damage detection from changes in curvature mode shapes abstract a damage in a structure alters its dynamic characteristics the change is characterized by changes in the eigenparameters i e natural frequency damping values and the mode shapes associated with each natural frequency considerable effort has been spent in obtaining a relationship between the changes in eigenparameters the damage location and the damage size most of the emphasis has been on using the changes in the natural frequencies and the damping values to determine the location and the size of the damage in this paper a new parameter called curvature mode shape is investigated as a possible candidate for identifying and locating damage in a structure by using a cantilever and a simply supported analytical beam model it is shown here that the absolute changes in the curvature mode shapes are localized in the region of damage and hence can be used to detect damage in a structure the changes in the curvature mode shapes increase with increasing size of damage this information can be used to obtain the amount of damage in the structure finite element analysis was used to obtain the displacement mode shapes of the two models by using a central difference approximation curvature mode shapes were then calculated from the displacement mode shapes

long route to consensus two stage coarsening in a binary choice voting model formation of consensus in binary yes no type of voting is a well defined process however even in presence of clear incentives the dynamics involved can be incredibly complex specifically formations of large groups of similarly opinionated individuals could create a condition of support bubbles or spontaneous polarization that renders consensus virtually unattainable e g the question of the uk exiting the eu there have been earlier attempts in capturing the dynamics of consensus formation in societies through simple z 2 symmetric models hoping to capture the essential dynamics of average behavior of a large number of individuals in a statistical sense however in absence of external noise they tend to reach a frozen state with fragmented and polarized states i e two or more groups of similarly opinionated groups with frozen dynamics here we show in a kinetic exchange opinion model considered on l l square lattices that while such frozen states could be avoided an exponentially slow approach to consensus is manifested specifically the system could either reach consensus in a time that scales as l 2 or a long lived metastable state termed a domain wall state for which formation of consensus takes a time scaling as l 3 6 the latter behavior is comparable to some voterlike models with intermediate states studied previously the late time anomaly in the timescale is reflected in the persistence probability of the model finally the interval of zero crossing of the average opinion i e the time interval over which the average opinion does not change sign is shown to follow a scale free distribution which is compared with that seen in the opinion surveys regarding brexit and associated issues since the late 1970s the issue of minority spreading is also addressed by calculating the exit probability

pair approximation for the noisy threshold q voter model in the standard q voter model a given agent can change its opinion only if there is a full consensus of the opposite opinion within a group of influence of size q a more realistic extension is the threshold q voter where a minimal agreement at least 0 q 0 q opposite opinions is sufficient to flip the central agent s opinion including also the possibility of independent nonconformist choices variants of this model including nonconformist behavior have been previously studied in fully connected networks mean field limit here we investigate its dynamics in random networks particularly while in the mean field case it is irrelevant whether repetitions in the influence group are allowed we show that this is not the case in networks and we study the impact of both cases with or without repetition furthermore the results of computer simulations are compared with the predictions of the pair approximation derived for uncorrelated networks of arbitrary degree distributions

langevin approach for the dynamics of the contact process on annealed scale free networks we study the dynamics of the contact process one of the simplest nonequilibrium stochastic processes taking place on a scale free network we consider the network topology as annealed i e all links are rewired at each microscopic time step so that no dynamical correlation can build up this is a practical implementation of the absence of correlations assumed by mean field approaches we present a detailed analysis of the contact process in terms of a langevin equation including explicitly the effects of stochastic fluctuations in the number of particles in finite networks this allows us to determine analytically the survival time for spreading experiments and the density of active sites in surviving runs the fluctuations in the topological structure induce anomalous scaling effects with respect to the system size when the degree distribution has a hard upper bound when the upper bound is soft the presence of outliers with huge connectivity perturbs the picture even more inducing an apparent shift of the critical point in light of these findings recent theoretical and numerical results in the literature are critically reviewed

rare region effects in the contact process on networks networks and dynamical processes occurring on them have become a paradigmatic representation of complex systems studying the role of quenched disorder both intrinsic to nodes and topological is a key challenge with this in mind here we analyze the contact process i e the simplest model for propagation phenomena with node dependent infection rates i e intrinsic quenched disorder on complex networks we find griffiths phases and other rare region effects leading rather generically to anomalously slow algebraic logarithmic etc relaxation on erd ifmmode mbox h o else h o fi s r enyi networks we predict similar effects to exist for other topologies as long as a nonvanishing percolation threshold exists more strikingly we find that griffiths phases can also emerge char22 even with constant epidemic rates char22 as a consequence of mere topological heterogeneity in particular we find griffiths phases in finite dimensional networks as for instance a family of generalized small world networks these results have a broad spectrum of implications for propagation phenomena and other dynamical processes on networks and are relevant for the analysis of both models and empirical data

phase transitions in a two parameter model of opinion dynamics with random kinetic exchanges recently a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry breaking transition was reported m lallouache a s chakrabarti a chakraborti and b k chakrabarti phys rev e 82 056112 2010 we generalize the model to incorporate two parameters to represent conviction and to represent the influencing ability of individuals a phase boundary given by 1 2 is obtained separating the symmetric and symmetry broken phases the effect of the influencing term enhances the possibility of reaching a consensus in the society the time scale diverges near the phase boundary in a power law manner the order parameter and the condensate also show power law growth close to the phase boundary albeit with different exponents the exponents in general change along the phase boundary indicating a nonuniversality the relaxation times however become constant with increasing system size near the phase boundary indicating the absence of any diverging length scale consistently the fluctuations remain finite but show strong dependence on the trajectory along which it is estimated

complex networks effect of subtle changes in nature of randomness abstract in two different classes of network models namely the watts strogatz type and the euclidean type subtle changes have been introduced in the randomness in the watts strogatz type network rewiring has been done in different ways and although the qualitative results remain the same finite differences in the exponents are observed in the euclidean type networks where at least one finite phase transition occurs two models differing in a similar way have been considered the results show a possible shift in one of the phase transition points but no change in the values of the exponents the ws and euclidean type models are equivalent for extreme values of the parameters we compare their behaviour for intermediate values

distribution of infected mass in disease spreading in scale free networks we use scale free networks to study properties of the infected mass m of the network during a spreading process as a function of the infection probability q and the structural scaling exponent we use the standard sir model and investigate in detail the distribution of m we find that for dense networks this function is bimodal while for sparse networks it is a smoothly decreasing function with the distinction between the two being a function of q we thus recover the full crossover transition from one case to the other this has a result that on the same network a disease may die out immediately or persist for a considerable time depending on the initial point where it was originated thus we show that the disease evolution is significantly influenced by the structure of the underlying population

spreading and shortest paths in systems with sparse long range connections spreading according to simple rules e g of fire or diseases and shortest path distances are studied on d dimensional systems with a small density p per site of long range connections small world lattices the volume v t covered by the spreading quantity on an infinite system is exactly calculated in all dimensions as a function of time t from this the average shortest path distance l r can be calculated as a function of euclidean distance r it is found that l r approximately r for r r c the characteristic length r c which governs the behavior of shortest path lengths diverges logarithmically with l for all p 0

proper orthogonal decomposition pod of a class of vibroimpact oscillations abstract this study employs the method of proper orthogonal decomposition pod also known as the karhunen loeve k l method to extract dominant coherent structures modes that approximate the system behavior from time series data these mode shapes can be used in a galerkin reconstruction process to obtain lower dimensional models for the structural systems under consideration the mode shapes and the energies obtained by this process can also be used to predict certain kinds of periodic or non periodic non linear motions the k l method has been applied successfully to fluid dynamical thermal processes and signal processing however only a handful of works exist in the area of vibration analysis and structural mechanics an extensive k l analysis is performed numerically for two vibroimpacting systems a beam and a rotor lower dimensional models are created and used to study non linear energy transmission from low to higher k l modes extensive reconstructions are also performed to prove the efficacy of the k l method to provide accurate low dimensional dynamical models in addition experimental investigations are presented for the case of the overhung impacting rotor and qualitative comparisons with the theoretical analysis are presented

a connection between a system of random walks and rumor transmission abstract we establish a relationship between the phenomenon of rumor transmission on a population and a probabilistic model of interacting particles on the complete graph more precisely we consider variations of the maki thompson epidemic model and the frog model of random walks which were introduced in the scientific literature independently and in different contexts we analyze the markov chains which describe these models and show a coupling between them our connection shows how the propagation of a rumor in a closed homogeneously mixing population can be described by a system of random walks on the complete graph additionally we discuss further applications of the random walk model which are relevant to the modeling of different biological dynamics

space time code design for correlated ricean mimo channels at finite snr space time code stc designs commonly rely on the assumptions of independent and identically distributed i i d rayleigh channels being either slow or fast fading and high signal to noise ratio snr however it has been shown that poor scattering conditions can have detrimental effects on the performance of stcs and that the behavior of codes at high snr is radically different from the finite snr behavior this calls for new design criteria that correctly predict the behavior of codes in correlated channels at finite snr in this paper we investigate how spatially and temporally correlated ricean fading affects the performance of stcs at finite snr we derive a code design criterion leading to robust stcs in a wide variety of propagation conditions and do not require any channel knowledge at the transmitter codes satisfying this criterion are shown to perform sensibly better in correlated channels than codes designed only for i i d slow or fast rayleigh fading channels examples of space time trellis codes and algebraic codes are proposed in order to illustrate the developed criterion

finite snr performance analysis of space time coding in correlated ricean mimo channels the performance analysis and the subsequent design of space time codes stc in multiantenna channels commonly assume an infinite signal to noise ratio snr this assumption has been shown to be justified in uncorrelated rayleigh fading channels by contrast this correspondence investigates stc in all snr regimes and in the broad class of space time correlated ricean fading multiple input multiple output mimo channels for rank deficient codes it is proven analytically that the error probability is significantly affected by spatial correlations and coherent components irrespective of the snr range and the temporal correlation for full rank codes the performance and the code design are shown to be affected by spatial correlations and or coherent paths only at finite snr in slow fading channels whereas in time varying channels they are affected in all snr regimes hence there is no guarantee that stc designed for independent and indentically distributed i i d rayleigh fading channels perform adequately in space time correlated rayleigh ricean channels simulation examples confirm the conclusions drawn from the analytical derivations they further illustrate that the use of a high snr assumption does not allow to accurately estimate the behavior of stc in practical scenarios and should thus be used with care

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

the shortest path of saws with bridges the shortest paths of self avoiding walks saws with bridge lengths b 1 2 3 and 2 are studied by exact series expansions and by monte carlo simulation methods on the square and simple cubic lattices in the series work saw configurations of up to 24 and 14 steps are generated on the square and simple cubic lattices respectively assuming the shortest path sn between two sites which are separated by n steps along the chain has the scaling form sn approximately an bn1 delta it is found that delta approximately 1 and delta approximately 1 2 on the square and simple cubic lattices respectively independent of the bridge length the problem is also investigated by the mellin pade approximation method using monte carlo data on the square lattice the latter method gives results consistent with those of the series expansion study the authors results are not consistent with earlier predictions

shortest paths on systems with power law distributed long range connections we discuss shortest path lengths l r on periodic rings of size l supplemented with an average of pl randomly located long range links whose lengths are distributed according to p l approximately l mu using rescaling arguments and numerical simulation on systems of up to 10 7 sites we show that a characteristic length xi exists such that l r approximately r for r xi for small p we find that the shortest path length satisfies the scaling relation l r mu p xi f mu r xi three regions with different asymptotic behaviors are found respectively a mu 2 where theta s 1 b 1 mu 2 where 0 theta s mu 1 2 and c mu 1 where l r behaves logarithmically i e theta s 0 the characteristic length xi is of the form xi approximately p nu with nu 1 2 mu in region b but depends on l as well in region c a directed model of shortest paths is solved and compared with numerical results

critical behavior of propagation on small world networks we report numerical evidence that an epidemiclike model which can be interpreted as the propagation of a rumor exhibits critical behavior at a finite randomness of the underlying small world network the transition occurs between a regime where the rumor dies in a small neighborhood of its origin and a regime where it spreads over a finite fraction of the whole population critical exponents are evaluated through finite size scaling analysis and the dependence of the critical randomness with the network connectivity is studied the behavior of this system as a function of the small network randomness bears noticeable similarities with an epidemiological model reported recently m kuperman and g abramson phys rev lett 86 2909 2001 in spite of substantial differences in the respective dynamical rules

mapping the q voter model from a single chain to complex networks abstract we propose and compare six different ways of mapping the modified q voter model to complex networks considering square lattices barabasi albert watts strogatz and real twitter networks we ask the question if always a particular choice of the group of influence of a fixed size q leads to different behavior at the macroscopic level using monte carlo simulations we show that the answer depends on the relative average path length of the network and for real life topologies the differences between the considered mappings may be negligible

ising model on a self avoiding walk fluctuation arguments combined with basic features of the geometry of self avoiding walks saws are shown to lead to zero transition temperature tc for the ising model on a saw the ising model on a non random fractal representing the essential geometrical features of saws is treated exactly by a decimation method it also leads to tc 0 and to ising saw critical behavior different from that on an ising chain

two dimensional sir epidemics with long range infection we extend a recent study of susceptible infected removed epidemic processes with long range infection referred to as i in the following from 1 dimensional lattices to lattices in two dimensions as in i we use hashing to simulate very large lattices for which finite size effects can be neglected in spite of the assumed power law p x x 2 for the probability that a site can infect another site a distance vector x apart as in i we present detailed results for the critical case for the supercritical case with 2 and for the supercritical case with 0 2 for the latter we verify the stretched exponential growth of the infected cluster with time predicted by m biskup for 2 we find generic power laws with dependent exponents in the supercritical phase but no kosterlitz thouless kt like critical point as in 1 d instead of diverging exponentially with the distance from the critical point the correlation length increases with an inverse power as in an ordinary critical point finally we study the dependence of the critical exponents on in the regime 0 2 and compare with field theoretic predictions in particular we discuss in detail whether the critical behavior for slightly less than 2 is in the short range universality class as conjectured recently by f linder et al as in i we also consider a modified version of the model where only some of the contacts are long range the others being between nearest neighbors if the number of the latter reaches the percolation threshold the critical behavior is changed but the supercritical behavior stays qualitatively the same

maximal planar networks with large clustering coefficient and power law degree distribution in this article we propose a simple rule that generates scale free networks with very large clustering coefficient and very small average distance these networks are called random apollonian networks rans as they can be considered as a variation of apollonian networks we obtain the analytic results of power law exponent ensuremath gamma 3 and clustering coefficient c frac 46 3 ensuremath 36 phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex frac 3 2 ensuremath approx 0 74 which agree with the simulation results very well we prove that the increasing tendency of average distance of rans is a little slower than the logarithm of the number of nodes in rans since most real life networks are both scale free and small world networks rans may perform well in mimicking the reality the rans possess hierarchical structure as c k ensuremath sim k ensuremath 1 that are in accord with the observations of many real life networks in addition we prove that rans are maximal planar networks which are of particular practicability for layout of printed circuits and so on the percolation and epidemic spreading process are also studied and the comparisons between rans and barab asi albert ba as well as newman watts nw networks are shown we find that when the network order n the total number of nodes is relatively small as n ensuremath sim 10 4 the performance of rans under intentional attack is not sensitive to n while that of ba networks is much affected by n and the diseases spread slower in rans than ba networks in the early stage of the suseptible infected process indicating that the large clustering coefficient may slow the spreading velocity especially in the outbreaks

between disorder and order a case study of power law abstract power law is an important feature of phenomena in long memory behaviors zipf ever found power law in the distribution of the word frequencies in physics the terms order and disorder are thermodynamic or statistical physics concepts originally and a lot of research work has focused on self organization of the disorder ingredients of simple physical systems it is interesting what make disorder order transition we devise an experiment based method about random symbolic sequences to research regular pattern between disorder and order the experiment results reveal power law is indeed an important regularity in transition from disorder to order about these results the preliminary study and analysis has been done to explain the reasons

navigation in a small world with local information it is commonly known that there exist short paths between vertices in a network showing the small world effect yet vertices for example the individuals living in society usually are not able to find the shortest paths due to the very serious limit of information to study this issue theoretically here the navigation process of launching messages toward designated targets is investigated on a variant of the one dimensional small world network swn in the network structure considered the probability of a shortcut falling between a pair of nodes is proportional to r alpha where r is the lattice distance between the nodes when alpha 0 it reduces to the swn model with random shortcuts the system shows the dynamic small world effect which is different from the well studied static sw effect we study the effective network diameter the path length as a function of the lattice distance and the dynamics they are controlled by multiple parameters and we use data collapse to show that the parameters are correlated the central finding is that in the one dimensional network studied the dynamic sw effect exists for 0 alpha 2 for each given value of alpha in this region the point where the dynamic sw effect arises is m l approximately 1 where m is the number of useful shortcuts and l is their average reduced effective length

zero temperature dynamics for the ferromagnetic ising model on random graphs abstract we consider glauber dynamics at zero temperature for the ferromagnetic ising model on the usual random graph model on n vertices with on average edges incident to each vertex in the limit as n based on numerical simulations svenson phys rev e 64 2001 036122 reported that the dynamics fails to reach a global energy minimum for a range of values of the present paper provides a mathematically rigorous proof that this failure to find the global minimum in fact happens for all 0 a lower bound on the residual energy is also given

a rumor spreading model with variable forgetting rate abstract a rumor spreading model with the consideration of forgetting rate changing over time is examined in small world networks the mean field equations are derived to describe the dynamics of rumor spreading in small world networks further numerical solutions are conducted on livejournal an online social blogging platform to better understand the performance of the model results show that the forgetting rate has a significant impact on the final size of rumor spreading the larger the initial forgetting rate or the faster the forgetting speed the smaller the final size of the rumor spreading numerical solutions also show that the final size of rumor spreading is much larger under a variable forgetting rate compared to that under a constant forgetting rate

effect of the nature of randomness on quenching dynamics of the ising model on complex networks randomness is known to affect the dynamical behavior of many systems to a large extent in this paper we investigate how the nature of randomness affects the dynamics in a zero temperature quench of the ising model on two types of random networks in both networks which are embedded in a one dimensional space the first neighbor connections exist and the average degree is 4 per node in random model a the second neighbor connections are rewired with a probability p while in random model b additional connections between neighbors at a euclidean distance l l 1 are introduced with a probability p l proportionally l we find that for both models the dynamics leads to freezing such that the system gets locked in a disordered state the point at which the disorder of the nonequilibrium steady state is maximum is located the behavior of dynamical quantities such as residual energy order parameter and persistence are discussed and compared overall the behavior of physical quantities are similar although subtle differences are observed due to the difference in the nature of randomness

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

phase transition of a one dimensional ising model with distance dependent connections the critical behavior of the ising model on a one dimensional network which has long range connections at distances l 1 with the probability theta l approximately l m is studied by using monte carlo simulations through analyzing the ising model on networks with different m values this paper discusses the impact of the global correlation which decays with the increase of m on the phase transition of the ising model adding the analysis of the finite size scaling of the order parameter m it is observed that in the whole range of 0 m 2 a finite temperature transition exists and the critical exponents show consistence with mean field values which indicates a mean field nature of the phase transition

damage detection using a modified laplacian operator on mode shape data abstract localized damage to a structure affects its dynamic properties and much work has been undertaken investigating the variation of natural frequencies with damage however use of mode shape data has seen much less effort this paper develops and presents a technique for identifying the location of structural damage in a beam the procedure operates solely on the mode shape from the damaged structure and does not requirea prioriknowledge of the undamaged structure the procedure is developed using a one dimensional finite element model of a beam and demonstrated by experiment when damage is severe a localized thickness reduction of more than 10 applying a finite difference approximation of laplace s differential operator to the mode shape successfully identifies the location of the damage however when damage is less severe further processing of the laplacian output is required before the location can be determined this post processing enables the location of thickness reductions of less than 0 5 to be identified the procedure is best suited to the mode shape obtained from the fundamental natural frequency the mode shapes from higher natural frequencies can be used to verify the location of damage but they are not as sensitive as the lower modes

the ising model on a saw using a renormalization group calculation the authors show that the most probable value of the static correlation function of the ising model on a saw decays as a stretched exponential with an exponent equal to the dimension d of the saw they prove that the thermal exponent vt equals d 1 on the basis of extensive monte carlo simulations they conclude that the spin spin autocorrelation function also decays as a stretched exponential they find evidence for a breakdown of dynamical scaling

blackmail propagation on small world networks abstract the dynamics of the blackmail propagation model based on small world networks is investigated it is found that for a given transmitting probability the dynamical behavior of blackmail propagation transits from linear growth type to logistical growth one with the network randomness p increases the transition takes place at the critical network randomness p c 1 n where n is the total number of nodes in the network for a given network randomness p the dynamical behavior of blackmail propagation transits from exponential decrease type to logistical growth one with the transmitting probability increases the transition occurs at the critical transmitting probability c 1 k where k is the average number of the nearest neighbors the present work will be useful for understanding computer virus epidemics and other spreading phenomena on communication and social networks

spectral dimension and the shortest path of saw s with multi neighbour interactions the spectral dimension and the shortest path of self avoiding walks saws with bridge length interaction range b 1 2 3 2 are studied numerically the spectral dimension is calculated by performing exact multi neighbour random walks on the monte carlo generated saw configurations it is found that the spectral dimension is not affected by the finite range of interactions finite bridge length and approach to ds 1 both in dimensions d 2 and 3 the shortest path length sn of the n step saw with local bridges is also investigated it is shown that sn n a n delta b c n the authors numerical simulation results indicate that the exponent delta is independent of the dimensionality and is about 3 16 in dimensions d 2 5

nonconservative kinetic exchange model of opinion dynamics with randomness and bounded confidence the concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values 1 1 the characteristics of the unrestricted model which has one parameter representing conviction undergo drastic changes with the introduction of bounded confidence parametrized by three distinct regions are identified in the phase diagram in the plane and the evidences of a first order phase transition for 0 3 are presented a neutral state with all opinions equal to zero occurs for c1 2 3 independent of while for c 1 c 2 an ordered region is seen to exist where opinions of only one sign prevail at c 2 a transition to a disordered state is observed where individual opinions of both signs coexist and move closer to the extreme values 1 as is increased for confidence level 0 3 the ordered phase exists for a narrow range of only the line 0 is apparently a line of discontinuity and this limit is discussed in some detail

stochastic bifurcations in the nonlinear parallel ising model we investigate the phase transitions of a nonlinear parallel version of the ising model characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one this model arises in problems of opinion formation the mean field approximation shows chaotic oscillations by changing the couplings or the connectivity the spatial model shows bifurcations in the average magnetization similar to that seen in the mean field approximation induced by the change of the topology after rewiring short range to long range connection as predicted by the small world effect these coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins induced by long range couplings similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution degree of asynchronism of the updating we also examined the effects of inhomogeneity mixing ferromagnetic and antiferromagnetic coupling which induces an unexpected bifurcation diagram with a bubbling behavior as also happens for dilution

small world phenomena and the statistics of linear polymers a regular lattice in which the sites can have long range connections at a distance l with a probabilty p l l in addition to the short range nearest neighbour connections shows small world behaviour for 0 c in the most appropriate physical example of such a system namely the linear polymer network the exponent is related to the exponents of the corresponding n vector model in the n 0 limit and its value is less than c still the polymer networks do not show small world behaviour here we show that this is due to a small value constraint on the number q of long range connections per monomer in the network in the general q space we obtain a phase boundary separating regions with and without small world behaviour and show that the polymer network falls marginally in the regular lattice region

ising model in small world networks the ising model in small world networks generated from two and three dimensional regular lattices has been studied monte carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems in the thermodynamic limit the phase transition has a mean field character for any finite value of the rewiring probability p which measures the disorder strength of a given network for small values of p both the transition temperature and critical energy change with p as a power law in the limit stackrel ensuremath rightarrow p 0 the heat capacity at the transition temperature diverges logarithmically in two dimensional 2d networks and as a power law in 3d

constrained opinion dynamics freezing and slow evolution we study opinion formation in a population of leftists centrists and rightist in an interaction between neighbouring agents a centrist and a leftist can become both centrists or leftists and similarly for a centrist and a rightist while leftists and rightists do not affect each other the evolution is controlled by the initial density of centrists 0 for any spatial dimension the system reaches a centrist consensus with probability 0 while with probability 1 0 the final state is either an extremist consensus or a frozen population of leftists and rightists in one dimension we determine the opinion evolution by mapping the system onto a spin 1 ising model with zero temperature glauber kinetics the approach to the final state is governed by a t long time tail with 2 0 as 0 0 in the one dimensional frozen state the length distribution of single opinion domains has an algebraic small size tail x 2 1 and the average domain length is l2 where l is the length of the system

structural damage detection based on proper orthogonal decomposition experimental verification the present paper describes a new structural damage detection method based on the monitoring of vibrational properties of the structure sensors record the accelerations of several points of the structure the recorded data are then used to compute the proper orthogonal modes the comparison between the proper orthogonal modes of the undamaged structure and those of the damaged structure provides information on damage location experimental results are presented

large scale topological and dynamical properties of the internet we study the large scale topological and dynamical properties of real internet maps at the autonomous system level collected in a 3 yr time interval we find that the connectivity structure of the internet presents statistical distributions settled in a well defined stationary state the large scale properties are characterized by a scale free topology consistent with previous observations correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the internet the study of the internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models we compare the properties of growing network models with the present real internet data analysis

on the application of karhunen loeve transform to transient dynamic systems abstract the karhunen loeve transform klt has become a popular method in various fields of engineering science due to its ability to identify the most prominent features in the underlying system dynamics the klt is a favorable method for such tasks as process monitoring model order reduction or optimum control however it is a well known fact that the klt is case sensitive that is that changes in the dynamic system behavior can decisively affect the klt results as much as this property is desired for monitoring problems it limits the performance of klt in model order reduction or optimum control problems if systems are subject to structural changes recent research interest focuses on extending applications of klt to systems with transient dynamic behavior or changing boundary conditions approaches have been published that circumvent the limitations of klt by either assuming reasonable comparability of system dynamics or by measuring the representative performance of klt bases a posteriori however such methods require additional simulations of the full size system and thus jeopardize the idea of model order reduction in this paper we introduce a novel a priori measure to evaluate the performance of the current klt basis this procedure can be of great help in either monitoring or adaptive control of systems that show intermittent transient and quasi stationary dynamic behavior this a priori measure prepares the path for adaptive model order reduction schemes moreover it can be used to measure the stationarity of multidimensional dynamic processes

geography in a scale free network model we offer an example of a network model with a power law degree distribution p k approximately k alpha for nodes but which nevertheless has a well defined geography and a nonzero threshold percolation probability for alpha 2 the range of real world contact networks this is different from p c 0 for alpha 3 results for the original well mixed scale free networks in our lattice based scale free network individuals link to nearby neighbors on a lattice even considerable additional small world links do not change our conclusion of nonzero thresholds when applied to disease propagation these results suggest that random immunization may be more successful in controlling human epidemics than previously suggested if there is geographical clustering

using svd to detect damage in structures with different operational conditions the aim of this article is to present a method based on the use of singular value decomposition svd for detecting damage in structures at an early stage the main advantage of the proposed technique is firstly the capability to deal with structures with different operating conditions i e with dynamic characteristics which may change during the lifetime secondly no mathematical model of the analyzed structure is required a priori such that it can be applied to systems of arbitrary complexity application of this method to simulated data for a truss type structure is illustrated with results from an experimental investigation on a cantilever beam

disorder induced phase transition in kinetic models of opinion dynamics abstract we propose a model of continuous opinion dynamics where mutual interactions can be both positive and negative different types of distributions for the interactions all characterized by a single parameter p denoting the fraction of negative interactions are considered results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p p c below which a consensus is reached although the order disorder transition is analogous to a ferromagnetic paramagnetic phase transition with comparable critical exponents the model is characterized by some distinctive features relevant to a social system

epidemics disorder and percolation abstract spatial models for spread of an epidemic may be mapped onto bond percolation we point out that with disorder in the strength of contacts between individuals patchiness in the spread of the epidemic is very likely and the criterion for epidemic outbreak depends strongly on the disorder because the critical region of the corresponding percolation model is broadened in some networks the percolation threshold is zero if another kind of disorder is present namely divergent fluctuations in the number of contacts we give an example a network with a well defined geography where this is not necessarily so and discuss whether real infection networks are likely to have this property

percolation in a kinetic opinion exchange model we study the percolation transition of the geometrical clusters in the square lattice lccc model a kinetic opinion exchange model introduced by lallouache chakrabarti chakraborti and chakrabarti phys rev e 82 056112 2010 with the change in conviction and influencing parameter the cluster is comprised of the adjacent sites having an opinion value greater than or equal to a prefixed threshold value of opinion the transition point is different from that obtained for the transition of the order parameter average opinion value found by lallouache et al although the transition point varies with the change in the threshold value of the opinion the critical exponents for the percolation transition obtained from the data collapses of the maximum cluster size the cluster size distribution and the binder cumulant remain the same the exponents are also independent of the values of conviction and influencing parameters indicating the robustness of this transition the exponents do not match any other known percolation exponents e g the static ising dynamic ising and standard percolation this means that the lccc model belongs to a separate universality class

on proper orthogonal co ordinates as indicators of modal activity proper orthogonal decomposition pod is applied for examining modal activity the extraction of proper orthogonal modal co ordinates pocs is outlined the proper orthogonal values povs are the mean squared values of the pocs the number of povs above the noise floor provides a bound on the number of significant modes based on povs above the noise floor the ideas are illustrated on a linear cantilevered beam experiment the displacement ensembles are obtained by processing six strain measurements coherent proper orthogonal modes poms and povs above the noise floor together confirm that six active modes are detected in the system the distribution of modal components in pocs is discussed the characteristics of the poms povs and pocs are then examined in the presence of added noise

on the structural properties of small world networks with range limited shortcut links abstract we explore a new variant of small world networks swns in which an additional parameter r sets the length scale over which shortcuts are uniformly distributed when r 0 we have an ordered network whereas r 1 corresponds to the original watts strogatz swn model these limited range swns have a similar degree distribution and scaling properties as the original swn model we observe the small world phenomenon for r 1 indicating that global shortcuts are not necessary for the small world effect for limited range swns the average path length changes nonmonotonically with system size whereas for the original swn model it increases monotonically we propose an expression for the average path length for limited range swns based on numerical simulations and analytical approximations

the susceptible infected recovered model on a euclidean network we consider a susceptible infected recovered sir epidemic model on a euclidean network in one dimension in which nodes at a distance l are connected with probability p l l in addition to nearest neighbors the topology of the network changes as is varied and its effect on the sir model is studied r t the recovered fraction of population up to time t and the total duration of the epidemic are calculated for different values of the infection probabilities q and a threshold behavior is observed for all up to 2 0 above the threshold value q qc the saturation value rsat attains a finite value both rsat and show scaling behavior in a finite system of size n and qc is constant for 0 qc the results are compared to static percolation phenomena and also to mean field results for finite systems discussions on the properties of the euclidean network are made in the light of the present results

opinion formation in kinetic exchange models spontaneous symmetry breaking transition we propose a minimal multiagent model for the collective dynamics of opinion formation in the society by modifying kinetic exchange dynamics studied in the context of income money or wealth distributions in a society this model has an intriguing spontaneous symmetry breaking transition to polarized opinion state starting from nonpolarized opinion state in order to analyze the model we introduce an iterative map version of the model which has very similar statistical characteristics an approximate theoretical analysis of the numerical results is also given based on the iterative map version

size of outbreaks near the epidemic threshold the spread of infectious diseases near the epidemic threshold is investigated scaling laws for the size and the duration of outbreaks originating from a single infected individual in a large susceptible population are obtained the maximal size of an outbreak n ensuremath ast scales as n 2 3 with n the population size this scaling law implies that the average outbreak size n scales as n 1 3 moreover the maximal and the average duration of an outbreak grow as t ensuremath ast ensuremath sim n 1 3 and t ensuremath sim text ln phantom rule 0 2em 0ex n respectively

superdiffusion in a class of networks with marginal long range connections a class of cubic networks composed of a regular one dimensional lattice and a set of long range links is introduced networks parametrized by a positive integer k are constructed by starting from a one dimensional lattice and iteratively connecting each site of degree 2 with a kth neighboring site of degree 2 specifying the way pairs of sites to be connected are selected various random and regular networks are defined all of which have a power law edge length distribution of the form p l approximately l s with the marginal exponent s 1 in all these networks lengths of shortest paths grow as a power of the distance and random walk is superdiffusive applying a renormalization group method the corresponding shortest path dimensions and random walk dimensions are calculated exactly for k 1 networks and for k 2 regular networks in other cases they are estimated by numerical methods although s 1 holds for all representatives of this class the above quantities are found to depend on the details of the structure of networks controlled by k and other parameters

small world networks links with long tailed distributions small world networks swn obtained by randomly adding to a regular structure additional links al are of current interest in this paper we explore based on physical models a new variant of swn in which the probability of realizing an al depends on the chemical distance between the connected sites we assume a power law probability distribution and study random walkers on the network focusing especially on their probability of being at the origin we connect the results to l evy flights which follow from a mean field variant of our model

mean field solution of the small world network model the small world network model is a simple model of the structure of social networks which possesses characteristics of both regular lattices and random graphs the model consists of a one dimensional lattice with a low density of shortcuts added between randomly selected pairs of points these shortcuts greatly reduce the typical path length between any two points on the lattice we present a mean field solution for the average path length and for the distribution of path lengths in the model this solution is exact in the limit of large system size and either a large or small number of shortcuts

a new view of performance analysis of transmit diversity schemes in correlated rayleigh fading this article provides a new formulation for the pairwise error probability for any coherently demodulated system in arbitrarily correlated rayleigh fading the novelty of the result is that the error probability expression can be described as a function of the eigenvalues of a signal only matrix we also provide the relationship between the pole location of the characteristic function and the resulting error probability this result allows us to approximate and bound the desired probability a new simple bound on the pairwise error probability is derived that is better than the standard chernoff bound and asymptotically tight with the signal to noise ratio snr to the true probability

contrarian like behavior and system size stochastic resonance in an opinion spreading model abstract we have recently shown that a stochastic driving in an opinion spreading model has a tremendous impact on the system dynamics spontaneously leading to system s agents which are analogous to galam s contrarians we have analyzed the existence of stochastic resonance phenomena in this social model in the presence of such contrarians we have found that the system does not show conventional stochastic resonance but interestingly it does exhibit system size stochastic resonance

phase transitions in a network with a range dependent connection probability we consider a one dimensional network in which the nodes at euclidean distance l can have long range connections with a probability p l approximately l delta in addition to nearest neighbor connections this system has been shown to exhibit small world behavior for delta 2 above which its behavior is like a regular lattice from the study of the clustering coefficients we show that there is a transition to a random network at delta 1 the finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicates that a continuous phase transition occurs at this point using these results we find that the two transitions occurring in this network can be detected in any dimension by the behavior of a single quantity the average bond length the phase transitions in all dimensions are nontrivial in nature

systematic space time trellis code construction for correlated rayleigh fading channels the potential for capacity increase in multiple antenna wireless communication systems has drawn considerable attention to space time codes however most of the existing space time code construction methods have assumed ideal channel models either quasi static fading or fast fading in this work we propose a systematic space time trellis code construction method for correlated fading channels we derive the performance criteria that take into account both spatial and temporal channel correlation assuming that the space time correlation matrix is of full rank moreover we introduce a new design criterion and analyze the properties of the space time trellis codes satisfying the proposed criterion using the design criterion we develop a code construction procedure that jointly considers diversity advantage and coding advantage for an arbitrary number of transmit antennas and any memoryless modulation the flexibility of the proposed code construction method is demonstrated by designing space time trellis codes for two three and four transmit antennas with quaternary phase shift keying qpsk 8psk phase shift keying and 4ask amplitude shift keying modulations the simulation results demonstrate that not only can our method generate new codes for an arbitrary number of antennas but in some special cases where previously proposed codes exist our codes also perform very well

random walk on self avoiding walk a model for conductivity of linear polymers random walks on self avoiding walks saws are studied using monte carlo techniques on a square lattice with nearest neighbour hopping along the chain and between saw points which are nearest neighbours on the embedding lattice the average of the square of the end to end distance for random walks of t steps on saws of length n is fitted to the scaling forms rt2 varies as ndelta tk for t or approximately ntheta where theta approximately 2 nu s k nu s being the average end to end distance exponent for saws the observed value of the exponent delta is supported by the authors real space renormalisation group result for the conductivity of saw chains the exponent k has been related to the effective fractal dimension of the saw chain

multistable binary decision making on networks we propose a simple model for a binary decision making process on a graph motivated by modeling social decision making with cooperative individuals the model is similar to a random field ising model or fiber bundle model but with key differences on heterogeneous networks for many types of disorder and interactions between the nodes we predict discontinuous phase transitions with mean field theory which are largely independent of network structure we show how these phase transitions can also be understood by studying microscopic avalanches and describe how network structure enhances fluctuations in the distribution of avalanches we suggest theoretically the existence of a glassy spectrum of equilibria associated with a typical phase even on infinite graphs so long as the first moment of the degree distribution is finite this behavior implies that the model is robust against noise below a certain scale and also that phase transitions can switch from discontinuous to continuous on networks with too few edges numerical simulations suggest that our theory is accurate

multiscale resurgent epidemics in a hierarchical metapopulation model abstract although population structure has long been recognized as relevant to the spread of infectious disease traditional mathematical models have understated the role of nonhomogenous mixing in populations with geographical and social structure recently a wide variety of spatial and network models have been proposed that incorporate various aspects of interaction structure among individuals however these more complex models necessarily suffer from limited tractability rendering general conclusions difficult to draw in seeking a compromise between parsimony and realism we introduce a class of metapopulation models in which we assume homogeneous mixing holds within local contexts and that these contexts are embedded in a nested hierarchy of successively larger domains we model the movement of individuals between contexts via simple transport parameters and allow diseases to spread stochastically our model exhibits some important stylized features of real epidemics including extreme size variation and temporal heterogeneity that are difficult to characterize with traditional measures in particular our results suggest that when epidemics do occur the basic reproduction number r 0 may bear little relation to their final size informed by our model s behavior we suggest measures for characterizing epidemic thresholds and discuss implications for the control of epidemics math model population structure

dynamics of majority rule in two state interacting spin systems we introduce a two state opinion dynamics model where agents evolve by majority rule in each update a group of agents is specified whose members then all adopt the local majority state in the mean field limit where a group consists of randomly selected agents consensus is reached in a time that scales ln n where n is the number of agents on finite dimensional lattices where a group is a contiguous cluster the consensus time fluctuates strongly between realizations and grows as a dimension dependent power of n the upper critical dimension appears to be larger than 4 the final opinion always equals that of the initial majority except in one dimension

random pseudofractal networks with competition abstract in this paper we present a simple rule which assigns fitness to each edge to generate random pseudofractal networks rpns this rpn model is both scale free and small world we obtain the theoretical results that the power law exponent is 2 1 1 for the tunable parameter 1 and that the degree distribution is of an exponential form for others analytical results also show that an rpn has a large clustering coefficient and can process hierarchical structure as c k k 1 that is in accordance with many real networks and we prove that the mean distance l n scales slower logarithmically with network size n in particular we explain the effect of nodes with degree 2 on the clustering coefficient these results agree with numerical simulations very well

scaling and percolation in the small world network model in this paper we study the small world network model of watts and strogatz which mimics some aspects of the structure of networks of social interactions we argue that there is one nontrivial length scale in the model analogous to the correlation length in other systems which is well defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero giving a normal critical point in this limit this length scale governs the crossover from large to small world behavior in the model as well as the number of vertices in a neighborhood of given radius on the network we derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex vertex distance on the network and using series expansion and pad e approximants find an approximate analytic form for the scaling function we calculate the effective dimension of small world graphs and show that this dimension varies as a function of the length scale on which it is measured in a manner reminiscent of multifractals we also study the problem of site percolation on small world networks as a simple model of disease propagation and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms in epidemiological terms the point at which an epidemic occurs the typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph all our analytic results are confirmed by extensive numerical simulations of the model

scaling behavior of the contact process in networks with long range connections we present simulation results for the contact process on regular cubic networks that are composed of a one dimensional lattice and a set of long edges with unbounded length networks with different sets of long edges are considered that are characterized by different shortest path dimensions and random walk dimensions we provide numerical evidence that an absorbing phase transition occurs at some finite value of the infection rate and the corresponding dynamical critical exponents depend on the underlying network furthermore the time dependent quantities exhibit log periodic oscillations in agreement with the discrete scale invariance of the networks in case of spreading from an initial active seed the critical exponents are found to depend on the location of the initial seed and break the hyperscaling law of the directed percolation universality class due to the inhomogeneity of the networks however if the cluster spreading quantities are averaged over initial sites the hyperscaling law is restored

karhunen loeve modes of a truss transient response reconstruction and experimental verification karhunen loeve k l or proper orthogonal decomposition modes are used to discretize the dynamics of a four bay linear truss this is achieved by defining global k l modal amplitudes and employing the orthogonality relations between k l modes that are inherent in the k l decomposition it is found that the k l based low order models can capture satisfactory the transient dynamics of the truss even when only a limited number of them is used for the order reduction a comparison between the exact and low order dynamics in the frequency domain reveals that the low order models capture the leading resonances of the truss a series of experiments with a practical three bay truss is then performed to validate the theoretical k l decomposition a comparison between theory and experiment indicates agreement between the predicted and realized dominant k l mode shapes but less so in the higher order modes the reasons for this discrepancy between theory and experiment are discussed and possible applications of the k l based order reduction to passive and active control of practical large scale flexible systems are outlined

physical interpretation of the proper orthogonal modes using the singular value decomposition abstract proper orthogonal decomposition is a statistical pattern analysis technique for finding the dominant structures called the proper orthogonal modes in an ensemble of spatially distributed data while the proper orthogonal modes are obtained through a statistical formulation they can be physically interpreted in the field of structural dynamics the purpose of this paper is thus to provide some insights into the physical interpretation of the proper orthogonal modes using the singular value decomposition

percolation in networks with long range connections abstract two dimensional lattices of points are connected with long range links whose lengths are distributed according to p r r by changing the decay exponent one can go from d dimensional short range networks to dimensional networks topologically similar to random graphs percolation on these networks is numerically studied for systems of up to 10 7 sites the shortest path fractal and chemical dimensions are determined at the critical threshold as a function of the decay exponent

topological bifurcations in a model society of reasonable contrarians people are often divided into conformists and contrarians the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority in practice however the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion which denotes a social norm such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets we present the opinion dynamics of a society of reasonable contrarian agents the model is a cellular automaton of ising type with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms we introduce the entropy of the collective variable as a way of comparing deterministic mean field and probabilistic simulations bifurcation diagrams in the mean field approximation the model exhibits bifurcations and a chaotic phase interpreted as coherent oscillations of the whole society however in a one dimensional spatial arrangement one observes incoherent oscillations and a constant average in simulations on watts strogatz networks with a small world effect the mean field behavior is recovered with a bifurcation diagram that resembles the mean field one but where the rewiring probability is used as the control parameter similar bifurcation diagrams are found for scale free networks and we are able to compute an effective connectivity for such networks

stability analysis of i2s2r rumor spreading model in complex networks abstract in this paper we propose i 2 s 2 r rumor spreading model with general incidence function in homogeneous networks and i 2 s 2 r rumor spreading model in heterogeneous network in the first model we establish a dynamic model for rumor propagation called i 2 s 2 r in which we consider two general incidence functions then the basic reproduction number the locally stability and the global stability of rumor free equilibrium are discussed in the second model we mainly consider another network structure i e heterogeneous network thus we propose a new dynamic model for rumor spreading by deriving the mean field equation the basic reproduction number is obtained moreover the global stability of rumor free equilibrium is established by comparison principle by using a monotone iterative algorithm the global attractivity of the positive equilibrium is proved finally we obtain some important conclusions with numerical simulations

on the theory of space time codes for psk modulation the design of space time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas the lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband differences between modulated codewords which is difficult to relate to traditional code designs over finite fields and rings we present general binary design criteria for psk modulated space time codes for linear bpsk qpsk codes the rank of binary projections of the unmodulated codewords as binary matrices over the binary field is a sufficient design criterion full binary rank guarantees full spatial diversity this criterion accounts for much of what is currently known about psk modulated space time codes we develop new fundamental code constructions for both quasi static and time varying channels these are perhaps the first general constructions other than delay diversity schemes that guarantee full spatial diversity for an arbitrary number of transmit antennas

modulated scale free network in euclidean space a random network is grown by introducing at unit rate randomly selected nodes on the euclidean space a node is randomly connected to its ith predecessor of degree k i with a directed link of length l using a probability proportional to k i l alpha our numerical study indicates that the network is scale free for all values of alpha alpha c and the degree distribution decays stretched exponentially for the other values of alpha the link length distribution follows a power law d l approximately l delta where delta is calculated exactly for the whole range of values of alpha