continuum approach to computational multiscale modeling of propagating fracture a new approach to two scale modeling of propagating fracture based on computational homogenization fe2 is presented the specific features of the approach are a a continuum setting for representation of the fracture at both scales based on the continuum strong discontinuity approach csda and b the use for the considered non smooth discontinuous problem of the same computational homogenization framework than for classical smooth cases as a key issue the approach retrieves a characteristic length computed at the lower scale which is exported to the upper one and used therein as a regularization parameter for a propagating strong discontinuity kinematics this guarantees the correct transfer of fracture energy between scales and the proper dissipation at the upper scale representative simulations show that the resulting formulation provides consistent results which are objective with respect to size and bias of the upper scale mesh and with respect to the size of the lower scale rve failure cell as well as the capability to model propagating cracks at the upper scale in combination with crack path field and strain injection techniques the continuum character of the approach confers to the formulation a minimal intrusive character with respect to standard procedures for multi scale computational homogenization

gaussian interference channel capacity to within one bit the capacity of the two user gaussian interference channel has been open for 30 years the understanding on this problem has been limited the best known achievable region is due to han and kobayashi but its characterization is very complicated it is also not known how tight the existing outer bounds are in this work we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges and by deriving new outer bounds we show that a very simple and explicit han kobayashi type scheme can achieve to within a single bit per second per hertz bit s hz of the capacity for all values of the channel parameters we also show that the scheme is asymptotically optimal at certain high signal to noise ratio snr regimes using our results we provide a natural generalization of the point to point classical notion of degrees of freedom to interference limited scenarios

discontinuous displacement approximation for capturing plastic localization it is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries interfaces of the finite element subdivision the regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept as a by product of the regularization an intrinsic band width is introduced as a constitutive property rather than a geometric feature of the finite element mesh in this way the spurious mesh sensitivity which is obtained when the displacement approximation is continuous can be avoided another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material an interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface up to within a scalar factor an analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a shear band for a general plasticity model the significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress it is shown that a unique structural post peak response in accordance with non linear fracture mechanics can be achieved when the plastic softening modulus is properly related to the bandwidth the paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope

a damage model with evolving nonlocal interactions we present a damage model for softening materials with evolving nonlocal interactions the thermodynamic implications and the material stability issue are addressed the proposed nonlocal averaging scheme provides the obtained constitutive models with an evolving nonlocal interaction which is activated only when damage occurs in the analysis of structures made of quasi brittle materials this feature helps not only to overcome some issues with the incorrect initiation of damage but also to better control the evolving size of the active fracture process zone this is an essential feature that is usually not considered in depth in many existing nonlocal approaches to the continuum modelling of quasi brittle fracture numerical examples are given to demonstrate features of the proposed modelling approach

an analytical solution with local elastoplastic models for the evolution of dynamic softening strain softening is associated with the evolution of localization with the use of the similarity method a closed form solution for wave propagation in a strain softening bar is derived in the paper through a partitioned modeling procedure with local elastoplastic constitutive models the initial point of the localization is taken as the point at which the type of governing differential equation transforms from a hyperbolic one to an elliptic one due to material softening the evolution of localization is then represented by a moving material surface between the softening domain and non softening domain the motion of the material surface is of diffusion type representing macroscopically the progressive percolation of heterogeneous flow or microdamage the evolution of relevant field variables along the bar is shown and the effects of the model parameters on the solution are discussed to demonstrate the proposed procedure the analytical solution is unique and stable for the given set of boundary and initial data and material properties based on the theory of differential equations

fixed rate transmission over fading interference channels using point to point gaussian codes this paper investigates transmission schemes for fixed rate communications over a rayleigh block fading interference channel there are two source destination pairs where each source in the presence of a short term power constraint intends to communicate with its dedicated destination at a fixed data rate it encodes its messages using a point to point gaussian codebook the two users transmissions can be conducted orthogonally or non orthogonally in the latter case each destination performs either direct decoding by treating the interference as noise or successive interference cancellation sic to recover its desired message for each scheme we seek solutions of a power control problem to efficiently assign power to the sources such that the codewords can be successfully decoded at destinations however because of the random nature of fading the power control problem for some channel realizations may not have any feasible solution and the transmission will be in outage thus for each transmission scheme we first compute a lower bound and an upper bound on the outage probability next we use these results to find an outer bound and an inner bound on the epsilon outage achievable rate region i e the rate region in which the outage probability is below a certain value epsilon

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

theoretical and computational issues in modelling material failure in strong discontinuity scenarios the paper deals with several aspects related to numerical modelling of material failure in strong discontinuity settings a the onset and development of local material failure in terms of continuum constitutive models equipped with strain softening closed forms formulas for the solutions of the discontinuous material bifurcation problem are given for a class of those models b finite elements with embedded discontinuities nodal and elemental enrichments families are formulated in the continuum strong discontinuity approach csda c instability treatment a discrete viscous perturbation method at the failure surfaces is presented as a way to substantially improve the robustness of the numerical simulations

effect of deviatoric nonassociativity on the failure prediction for elastic plastic materials abstract this paper presents a theoretical study of the effect of nonassociativity of the plastic flow rule on the critical plastic modulus for discontinuous bifurcation in an elastic plastic material nonassociativity in both the spherical and the deviatoric spaces are considered with an emphasis on the effect of nonassociativity in the deviatoric space a particular form of nonassociativity in the deviatoric space is introduced where the projections of the plastic flow direction and the normal to the yield surface are assumed to have the same length but the projection of plastic flow direction is allowed to lag that of the normal by an angle it is shown that even for the simple yield surface of von mises nonassociativity in the deviatoric space can lead to a bifurcation for a load parameter significantly lower than the value predicted with an associated flow rule

discontinuous bifurcation analysis of thermodynamically consistent gradient poroplastic materials abstract in this work analytical and numerical solutions of the condition for discontinuous bifurcation of thermodynamically consistent gradient based poroplastic materials are obtained and evaluated the main aim is the analysis of the potentials for localized failure modes in the form of discontinuous bifurcation in partially saturated gradient based poroplastic materials as well as the dependence of these potentials on the current hydraulic and stress conditions also the main differences with the localization conditions of the related local theory for poroplastic materials are evaluated to perfectly understand the regularization capabilities of the non local gradient based one firstly the condition for discontinuous bifurcation is formulated from wave propagation analyses in poroplastic media the material formulation employed in this work for the spectral properties evaluation of the discontinuous bifurcation condition is the thermodynamically consistent gradient based modified cam clay model for partially saturated porous media previously proposed by the authors the main and novel feature of this constitutive theory is the inclusion of a gradient internal length of the porous phase which together with the characteristic length of the solid skeleton comprehensively defined the non local characteristics of the represented porous material after presenting the fundamental equations of the thermodynamically consistent gradient based poroplastic constitutive model the analytical expressions of the critical hardening softening modulus for discontinuous bifurcation under both drained and undrained conditions are obtained as a particular case the related local constitutive model is also evaluated from the discontinuous bifurcation condition stand point then the localization analysis of the thermodynamically consistent non local and local poroplastic cam clay theories is performed the results demonstrate on the one hand and related to the local poroplastic material the decisive role of the pore pressure and of the volumetric non associativity degree on the location of the transition point between ductile and brittle failure regimes in the stress space on the other hand the results demonstrate as well the regularization capabilities of the non local gradient based poroplastic theory with exception of a particular stress condition which is also evaluated in this work finally it is also shown that due to dependence of the characteristic lengths for the pore and skeleton phases on the hydraulic and stress conditions the non local theory is able to reproduce the strong reduction of failure diffusion that takes place under both low confinement and low pore pressure of partially saturated porous materials without loosing however the ellipticity of the related differential equations

discontinuous bifurcation states for associated smooth plasticity and damage with isotropic elasticity abstract for many constitutive equations the tangent tensor consists of a rank one modification to the isotropic elasticity tensor with a total of two elasticity parameters and one parameter describing the current state of inelasticity for small deformations general expressions are derived for the loss of ellipticity the corresponding normal to the bifurcation plane and the mode of discontinuous bifurcation for the velocity gradient if the principal basis of an evolution tensor is used the current stress or strain state is characterized by two additional parameters the small number of material and state parameters makes it feasible to use contour plots to iilustrate all possible combinations that can provide a discontinuous bifurcation these bifurcation maps can be used to illustrate the bifurcation properties of a particular plasticity or continuum damage constitutive model conversely the bifurcation maps can be used in conjunction with experimental data on bifurcation features to assist in the development of constitutive equations that provide the correct failure criterion for a given material under all possible stress paths

numerical analyses of discontinuous material bifurcation strong and weak discontinuities abstract in this paper an algorithmic formulation for numerical analyses of material bifurcation is presented conditions for the onset of both weak discontinuities discontinuous strain rates and strong discontinuities discontinuous velocity fields are summarized based on a recently proposed plasticity model formulated within the logarithmic strain space the condition for the formation of strong discontinuities is extended to anisotropic finite strain plasticity theory the resulting equations associated with the mode of bifurcation are solved numerically for that purpose an equivalent optimization problem is considered the algorithmic formulation is based on newton s method using a consistent linearization to enlarge the radius of convergence a line search strategy is applied the applicability of the proposed implementation as well as its performance and numerical robustness is investigated by means of three dimensional numerical bifurcation analyses of a drucker prager type plasticity model

the generalized diversity multiplexing tradeoff of the mimo z interference channel the generalized diversity multiplexing tradeoff gdmt of the two user quasi static fading multi input multi output mimo z interference channel z ic is established for the general case with an arbitrary number of antennas at each node under the assumptions of full channel state information at the transmitters csit and a short term average power constraint in the gdmt framework which captures the rate versus reliability tradeoff in the high signal to noise ratio snr regime the direct link snr and cross link interference to noise ratio inr are allowed to be disparate so that their ratios relative to a nominal snr in the decibel scale i e the snr and inr exponents are arbitrary and fixed it is shown that a simple han kobayashi message splitting partial interference decoding scheme that uses only partial csit in which the second transmitter s signal depends only on its cross link channel matrix and the first user s transmit signal does not need any csit can achieve the full csit gdmt of the mimo z ic the gdmt of the mimo z ic under the no csit assumption is also obtained for some range of multiplexing gains the size of this range depends on the numbers of antennas at the four nodes and the snr and inr exponents of the direct and cross links respectively for certain classes of channels including those in which the interfered receiver has more antennas than do the other nodes or when the inr exponent is greater than a certain threshold the gdmt of the mimo z ic under the no csit assumption is also completely characterized

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

a variational multiscale approach to strain localization formulation for multidimensional problems abstract the multiscale approach to strain localization problems developed earlier is generalized to higher dimensions the key idea is the identification of the fine scale field with a component of the displacement that has a large gradient the difference between the total displacement and the fine scale is the coarse scale field the formulation is variationally based with the weak form as the point of departure with suitable assumptions on the space of fine scale fields the weak form is separable into coarse and fine scale parts the weak form of the fine scale problem is used to eliminate the fine scales from the formulation this is achieved by way of a projection onto the fine scale space and allows a reformulation of the full problem in terms of coarse scale components alone in this framework fine scale interpolations are identified that ensure sharp resolution of localized displacement irrespective of the underlying finite element mesh it is demonstrated that by correctly accounting for the microstructural fine scale behavior the formulation results in solutions devoid of pathological mesh sensitivity for problems wherein the detailed structure of the localized displacement is of interest recovery of the fine scale components can be performed to reconstruct the entire displacement field several numerical examples are presented that demonstrate the robustness of the formulation

a new achievable rate region for the interference channel a new achievable rate region for the general interference channel which extends previous results is presented and evaluated the technique used is a generalization of superposition coding to the multivariable case a detailed computation for the gaussian channel case clarifies to what extent the new region improves previous ones the capacity of a class of gaussian interference channels is also established

strain localization short to long correlation length transition abstract the current study considers the problem of the strain localization as being a dynamic transition in the range of the correlation length using the particle dynamic method within the framework of statistical physics the proposed model re examines the assumptions and simplifications of the traditional quasi static continuum localization theories special attention is focused on the softening regime mystery of the vanishing fault width and the reasons for this pathological result the proposed model suggests an objective and physically acceptable measure of the fault width

localization analysis via a geometrical method a geometrical technique is proposed in order to solve explicitly the critical conditions at localization for a quite general constitutive behaviour with isotropic elastic properties these critical conditions are shown to be closely related to the spectral properties eigenvalues and eigenvectors of the sum and difference of two tensors describing the inelastic effects when these two tensors are coaxial it is shown that the normal to a potential localization plane always lies in one of their principal planes it is also demonstrated that depending on the constitutive behaviour and the loading conditions several expressions for the critical hardening modulus at localization are available and their respective domain of validity well defined the roles and interactions of both deviatoric and hydrostatic non associativities in the critical conditions of localization are emphasized

embedded localization band in undrained soil based on regularized strong discontinuity theory and fe analysis abstract the paper presents a novel approach to the analysis of a developing localization zone in undrained soil considered as a mixture of a solid skeleton and fluid filled pores where the solid phase is considered as elastic plastic the basic feature is the concept of regularized displacement and pore pressure discontinuities which are assumed to occur across an internal discontinuity surface in this respect the present developments are extensions of those suggested by simo et al 1993 comput mech 12 277 296 and more recently by larsson and runesson 1995 j engng mech asce in press a finite element formulation is proposed on the basis of a mixed variational formulation in the spirit of the enhanced strain concept by simo and rifai 1990 int j numer meth engng 29 1595 1638 in this fashion the localization zone is embedded into a base element for the ordinary analysis of the non localized mixture problem

a partitioned modeling approach with moving jump conditions for localization abstract although many investigations have been performed on localization problems there still exist some pressing issues specifically it is difficult to show in general well posed governing equations based on the essential features of localization phenomena a partitioned modeling approach is proposed here via moving jump conditions for localization problems by taking the initial point of localization as that point where the type of the governing differential equation changes i e a hyperbolic to an elliptic type for dynamic problems and an elliptic to another elliptic type for static problems a moving boundary between localized and non localized deformation zones is defined through jump forms of conservation laws across the boundary as a result localization problems might be considered in the same category as shocks in fluids and solidification in heat transfer to illustrate the proposed procedure one dimensional analytical solutions are given with an emphasis on the definition of boundary conditions and the experimental means to determine model parameters associated with localization future research is then discussed on an extension to general cases

analytical and numerical tests for loss of material stability material instability occurs when ellipticity is lost for symmetric constitutive equations prior to loss of ellipticity it is possible that the second order work of hill or drucker becomes negative there are implications in the literature that numerical solutions cease to be meaningful when a material strain softens and the second order work is not positive the instant that the second order work is zero or negative simultaneously with the additional restriction that the strain increments satisfy compatibility is equivalent to the loss of the ellipticity criterion for symmetric constitutive relations the loss of ellipticity criterion is the appropriate one for identifying when numerical solutions cease to show convergence and may also be a suitable criterion for identifying the instant at which material failure is initiated an analytical development is provided for loss of ellipticity together with an explicit expression for the normal to the bifurcation plane numerical solutions are given for several sample problems for all cases the numerical solutions based on the finite element method conform to the theoretical expectations that unique numerical solutions exist prior to the point at which ellipticity is lost

bifurcations in elastic plastic materials abstract when strain softening elastic plastic materials are loaded into the plastic regime they often exhibit deformations that are localized into small regions at some point in the loading process this intense localized deformation limits the formability of materials and will often quickly lead to failure with continued loading localized deformation is often associated with satisfaction of the classical discontinuous bifurcation criterion here we propose that the loss of strong ellipticity criterion should be used in place of the classical discontinuous bifurcation criterion as a necessary condition for localization the application of the strong ellipticity criterion implies that a bifurcation mode associated with loss of positive definiteness of the symmetric part of the acoustic tensor must be identified rather than a mode associated with the first zero eigenvalue of the acoustic tensor itself the eigensystem for the symmetric part of the tangent modulus tensor is obtained for several different plasticity models this eigensystem provides information about deformation modes associated with both diffuse and discontinuous bifurcations material properties boundary conditions and body geometry are all shown to affect the diffuse and localized deformation modes that are generated numerous experimental observations of necking and localization in metal specimens subject to various boundary conditions are explained with the proposed approach

decohesive carrying capacity of a disk under tension and in plane torsion abstract an elastic perfectly plastic circular disk with rigid circular inclusion of the radius a subjected to simultaneous uniform radial tension and in plane torsion is considered external radius of the disk is assumed to be infinitely large just to simplify the boundary conditions limit load carrying capacity of such a disk cannot be reached it is preceded by decohesive carrying capacity dcc defined by infinitely large radial strains e r they attain their upper bound for r a then the shearing strains r at r a increase infinitely as well in contradistinction to the limit carrying capacity the decohesive carrying capacity depends essentially on poisson s ratio v interaction curves corresponding to dcc are shown in the plane of external loadings a comparison with the condition of discontinuous bifurcation under uniform stresses and strains is given and full agreement is found though in the case under consideration the state of stress is evidently non uniform diagrams of stress and strain distribution at the moment of decohesion are also presented

on the han kobayashi region for theinterference channel in this correspondence we derive a simplified description of the han kobayashi rate region for the general interference channel using this result we establish that the recently discovered chong motani garg rate region is a new representation of the han kobayashi region moreover a tighter bound for the cardinality of the time sharing auxiliary random variable emerges from our simplified description

uniqueness and localization i associative and non associative elastoplasticity abstract localization of deformation into a planar band in the incremental response of elasto plastic material is studied in the case of small strains and rotations the critical hardening modulus for localization is given in an explicit form uncoupled from the band normal for an arbitrary rate independent non associative plasticity loss of uniqueness of the response is investigated in terms of positiveness of the second order work density criteria for loss of second order work positiveness and localization are compared for plane stress and plane strain in these cases for the associative flow rule the threshold for the second order work positiveness coincides with the threshold for shear band formation this coincidence may not however occur if localization into splitting mode is attained

acceleration waves in elasto plasticity a spectral analysis of the acceleration wave problem in general elasto plastic materials is carried out whereby explicit expressions for the eigenvalues and eigenvectors are obtained in case of nonassociated plasticity all eigenvectors become nonorthogonal and one eigenvalue always remains unchanged and equal to the shear modulus for a very broad class of nonassociated plasticity models it is shown that the eigenvalues are always real implying that so called divergence instability can occur while flutter instability can never occur it is found that a certain value of the hardening modulus exists for which specific propagation directions will always imply that all wave speeds are identical and equal to the elastic distortion wave speed moreover in this situation the eigenvectors are arbitrary corresponding to a state of diffuse wave modes the criteria of von mises and rankine are used to illustrate some of the findings

on the localization properties of multiplicative hyperelasto plastic continua with strong discontinuities abstract the objective of this work is to examine the large strain localization properties of hyperelasto plastic materials which are based on the multiplicative decomposition of the deformation gradient thereby the case of strong discontinuities is investigated to this end first an explicit expression for the spatial tangent operator is given taking into account anisotropic as well as nonassociated material behaviour then the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail based on these two results the localization condition is derived with special emphasis on the loading conditions inside and outside an anticipated localization band thereby the intriguingly simple structure of the tangent operator which resembles the structure of the geometrically linear theory is extensively exploited this similarity carries over to the general representation for the critical hardening modulus which is exemplified for isotropic materials as a result analytical solutions are available under the assumption of small elastic strains which is justified for metals finally examples are given for the special case of the associated von mises flow rule to this end the critical localization direction and the critical hardening modulus are investigated with respect to the amount of finite elastic strain within different modes of homogeneous elasto plastic deformations

capturing strain localization in dense sands with random density summary this paper presents a three invariant constitutive framework suitable for the numerical analyses of localization instabilities in granular materials exhibiting unstructured random density a recently proposed elastoplastic model for sands based on critical state plasticity is enhanced with the third stress invariant to capture the difference in the compressive and extensional yield strengths commonly observed in geomaterials undergoing plastic deformation the new three invariant constitutive model similar to its two invariant predecessor is capable of accounting for meso scale inhomogeneities as well as material and geometric nonlinearities details regarding the numerical implementation of the model into a fully nonlinear finite element framework are presented and a closed form expression for the consistent tangent operator whose spectral form is used in the strain localization analyses is derived an algorithm based on the spectral form of the so called acoustic tensor is proposed to search for the necessary conditions for deformation bands to develop the aforementioned framework is utilized in a series of boundary value problems on dense sand specimens whose density fields are modelled as exponentially distributed unstructured random fields to account for the effect of inhomogeneities at the meso scale and the intrinsic uncertainty associated with them copyright 2006 john wiley sons ltd

benchmarking on bifurcation and localization in j2 plasticity for plane stress and plane strain conditions this paper studies the phenomenon of strain bifurcation and localization in j2 plasticity under plane stress and plane strain conditions necessary conditions for the outcome of bifurcation localization stress boundedness and decohesion are analytically established it is shown that the explicit consideration of these conditions allows for the determination of localization angles in certain situations of interest that can be used to conduct benchmark tests on finite element formulations the relative merits of irreducible stabilized mixed and displacement and or strain enhanced formulations are discussed numerical examples show that the mixed displacement pressure formulation is to be preferred to the standard irreducible schemes in order to predict correct failure mechanisms with localized patterns of plastic deformation mixed elements are shown to be practically free from mesh directional bias dependence

the capacity of the gaussian interference channel under strong interference corresp the capacity region of a gaussian interference channel with two separate messages is obtained for the case of moderately strong interference it is shown that the region coincides with the one where both messages are required in both receiving terminals

diversity multiplexing tradeoff for the interference channel with a relay we study the diversity multiplexing tradeoff dmt for the slow fading interference channel with a relay icr we derive four inner bounds on the dmt region the first is based on the compress and forward cf relaying scheme the second is based on the decode and forward df relaying scheme and the last two bounds are based on the half duplex hd and full duplex fd amplify and forward af schemes for the cf and df schemes we find conditions on the channel parameters and the multiplexing gains under which the corresponding inner bound achieves the optimal dmt region we also identify the cases in which the dmt region of the icr corresponds to that of two parallel slow fading relay channels implying that interference does not decrease the dmt for each pair and that a single relay can be dmt optimal for two pairs simultaneously for the hd af scheme we derive conditions on the channel coefficients under which the proposed scheme achieves the optimal dmt for the af based relay channel finally we identify the conditions under which adding a relay strictly enlarges the dmt region relative to the interference channel without a relay

comments on loss of strong ellipticity in elastoplasticity the loss of strong ellipticity is analyzed for a rate independent infinitesimal elastoplastic model this local stability condition corresponds to the loss of positive definiteness of the symmetric part of the acoustic tensor first in the case of multisurface plasticity some expressions for the plastic hardening moduli are obtained for various bifurcation criteria next explicit expressions for the critical plastic hardening modulus and the critical orientation are obtained in the case of single surface plasticity hill type comparison solid the analysis is based on a geometric method linear isotropic elasticity and a general nonassociative flow rule are assumed however the principal axes of the second order tensors of the plastic potential and yield surfaces gradients are coaxial it is shown that similar to the loss of ellipticity the direction of the critical orientation is identical to one of the principal directions except in the particular case where the gradient of the plastic potential and yield surfaces each have a double eigenvalue in particular explicit expression for the plastic hardening modulus using the same geometric method is also presented for the raniecki type comparison solid as an illustrative example the critical orientation for the loss of strong ellipticity and the classical shear band localization loss of ellipticity are compared for axially symmetric compression and tension

efficiency of information spreading in a population of diffusing agents we introduce a model for information spreading among a population of n agents diffusing on a square l x l lattice starting from an informed agent source information passing from informed to unaware agents occurs whenever the relative distance is or 1 numerical simulations show that the time required for the information to reach all agents scales as n alpha l beta where alpha and beta are noninteger a decay factor z takes into account the degeneration of information as it passes from one agent to another the final average degree of information of the population tau av z is thus history dependent we find that the behavior of tau av z is nonmonotonic with respect to n and l and displays a set of minima part of the results are recovered with analytical approximations

effects of mixing in threshold models of social behavior we consider the dynamics of an extension of the influential granovetter model of social behavior where individuals are affected by their personal preferences and observation of the neighbors behavior individuals are arranged in a network usually the square lattice and each has a state and a fixed threshold for behavior changes we simulate the system asynchronously by picking a random individual and we either update its state or exchange it with another randomly chosen individual mixing we describe the dynamics analytically in the fast mixing limit by using the mean field approximation and investigate it mainly numerically in the case of finite mixing we show that the dynamics converge to a manifold in state space which determines the possible equilibria and show how to estimate the projection of this manifold by using simulated trajectories emitted from different initial points we show that the effects of considering the network can be decomposed into finite neighborhood effects and finite mixing rate effects which have qualitatively similar effects both of these effects increase the tendency of the system to move from a less desired equilibrium to the ground state our findings can be used to probe shifts in behavioral norms and have implications for the role of information flow in determining when social norms that have become unpopular in particular communities such as foot binding or female genital cutting persist or vanish

on failure indicators in multidissipative materials abstract multi dissipative constitutive descriptions of irreversible material degradation result in tangent operators that are made up of multiple rank one updates of the elasticity tensors multisurface elastoplasticity plastic yielding combined with elastic degradation and multicrack models are representative examples the spectral properties of these tangent operators determine failure conditions at the material level in terms of loss of uniqueness and discontinuous bifurcation of the incremental response these failure properties are analysed herein by studying the eigensolution of the sum of n rank one m m matrices and the eigensolution of n rank one updates of the m m identity matrix whereby the tangent material tensors are written in matrix form analytical eigensolutions are presented and interpreted mechanically in terms of continuous and discontinuous failure indicators in the light of these spectral properties the failure indicators of single dissipative materials are revisited and explicit results are presented for double dissipative models in the form of plasticity combined with elastic damage in particular it is shown that the activation and interaction of two dissipation processes may destabilize the tangent operators beyond the state resulting from a single active mechanism

bounds and approximations for elastodynamic wave speeds in tetragonal media this paper presents an analytical study of elastodynamic waves propagating along an arbitrary direction in anisotropic materials with tetragonal symmetry upper and lower bounds are developed on the wave speeds through an additive decomposition of the acoustic tensor into an associated hexagonal counterpart and a rank one modification the eigenproperties of which can be determined analytically the bounds are obtained by applying the minimax property of eigenvalues linear approximations of the wave speeds are obtained from a first order expansion of the eigenvalues of the acoustic tensor with respect to a tetragonality index about the value of that index for which tetragonal symmetry degenerates to hexagonal symmetry a numerical example shows that the linear approximations agree remarkably well with the exact values of the wave speeds

potts model for exaggeration of a simple rumor transmitted by recreant rumormongers a simple rumor transmitted by recreant rumormongers is considered quantitatively the simple message contained in the rumor is represented by a simple proposition that has been universally quantified the operations to change the proposition by rumormongers are established to describe the rumor s transmission along different channels mathematically a spin chain is introduced in which spins represent the operations the addition of spins is established according to the laws of operations the result of a rumor s transmission is given by the chain s spin sum the model which is favorable for a social prognostication can determine quantitatively how the social guide and the competition among various opinions affect the exaggeration of the simple rumor transmitted by recreant rumormongers it proves that the rumor forms potts like spin chains in the case with maximum information entropy the approximate calculation shows that the rumor may be aggrandized little or aggrandized normally even sometimes catastrophically moreover the exaggeration is greater when the guide is larger and the competition is lower

relation between structure and size in social networks in the context of complex network systems we model social networks with the property that there is certain degradation of the information flowing through the network we analyze different kinds of networks from regular lattices to random graphs we define an average coordination degree for the network which can be associated with a certain notion of efficiency assuming that there is a limit to the information a person may handle we show that there exists a close relationship between the structure of the network and its maximum size

on the axioms of plasticity abstract in the present paper some propositions usually considered as independent axioms in plasticity theory including ii yushin s postulate are obtained as consequences of a general axiomatic structure of continuum damage mechanics this fact indicates that continuum damage mechanics and plasticity theory have common conceptual foundations notwithstanding that their phenomenological manifestations are different for many aspects the formal framework used is able to consider different plasticity constitutive models and some of the non classical situations discussed recently in technical literature on the basic concepts of plasticity theory as the loss of convexity of the yield surface and the violation of ii yushin s postulate in non associative plasticity a comparative analysis with other proposals on foundations of plasticity in technical literature is developed

properties of discontinuous bifurcation solutions in elasto plasticity explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic plastic materials are presented it then follows that the classical value of the critical hardening modulus derived by rice 1976 proc 14th iutam congr delft the netherlands pp 207 220 north holland amsterdam is in fact the only possible one furthermore from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived for non associated volumetric flow rules while the devialoric portion is associated the considered yield and potential functions may depend on all three stress invariants and may involve mixed isotropic and kinematic hardening the result obtained by rudnicki and rice 1975 j mech phys solids 23 371 394 for a drucker pruger material appear as a special case other criteria that are investigated arc those of coulomb and rankine less

diversity multiplexing tradeoff in two user fading interference channels we analyze the two user single antenna fading interference channel with perfect receive channel state information csi and no transmit csi the diversity multiplexing tradeoff dmt region of a fixed power split han and kobayashi hk type superposition coding scheme is considered and design criteria for the corresponding superposition codes are derived we demonstrate that this scheme is dmt optimal under strong and very strong interference by showing that it achieves a dmt region outer bound that we derive n addition we show that under very strong interference decoding interference while treating the intended signal as noise subtracting the result out and then decoding the desired signal a process known as stripping achieves the optimal dmt region our proofs reveal code design criteria for achieving dmt optimality in the cases where we can demonstrate it

nonlocal constitutive models with gradients of internal variables derived from a micro macro homogenization procedure finite element simulations involving strain softening materials or finite strains are faced with problems of loss of uniqueness and strain localization if localization occurs the size of the region where the strains concentrate is determined by the mesh size and no convergence can be obtained with mesh refinement a non local approach has been proposed recently by andrieux et al 15 16 in order to solve the problem with this approach spatial gradients of internal variables are incorporated in the macroscopic constitutive equations via a homogenization procedure in this paper this new formulation is investigated and numerical algorithms are presented for the one dimensional case the results of the numerical simulations demonstrate that the size of the strain localization zone cannot be arbitrarily small anymore c 1999 elsevier science s a all rights reserved

signaling over two user parallel gaussian interference channels outage analysis this paper presents an outage analysis for a two user parallel gaussian interference channel consisting of two sub channels each sub channel is modeled as a two user gaussian interference channel with quasi static and flat fading both users employ single layer gaussian code books and maintain a statistical correlation rho between the signals transmitted over the underlying sub channels when joint decoding jd is performed at the receivers setting rho 0 minimizes the outage probability regardless of the value of the signal to noise ratio snr it is shown however that if the receivers treat interference as noise tin or cancel interference ci the value of optimum rho approaches 1 as snr goes to infinity motivated by these observations we let rho 0 under jd and rho 1 under tin and ci and compute the outage probability in finite snr assuming that the direct and crossover channel coefficients are independent zero mean complex gaussian random variables with possibly different variances in the asymptote of large snr and assuming the transmission rate per user is r log mathrm snr it is shown that the outage probability scales like mathrm snr 1 r under both tin and ci while it vanishes at least as fast as mathrm snr min 2 r 4 1 r log mathrm snr under jd this paper is concluded by extending some of the results to a two user parallel gaussian interference channel with an arbitrary number of sub channels

two scale shear band evolution by local partition of unity we introduce a methodology to model shear band evolution in the quasi static regime using the extended finite element method we enrich the finite element polynomial displacement field with a fine scale function which models the high displacement gradient in the shear band for this purpose we use a local partition of unity and a parameterized displacement enrichment based on closed form solutions for one dimensional shear bands a stabilized consistent penalty method is used to circumvent locking in the regularized elasto viscoplastic plane strain regime and to guarantee element stability the loss of stability of the boundary value problem is used as an indicator of shear band initiation point and direction shear band development examples are shown illustrating the capabilities of the method to track shear band evolution and strains as high as 1000 copyright 2005 john wiley sons ltd