nonadditive conditional entropy and its significance for local realism based on the form invariance of the structures given by khinchin s axiomatic foundations of information theory and the pseudoadditivity of the tsallis entropy indexed by q the concept of conditional entropy is generalized to the case of nonadditive nonextensive composite systems the proposed nonadditive conditional entropy is classically nonnegative but can be negative in the quantum context indicating its utility for characterizing quantum entanglement a criterion deduced from it for separability of density matrices for validity of local realism is examined in detail by employing a bipartite spin 1 2 system it is found that the strongest criterion is obtained in the limit q

a theoretical and computational framework for anisotropic continuum damage mechanics at large strains abstract the main objective of this work is the formulation and algorithmic treatment of anisotropic continuum damage mechanics at large strains based on the concept of a fictitious isotropic undamaged configuration an additional linear tangent map is introduced which allows the interpretation as a damage deformation gradient then the corresponding finger tensor denoted as damage metric constructs a second order internal variable due to the principle of strain energy equivalence with respect to the fictitious effective space and the standard reference configuration the free energy function can be computed via push forward operations within the nominal setting referring to the framework of standard dissipative materials associated evolution equations are constructed which substantially affect the anisotropic nature of the damage formulation the numerical integration of these ordinary differential equations is highlighted whereby two different schemes and higher order methods are taken into account finally some numerical examples demonstrate the applicability of the proposed framework

numerical studies of time independent and time dependent scattering by several elliptical cylinders a numerical solution to the problem of time dependent scattering by an array of elliptical cylinders with parallel axes is presented the solution is an exact one based on the separation of variables technique in the elliptical coordinate system the addition theorem for mathieu functions and numerical integration time independent solutions are described by a system of linear equations of infinite order which are truncated for numerical computations time dependent solutions are obtained by numerical integration involving a large number of these solutions first results of a software package generating these solutions are presented wave propagation around three impenetrable elliptical scatterers as far as we know this method described has never been used for time dependent multiple scattering

modeling and analysis of a phase field system for damage and phase separation processes in solids abstract in this work we analytically investigate a multi component system for describing phase separation and damage processes in solids the model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an elliptic system with material dependent coefficients for the strain tensor and a doubly nonlinear differential inclusion for the damage function the main aim of this paper is to show existence of weak solutions for the introduced model where in contrast to existing damage models in the literature different elastic properties of damaged and undamaged material are regarded to prove existence of weak solutions for the introduced model we start with an approximation system then by passing to the limit existence results of weak solutions for the proposed model are obtained via suitable variational techniques

a new formalism for time dependent wave scattering from a bounded obstacle a time dependent three dimensional acoustic scattering problem is considered an incoming wave packet is scattered by a bounded simply connected obstacle with locally lipschitz boundary the obstacle is assumed to have a constant boundary acoustic impedance the limit cases of acoustically soft and acoustically hard obstacles are considered the scattered acoustic field is the solution of an exterior problem for the wave equation a new numerical method to compute the scattered acoustic field is proposed this numerical method obtains the time dependent scattered field as a superposition of time harmonic acoustic waves and computes the time harmonic acoustic waves by a new operator expansion method that is the time harmonic acoustic waves are solutions of an exterior boundary value problem for the helmholtz equation the method used to compute the time harmonic waves improves on the method proposed by misici pacelli and zirilli j acoust soc am 103 106 113 1998 and is based on a perturbative series of the type of the one proposed in the operator expansion method by milder j acoust soc am 89 529 541 1991 computationally the method is highly parallelizable with respect to time and space variables some numerical experiments on test problems obtained with a parallel implementation of the numerical method proposed are shown and discussed from the numerical and the physical point of view the website http www econ unian it recchioni w1 shows four animations relative to the numerical experiments

characterizing nonclassical correlations via local quantum uncertainty quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system nothing yet seems to prevent a single physical quantity such as one spin component from being measured with arbitrary precision here we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations when revealed on local observables of a bipartite system such uncertainty defines an entire class of bona fide measures of nonclassical correlations for the case of 2 ifmmode times else texttimes fi d systems we find that a unique measure is defined which we evaluate in closed form we then discuss the role that these correlations which are of the discord type can play in the context of quantum metrology we show in particular that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision as quantified by the quantum fisher information in the optimal phase estimation protocol

generalized conditional entropy in bipartite quantum systems we analyze for a general concave entropic form the associated conditional entropy of a quantum system a b obtained as a result of a local measurement on one of the systems b this quantity is a measure of the average mixedness of a after such measurement and its minimum over all local measurements is shown to be the associated entanglement of formation between a and a purifying third system c in the case of the von neumann entropy this minimum determines also the quantum discord for classically correlated states and mixtures of a pure state with the maximally mixed state we show that the minimizing measurement can be determined analytically and is universal i e the same for all concave forms while these properties no longer hold for general states we also show that in the special case of the linear entropy an explicit expression for the associated conditional entropy can be obtained whose minimum among projective measurements in a general qudit qubit state can be determined analytically in terms of the largest eigenvalue of a simple 3 3 correlation matrix such minimum determines the maximum conditional purity of a and the associated minimizing measurement is shown to be also universal in the vicinity of maximal mixedness results for x states including typical reduced states of spin pairs in xy chains at weak and strong transverse fields are also provided and indicate that the measurements minimizing the von neumann and linear conditional entropies are typically coincident in these states being determined essentially by the main correlation they can differ however substantially from that minimizing the geometric discord

new features of quantum discord uncovered by q entropies the notion of quantum discord introduced by ollivier and zurek phys rev lett 88 2001 017901 see also henderson and vedral j phys a 34 2001 6899 has attracted increasing attention in recent years as an entropic quantifier of non classical features pertaining to the correlations exhibited by bipartite quantum systems here we generalize the notion so as to encompass power law q entropies that reduce to the standard shannon entropy in the limit q 1 and study the concomitant consequences the ensuing new discord like measures we advance describe aspects of non classicality that are different from those associated with the standard quantum discord a particular manifestation of this difference concerns a feature related to order let d1 stand for the standard shannon based discord measure and dq for the q 1 one if two quantum states a b are such that d1 a d1 b this order relation does not remain invariant under a change from d1 to dq

a quasistatic evolution model for the interaction between fracture and damage this paper is devoted to the investigation of a quasistatic evolution model for a continuum which undergoes damage and possibly fracture in both cases the model appears to be ill posed so that it is necessary to introduce a relaxed variational evolution preserving the irreversibility of the process the minimality at each time and the energy balance from a mechanical point of view it turns out that the material prefers to form microstructures through the creation of fine mixtures between the damaged and healthy parts of the medium the brutal character of the damage process is then replaced by a progressive one where the original damage internal variable that is the characteristic function of the damaged part is replaced by the local volume fraction the analysis rests on a locality property for mixtures which enables us to use an alternative formula for the lower semicontinuous envelope of the elastic energy in terms of the g closure set

a fast high order solver for problems of scattering by heterogeneous bodies a new high order integral algorithm for the solution of scattering problems by heterogeneous bodies is presented here a scatterer is described by a continuously or discontinuously varying refractive index n x within a two dimensional 2d bounded region solutions of the associated helmholtz equation under given incident fields are then obtained by high order inversion of the lippmann schwinger integral equation the algorithm runs in o nlog n operations where n is the number of discretization points a wide variety of numerical examples provided include applications to highly singular geometries high contrast configurations as well as acoustically electrically large problems for which supercomputing resources have been used recently our method provides highly accurate solutions for such problems on small desktop computers in cpu times of the order of seconds

quantum discord a measure of the quantumness of correlations two classically identical expressions for the mutual information generally differ when the systems involved are quantum this difference defines the quantum discord it can be used as a measure of the quantumness of correlations separability of the density matrix describing a pair of systems does not guarantee vanishing of the discord thus showing that absence of entanglement does not imply classicality we relate this to the quantum superposition principle and consider the vanishing of discord as a criterion for the preferred effectively classical states of a system i e the pointer states

on a model for phase separation in binary alloys driven by mechanical effects this work is concerned with the mathematical analysis of a system of partial differential equations modeling the effect of phase separation driven by mechanical actions in binary alloys like tin lead solders the system combines the quasistationary balance of linear momentum with a fourth order evolution equation of cahn hilliard type for the phase separation and it is highly nonlinearly coupled existence and uniqueness results are shown tel 0382505631 email bonetti dimat unipv it

generalized nonadditive entropies and quantum entanglement we examine the inference of quantum density operators from incomplete information by means of the maximization of general nonadditive entropic forms extended thermodynamic relations are given when applied to a bipartite spin 1 2 system the formalism allows one to avoid fake entanglement for data based on the bell clauser horne shimony holt observable and in general on any set of bell constraints particular results obtained with the tsallis entropy and with an introduced exponential entropic form are also discussed

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

a variational view of partial brittle damage evolution under time dependent loading an elastic material undergoes the simplest form of damage in which it passes from its original state to a weaker elastic state elaborating on prior work 14 we establish the existence of a relaxed variational evolution where at each time the two states of the material combine to form a fine mixture optimal from the standpoint of the applied load at that time yet preserving the irreversibility of the damaging process

threshold based quasi static brittle damage evolution we introduce models for static and quasi static damage in elastic materials based on a strain threshold and then investigate the relationship between these threshold models and the energy based models introduced in francfort and marigo eur j mech a solids 12 149 189 1993 and francfort and garroni ration mech anal 182 1 125 152 2006 a somewhat surprising result is that while classical solutions for the energy models are also threshold solutions this is shown not to be the case for nonclassical solutions that is solutions with microstructure a new and arguably more physical definition of solutions with microstructure for the energy based model is then given in which the energy minimality property is satisfied by sequences of sets that generate the effective elastic tensors rather than by the tensors themselves we prove existence for this energy based problem and show that these solutions are also threshold solutions a by product of this analysis is that all local minimizers in both the classical setting and for the new microstructure definition are also global minimizers

unified view of quantum and classical correlations we discuss the problem of the separation of total correlations in a given quantum state into entanglement dissonance and classical correlations using the concept of relative entropy as a distance measure of correlations this allows us to put all correlations on an equal footing entanglement and dissonance whose definition is introduced here jointly belong to what is known as quantum discord our methods are completely applicable for multipartite systems of arbitrary dimensions we investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states

damage gradient of damage and principle of virtual power a theory of continuum damage mechanics is developed within the framework of the principle of virtual power because the damage in a solid results from microscopic movements we decided to include the power of these microscopic movements in the power of the internal forces the microscopic velocities are related to the damage rate the power of the internal forces we choose depends on the damage velocity and its gradient to take into account the interactions models issued from this theory are presented they are coherent from the mechanical and mathematical points of view the numerical computations show no mesh sensitivity they describe with good agreement the main experimental properties concrete is chosen as an example to illustrate the theory a model using two damage quantities is also presented it yields the correct description of the unilateral phenomenon observed in concrete finally an extension of the existing models is proposed to describe the fatigue damage behaviour

young measure quasi static damage evolution an existence result for the quasi static evolution of incomplete damage in elastic materials is presented the absence of gradient terms in the damage variable causes a critical lack of compactness therefore the analysis is developed in the framework of young measures where a notion of solution is defined presenting some improvements with respect to previous contributions the main new feature in the proof of the existence result regards a delicate construction of the joint recovery sequence

conditional renyi entropies there is no generally accepted definition of conditional renyi entropy the unconditional renyi entropy depends on a parameter which for the case of min entropy takes the value even for this particular case there are several proposals for the definition of conditional entropy this paper describes three general definitions of conditional renyi entropy that were found or suggested in the literature their properties are studied and their values as a function of are compared the particular case of min entropy is widely used in cryptography as a security parameter this case is studied in some detail

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

theory of ground state factorization in quantum cooperative systems we introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems the method allows us to determine rigorously the existence location and exact form of separable ground states in a large variety of generally nonexactly solvable spin models belonging to different universality classes the theory applies to translationally invariant systems irrespective of spatial dimensionality and for spin spin interactions of arbitrary range