exact cumulant kramers moyal like expansion abstract we derive an exact equation a cumulant kramers moyal equation ckme quite similar to the kramers moyal equation kme for the probability distribution of a markovian dynamical system it can be applied to any well behaved converging cumulants continuous time systems such as langevin equations or other models an interesting but significant difference with respect to the kme is that their jump moments are proportional to cumulants of the dynamical variables but not proportional to central moments as is the case for the kme in fact they still obey a weaker version of pawula s theorem namely marcinkiewicz s theorem we compare the results derived from the equations herein with the ones obtained by computing via gaussian and biased and unbiased poisson langevin dynamics and a poisson non langevin model we obtain the exact ckme time evolution equation for the systems and in several cases those are distinct from the fokker planck equation or the kme

on the maslov index in this paper we give four definitions of maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other moreover relationships of several symplectic and differential geometric analytic and topological invariants including triple maslov indices eta invariants spectral flow and signatures of quadratic forms to the maslov index are developed and formulae relating them are given the broad presentation is designed with a view to applications both in geometry and in analysis 1994 john wiley sons inc

a new simple third order shear deformation theory of plates an improved simple third order shear deformation theory for the analysis of shear flexible plates is presented in this paper this new plate theory is composed of three parts the simple third order kinematics of displacements reduced from the higher order displacement field derived previously by the author a system of 10th order differential equilibrium equations in terms of the three generalized displacements of bending plates five boundary conditions at each edge of plate boundaries although the resulting displacement field is the same as that proposed by murthy the variational consistent governing equations and the associated proper boundary conditions are derived and identified in this work for the first time in the literature the applications and accuracy of the present shear deformation theory of plates are demonstrated by analytically solving the differential governing equations of a twisting plate a bending beam and two bending plates to which the 3 d elasticity solutions are available and excellent agreements are achieved even for the torsion of a plate with square cross section as well the local effects of stresses at plate boundaries can be characterized accurately these analytical solutions clearly show that the simple third order shear deformation theory developed in this work indeed gives better results than the first order shear deformation theories and other simple higher order shear deformation theories since the present third order shear flexible theory is based on a more rigorous kinematics of displacements and consists of not only a system of variational consistent differential equations but also a group of consistent boundary conditions associated with the differential equations the present simple third order shear deformation theory can easily be applied to the static and dynamic finite element analysis of laminated plates just like the applications of other popular shear flexible plate theories and improved results could be obtained from the present simple third order shear deformable theories of plates

brownian dynamics time averaging and colored noise we propose a method to obtain the equilibrium distribution for positions and velocities of a one dimensional particle via time averaging and laplace transformations we apply it to the case of a damped harmonic oscillator in contact with a thermal bath the present method allows us to treat among other cases a gaussian noise function exponentially correlated in time e g gaussian colored noise we obtain the exact equilibrium solution and study some of its properties

high action orbits for tonelli lagrangians and superlinear hamiltonians on compact configuration spaces abstract multiplicity results for solutions of various boundary value problems are known for dynamical systems on compact configuration manifolds given by lagrangians or hamiltonians which have quadratic growth in the velocities or in the momenta such results are based on the richness of the topology of the space of curves satisfying the given boundary conditions in this note we show how these results can be extended to the classical setting of tonelli lagrangians lagrangians which are c 2 convex and superlinear in the velocities or to hamiltonians which are superlinear in the momenta and have a coercive action integrand

a study on the action of non gaussian noise on a brownian particle abstract we analytically address the non equilibrium problem of a brownian particle in contact with a thermal reservoir by means of a non gaussian langevin noise term t the presence of noise kurtosis is akin to a second temperature reservoir acting on the system and we exploit its consequences by means of studying a converging exact form for the stationary probability distribution

thermostatistics of small nonlinear systems gaussian thermal bath we discuss the statistical properties of small mechanothermodynamic systems one and two particle cases subject to nonlinear coupling and in contact with standard gaussian reservoirs we use a method that applies averages in the laplace fourier space which relates to a generalization of the final value theorem the key advantage of this method lies in the possibility of eschewing the explicit computation of the propagator traditionally required in alternative methods like path integral calculations which is hardly obtainable in the majority of the cases for one particle equilibrium systems we are able to compute the instantaneous equilibrium probability density functions of injected and dissipated power as well as the respective large deviation functions our thorough calculations explicitly show that for such models nonlinearities are irrelevant in the long term statistics which preserve the exact same values as computed for linear cases actually we verify that the thermostatistical effect of the nonlinearities is constricted to the transient towards equilibrium since it affects the average total energy of the system for the two particle system we consider each element in contact with a heat reservoir at different temperatures and focus on the problem of heat flux between them contrarily to the one particle case in this steady state nonequilibrium model we prove that the heat flux probability density function reflects the existence of nonlinearities in the system an important consequence of that it is the temperature dependence of the conductance which is unobserved in linear harmonic models our results are complemented by fluctuation relations for the injected power equilibrium case and heat flux nonequilibrium case

multiple periodic points of the poincare map of lagrangian systems on tori in this paper suppose l t x p 1 over 2 a x p cdot p v t x a is positive definite and symmetric and both a and v are c 3 and 1 periodic in all of their variables we prove that the poincare map i e the time 1 solution map of the lagrangian system

periodic orbits of hamiltonian homeomorphisms of surfaces john franks and michael handel fh2 have recently proved that any nontrivial hamiltonian diffeomorphism of a closed surface of genus at least one has periodic orbits of arbitrarily large period they proved a similar result for a nontrivial area preserving diffeomorphism of a sphere with at least three fixed points we extend these results to the case of the homeomorphisms when the genus is at least one we prove moreover that the periodic orbits may be chosen contractible if the set of contractible fixed points is contained in a disk when the surface is a sphere we extend the result to the case of a nontrivial homeomorphism with no wandering points the proofs make use of an equivariant foliated version of brouwer s plane translation theorem see b proposition 2 1 and some properties of the linking number of fixed points

meshless implementation of arbitrary 3d shell structures based on a modified first order shear deformation theory abstract a meshless implementation of arbitrary 3d shell structures based on a modified first order shear deformation theory fsdt is investigated in this paper the fsdt is improved in this manuscript in order to assume a parabolic distribution of the shear strain to correct the constant shear stress in the mindlin reissner theory and to get closer to a realistic distribution of the shear strain through the thickness the radial point interpolation method is used in the construction of shape functions based on arbitrarily distributed nodes of general spatial shell geometry the convergence of the proposed model is compared to other well known formulations found in the literature considering isotropic and functionally graded spatial shell structures the results obtained using the proposed meshless method demonstrate that the improved fsdt is very successful compared to closed form solutions and finite element results using different shell theories the effect of the material distribution on the deflections and stresses is also analyzed

a new obstruction to embedding lagrangian tori n let 2n be endowed with the canonical symplectic form a i 1 dxi dy i and consider a lagrangian embedding of a compact manifold j l r 2 a a well known result due to g r o m o v g states that the cohomology class of a in h z e 2 l is non zero we identify l with its image in r2 an equivalent assertion is that the liouville form 2 y 7 1 xldy i pulls back to a closed form j 2 on l whose cohomology class does not vanish g r o m o v s proof uses subtle properties of holomorphic maps into c he shows that there is always a holomorphic disk a in c with boundary in l on such a disk a is positive hence sa a soa 2 0 in this paper we shall only consider the case l t and give an elementary proof of gromov s result elementary should be understood in the sense of number theory that is without using holomorphic functions in fact our result is somewhat more precise and can be stated as follows

multiple brake orbits in bounded convex symmetric domains abstract in this paper we prove that there exist at least two geometrically distinct brake orbits in every bounded convex symmetric domain in r n for n 2

first passage times for the uhlenbeck ornstein process a numerical solution is obtained for the laplace transformed backward kramers equation from which the mean first passage time may be obtained the main difficulties are associated with a the parabolic nature of the time development operator and b the existence of a double structure in the solution near the absorbing barrier both of these difficulties are resolved by computational methods derived from boundary layer theory the reliability of the method is assessed by comparing its results with an earlier analytic solution for the case of a uniform force field the authors also present the results for a harmonic force field for which no analytic solution is yet known

exact time average distribution for a stationary non markovian massive brownian particle coupled to two heat baths using a time averaging technique we obtain exactly the probability distribution for position and velocity of a brownian particle under the influence of two heat baths at different temperatures these baths are expressed by a white noise term representing the fast dynamics and a colored noise term representing the slow dynamics our exact solution scheme accounts for inertial effects that are not present in approaches that assume the brownian particle in the overdamped limit we are also able to obtain the contributions associated with the fast noise that are usually neglected by other approaches

augmented levy michell equations for flexural plates abstract a new sixth order isotropic elastic and flexural plate theory is presented based on the fourth order equations of levy 1877 and michell 1900 the lack of surface loading in these levy michell equations is overcome by including the dominant flexural component of dougall s 1904 solution for a point load on the surface of a three dimensional isotropic elastic layer the augmented plate equations are arranged to fit the form of a consistent sixth order system of isotropic plate equations which include the well known work of reissner and static equations of mindlin numerical applications to two three dimensional problems with analytical solutions show good comparative results

finite element vibration analysis of composite beams based on higher order beam theory abstract this paper presents a new finite element formulation for the free vibration analysis of composite beams based on the third order beam theory this work also studies the influence of the mass components resulting from higher order displacements on the frequencies of flexural vibration by using hamilton s principle the variational consistent equation of motion in matrix form corresponding to the third order shear deformation theory is derived the resulting mass matrices are decomposed into three parts i e the usual part including the rotary inertia corresponding to first order theory the part resulting from higher order displacement and the part resulting from the coupling between the different components of the axial displacement the numerical examples show that the higher order and coupling mass matrices have a significant influence on the frequencies of high mode flexural vibration the present element formulation for composite beams can be easily extended to composite plates and shells

exact nonequilibrium work generating function for a small classical system we obtain the exact nonequilibrium work generating function newgf for a small system consisting of a massive brownian particle connected to internal and external springs the external work is provided to the system for a finite time interval the jarzynski equality obtained in this case directly from the newgf is shown to be valid for the present model in an exact way regardless of the rate of external work

the conley conjecture for hamiltonian systems on the cotangent bundle and its analogue for lagrangian systems abstract in this paper the conley conjecture which was recently proved by franks and handel j franks m handel periodic points of hamiltonian surface diffeomorphism geom topol 7 2003 713 756 for surfaces of positive genus hingston n hingston subharmonic solutions of hamiltonian equations on tori ann math in press for tori and ginzburg v l ginzburg the conley conjecture arxiv math sg 0610956v1 for closed symplectically aspherical manifolds is proved for c 1 hamiltonian systems on the cotangent bundle of a c 3 smooth compact manifold m without boundary of a time 1 periodic c 2 smooth hamiltonian h r t m r which is strongly convex and has quadratic growth on the fibers namely we show that such a hamiltonian system has an infinite sequence of contractible integral periodic solutions such that any one of them cannot be obtained from others by iterations if h also satisfies h t q p h t q p for any t q p r t m it is shown that the time 1 map of the hamiltonian system if exists has infinitely many periodic points siting in the zero section of t m if m is c 5 smooth and dim m 1 h is of c 4 class and independent of time t then for any 0 the corresponding system has an infinite sequence of contractible periodic solutions of periods of integral multiple of such that any one of them cannot be obtained from others by iterations or rotations these results are obtained by proving similar results for the lagrangian system of the fenchel transform of h l r t m r which is proved to be strongly convex and to have quadratic growth in the velocities yet

brownian motion as a problem of eliminating fast variables abstract the hamilton equations for a brownian particle involve its mass as a large parameter as a consequence its motion is relatively slow and the fast motion of the surrounding fluid molecules can be eliminated by the standard method of eliminating fast variables the result is equivalent to the known langevin equation plus additional higher orders all coefficients are expressed in terms of correlation functions of the microscopic force on the particle

infinitely many periodic solution orbits of autonomous lagrangian systems on tori we prove that for any 0 the autonomous lagrangian system ddtlx x x lx x x 0 on the standard n dimensional torus possesses infinitely many geometrically distinct contractible periodic solution orbits whose periods are integer multiples of provided that the lagrangian function satisfies l x p 12ap p v x where a is a positive definite symmetric real matrix and v is c3 and 1 periodic in all of its variables

a refined two dimensional theory for thick cylindrical shells abstract a higher order two dimensional theory for thick cylindrical shells is presented in this paper the shell equations given here do not only incorporate the effect of transverse shear deformations but also account for the initial curvature as well as the radial stress the proposed theory presents a very good approximation for the shell constitutive equations and the nonlinear distributions of the in plane stresses across the thickness of the shell the latter is very important in the thick shells analysis the formulation is based on 1 1 assumed out of plane stress components which satisfy the given traction boundary conditions 2 2 three dimensional elasticity equations with an integral form of the equilibrium equations and 3 3 stress resultants and stress couples acting on the middle surface of the shell average displacements along the normal at a point on the middle surface and average rotations of the normal the proposed shell equations can be conveniently used in the finite element analysis an application of this theory to the finite element analysis of circular arches is given in this paper a more convenient form of the proposed shell equations for finite element analysis and its application to cylindrical shells will be presented in a follow up paper

the conley conjecture we prove the conley conjecture for a closed symplectically aspherical symplectic manifold a hamiltonian diffeomorphism of such a manifold has infinitely many periodic points more precisely we show that a hamiltonian diffeomorphism with finitely many fixed points has simple periodic points of arbitrarily large period this theorem generalizes for instance a recent result of hingston establishing the conley conjecture for tori

a refined nonlinear theory of plates with transverse shear deformation abstract a higher order shear deformation theory of plates accounting for the von karman strains is presented the theory contains the same dependent unknowns as in the hencky mindlin type first order shear deformation theory and accounts for parabolic distribution of the transverse shear strains through the thickness of the plate exact solutions of simply supported plates are obtained using the linear theory and the results are compared with the exact solutions of 3 d elasticity theory the first order shear deformation theory and the classical plate theory the present theory predicts the deflections stresses and frequencies more accurately when compared to the first order theory and the classical plate theory

analysis of cracked plate using higher order shear deformation theory asymptotic crack tip fields and xiga implementation abstract in this work an extended isogeometric analysis xiga is used for the analysis of through thickness crack in a homogeneous and isotropic plate in isogeometric analysis iga non uniform rational b splines nurbs are used as a basis function the plate kinematics is modelled by reddy s higher order shear deformation theory hsdt the c 1 continuity requirement of hsdt can be easily fulfilled by the nurbs basis functions in order to obtain the plate fracture parameters moment intensity factors the expressions of crack tip fields auxiliary fields are derived using separation of variables and eigen function approach a new expression for moment intensity factors is developed using auxiliary fields solution crack tip fields and interaction integral approach several cracked plate problems are solved by xiga using hsdt the results obtained by hsdt based xiga hsdt xiga are compared with the fsdt based xiga fsdt xiga and literature solutions