with an in situ measurement showing a fair agreement

theoretical studies of self organized criticality these notes are intended to provide a pedagogical introduction to the abelian sandpile model of self organized criticality and its related models the abelian group the algebra of particle addition operators the burning test for recurrent states equivalence to the spanning trees problem are described the exact solution of the directed version of the model in any dimension is explained the model s equivalence to scheidegger s model of river basins takayasu s aggregation model and the voter model is discussed for the undirected case the solution for one dimensional lattices and the bethe lattice is briefly described known results about the two dimensional case are summarized generalization to the abelian distributed processors model is discussed time dependent properties and the universality of critical behavior in sandpiles are briefly discussed i conclude by listing some still unsolved problems

effect of quenched disorder on moving interfaces in two dimensions abstract we consider the morphology and dynamics of an interface driven through a random two dimensional medium by an applied force the onset of motion is a critical phenomenon with mean velocity v c above the threshold force c fluctuations in the velocity exhibit a power law noise spectrum at large length scales the moving interfaces are self affine with roughness exponent 0 5 there is a crossover to different scaling behavior below the correlation length c v the type of scaling at small lengths depends upon the nature and strength of the disorder two examples are considered a magnetic domain wall model exhibiting self similar structure characteristic of percolation and a fluid invasion model which produces self affine scaling

crossover from isotropic to directed percolation we generalize the directed percolation dp model by relaxing the strict directionality of dp such that propagation can occur in either direction but with anisotropic probabilities we denote the probabilities as p p pd and p p 1 pd with p representing the average occupation probability and pd controlling the anisotropy the leath alexandrowicz method is used to grow a cluster from an active seed site we call this model with two main growth directions biased directed percolation bdp standard isotropic percolation ip and dp are the two limiting cases of the bdp model corresponding to pd 1 2 and pd 0 1 respectively in this work besides ip and dp we also consider the 1 2 pd 1 region extensive monte carlo simulations are carried out on the square and the simple cubic lattices and the numerical data are analyzed by finite size scaling we locate the percolation thresholds of the bdp model for pd 0 6 and 0 8 and determine various critical exponents these exponents are found to be consistent with those for standard dp we also determine the renormalization exponent associated with the asymmetric perturbation due to pd 1 2 6 0 near ip and confirm that such an asymmetric scaling field is relevant at ip