discontinuous galerkin method based on peridynamic theory for linear elasticity modeling of discontinuities shock waves crack surfaces etc in solid mechanics is one of the major research areas in modeling the mechanical behavior of materials among the numerical methods the discontinuous galerkin method dgm poses some advantages in solving these problems in this study a novel formulation for dgm is derived for elastostatics based on the peridynamic theory derivation of the proposed formulation is presented numerical analyses are performed for different problems and the numerical results are compared to that of the known exact solutions of the problems the proposed weak formulation is stable and coercive peridynamic discontinuous galerkin formulation is found to be robust and successful in modeling elastostatic problems copyright 2011 john wiley sons ltd

on 2d elliptic discontinuous galerkin methods we discuss the discretization using discontinuous galerkin dg formulation of an elliptic poisson problem two commonly used dg schemes are investigated the original average flux proposed by bassi and rebay j comput phys 1997 131 267 and the local discontinuous galerkin ldg siam j numer anal 1998 35 2440 2463 scheme in this paper we expand on previous expositions discontinuous galerkin methods theory computation and applications springer berlin 2000 135 146 siam j sci comput 2002 24 2 524 547 int j numer meth engng 2003 58 2 1119 1148 by adopting a matrix based notation with a view to highlighting the steps required in a numerical implementation of the dg method through consideration of standard c0 type expansion bases as opposed to elementally orthogonal expansions with the matrix formulation we are able to apply static condensation techniques to improve efficiency of the direct solver when high order expansions are adopted the use of c0 type expansions also permits the direct enforcement of dirichlet boundary conditions through a lifting approach where the ldg flux does not require further stabilization in our construction we also adopt a formulation of the continuous dg fluxes that permits a more general interpretation of their numerical implementation in particular it allows us to determine the conditions under which the ldg method provides a near local stencil finally a study of the conditioning and the size of the null space of the matrix systems resulting from the dg discretization of the elliptic problem is undertaken copyright 2005 john wiley sons ltd

the bender dunne basis operators as hilbert space operators the bender dunne basis operators t m n 2 n k 0nnkqkp mqn k where q and p are the position and momentum operators respectively are formal integral operators in position representation in the entire real line r for positive integers n and m we show by explicit construction of a dense domain that the operators t m n s are densely defined operators in the hilbert space l2 r

a finite element method by patch reconstruction for the stokes problem using mixed formulations abstract in this paper we develop a patch reconstruction finite element method for the stokes problem the weak formulation of the interior penalty discontinuous galerkin is employed the proposed method has a great flexibility in velocity pressure space pairs whose stability properties are confirmed by the inf sup tests numerical examples show the applicability and efficiency of the proposed method

quantum time of arrival goursat problem the construction of quantum time of arrival operator conjugate to the system hamiltonian leads to a particular linear homogeneous goursat problem in this work we demonstrate how to approximate the solution of the mentioned differential equation both semi analytically and numerically with the goal of calculating the largest eigenvalue of the associated confined time of arrival operator in the analytical approximation we used the partial sum expansion of the solution and showed that the resulting largest eigenvalue converges as the number of terms increases the result shows that for the parameters considered in this paper the approximation is sufficient up to the fourth order correction term in the numerical approximation we develop a non iterative formula to obtain the numerical solution of the goursat problem the performance of the non iterative method is compared with the known numerical techniques in literature numerical results show that the non iterative algorithm is more accurate and faster

on discontinuous galerkin methods discontinuous galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present several alternatives for treating the diffusion and advective fluxes have been introduced this report summarizes some of the methods that have been proposed several numerical examples are included in the paper these present discontinuous galerkin solutions of one dimensional problems with a scalar variable results are presented for diffusion reaction problems and advection diffusion problems we discuss the performance of various formulations with respect to accuracy as well as stability of the method copyright 2003 john wiley sons ltd

derivation of the relativistic proper time quantum evolution equations from canonical invariance based on 1 the spectral resolution of the energy operator 2 the linearity of correspondence between physical observables and quantum self adjoint operators 3 the definition of conjugate coordinate momentum variables in classical mechanics and 4 the fact that the physical point in phase space remains unchanged under canonical transformations between one pair of conjugate variables to another we are able to show that the proper time rest energy transformation matrices are given as aexp iests from which we obtain the proper time rest energy evolution equation for special relativistic situations this equation can be reduced to the usual dynamical equations where t is the reference time and e is the total energy extension of these equations to accelerating frames is then provided

weyl ordered series form for the angle variable of the time dependent oscillator the definition of the phase variable for a classical time dependent oscillator as the natural variable canonically conjugated to the ermakov invariant is revised some implications of the result at the quantum level are discussed and an exact formal expression in terms of weyl ordered operators is given for the associated phase operator

spectral problems for the weyl ordered form of operators 1pnqn in this paper we consider quantization of powers of the ratio between the hamiltonian coordinates for position and momentum in one dimensional systems the domain of the operators consists of square integrable functions over a finite real interval to ensure boundedness and self adjointness the spectral problems for the operators that result from using weyl ordering are discussed by introducing fredholm integral operator forms in position representation and the symmetry of the actions of the parity and time reversal operators on the kernels is discussed finally the general structures and properties of the eigenfunctions and eigenvalues are also derived and analyzed

optimal layout design of three dimensional geometrically non linear structures using the element connectivity parameterization method the topology design optimization of three dimensional geometrically non linear continuum structures is still difficult not only because of the size of the problem but also because of the unstable continuum finite elements that arise during the optimization to overcome these difficulties the element connectivity parameterization ecp method with two implementation formulations is proposed in ecp structural layouts are represented by inter element connectivity which is controlled by the stiffness of element connecting zero length links depending on the link location ecp may be classified as an external ecp e ecp or an internal ecp i ecp in this paper i ecp is newly developed to substantially enhance computational efficiency the main idea in i ecp is to reduce system matrix size by eliminating some internal degrees of freedom associated with the links at voxel level as for ecp implementation with commercial software e ecp developed earlier for two dimensional problems is easier to use even for three dimensional problems because it requires only numerical analysis results for design sensitivity calculation the characteristics of the i ecp and e ecp methods are compared and these methods are validated with numerical examples copyright 2006 john wiley sons ltd

self adjoint lyapunov variables temporal ordering and irreversible representations of schrodinger evolution in nonrelativistic quantum mechanics time enters as a parameter in the schrodinger equation however there are various situations where the need arises to view time as a dynamical variable in this paper we consider the dynamical role of time through the construction of a lyapunov variable i e a self adjoint quantum observable whose expectation value varies monotonically as time increases it is shown in a constructive way that a certain class of models admits a lyapunov variable and that the existence of a lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation in addition it is proven that in the irreversible representation there exists a natural time ordering observable splitting the hilbert space at each t 0 into past and future subspaces

efficient dg like formulation equipped with curved boundary edges for solving elasto acoustic scattering problems summary a discontinuous galerkin dg based approach is proposed for computing the scattered field from an elastic bounded object immersed in an infinite homogeneous fluid medium the proposed method possesses two distinctive features first it employs higher order polynomial shape functions needed to address the high frequency propagation regime second it is equipped with curved boundary edges to provide an accurate representation of the fluid structure interface the most salient benefits resulting from the latter feature as demonstrated by the numerical investigation are the following i an improvement by at least two orders of magnitude on the relative error and ii the disappearance of spurious resonance frequencies in the surrounding fluid medium in addition the reported numerical results reveal that when using cubic polynomials with less than three elements per wavelength the proposed dg method computes the scattered field with a relative error below 1 for an elastic scatterer of about 30 wavelengths this observation highlights the potential of the proposed solution methodology for efficiently solving mid frequency to high frequency elasto acoustic scattering problems copyright 2014 john wiley sons ltd

pauli s theorem and quantum canonical pairs the consistency of a bounded self adjoint time operator canonically conjugate to a hamiltonian with non empty point spectrum in single hilbert space pauli s wellknown theorem implies that the existence of a selfadjoint time operator canonically conjugate to a given hamiltonian requires the hamiltonian to possess complet

generalized weyl transform for operator ordering polynomial functions in phase space the generalized weyl transforms were developed from the hermiticity condition and the ordering rules were represented by characteristic real valued functions the integral transforms give rise to transformation equations between weyl quantization and differently ordered operators the transforms also simplify evaluation of commutator and anticommutator of a set of operators following the same ordering rule

an element wise locally conservative galerkin lcg method for solving diffusion and convection diffusion problems an element wise locally conservative galerkin lcg method is employed to solve the conservation equations of diffusion and convection diffusion this approach allows the system of simultaneous equations to be solved over each element thus the traditional assembly of elemental contributions into a global matrix system is avoided this simplifies the calculation procedure over the standard global continuous galerkin method in addition to explicitly establishing element wise flux conservation in the lcg method elements are treated as sub domains with weakly imposed neumann boundary conditions the lcg method obtains a continuous and unique nodal solution from the surrounding element contributions via averaging it is also shown in this paper that the proposed lcg method is identical to the standard global galerkin gg method at both steady and unsteady states for an inside node thus the method has all the advantages of the standard gg method while explicitly conserving fluxes over each element several problems of diffusion and convection diffusion are solved on both structured and unstructured grids to demonstrate the accuracy and robustness of the lcg method both linear and quadratic elements are used in the calculations for convection dominated problems petrov galerkin weighting and high order characteristic based temporal schemes have been implemented into the lcg formulation

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

the rigged hilbert space of the algebra of the one dimensional rectangular barrier potential the rigged hilbert space of the algebra of the one dimensional rectangular barrier potential is constructed the one dimensional rectangular potential provides another opportunity to show that the rigged hilbert space fully accounts for dirac s bra ket formalism the analogy between dirac s formalism and fourier methods is pointed out

on the algebraic difference equations un 2 un ψ un 1 in r related to a family of elliptic quartics in the plane abstract we study difference equations of the type u n 2 u n u n 1 in r with invariant curves given by x 2 y 2 d x y x y c x 2 y 2 b x y a x y k 0 this completes the results about multiplicative difference equations of the type u n 2 u n u n 1 obtained in the previous paper we reduce first these additive difference equations to u n 2 u n u n 1 1 u n 1 2 we study specially the case 0 2 using the parametrization of the above elliptic quartics by weierstrass elliptic functions we show that the solutions behave somewhat as in the multiplicative case if 0 there is divergence if the starting point u 1 u 0 is not the locally stable fixed point 0 0 and density of periodic initial points and of initial points with dense orbit in the quartic with invariant pointwise chaotic behavior we show that the period can be every number n 3 depending on and on the starting point

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

wigner quantisation of arrival time and oscillator phase by means of the wigner distribution function an expression is derived for the quasiprobability that a free particle in one dimension arrives at the origin during a given time interval and also for the quasiprobability that the phase of a one dimensional harmonic oscillator lies in a given segment of the circle it is shown that the best bounds on these quasiprobabilities p are 0 1559 or p or 1 0077 independent of the size of the interval it is shown that on disjoint unions of infinitely many intervals the quasiprobabilities may add up to any positive or negative real value it is briefly indicated how negative probabilities can be avoided altogether in an alternative approach to the quantisation of arrival time and oscillator phase

pulse wave propagation in a model human arterial network assessment of 1 d visco elastic simulations against in vitro measurements a numerical model based on the nonlinear one dimensional 1 d equations of pressure and flow wave propagation in conduit arteries is tested against a well defined experimental 1 1 replica of the human arterial tree the tree consists of 37 silicone branches representing the largest central systemic arteries in the human including the aorta carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs the set up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow terminal branches end in simple resistance models consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure the parameters required by the numerical algorithm are directly measured in the in vitro set up and no data fitting is involved comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1 d time domain formulation to capture the main features of pulse wave propagation measured throughout the system test as a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation the experimental set up generates waveforms at terminal branches with additional non physiological oscillations the frequencies of these oscillations are well captured by the 1 d model even though amplitudes are overestimated adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect suggesting that wall visco elasticity might play an important role in the experimental results nevertheless average relative root mean square errors between simulations and experimental waveforms are smaller than 4 for pressure and 19 for the flow at all 70 locations studied

squeezing of arbitrary order the ups and downs we show how using classical von neumann index theory makes possible a universal treatment of squeezing of arbitrary order universal means that the same approach applied to displacement order 1 a

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

some properties of the k dimensional lyness map this paper is devoted to study some properties of the k dimensional lyness map f x1 xk x2 xk a ki 2xi x1 our main result presents a rational vector field that gives a lie symmetry for f this vector field is used for k 5 to give information about the nature of the invariant sets under f when k is odd we also present a new as far as we know first integral for ff which allows us to deduce in a very simple way several properties of the dynamical system generated by f in particular for this case we prove that except on a given codimension one algebraic set none of the positive initial conditions can be a periodic point of odd period

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

numerical simulation of axisymmetric viscous flows by means of a particle method a vortex particle method for the simulation of axisymmetric viscous flow is presented the flow is assumed to be laminar and incompressible the navier stokes equations are expressed in an integral velocity vorticity formulation the inviscid scheme is based on nitsche s method for axisymmetric vortex sheets meanwhile two techniques are proposed for dealing with the viscous term the first uses an integral green s function method while the second is based on a diffusion velocity approach both are obtained by extension of existing methods for 2d flows the problem of satisfying boundary conditions along the axis of symmetry is specifically addressed the problem is solved by using cut off functions that are derived from the green s function of the axisymmetric diffusion equation the scheme is applied to simulate the evolution of vortex rings at intermediate reynolds number the processes of entrainment and wake formation are evident in the calculations as well as the extension of the support of vorticity due to viscous diffusion

discontinuous galerkin finite element in time for solving periodic differential equations the dynamics of rotating systems can be modeled by ordinary differential equations with periodic time varying coefficients and forcing discontinuous galerkin dg methods which are known to be higher order accurate a stable and locally conservative are used to solve such equations in this work dg methods are shown to find the steady state periodic solution of a constant coefficient structural dynamics problem with periodic forcing and b helicopter rotor rigid blade flapping equation which is a parametric ordinary differential equation with periodic time varying coefficients and periodic forcing convergence of the numerical solution obtained is studied for both the above equations while h and p are refined separately it is found that the dg method works well for these problems and allows the development of an element level error estimate which can be used to monitor convergence and hence develop adaptive schemes it is clear from the results that even though higher order polynomials result in much faster convergence with reduced computational effort it also results in deterioration of the numerical performance for p 12 two adaptive strategies based on the element level displacement jump norm i e h and hp refinement are proposed and demonstrated on problems with higher harmonic forcing primary controls and parametric variations

studying discrete dynamical systems through differential equations abstract in this paper we consider dynamical systems generated by a diffeomorphism f defined on u an open subset of r n and give conditions over f which imply that their dynamics can be understood by studying the flow of an associated differential equation x x x also defined on u in particular the case where f has n 1 functionally independent first integrals is considered in this case x is constructed by imposing that it shares with f the same set of first integrals and that the functional equation f x det d f x x x u has some non zero solution several examples for n 2 3 are presented most of them coming from several well known difference equations

reply to comment on almost periodic time observables for bound quantum systems in a recent paper hall 2008 j phys a math gen 41 255301 i made several critical remarks on a hermitian time operator proposed by galapon 2002 proc r soc a 458 2671 galapon has correctly pointed out that remarks pertaining to denseness of the commutator domain are wrong galapon 2008 j phys a math theor 42 018001 however the other remarks still apply and it is further noted that a given quantum system can be a member of this domain only at a set of times of total measure zero

a generalized weyl relation approach to the time operator and its connection to the survival probability the time operator an operator which satisfies the canonical commutation relation with the hamiltonian is investigated on the basis of a certain algebraic relation for a pair of operators t and h where t is symmetric and h self adjoint this relation is equivalent to the weyl relation in the case of self adjoint t and is satisfied by the aharonov bohm time operator t0 and the free hamiltonian h0 for the one dimensional free particle system in order to see the qualitative properties of t0 the operators t and h satisfying this algebraic relation are examined in particular it is shown that the standard deviation of t is directly connected to the survival probability and h is absolutely continuous hence it is concluded that the existence of the operator t implies the existence of scattering states it is also shown that the minimum uncertainty states do not exist other examples of these operators t and h than the one dimensional free particle system are demonstrated

a spacetime discontinuous galerkin method for hyperbolic heat conduction non fourier conduction models remedy the paradox of infinite signal speed in the traditional parabolic heat equation for applications involving very short length or time scales hyperbolic conduction models better represent the physical thermal transport processes this paper reviews the maxwell cattaneo vernotte modification of the fourier conduction law and describes its implementation within a spacetime discontinuous galerkin sdg finite element method that admits jumps in the primary variables across element boundaries with arbitrary orientation in space and time a causal advancing front meshing procedure enables a patch wise solution procedure with linear complexity in the number of spacetime elements an h adaptive scheme and a special sdg shock capturing operator accurately resolve sharp solution features in both space and time numerical results for one spatial dimension demonstrate the convergence properties of the sdg method as well as the effectiveness of the shock capturing method simulations in two spatial dimensions demonstrate the proposed method s ability to accurately resolve continuous and discontinuous thermal waves in problems where rapid and localized heating of the conducting medium takes place

quantum like picture for intrinsic classical arrival distributions we introduce a marginal quantum like picture for the arrival of classical quantities in which the representation vectors are the quantities that evolve and probability densities remain static the representation functions can be seen as probe functions which are the evolution of delta functions with support on a curve in phase space the time fronts this procedure provides a classical analog as well as a clear physical interpretation of the time eigenstates used in quantum systems

self adjoint time operator is the rule for discrete semi bounded hamiltonians we prove explicitly that to every discrete semibounded hamiltonian with constant degeneracy and with a finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span th

regular article a discontinuous galerkin ale method for compressible viscous flows in moving domains we present a matrix free discontinuous galerkin method for simulating compressible viscous flows in two and three dimensional moving domains to this end we solve the navier stokes equations in an arbitrary lagrangian eulerian ale framework spatial discretization is based on standard structured and unstructured grids but using an orthogonal hierarchical spectral basis the method is third order accurate in time and converges exponentially fast in space for smooth solutions a novelty of the method is the use of a force directed algorithm from graph theory that requires no matrix inversion to efficiently update the grid while minimizing distortions we present several simulations using the new method including validation with published results from a pitching airfoil and new results for flow past a three dimensional wing subject to large flapping insect like motion

hamiltonian dynamics on the symplectic extended phase space for autonomous and non autonomous systems we will present a consistent description of hamiltonian dynamics on the symplectic extended phase space that is analogous to that of a time independent hamiltonian system on the conventional symplectic phase space the extended hamiltonian h1 and the pertaining extended symplectic structure that establish the proper canonical extension of a conventional hamiltonian h will be derived from a generalized formulation of hamilton s variational principle the extended canonical transformation theory then naturally permits transformations that also map the time scales of the original and destination system while preserving the extended hamiltonian h1 and hence the form of the canonical equations derived from h1 the lorentz transformation as well as time scaling transformations in celestial mechanics will be shown to represent particular canonical transformations in the symplectic extended phase space furthermore the generalized canonical transformation approach allows us to directly map explicitly time dependent hamiltonians into time independent ones an extended generating function that defines transformations of this kind will be presented for the time dependent damped harmonic oscillator and for a general class of explicitly time dependent potentials in the appendix we will re establish the proper form of the extended hamiltonian h1 by means of a legendre transformation of the extended lagrangian l1

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

numerical analysis of growing crack problems using particle discretization scheme this paper presents the particle discretization scheme pds to analyze brittle failure of solids the scheme uses characteristic functions of voronoi and delaunay tessellations to discretize a function and its derivatives respectively a discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks without making any extra computation to accommodate new displacement discontinuities when the scheme is implemented to a finite element method fem the resulting stiffness matrix coincides with the one that is obtained by using linear elements the accuracy of computing a stress intensity factor at a crack tip is examined it is shown that the accuracy is better than that of a fem with linear elements when the rotational degree of freedom is included in discretizing displacement functions three three dimensional growing crack problems are solved by means of the pds and the results are presented copyright 2009 john wiley sons ltd

a drop of ink falls from my pen it comes to earth i know not when the authors obtain for a brownian particle in a uniform force field the mean and asymptotic first passage times as functions of the particle s initial position and velocity with the recurrence times given as a special case they discuss the region of phase space for which the diffusion model of brownian motion provides an adequate approximation and conclude that there is no possibility of obtaining the recurrence times within that model they find that the nature of the boundary value problem is profoundly altered when the motion is treated as a process in phase rather than configuration space because the time development operator is then parabolic rather than elliptic they argue that such a change in the treatment of brownian motion places it within the sphere of transport theory rather than diffusion theory and that consequently results such as ours have relevance to the study of phenomena such as radiative transfer and neutron transport

dichotomy of a perturbed lyness difference equation abstract we investigate in this paper the perturbed lyness difference equation bx n 2 x n x n 1 x n 2 n 0 1 2 where b are arbitrary positive real numbers and 0 and the initial values x 1 x 0 0 which is a generalization of the lyness difference equation x n 2 x n a x n 1 extensively studied it is known that for the lyness difference equation i e the perturbed lyness difference equation with 0 all its solutions are periodic or strictly oscillatory however one here finds that this perturbed lyness difference equation possesses the following dichotomy for 0 b all of its solutions are globally asymptotically stable for b all the sequences generated by it converge to we hence find that there exists the essential difference for the properties of solutions between the unperturbed lyness difference equation and the perturbed lyness difference equation

time dependent diffeomorphisms as quantum canonical transformations and the time dependent harmonic oscillator quantum canonical transformations corresponding to time dependent diffeomorphisms of the configuration space are studied a special class of these transformations which correspond to time dependent dilatations is used to identify a previously unknown class of exactly solvable time dependent harmonic oscillators the caldirola kanai oscillator belongs to this class for a general time dependent harmonic oscillator it is shown that choosing the dilatation parameter to satisfy the classical equation of motion one obtains the solution of the schrodinger equation a simple generalization of this result leads to the reduction of the schrodinger equation to a second order ordinary differential equation whose special case is the auxiliary equation of the lewis riesenfeld invariant theory the time evolution operator is expressed in terms of a positive real solution of this equation in a closed form and the time dependent position and momentum operators are calculated

zeeman s monotonicity conjecture abstract in this paper we prove a conjecture of zeeman 1 about the monotonicity of the rotation number of a family of diffeomorphisms of the first quadrant q of r 2

comment on almost periodic time observables for bound quantum systems hall 2008 j phys a math theor 41 255301 makes two claims on a time operator constructed in galapon 2002 proc r soc a 458 2671 we discuss why both claims are wrong

quantum first time of arrival operators this paper undertakes the problem of constructing first time of arrival operators for arbitrary everywhere analytic potentials in the space of operators spanned by the bender dunne basis bender and dunne 1989 phys rev d 40 3504 the operators are conjugate with their respective system hamiltonians and reduce to their corresponding classical time of arrival expressions for infinitesimal the supraquantized time of arrival operators galapon 2004 j math phys 45 3180 and the confined time of arrival operators galapon et al 2004 phys rev lett 93 180406 galapon 2006 j mod phys a 21 6351 are then shown to be two distinct representations of the time of arrival operators constructed in the bender dunne space

a general discontinuous galerkin method for finite hyperelasticity formulation and numerical applications a discontinuous galerkin formulation of the boundary value problem of finite deformation elasticity is presented the primary purpose is to establish a discontinuous galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the dg concept can show its superiority compared to the continuous formulation the method is based on a general hu washizu de veubeke functional allowing for displacement and stress discontinuities in the domain interior it is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation the consistency and linearized stability of the method in the non linear range as well as its convergence rate are proven an implementation in three dimensions is developed showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner in order to demonstrate the versatility accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided copyright 2006 john wiley sons ltd

conjugate dynamical systems classical analogue of the quantum energy translation an aspect of quantum mechanics that has not been fully understood is the energy shift generated by the time operator in this study we introduce the use of the eigensurfaces of dynamical variables and commutators in classical mechanics to study the classical analogue of the quantum translation of energy we determine that there is a conjugate dynamical system that is conjugate to hamilton s equations of motion and then we generate the analogue of the time operator and use it in the translation of points along the energy direction i e the classical analogue of the pauli theorem the theory is illustrated with a nonlinear oscillator model

global behaviour of the period function of the sum of two quasi homogeneous vector fields abstract we study the global behaviour of the period function on the period annulus of degenerate centres for two families of planar polynomial vector fields these families are the quasi homogeneous vector fields and the vector fields given by the sum of two quasi homogeneous hamiltonian ones in the first case we prove that the period function is globally decreasing extending previous results that deal either with the hamiltonian quasi homogeneous case or with the general homogeneous situation in the second family and after adding some more additional hypotheses we show that the period function of the origin is either decreasing or has at most one critical period and that both possibilities may happen this result also extends some previous results that deal with the situation where both vector fields are homogeneous and the origin is a non degenerate centre