unique real variable expressions of displacement and traction fundamental solutions covering all transversely isotropic elastic materials for 3d bem a general efficient and robust boundary element method bem formulation for the numerical solution of three dimensional linear elastic problems in transversely isotropic solids is developed in the present work the bem formulation is based on the closed form real variable expressions of the fundamental solution in displacements uik and in tractions tik originated by a unit point force valid for any combination of material properties and for any orientation of the radius vector between the source and field points a compact expression of this kind for uik was introduced by ting and lee q j mech appl math 1997 50 407 426 in terms of the stroh eigenvalues on the oblique plane normal to the radius vector working from this expression of uik and after a revision of their final formula a new approach based on the application of the rotational symmetry of the material for deducing the derivative kernel uik j and the corresponding stress kernel ijk and traction kernel tik has been developed in the present work these expressions of uik uik j ijk and tik do not suffer from the difficulties of some previous expressions obtained by other authors in different ways with complex valued functions appearing for some combinations of material parameters and or with division by zero for the radius vector at the rotational symmetry axis the expressions of uik uik j ijk and tik have been presented in a form suitable for an efficient computational implementation the correctness of these expressions and of their implementation in a three dimensional collocational bem code has been tested numerically by solving problems with known analytical solutions for different classes of transversely isotropic materials copyright 2007 john wiley sons ltd

anisotropic elastic plates with holes cracks inclusions subjected to out of plane bending moments the problems of anisotropic plates containing holes cracks and or inclusions have been studied extensively for two dimensional deformations although the correspondence between the two dimensional problems and the plate bending problems has been observed long time ago without clarifying the involved mathematical details one still cannot get the solutions of the plate bending problems directly from the solutions of the corresponding two dimensional problems based upon the correspondence relation recently we developed a stroh like formalism for the bending theory of anisotropic plates by this newly developed formalism most of the relations for bending problems can be organized into the forms for two dimensional problems thus by using the stroh like formalism the analytical solutions for problems of anisotropic plates with holes cracks inclusions subjected to out of plane bending moments can be obtained directly from the solutions of the corresponding two dimensional problems the stresses or resultant bending moments around the hole crack inclusion boundaries are also given explicitly in this paper since the explicit closed form solutions for the present cases have not been found in the literature comparison is made with some special cases of which the analytical solutions exist which shows that our solutions are exact simple and general

a short characterization of relative entropy we prove characterization theorems for relative entropy also known as kullback leibler divergence q logarithmic entropy also known as tsallis entropy and q logarithmic relative entropy all three have been characterized axiomatically before but we show that earlier proofs can be simplified considerably at the same time relaxing some of the hypotheses

sextic formalism in anisotropic elasticity for almost non semisimple matrix n abstract the sextic formalism of stroh for anisotropic elasticity leads to the eigen relation n p in which n is a 6 6 real matrix the orthogonality and closure relations as well as many other relations involving the eigenvalues p and the eigenvectors x are based on the assumption that n is simple or semisimple so that the six eigenvectors span a six dimensional space problems arise when n is non semisimple in fact there are problems even when n is almost non semisimple we present a modified formalism which is valid regardless of whether n is simple almost non semisimple or non semisimple the modified formalism does not apply when n is semisimple

on uniqueness theorems for tsallis entropy and tsallis relative entropy the uniqueness theorem for tsallis entropy was presented in h suyari ieee trans inf theory vol 50 pp 1783 1787 aug 2004 by introducing the generalized shannon khinchin axiom in the present correspondence this result is generalized and simplified as follows generalization the uniqueness theorem for tsallis relative entropy is shown by means of the generalized hobson s axiom simplification the uniqueness theorem for tsallis entropy is shown by means of the generalized faddeev s axiom

deconstructing plane anisotropic elasticity part i the latent structure of lekhnitskii s formalism abstract general solutions of the stress and displacements in two dimensional anisotropic elasticity may be represented by eigenvectors and analytic functions of the complex variables x iy but the representation takes different forms for five distinct types of materials as determined by the elastic compliance matrix in this paper explicit expressions of the general solutions are derived for each type of anisotropic materials in terms of the eigenvalues i and the elements of it is shown that for degenerate and extra degenerate materials the generalized eigenvectors and associated eigensolutions may be obtained by the derivative rule the barnett lothe tensors are defined in terms of unnormalized eigenvectors by the same set of relations regardless of material degeneracy explicit expressions of these tensors are given in concise forms depending only on the multiplicity of the eigenvalues the six dimensional matrix formalism and normalization of the eigenvectors are found to be neither essential nor expedient for the analysis except as a device for abridged expressions of matrix identities

fractional sturm liouville eigen problems we first consider a regular fractional sturm liouville problem of two kinds rfslp i and rfslp ii of order 0 2 the corresponding fractional differential operators in these problems are both of riemann liouville and caputo type of the same fractional order 2 0 1 we obtain the analytical eigensolutions to rfslp i ii as non polynomial functions which we define as jacobi poly fractonomials these eigenfunctions are orthogonal with respect to the weight function associated with rfslp i ii subsequently we extend the fractional operators to a new family of singular fractional sturm liouville problems of two kinds sfslp i and sfslp ii we show that the primary regular boundary value problems rfslp i ii are indeed asymptotic cases for the singular counterparts sfslp i ii furthermore we prove that the eigenvalues of the singular problems are real valued and the corresponding eigenfunctions are orthogonal in addition we obtain the eigen solutions to sfslp i ii analytically also as non polynomial functions hence completing the whole family of the jacobi poly fractonomials in numerical examples we employ the new poly fractonomial bases to demonstrate the exponential convergence of the approximation in agreement with the theoretical results

chaos and chaos synchronization of a symmetric gyro with linear plus cubic damping the dynamic behavior of a symmetric gyro with linear plus cubic damping which is subjected to a harmonic excitation is studied in this paper the liapunov direct method has been used to obtain the sufficient conditions of the stability of the equilibrium points of the system by applying numerical results time history phase diagrams poincare maps liapunov exponents and liapunov dimensions are presented to observe periodic and chaotic motions besides several control methods the delayed feedback control the addition of constant motor torque the addition of period force and adaptive control algorithm aca have been used to control chaos effectively finally attention is shifted to the synchronization of chaos in the two identical chaotic motions of symmetric gyros the results show that one can make two identical chaotic systems to synchronize through applying four different kinds of one way coupling furthermore the synchronization time is also examined

robust synchronization of chaotic horizontal platform systems with phase difference this paper studies a robust synchronization of non autonomous chaotic systems with parameter mismatch in the synchronization scheme a linear state error feedback control is used to couple the master and slave horizontal platform systems excited by harmonic external forces between which there exists a phase mismatch a new definition of global synchronization with error bound is introduced using lyapunov s stability theory the sufficient synchronization criteria for the scheme are proven and the corresponding synchronization error bound is estimated the synchronization criteria are further optimized by optimally designing a quadratic lyapunov function to more precisely estimate the synchronization error bound the illustrative simulations verify the effectiveness of these criteria the estimated synchronization error bound is compared with numerical one in the examples

a mass balance based numerical method for the fractional advection dispersion equation theory and application 1 the inherent heterogeneity of many geophysical systems often gives rise to fast and slow pathways to water and chemical movement and one approach to model solute transport through such media is the continuous time random walk ctrw one special asymptotic case of the ctrw is the fractional advection dispersion equation fade which has proven to be a promising alternative to model anomalous dispersion and has been increasingly used in hydrology to model chemical transport in both surface and subsurface water most practical problems in hydrology have complicated initial and boundary conditions and need to be solved numerically but the numerical solution of the fade is not trivial in this paper we present a finite volume approach to solve the fade where the spatial derivative of the dispersion term is fractional we also give methods to solve different boundary conditions often encountered in practical applications the linear system resulting from the temporal spatial discretization is solved using a semi implicit scheme the numerical method is derived on the basis of mass balance and its accuracy is tested against analytical solutions the method is then applied to simulate tracer movement in a stream and a near saturated hillslope in a naturally structured upland podzol field in northeast scotland

synchronization multistability and basin crisis in coupled pendula abstract the synchronization dynamics of two linearly coupled pendula is studied in this paper based on the lyapunov stability theory and linear matrix inequality lmi some necessary and sufficient conditions for global asymptotic synchronization are derived from which an estimated threshold coupling k th for the on set of full synchronization is obtained the numerical value of k th determined from the average energies of the systems is in good agreement with theoretical analysis prior to the on set of synchronization the boundary crisis of the chaotic attractor is identified in the bistable states where two asymmetric periodic attractors co exist it is shown that the coupled pendula can attain multistable states via a new dynamical transition the basin crisis that occur prior to the on set of stable synchronization the essential feature of basin crisis is that the two co existing attractors are destroyed while new three or more co existing attractors of the same or different periodicity are created in addition the linear perturbation technique and the routh hurwitz criteria are employed to investigate the stability of steady states and clearly identify the different types of bifurcations likely to be encountered finally two parameter phase plots show various regions of chaos hyperchaos and periodicity

master slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control global chaos synchronization of two identical non autonomous horizontal platform systems coupled by linear state error feedback controller is investigated the sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time varied systems and lyapunov s direct method of which the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices in the examples the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified it is analytically and numerically examined that the synchronization criteria based on lyapunov s direct method are sharper than the criteria based on the stability theory of linear time varied systems

chaos synchronization and parameter identification for gyroscope system synchronization of chaos for a two degree of freedom heavy symmetric gyroscope system are studied in this paper because of the nonlinear terms of the system the system exhibits both regular and chaotic motions by lyapunov stability theory with control terms by adaptive control and by random optimization method the synchronization of two identical systems and tracking of the parameter of the systems are studied

chaos synchronization of a horizontal platform system chaos and chaos synchronization of the horizontal platform system are studied in this paper because of the non linear terms of the systems the systems exhibit both regular and chaotic motions by applying various numerical results such as phase portraits poincare maps time history and power spectrum analysis the behaviors of the periodic and chaos synchronization are presented the effects of the change of parameters in the system can be found in the bifurcation diagrams chaos synchronization of feedback methods in two coupled systems has been studied by lyapunov exponent and coupling strength besides phase effect of external excitations and the transient time in unidirectional synchronization also have been researched

the stroh formalism for anisotropic materials that possess an almost extraordinary degenerate matrix n abstract it has been discovered recently that the 6 x 6 elasticity matrix n for an anisotropic elastic material under a two dimensional deformation can be extraordinary degenerate i e n can have three identical pairs of complex conjugate eigenvalues but has only one pair of complex conjugate eigenvector the stroh formalism and the modified formalism for a simple degenerate n available in the literature need to be revised what is more likely to happen in applications is that the matrix n is almost extraordinary degenerate in that case the orthonormalized eigenvectors can be very large causing certain numerical problems we therefore present in this paper a modified formalism that is applicable to the case when n can be extraordinary degenerate or almost extraordinary degenerate

surface waves in anisotropic elastic materials for which the matrix n υ is extraordinary degenerate degenerate or semisimple the 6 x 6 real matrix n for anisotropic elastic materials under a two dimensional steady state motion with speed is extraordinary degenerate when n has three identical complex eigenvalues p but has only one associated eigenvector it has been an open question if such an n exists for surface waves in this paper we first modify the solution for ordinary surface waves to the case when n is extraordinary degenerate the displacement consists of three waves one of which decays exponentially as in the ordinary surface waves according to e ndash 2 where is a positive constant the other two waves decay in proportion to 2endash 2 and x 22endash 2 we then consider a class of materials that has seven independent elastic constants for two dimensional deformations for this class of materials it is shown that there is a five parameter family of extraordinary degenerate n for surface waves thus not only an extraordinary degenerate n for surface waves exists its existence is not as rare as one might have expected we also study surface waves for which n is degenerate or semisimple in the former n has two or three identical complex eigenvalues but has two independent eigenvectors in the latter two of the three eigenvalues are identical but n has three independent eigenvectors it is shown that there are families of degenerate and semisimple n for surface waves

design and implementation of fuzzy sliding mode controllers for generalized projective synchronization of chaos horizontal platform systems this paper presents robust chattering free fuzzy sliding mode control fsmc as a way to achieve generalized projective synchronization gps of two horizontal chaos platform vibration systems with system uncertainty and external disturbance an appropriate sliding surface is acquired through an smc design such that the error state trajectories of a master slave system will reach such a sliding surface and approaches to the origin based on the lyapunov stability theory we address the design schemes of integration fuzzy sliding mode control where the reaching law is proposed by a set of linguistic rules and the control input is chattering free as a consequence the system is simulated and experimented to demonstrate that the error state tends to be stabilized and the chattering problem can be thus resolved implying that the slave horizontal platform system hps is gps with the master hps

master slave synchronization criteria for horizontal platform systems using time delay feedback control abstract this paper is concerned with master slave synchronization for two identical non autonomous horizontal platform systems by using time delay feedback control compared with some existing results on synchronization for horizontal platform systems the effect of the time delay in the feedback control on master slave synchronization is investigated applying a delay decomposition approach some delay dependent synchronization criteria are established and formulated in the form of linear matrix inequalities lmis sufficient conditions about the existence of a time delay feedback controller are derived by employing these newly obtained synchronization criteria the controller gains can be achieved by solving a set of lmis one simulation example is given to illustrate the effectiveness of synchronization criteria and the design method

modeling cardiac pacemakers with relaxation oscillators abstract a modified van der pol oscillator model was designed in order to reproduce the time series of the action potential generated by a natural pacemaker of the heart i e the sa or the av node the main motivation was that the models published up to now were not altogether adequate for research on the heart based on either the classical van der pol oscillator or other nonlinear oscillators these models were interesting rather because of the physical phenomena that could be obtained chaos and synchronization however they were unable to simulate many important physiological features of true physiological action potentials we based our research on the experience of other groups which modeled neuronal oscillators there complex nonlinear oscillators were used whose most important feature was a certain topology of the phase space in our case we modified the phase space of the classical van der pol oscillator by adding two fixed points a saddle and a node in addition a damping term asymmetric with respect to the voltage was introduced introduction of these new features into the van der pol oscillator allowed to change the firing frequency of the pacemaker node without changing the length of the refractory period an important physiological detail we also show different ways of changing the pacemaker rhythm a comparison of the properties of the signal obtained from our model with the features of the action potentials measured by other groups is made

deconstructing plane anisotropic elasticity part ii stroh s formalism sans frills abstract eigensolutions for all types of anisotropic elastic materials are obtained in terms of the eigenvalues and the anisotropic elastic stiffness the generalized eigenvectors and eigensolutions in the degenerate and extra degenerate cases are obtained by the derivative rule a complete set of unnormlized eigenvectors now given in terms of the elastic moduli define the barnett lothe tensors by the same expressions irrespective of material degeneracy explicit expressions of the barnett lothe tensors are obtained in various forms depending on the multiplicity of eigenvalues these expressions complement the alternative expressions of part i in terms of the elastic compliances a new family of extra degenerate materials is found suggesting the superabundance of such materials a concise proof of the equivalence of the eigensystems of the compliance based and elasticity based formalisms is given eigenrelations applicable to all cases of material degeneracy are presented in both three dimensional and six dimensional matrix formalisms

new solutions to pressuring shearing torsion and extension of a cylindrically anisotropic elastic circular tube or bar the problem of a cylindrically anisotropic elastic circular tube or bar subjected to a uniform pressure shearing torsion or extension has been studied by ting the stroh formalism for twodimensio

a unified formalism for elastostatics or steady state motion of compressible or incompressible anisotropic elastic materials abstract for a two dimensional deformation of an anisotropic elastic material the lekhnitski formalism applies to elastostatics only it does not apply to steady state motion such as surface waves or a moving line dislocation the stroh formalism applies to elastostatics as well as steady state motion however it does not apply to an incompressible material because some of the elastic stiffnesses become unbounded in the incompressible limit modifying a new formalism studied recently a more explicit and remarkably simple expression of the matrices in the new formalism is given and a unified formalism that is applicable to elastostatics as well as steady state motion of a compressible or incompressible anisotropic elastic material is obtained as an application the secular equation is presented for surface waves propagating in a monoclinic material with the symmetry plane at x 3 0 that has a more explicit expression than what is available in the literature for a general anisotropic elastic material explicit expressions are obtained for the sextic equation for the eigenvalues p and the eigenvectors b and a for any steady state wave speed the explicit expressions recover results related to one component surface waves when the material is incompressible it is shown that the eigenvalues p remain complex for elastostatics we also show that when the material is incompressible a monoclinic material with the symmetry plane at x 3 0 behaves like that of an orthotropic material

a space time spectral collocation method for the two dimensional variable order fractional percolation equations abstract in this article we introduce a space time spectral collocation method for solving the two dimensional variable order fractional percolation equations the method is based on a legendre gauss lobatto lgl spectral collocation method for discretizing spatial and the spectral collocation method for the time integration of the resulting linear first order system of ordinary differential equation optimal priori error estimates in l 2 norms for the semi discrete and full discrete formulation are derived the method has spectral accuracy in both space and time numerical results confirm the exponential convergence of the proposed method in both space and time

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

general solution for eshelby s problem of 2d arbitrarily shaped piezoelectric inclusions abstract eshelby s problem of piezoelectric inclusions arises sometimes in exploiting the electromechanical coupling effect in piezoelectric media for example it intervenes in the nanostructure design of strained semiconductor devices involving strain induced quantum dot qd and quantum wire qwr growth using the extended stroh formalism the present work gives a general analytical solution for eshelby s problem of two dimensional arbitrarily shaped piezoelectric inclusions the key step toward obtaining this general solution is the derivation of a simple and compact boundary integral expression for the eigenfunctions in the extended stroh formalism applied to eshelby s problem the simplicity and compactness of the boundary integral expression derived make it much less difficult to analytically tackle eshelby s piezoelectric problem for a large variety of non elliptical inclusions in the present work explicit analytical solutions are obtained and detailed for all polygonal inclusions and for the inclusions characterized by jordan s curves and laurent s polynomials by considering the piezoelectric material gaas 110 the analytical solutions provided are illustrated numerically to verify the coincidence between different expressions and to clarify the jump across the boundary of the inclusion and the singularity around the corner of the inclusion

numerical treatment for solving the perturbed fractional pdes using hybrid techniques in this article an accurate numerical approach is introduced in this approach we mixed between the fractional finite difference method and the restrictive taylor approximation rta the proposed method is implemented to solve numerically the perturbed fractional partial differential equations fpdes special attention is given to study the stability and consistency of the method by means of gerschgorin theorem and using the stability matrix analysis two numerical examples are given and compared with the exact solution

diversity as a concept and its measurement abstract this paper puts forth the view that diversity is an average property of a community and identifies that property as species rarity an intrinsic diversity ordering of communities is defined and is shown to be equivalent to stochastic ordering also the sensitivity of an index to rare species is developed culminating in a crossing point theorem and a response theory to perturbations diversity decompositions analogous to the analysis of variance are discussed for two way classifications and mixtures the paper concludes with a brief survey of genetic diversity linguistic diversity industrial concentration and income inequality

dynamics and synchronization of coupled self sustained electromechanical devices abstract the dynamics and synchronization of two coupled self excited devices are considered the stability and duration of the synchronization process between two coupled self sustained electrical oscillators described by the rayleigh duffing oscillator are first analyzed the properties of the hill equation and the whittaker method are used to derive the stability conditions of the synchronization process secondly the averaging method is used to find the amplitudes of the oscillatory states of the self sustained electromechanical device consisting of an electrical rayleigh duffing oscillator coupled magnetically to a linear mechanical oscillator the synchronization of two such coupled devices is discussed and the stability boundaries of the synchronization process are derived using the floquet theory and the hill s determinant good agreement is obtained between the analytical and numerical results

a modified lekhnitskii formalism a la stroh for anisotropic elasticity and classifications of the 6 6 matrix n the stroh formalism for two dimensional deformations of anisotropic elastic materials computes the eigenvalue p and the eigenvector a from an eigenrelation the vector b is then determined from a depending on the number of repeated eigenvalues p and the number of independent eigenvectors a b the system has it can be classified into six groups the lekhnitskii formalism has no eigenrelation to speak of we present a modified lekhnitskii formalism that computes the eigenvalue p and the eigenvector b from an eigenrelation the vector a is then determined from b thus the modified lekhnitskii formalism is a dual to the stroh formalism not only does the modified formalism enable us to do the classifications it is much simpler than using the stroh formalism the six groups are the sp ss d1 d2 ed and es groups the es group does not exist for a real material the ss group that has p 1 p 2 p 3 and the d2 group that has p 1 p 2 p 3 can be identified without computing the eigenvalues p and the eigenvectors a b we show that the repeated eigenvalue p 1 p 2 in the ss and d2 groups is simply a root of the quadratic equation l 2 0 we present an explicit expression of p 3 for the ss group the ed group that has three identical p can also be identified without computing p and a b however we do present an explicit expression of p we show that monoclinic materials with the symmetry plane at x 3 0 cannot belong to the ed group the identification of the sp and d1 groups is the only one that requires computation of p but not a b for special classes of materials however they can be identified without computing p in all cases the eigenvectors and the generalized eigenvectors are obtained explicitly

multi scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions abstract in this paper we investigate the multi scale orthogonal basis method for fractional integral boundary value problems we apply the newton iteration method to linearize the nonlinear problems and employees the idea of collocation method to determine the coefficients of multi scale orthogonal basis then the approximation solution is obtained the error estimation and stable analysis are presented in detailed the final numerical experiments verify that the accuracy of our method

direct observation of homoclinic orbits in human heart rate variability homoclinic trajectories of the interbeat intervals between contractions of ventricles of the human heart are identified the interbeat intervals are extracted from 24 h holter ecg recordings three such recordings are discussed in detail mappings of the measured consecutive interbeat intervals are constructed in the second and in some cases in the fourth iterate of the map of interbeat intervals homoclinic trajectories associated with a hyperbolic saddle are found the homoclinic trajectories are often persistent for many interbeat intervals sometimes spanning many thousands of heartbeats several features typical for homoclinic trajectories found in other systems were identified including a signature of the gluing bifurcation the homoclinic trajectories are present both in recordings of heart rate variability obtained from patients with an increased number of arrhythmias and in cases in which the sinus rhythm is dominant the results presented are a strong indication of the importance of deterministic nonlinear instabilities in human heart rate variability

on the most concise set of axioms and the uniqueness theorem for tsallis entropy we present the most concise set of axioms for tsallis entropy and rigorously prove the uniqueness theorem this set of axioms consists of only two distinct additivities pseudoadditivity and shannon additivity we then compare our axioms with the axioms presented by santos the peculiarity of pseudoadditivity as an axiom for tsallis entropy is also discussed

nonlinear dynamics of the heartbeat i the av junction passive conduit or active oscillator under physiologic conditions the av junction is traditionally regarded as a passive conduit for the conduction of impulses from the atria to the ventricles an alternative view namely that subsidiary pacemakers play an active role in normal electrophysiologic dynamics during sinus rhythm has been suggested based on nonlinear models of cardiac oscillators a central problem has been the development of a simple but explicit mathematical model for coupled nonlinear oscillators relevant both to stable and perturbed cardiac dynamics we use equations describing an analog electrical circuit with an external d c voltage source v0 and two nonlinear oscillators with intrinsic frequencies in the ratio of 3 2 comparable to the sa node and av junction rates the oscillators are coupled by means of a resistor 1 1 sa av phase locking of the oscillators occurs over a critical range of v0 externally driving the sa oscillator at increasing rates results in 3 2 av wenckebach periodicity and a 2 1 av block these findings appear with no assumptions about conduction time or refractoriness this dynamical model is consistent with the new interpretation that normal sinus rhythm may represent 1 1 coupling of two or more active nonlinear oscillators and also accounts for the appearance of an av block with critical changes in a single parameter such as the pacing rate