the bar partial neumann problem on product domains in mathbb c n let omega omega 1 times cdots times omega n subset mathbb c n where omega j subset mathbb c is a bounded domain with smooth boundary we study the solution operator to the overline partial neumann problem for 0 1 forms on in particular we construct singular functions which describe the singular behavior of the solution as a corollary our results carry over to the overline partial neumann problem for 0 q forms despite the singularities we show that the canonical solution to the overline partial equation obtained from the neumann operator does not exhibit singularities when given smooth data

non linear finite strip analysis of rectangular laminates under end shortening using classical plate theory the finite strip method is developed for predicting the geometrically non linear response of rectangular composite laminates with simply supported ends when subjected to uniform end shortening in their plane at the loaded ends lateral in plane expansion may be allowed freely or may be prevented completely in different versions of the approach the permitted laminate material properties are quite general encompassing anisotropy and full coupling between in plane and out of plane behaviour the analysis is based on the use of the classical plate theory and the non linearity is introduced in the strain displacement equations in the manner of the von karman assumptions three different types of finite strip are presented with either linear quadratic or cubic interpolation of the membrane displacement components across a strip in each case the bending displacement component varies cubically across a strip results are presented for isotropic plates and for unsymmetric cross ply angle ply and arbitrary laminates

vibration of shear deformable beams using a spline function approach b spline functions are used as trial functions in a rayleigh ritz analysis of the free vibration of shear deformable timoshenko beams in a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams this is identified as a shear locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a b spline function which is one order higher than that used to represent the rotation numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams the shear locking difficulty is completely eliminated this has clear significance for the analysis of shear deformable plates and shells when using b spline functions

vector opinion dynamics in a model for social influence we present numerical simulations of a model of social influence where the opinion of each agent is represented by a binary vector agents adjust their opinions as a result of random encounters whenever the difference between opinions is below a given threshold evolution leads to a steady state which highly depends on the threshold and a convergence parameter of the model we analyze the transition between clustered and homogeneous steady states results of the cases of complete mixing and small world networks are compared

dynamics of rumor propagation on small world networks we study the dynamics of an epidemiclike model for the spread of a rumor on a small world network it has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network randomness here by numerical means we perform a quantitative characterization of the evolution in the two regimes the variant of dynamic small worlds where the quenched disorder of small world networks is replaced by randomly changing connections between individuals is also analyzed in detail and compared with a mean field approximation

postbuckling analysis of composite laminated panels a description is given of the development of a spline e nite strip method for predicting the response of composite laminated prismatic panels to a progressive uniform end shortening the response is assumed to be geometrically nonlinear with the nonlinearity introduced in enhanced strain displacement equations in a total langrangian approach the set of nonlinear equilibrium equations obtained by appropriate energy minimization is solved using the newton raphson method the development of the properties of a e at e nite strip is made in the contexts of both e rst order shear deformation plate theory and classical plate theory and a number of strip models is available corresponding to different displacement e elds presented applications concern a box section and several longitudinally stiffened panels that include curved panels modeled as faceted shells comparison of the e nite strip predictions is made where possible with results from other sources and such comparison is shown to be close

opinion dynamics of random walking agents on a lattice the opinion dynamics of random walking agents on finite two dimensional lattices is studied in the model the opinion is continuous and both the lattice and the opinion can be either periodic or nonperiodic at each time step all agents move randomly on the lattice and update their opinions based on those of neighbors with whom the differences of opinion are not greater than a given threshold due to the effect of repeated averaging opinions first converge locally and eventually reach steady states as in other models with bounded confidence steady states in general are those with one or more opinion groups in which all agents have the same opinion when both the lattice and the opinion are periodic however metastable states can emerge in which the whole spectrum of location dependent opinions can coexist this result shows that when a set of continuous opinions forms a structure like a circle unlike the typically used linear opinions rich dynamic behavior can arise when there are geographical restrictions in real situations a complete consensus is rarely reached and metastable states here might be one of the explanations for these situations especially when opinions are not linear

global culture a noise induced transition in finite systems we analyze the effect of cultural drift modeled as noise in axelrod s model for the dissemination of culture the disordered multicultural frozen configurations are found not to be stable this general result is proven rigorously in d51 where the dynamics is described in terms of a lyapunov potential in d52 the dynamics is governed by the average relaxation time t of perturbations noise at a rate r t 21 induces monocultural configurations whereasr t 21 sustains disorder in the thermodynamic limit the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence

non linear analysis of rectangular laminates under end shortening using shear deformation plate theory consideration is given to the prediction of the geometrically non linear elastic response of rectangular composite laminates with simply supported ends when subjected to uniform end shortening in their plane at the loaded ends lateral in plane expansion is either allowed freely or is prevented completely material properties of the laminates are quite general encompassing anisotropy and full coupling between in plane and out of plane behaviour first order shear deformation plate theory is used as the mathematical model of laminate behaviour and the non linearity is introduced in the strain displacement equations in the manner of the von karman assumptions the finite strip method is used as the main numerical analysis procedure and subsidiary use is made of the finite element method close comparison of results generated using the two methods is demonstrated in applications ranging from isotropic plates to unsymmetric anisotropic laminates further comparison with the results of an earlier developed finite strip method wherein properties are based on the use of classical plate theory shows the effect of through thickness shearing action in different situations

dynamical response of networks under external perturbations exact results we give exact statistical distributions for the dynamic response of influence net works subjected to external perturbations we consider networks whose nodes have two internal states labeled 0 and 1 we let n0 nodes be frozen in state 0 n1 in state 1 and the remainingnodeschangebyadoptingthestateofaconnectednodewithafixedprobabilityper time step the frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes analytically extending n0 and n1 to be smaller than 1 enables modeling the case of weak coupling we solve the dynamical equations exactly for fully connected networks obtaining the equilibrium distribution transition probabilities between any two states and the characteristic time to equilibration our exact results are excellent approximations for other topologies including random regular lattice scale free and small world networks when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment this model can describe a variety of complex systems from magnetic spins to social networks to population genetics and was recently applied as a framework for early warning signals for real world self organized economic market crises

nonequilibrium transitions in complex networks a model of social interaction we analyze the nonequilibrium order disorder transition of axelrod s model of social interaction in several complex networks in a small world network we find a transition between an ordered homogeneous state and a disordered state the transition point is shifted by the degree of spatial disorder of the underlying network the network disorder favoring ordered configurations in random scale free networks the transition is only observed for finite size systems showing system size scaling while in the thermodynamic limit only ordered configurations are always obtained thus in the thermodynamic limit the transition disappears however in structured scale free networks the phase transition between an ordered and a disordered phase is restored

static pairwise annihilation in complex networks we study static annihilation on complex networks in which pairs of connected particles annihilate at a constant rate during time through a mean field formalism we compute the temporal evolution of the distribution of surviving sites with an arbitrary number of connections this general formalism which is exact for disordered networks is applied to kronecker erd os r enyi i e poisson and scale free networks we compare our theoretical results with extensive numerical simulations obtaining excellent agreement although the mean field approach applies in an exact way neither to ordered lattices nor to small world networks it qualitatively describes the annihilation dynamics in such structures our results indicate that the higher the connectivity of a given network element the faster it annihilates this fact has dramatic consequences in scale free networks for which once the hubs have been annihilated the network disintegrates and only isolated sites are left

sobolev estimates for the bar partial neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary neumann operator on domains inc n admitting a defining function that is plurisubharmonic on the boundary

localization of the kobayashi metric and the boundary continuity of proper holomorphic mappings a classical theorem of carath6odory 8 states that every biholomorphic map f d d2 between domains in the complex plane c bounded by simple closed jordan curves extends to a homeomorphism of 31 onto 2 there are some well known generalizations of this result to domains in ie a if d t and d2 are bounded pseudoconvex domains in 112 with if2 boundary and if the infinitezimal kobayashi metric on d2 grows sufficiently fast near the boundary of d2 ko2 g x xl d z bdz for some e e 0 1 then every proper holomorphic map f dt d2 extends to a h61der continuous map of 51 onto 32 2 3 10 25 29 32 this holds in particular if 92 is strictly pseudoconvex or if it is pseudoconvex with real analytic boundary the same result holds if d2 is only piecewise smooth strongly pseudoconvex 31 further results treat exceptional cases such as the balls 1 reinhardt domains 5 24 domains with many symmetries 4 and analytically bounded hartogs domains in c 2 i1 biholomorphic maps between certain types of nonpseudoconvex domains with real analytic boundaries were treated in 13 and 27 besides the papers mentioned above there is a vast literature concerning smooth extension of proper holomorphic maps of smoothly bounded pseudoconvex domains 6 7 12 14 to mention just a few in the present paper we obtain some results on the continuous extension of proper holomorphic maps f d1 2 under local assumptions on the boundaries bd1 and bd2 one of the main results is

random walk access times on partially disordered complex networks an effective medium theory an analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices considering transition rates f that are different for steps across lattice bonds from the rates f across network shortcuts the theory is developed for structures with arbitrary shortcut distributions and applied to a class of partially disordered traversal enhanced networks in which shortcuts of fixed length are distributed randomly with finite probability numerical simulations are found to be in excellent agreement with predictions of the effective medium theory on all aspects addressed by the latter access times for random walks on these partially disordered structures are compared to those on small world networks which on average appear to provide the most effective means of decreasing access times uniformly across the network

the cauchy riemann equations on product domains we establish the l 2 theory for the cauchy riemann equations on product domains provided that the cauchy riemann operator has closed range on each factor we deduce regularity of the canonical solution on p 1 forms in special sobolev spaces represented as tensor products of sobolev spaces on the factors of the product this leads to regularity results for smooth data