a new concept of geometric phase in parameter space coupling as a parameter we have obtained the geometric phase of the tripartite spin 1 2 system with spin spin coupling and discussed the influence of this coupling on the geometric phase we have discovered the coupling independent geometric phase and explained it based on this work we propose the concept of quasimagnetic field and assimilate the coupling into the parameter space by this theory the relation between the geometric phase and the solid angle in parameter space still holds for a system with spin spin coupling if the concept of the parameter is properly revised in the way we have elucidated

berry s phase and the planar three body problem berry s angular 2 form in seen as a correction to the symplectic structure in a separation of variables type scheme where the variables are canonically non separable this view is applied to the planar three body problem where the rotational and vibrational motions are not separable it is shown that the corrected symplectic structure gives the correct quantisation

a quadrilateral g1 conforming finite element for the kirchhoff plate model abstract a quadrilateral bi cubic g 1 conforming finite element for the analysis of kirchhoff plates is presented the rational version of the gregory patch proposed by loop et al 2009 is the starting point of our formulation this version of the gregory patch consists in rational enhancement of the bi cubic bezier interpolation representing a suitable tool for designing g 1 conforming quadrilateral element on c 0 conforming un structured meshes the element includes as additional degrees of freedom the edge rotations like in the loof formulations but is only displacement based because of the presence of the rational functions the second derivatives of the interpolation present a finite discontinuity at the corners of the element that prevent the element from passing the bending patch test the element so formulated does not present optimal rate of convergence under h refinement operation the formulation is enhanced enforcing these discontinuities to be zero by means of lagrange multipliers it is shown that with these constraints the element passes the patch test and presents optimal rate of convergence for unstructured mesh in this way the rational conforming approximation collapses into a conforming re arrangement of the complete bi cubic bezier interpolation some examples and benchmarks are presented in order to test the performance of the element for the kirchhoff plate model

on a computationally simple form of the generalized campbell baker hausdorff dynkin formula abstract in this paper a computationally simple form of the generalized campbell baker hausdorff dynkin formula gcbhd is given simplifications arise from both combinatorial explicit as well as algorithmic implicit arguments on generating the ph hall basis in a special form and introducing a specific structure representation of the vector field vector fields appearing in gcbhd are automatically transformed into the reduced ph hall basis the formula can be exploited in nonholonomic motion planning what is illustrated with examples

semiclassical asymptotics gauge fields and quantum chaos a gauge field is given by a connection on a principal bundle p m we consider the semiclassical behavior of a family of schrodinger operators associated with a gauge field in the limit as h 0 we relate the spectral theory of such operators to behavior of the hamiltonian flow on the natural phase space associated to a gauge field examining in particular situations where this flow exhibits chaotic behavior

optimal motion planning for nonholonomic systems using genetic algorithm with wavelet approximation an optimal motion planning scheme using genetic algorithm with wavelet approximation is proposed for nonholonomic systems the motion planning of nonholonomic systems can be formulated as an optimal control of a driftfree system a cost function is introduced to incorporate the control energy and the final state errors the control inputs are determined to minimize the cost functional by using the method of wavelet the infinite dimensional optimal control problem is truncated to a finite dimensional one based on the wavelet bases the genetic algorithm is employed to solve a feasible trajectory satisfying nonholonomic constraints the proposed scheme is applied to a free floating robot consisting of two one link arms connected to a main base via revolute joints the numerical results demonstrate that the genetic algorithm with the wavelet approximation is an effective approach to steer a nonholonomic system from its initial state to its final state 2006 published by elsevier inc

a comparative study of the hannay s angles associated with a damped harmonic oscillator and a generalized harmonic oscillator in this paper we show that a damped harmonic oscillator the simplest dissipative physical system is canonically equivalent to a generalized harmonic oscillator a conservative system even for time dependent parameters as a consequence the hannay s angles and the adiabatic invariants of the two systems appear to be the same modulo this equivalence this raises the question of whether this analogy can be extended to other nonlinear dissipative systems

an elastic viscoplastic quasistatic contact problem existence and uniqueness of a weak solution in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to internal tension or compression and caused by the opening and growth of micro cracks and micro cavities is also considered the variational formulation leads to a coupled system of evolutionary equations an existence and uniqueness result is established by using approximate problems the pseudomonotone operators theory schauder fixed point theorem and a comparison result

an elastic viscoplastic quasistatic contact problem with damage abstract in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to tension or compression is also considered the variational formulation leads to a coupled system of evolutionary equations for which an existence and uniqueness result is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are obtained and as a consequence the convergence of the algorithm is deduced finally some numerical simulations are presented to demonstrate the accuracy of the algorithm

the degenerate parametric oscillator and ince s equation we construct green s function for the quantum degenerate parametric oscillator in the coordinate representation in terms of standard solutions of ince s equation in a framework of a general approach to variable quadratic hamiltonians exact time dependent wavefunctions and their connections with dynamical invariants and su 1 1 group are also discussed an extension to the degenerate parametric oscillator with time dependent amplitude and phase is also mentioned

hannay berry phase and the restricted three vortex problem abstract asymptotic expansions for the hannay berry phase are computed for a class of hamiltonian systems in perturbed action angle form with slowly varying parameters where the parameters recur on a slow time scale a multi scale perturbation method is used which in principle can be carried to any desired order of accuracy as a specific application we use the method to examine the restricted three vortex problem a completely integrable configuration of two co rotating point vortices a distance d apart and a tracer particle rotating around one of the vortices with distance r in the asymptotic limit r d e we compute the particle trajectory through o e and find that the hannay berry phase is given by 2 3 r 0 d o 1 d 2 where r 0 is the conserved action

an implicit multi patch b spline interpolation for kirchhoff love space rod abstract the paper presents a novel formulation for the isogeometric analysis of assemblies of kirchhoff love space rod elements introducing a multi patch implicit g 1 formulation so that an automatic non singular stiffness operator is obtained without the need of adding continuity conditions the goal is achieved using a polar decomposition of the deformation of the first and last segments of the control polygon that allows to introduce directly the end rotations as degrees of freedom both parametric and geometric continuity can be obtained in this way we use bezier and b spline interpolations and we show that they are able to attain very good accuracy for developing a 3d exact curve element with geometric torsion pre twisted rod in the paper the performance of the multi patch elements is examined comparing the rates of convergence of the l 2 error norm for the multi patch and single patch formulations it is shown that the rate of convergence remains the same although in certain cases the accuracy is lower for the multi patch solutions

berry s phase and wavefunctions for time dependent hamilton systems an alternative derivation of berry s phase 1985 to that given by morales 1988 is given for non autonomous hamiltonian systems which admit an energy like first integral the generality of the problems treated is greater

berry s phase as the asymptotic limit of an exact evolution an example the authors exhibit for arbitrary time variations of the parameters of the generalised harmonic oscillator hamiltonian a canonical transformation which facilitates an exact analysis of quantal phase and classical angle formulae for berry s phase and hannay s angle are readily obtained by taking the adiabatic limit of the exact theory

non abelian geometric phase for general three dimensional quantum systems adiabatic u 2 geometric phases are studied for arbitrary quantum systems with a three dimensional hilbert space necessary and sufficient conditions for the occurrence of the non abelian geometrical phases are obtained without actually solving the full eigenvalue problem for the instantaneous hamiltonian the parameter space of such systems which has the structure of is explicitly constructed the results of this article are applicable for arbitrary multipole interaction hamiltonians and their linear combinations for spin j 1 systems in particular it is shown that the nuclear quadrupole hamiltonian does actually lead to non abelian geometric phases for j 1 this system being bosonic is time reversal invariant therefore it cannot support abelian adiabatic geometrical phases

angle variable holonomy in adiabatic excursion of an integrable hamiltonian if an integrable classical hamiltonian h describing bound motion depends on parameters which are changed very slowly then the adiabatic theorem states that the action variables i of the motion are conserved here the fate of the angle variables is analysed because of the unavoidable arbitrariness in their definition angle variables belonging to distinct initial and final hamiltonians cannot generally be compared however they can be compared if the hamiltonian is taken on a closed excursion in parameter space so that initial and final hamiltonians are the same the result shows that the angle variable change arising from such an excursion is not merely the time integral of the instantaneous frequency omega dh di but differs from it by a definite extra angle which depends only on the circuit in parameter space not on the duration of the process the 2 form which describes this angle variable holonomy is calculated

classical adiabatic angles and quantal adiabatic phase a semiclassical connection is established between quantal and classical properties of a system whose hamiltonian is slowly cycled by varying its parameters round a circuit the quantal property is a geometrical phase shift gamma n associated with an eigenstate with quantum numbers n nl the classical property is a shift delta theta l i in the lth angle variable for motion round a phase space torus with actions i il the connection is delta theta l delta gamma delta nl two applications are worked out in detail the generalised harmonic oscillator with quadratic hamiltonian whose parameters are the coefficients of q2 qp and p2 and the rotated rotator consisting of a particle sliding freely round a non circular hoop slowly turned round once in its own plane

berry s phase and hannay s angle from quantum canonical transformations using an action angle coherent states formalism introduced by the authors in a preceding paper it is shown that berry s phase and hannay s angle can both be derived from the same quantum unitary transformation their relationship is easily established in this framework

a factorization property of the berry phase it is shown that for systems with hamiltonians expressible in terms of the generators of a lie group the berry phase appears in the form of a product of a representation dependent term and a purely geometrical factor

semiclassical sum rules and generalized coherent states various semiclassical sum rules are obtained for matrix elements of smooth observables using semiclassical estimates of time evolved coherent states together with stationary phase theorems

isoholonomic problems and some applications we study the problem of finding the shortest loops with a given holonomy we show that the solutions are the trajectories of particles in yang mills potentials theorem 4 or equivalently the projections of kaluza klein geodesics theorem 2 applications to quantum mechanics berry s phase sect 3 and the optimal control of deformable bodies sect 6 are touched upon

two new triangular g1 conforming finite elements with cubic edge rotation for the analysis of kirchhoff plates abstract two triangular g 1 conforming elements based on the triangular gregory patch suitable for the analysis of the kirchhoff plate model are presented both have cubic normal derivative along the sides so that they can be effectively used in combination with generalized hermitian elements the gregory patch consists in a rational enhancement of the base polynomial spaces useful to design g 1 conforming elements on general c 0 conforming unstructured meshes because of the presence of the rational functions the second derivatives at the corners of the element present finite discontinuities that prevent the elements from passing the bending patch test the discontinuities are removed using a constrained version of the gregory patch with lagrange multipliers in this way the rational conforming space collapses into a conforming rearrangement of the original polynomial interpolant spaces the proposed formulation design elements that pass the bending patch test and present optimal rate of convergence on general unstructured meshes

large deformations of planar extensible beams and pantographic lattices heuristic homogenization experimental and numerical examples of equilibrium the aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call pantographic structures the interest in these materials was increased by the possibilities opened by the diffusion of technology of three dimensional printing they can be regarded once choosing a suitable length scale as families of beams also called fibres interconnected to each other by pivots and undergoing large displacements and large deformations there are however relatively few ready to use results in the literature of nonlinear beam theory in this paper we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by piola to formulate a continuum fully nonlinear beam model the homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems furthermore we consider pantographic structures find the corresponding homogenized second gradient deformation energies and study some planar problems numerical solutions for these two dimensional problems are obtained via minimization of energy and are compared with some experimental measurements in which elongation phenomena cannot be neglected

macroscopic description of microscopically strongly inhomogenous systems a mathematical basis for the synthesis of higher gradients metamaterials we consider the time evolution of a one dimensional n gradient continuum our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems referred to as microscopic because they are living on a smaller space scale we validate our construction by proving a convergence theorem of the microscopic system to the given continuum as the scale parameter goes to zero

an efficient blended mixed b spline formulation for removing membrane locking in plane curved kirchhoff rods abstract mixed formulations of the b type when applied to b spline representations bear significant computational cost and lead to a full stiffness matrix in this work we present an efficient mixed formulation for avoiding membrane locking of curved non polar plane rods in the context of isogeometric analysis an efficient spline reconstruction of the assumed axial strains obtained by means of a local projection at the element level is performed using the method proposed by thomas et al 2015 for the reconstruction of the geometry in this way a much smaller bandwidth of the stiffness matrix is obtained with respect to the non local b formulation with significant reduction of the computational cost the blended mixed formulation splits in two steps in the first step the local b operators are defined at the element level via projection of the strain measure both l 2 projection and discrete collocation approaches are considered successively by means of the spline reconstruction algorithm the global projection of the strain measures at the patch level is defined numerical experiments show that the proposed method in addition to completely remove membrane locking yields the same accuracy and rate of convergence as the non local b method

on a doubly nonlinear model for the evolution of damaging in viscoelastic materials we consider a model describing the evolution of damage in visco elastic materials where both the stiffness and the viscosity properties are assumed to degenerate as the damaging is complete the equation of motion ruling the evolution of macroscopic displacement is hyperbolic the evolution of the damage parameter is described by a doubly nonlinear parabolic variational inclusion due to the presence of two maximal monotone graphs involving the phase parameter and its time derivative existence of a solution is proved in some subinterval of time in which the damage process is not complete uniqueness is established in the case when one of the two monotone graphs is assumed to be lipschitz continuous

on natural strain measures of the non linear micropolar continuum we discuss three different ways of defining the strain measures in the non linear micropolar continuum a by a direct geometric approach b considering the strain measures as the fields required by the structure of local equilibrium conditions and c requiring the strain energy density of the polar elastic body to satisfy the principle of invariance under superposed rigid body deformations the geometric approach a generates several two point deformation measures as well as some lagrangian and eulerian strain measures the ways b and c allow one to choose those lagrangian strain measures which satisfy the additional mechanical requirements these uniquely selected relative strain measures are called the natural ones all the strain measures discussed here are formulated in the general coordinate free form they are valid for unrestricted translations stretches and changes of orientations of the micropolar body and are required to identically vanish in the absence of deformation the relation of the lagrangian stretch and wryness tensors derived here to the ones proposed in the literature is thoroughly discussed

nonlinear attitude and shape control of spacecraft with articulated appendages and reaction wheels three dimensional attitude and shape control problems are studied for a class of spacecraft with articulated appendages and reaction wheels a number of special cases of such attitude control problems have been studied previously we provide a unified formulation and a comprehensive set of results for planning of attitude and shape maneuvers of a spacecraft assuming that joint actuators and reaction wheels provide a sufficiently rich set of inputs the development is based on a nonlinear drift free control model that characterizes the attitude and shape change dynamics assuming zero angular momentum of the system controllability results are presented for the general case and specialized results are identified for interesting multibody spacecraft configurations these results are made explicit by providing computable formulas for the lie brackets in terms of the spacecraft geometry mass properties and shape constructive motion planning approaches are described to achieve spacecraft attitude and shape change maneuvers a distinct feature of these approaches is that they require only simple computations as is desirable for online implementation emphasis is given to the interplay between the shape change dynamics and the attitude change dynamics in achieving the maneuver planning objectives

on the removability of berry s phase the authors present a thorough analysis of the removability of the berry phase they show that for any system they can by properly restricting the parameter space turn the geometrical phase into an extra shift of the dynamical one however this extra shift in the dynamical phase retains its truly geometrical character the removability is thus only apparent and the geometrical phase can still be measured in interference experiments as indeed has already been done several times

geometric amplitude adiabatic invariants quantization and strong stability of hamiltonian systems considered is a linear set of ordinary differential equations with a matrix depending on a set of adiabatically varying parameters asymptotic solutions have been constructed as has been shown an important characteristic determining the qualitative portrait of the system is the real part of berry s complex geometric phase which we call the geometric amplitude for systems with purely imaginary eigenvalues the equivalence has been proven in the adiabatic approximation of system sets without geometric amplitude hamiltonian systems quantizable systems and strongly stable systems classification of the systems without geometric amplitude is given with respect to the kind of matrix of the initial system

one dimensional dynamic thermoviscoelastic contact with damage abstract the problem of thermoviscoelastic dynamic contact between a rod and a rigid obstacle when the material damage is taken into account is modeled and analyzed the contact is modeled by the normal compliance condition and the stress strain constitutive equation is of kelvin voigt type the damage which describes the reduction of the load carrying capacity of the rod evolves because of the opening of microcracks as a result of tension or compression when the damage reaches a critical value at a point on the rod the material cannot carry any load and the system breaks down mathematically this is expressed by the quenching of the solution the existence of a local weak solution is established using penalization and a priori estimates

nonlinear microstrain theories a hierarchy of higher order continua is presented that introduces additional degrees of freedom accounting for volume changes rotation and straining of an underlying microstructure an increase in the number of degrees of freedom represents a refinement of the material description in addition to available nonlinear cosserat and micromorphic theories general formulations of elastoviscoplastic behaviour are proposed for microdilatation and microstretch continua a microstrain theory is introduced that is based on six additional degrees of freedom describing the pure straining of the microstructural element in each case balance equations and boundary conditions are derived decompositions of the finite strain measures into elastic and plastic parts are provided the formulation of finite deformation elastoviscoplastic constitutive equations relies on the introduction of the free energy and dissipation potentials thus complying with requirements of continuum thermodynamics some guidelines for the selection of a suitable higher order model for a given material close the discussion

periodic solutions for doubly nonlinear evolution equations abstract we discuss the existence of periodic solution for the doubly nonlinear evolution equation a u t u t f t governed by a maximal monotone operator a and a subdifferential operator in a hilbert space h as the corresponding cauchy problem cannot be expected to be uniquely solvable the standard approach based on the poincare map may genuinely fail in order to overcome this difficulty we firstly address some approximate problems relying on a specific approximate periodicity condition then periodic solutions for the original problem are obtained by establishing energy estimates and by performing a limiting procedure as a by product a structural stability analysis is presented for the periodic problem and an application to nonlinear pdes is provided

continuum modelling of pantographic sheets for out of plane bifurcation and vibrational analysis a nonlinear two dimensional 2d continuum with a latent internal structure is introduced as a coarse model of a plane network of beams which in turn is assumed as a model of a pantographic structure made up by two families of equispaced beams superimposed and connected by pivots the deformation measures of the beams of the network and that of the 2d body are introduced and the former are expressed in terms of the latter by making some kinematical assumptions the expressions for the strain and kinetic energy densities of the network are then introduced and given in terms of the kinematic quantities of the 2d continuum to account for the modelling abilities of the 2d continuum in the linear range the eigenmode and eigenfrequencies of a given specimen are determined the buckling and post buckling behaviour of the same specimen subjected to two different loading conditions are analysed as tests in the nonlinear range the problems have been solved numerically by means of the comsol multiphysics finite element software

berry s transport and minimization of averaged distances in this paper we consider the metric approach to the berry s transport geometrical part of the adiabatic evolution of any pure or mixed state for possibly degenerate hamiltonians we emphasize that explicit formulae for the transport of such states need the introduction of an averaging procedure in analogy with the classical case this quantum averaging involves multiplying each energy eigenstate by a different phase and then integrating over these phases we show in particular how the transport of non stationary pure states rays and density matrices arise from the minimization of hilbert fubini study and bures averaged distances respectively

berry s phase hannay s angle and coherent states through the use of coherent states describing the action angle variables the authors establish a strict parallelism between berry s phase and hannay s angle in particular they define a geometrical transport for classical tori which leads to hannay s angle as in the case of berry s phase the transport can be associated with the minimization of a distance

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

on wave action and phase in the non canonical hamiltonian formulation the long timeevolution of disturbances to slowlyvarying solutions of partial differential equations is subject to the adiabatic invariance of the wave action generally this approximate conservati

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

the geometric phase for chaotic unitary families we consider the geometric phase for a family of quantum classical hamiltonians in which the effect of changing parameters is simply to induce unitary canonical transformations in this case the classical limit of the geometric phase is easily obtained even when the classical motion is chaotic the results agree with those previously obtained for general chaotic families but may be expressed in a simpler form not involving time integrals of correlation functions it is also straightforward to establish some results which are problematic in the general case for example the form of periodic orbit corrections and the closeness of the classical 2 form if the parameters are regarded as dynamical variables evolving slowly so as to maintain adiabaticity they are subject to geometric magnetism but not in contrast to the general case deterministic friction and born oppenheimer forces examples including families of translated and rotated systems are discussed

damageable contact between an elastic body and a rigid foundation in this work the contact problem between an elastic body and a rigid obstacle is studied including the development of material damage which results from internal compression or tension the variational problem is formulated as a first kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field the existence of a unique local weak solution is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are derived on the approximate solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally three two dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme

adiabatic invariance in the standard map adiabatic invariance of the action is investigated in the standard map under slow changes of the stochasticity parameter k a fixed action representation of the rotational tori is developed perturbatively in k and is connected with the usual kam representation at fixed winding number the notion of adiabatic invariance to a given order in k k 1 is then introduced it involves an approximation to exact dynamics by essentially a power series expansion in both k and a slowness parameter adiabatic invariance is explicitly verified to second order and the dependence of the nonadiabaticity on the form of the switching function and the slowness of the change is investigated the case of adiabatic switching to larger values of k k 1 is approached phenomenologically taking into account the problem of separatrix crossing it is shown that this crossing leads in general to nonadiabatic effects in the limit of infinitely slow change these reflect the finite widths or intrinsic action uncertainties associated with the main island chains crossed the latter are determined from the farey tree in the range of variation of the winding number an estimate of the critical slowness parameter corresponding to the onset of the intrinsic nonadiabatic effects is derived it involves typical time scales associated with the main island chains crossed

near optimal nonholonomic motion planning for a system of coupled rigid bodies how does a falling cat change her orientation in midair without violating angular momentum constraint this has become an interesting problem to both control engineers and roboticists in this paper we address this problem together with a constructive solution first we show that a falling cat problem is equivalent to the constructive nonlinear controllability problem thus the same principle and algorithm used by a falling cat can be used for space robotic applications such as reorientation of a satellite using rotors and attitude control of a space structure using internal motion and other robotic tasks such as dextrous manipulation with multifingered robotic hands and nonholonomic motion planning for mobile robots then using ideas from ritz approximation theory we develop a simple algorithm for motion planning of a falling cat finally we test the algorithm through simulation on two widely accepted models of a falling cat it is interesting to note that one set of simulation results closely resembles the real trajectories employed by a falling cat

time dependent implicit evolution equations on presente des theoremes d existence et d unicite pour des problemes de cauchy correspondant aux equations abstraites de la forme d b t u t dt a t u t f t ou b t est une famille dependante du temps d operateurs lineaires

parallel transport along a space curve and related phases the authors investigate geometrical properties of a space curve and of its spherical images they show that a space curve is characterised by two phase like quantities and comment on the relation of these quantities to the berry phase

the geometric phase for chaotic systems the geometric phase acquired by the eigenstates of cycled quantum systems is given by the flux of a two form through a surface in the system s parameter space we obtain the classical limit of this two form in a form applicable to systems whose classical dynamics is chaotic for integrable systems the expression is equivalent to the hannay two form we discuss various properties of the classical two form derive semiclassical corrections to it associated with classical periodic orbits and consider implications for the semiclassical density of degeneracies

existence and uniqueness of solutions for a dynamic one dimensional damage model we consider a one dimensional dynamic model that describes the evolution of damage caused by tension in a viscoelastic material the process is modeled by a coupled set of two differential inclusions for the elastic displacement and damage fields we establish the existence of local weak solutions the existence result is derived from the a priori estimates obtained for a sequence of regularized truncated and time retarded approximations we also establish the existence of the unique weak solution of a simplified version of the model

plane bias extension test for a continuum with two inextensible families of fibers a variational treatment with lagrange multipliers and a perturbation solution in the present paper a system constituted by two families of nearly inextensible fibers is studied the interest towards this kind of structures which can be suitably modeled by 2d continua with inextensible curves comes form both theoretical and applicative motivations indeed the advantageous weight strength ratio and the particularly safe behavior in fractures make them attractive in many engineering fields while the mechanical properties displayed by them are theoretically interesting and still not well understood in full generality we focused on dead loading traction boundary value problems assuming particular forms for the deformation energy associated to every node of the structure the main result of the paper consists in the determination of the nonlinear integral equations describing fibers directions for a specific class of deformation energies a perturbative analysis of a particular solution is also performed and some physical justification for one of the considered forms for the energy density are provided in the appendix

lie algebraic approach to fer s expansion for classical hamiltonian systems the so called fer s expansion is proposed as a solution for the time evolution operator of classical time dependent hamiltonian systems the quadratic hamiltonians treated as examples show that under very different regimes the second order approximation already gives extremely good results

berry phase in arbitrary dimensions we study the properties of the berry phase in quantum systems where momentum and position operators satisfy the r deformed heisenberg relations and the noninteger dimension d and angular momentum appear as parameters we focus on the dynamics of the generalized time dependent harmonic oscillator which satisfies the schr dinger wave mechanics formulated in arbitrary dimensions we also examine quantum systems which can be expressed as linear combination of generators with time dependent coefficients in arbitrary dimensions we show the explicit dependence of the berry phase on d and the parity of quantum systems which satisfy the r deformed heisenberg relations using an explicit relation of the fubini study metric in fractional dimensions we highlight a geometrical interpretation of d and of systems which are quantized in arbitrary dimensions