numerical simulation of unsteady viscous free surface flow abstract a finite element method is presented for the numerical simulation of time dependent incompressible viscous free surface flows the time dependent primitive equations are solved sequentially using explicit time marching procedure the method is based on a velocity correction approach to the time integration of the navier stokes equations in which only the incompressibility condition is treated implicitly a special arbitrary mixed lagrangian eulerian description has been used to avoid the typical problems encountered in a purely lagrangian description the method appears applicable for small computers problems requiring several thousand nodes can be solved on personal computers numerical experiments have been performed that show that this approach is reasonably efficient and robust for a range of complicated highly nonlinear problems

a hybrid element formulation for the three dimensional penalty finite element analysis of incompressible fluids this work presents a hybrid element formulation for the three dimensional penalty finite element analysis of incompressible newtonian fluids the formulation is based on a mixed variational statement in which velocity and stresses are treated as independent field variables the main advantage of this formulation is that it bypasses the use of ad hoc techniques such as selective reduced integration that are commonly used in penalty based finite element formulations and directly yields high accuracy for the velocity and stress fields without the need to carry out smoothing in addition since the stress degrees of freedom are condensed out at an element level the cost of solving for the global degrees of freedom is the same as in a standard penalty finite element method although the gain in accuracy for both the velocity and stress including the pressure fields is quite significant

spectral hp least squares finite element formulation for the navier stokes equations we consider the application of least squares finite element models combined with spectral hp methods for the numerical solution of viscous flow problems the paper presents the formulation validation and application of a spectral hp algorithm to the numerical solution of the navier stokes equations governing two and three dimensional stationary incompressible and low speed compressible flows the navier stokes equations are expressed as an equivalent set of first order equations by introducing vorticity or velocity gradients as additional independent variables and the least squares method is used to develop the finite element model high order element expansions are used to construct the discrete model the discrete model thus obtained is linearized by newton s method resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method spectral convergence of the l2 least squares functional and l2 error norms is verified using smooth solutions to the two dimensional stationary poisson and incompressible navier stokes equations numerical results for flow over a backward facing step steady flow past a circular cylinder three dimensional lid driven cavity flow and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

probabilistic characterization of nonlinear systems under α stable white noise via complex fractional moments abstract the probability density function of the response of a nonlinear system under external stable levy white noise is ruled by the so called fractional fokker planck equation in such equation the diffusive term is the riesz fractional derivative of the probability density function of the response the paper deals with the solution of such equation by using the complex fractional moments the analysis is performed in terms of probability density for a linear and a non linear half oscillator forced by levy white noise with different stability indexes numerical results are reported for a wide range of non linearity of the mechanical system and stability index of the levy white noise

multigrid methods to accelerate convergence of element by element solution algorithms for viscous incompressible flows abstract the use of iterative solvers for large systems of equations results in a slow convergence rate after the small wave length error components are resolved for a fixed convergence tolerance limit the error resolution capability of an iterative solver is a function of the mesh density two iterative solvers gmres and orthomin which utilize the element by element ebe data structure of the finite element mesh are studied to demonstrate this behavior a significant improvement in the accuracy of the solution and the rate of convergence is achieved for these iterative solvers by using a successive mesh refinement scheme like in a multigrid method this approach is found to better resolve both the large and the small scale flow phenomenon for a fine mesh while satisfying the convergence criterion in a fraction of the cpu time required by the standard iterative methods an iterative penalty finite element model is used to solve the governing equations for laminar incompressible isothermal fluid flows the solution accuracy and cpu time savings are demonstrated for two sample problems

an implicit algorithm within the arbitrary lagrangian eulerian formulation for solving incompressible fluid flow with large boundary motions abstract the objective of the paper is to present an implicit algorithm for incompressible fluid flow solution using the arbitrary lagrangian eulerian ale formulation and to investigate solution accuracy and stability of the algorithm the governing equations of the implicit procedure are derived using isoparametric interpolations for the fluid velocities and pressure the details suitable for general use are presented in our derivations of the fundamental equations and of the basic finite element balance equations the penalty method is utilized to eliminate the pressure on the element level accuracy and stability of the solutions are demonstrated in three examples for which the analytical solutions are known in the first example the burger s equation analogue to 1 d fluid flows is solved without and with fe mesh motion to show that the mesh motion practically does not affect the solutions in the second example the solitary wave motion with large displacements of the free boundary is solved as a benchmark problem in the third example the fluid flow in an infinite contractible and expandable pipe with prescribed large radial wall motion is solved this example is specifically attractive for biological flows as in blood vessels and lung airways all solutions presented show that the proposed algorithm is sufficiently accurate and stable since the algorithm is implicit high accuracy of results can be achieved with a relatively large time step

improved fractional step method for simulating fluid structure interaction using the pfem summary numerical difficulties are present in the particle finite element method even though it has been shown to be a powerful and effective approach to simulating fluid structure interaction to overcome problems of mass loss on the free surface and the added mass effect an improved fractional step method fsm that handles added mass terms in a mathematically exact way is developed a further benefit is that no assumptions regarding the structural response are made in handling added mass terms thus it is straightforward to incorporate material nonlinearity in fluid structure interaction fsi under this approach patch tests and comparisons with experimental data are presented in order to verify and validate the improved fsm for fsi applications the computational cost of this approach is shown to be negligible compared with the other aspects of the fsm particularly when the size of the structure and the fluid structure interface is small relative to the volume of fluid copyright 2014 john wiley sons ltd

tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing front delaunay triangulation a method of unstructured technical mesh generation for general three dimensional domains is presented a conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology the geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation a preliminary surface mesh is generated by an advancing front method with the nodes inserted by hard sphere packing in physical space in accordance with a prescribed mesh density interior nodes are inserted in a face centered cubic fcc crystal lattice arrangements coupled to octree spatial subdivision with the local lattice parameter determined by a prespecified nodal density function prior to triangulation of the volume the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume delaunay triangulation a joint delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing front approach the resulting mesh is finally improved upon by the application of local transformations the overall time complexity of the mesher is o n log n the robustness and versatility of the approach as well as the good quality of the resulting meshes is demostrated with the aid of selected examples

open loop and closed loop attitude dynamics and controls of miniature spacecraft using pseudowheels this paper presents open loop and closed loop attitude control strategies of miniature spacecraft using pseudowheels which are composed of multiple bimorphs and are mounted on the three principal axes of the spacecraft due to the conservation of angular momentum the vibrations of the bimorph excited by applied voltages can rotate the spacecraft by applying a sequence of rotations along the three axes the attitude of the spacecraft can be changed the modeling of the spacecraft pseudowheel system includes the inverse piezoelectric effect and the gravity gradient torques since one cannot guarantee that a solution will be found for every rotation sequence this paper proposes an approach to solve this problem in addition the voltages applied to the bimorphs are reduced to meet the specifications of the voltage amplifiers furthermore a closed loop attitude control strategy is presented to reduce the applied voltages and to compensate the attitude error caused by the gravity gradient torques

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

penalty finite element analysis of 3 d navier stokes equations abstract the steady state navier stokes equations in three dimensions are solved by a penalty finite element method for the problems of wall driven cavity flow in a cubical box and natural convection in a cubical cavity subjected to differential side heating the present solutions are compared with recent finite difference solutions of the wall driven cavity problem for reynolds numbersre 100 and 400 the agreement is found to be very good

some multidimensional fractional integral operators involving a general class of polynomials in this paper the authors present a systematic investigation of two novel families of multidimensional fractional integral operators involving a general class of polynomials with essentially arbitrary coefficients the various theorems established here involve compositions inversion formulas and multidimensional mellin transforms and convolutions of these general fractional integral operators each of the results obtained in this paper would unify and extend the corresponding known or new result for simpler families of fractional integral operators which were studied in several earlier works on the subject

two dimensional mesh generation adaptive remeshing and refinement this paper discusses the generation of unstructured triangular meshes by the advancing front technique we also employ the technique to discretize surfaces a simple and effective algorithm for the specification of element sizes is described a similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable the isolines are obtained from the fe calculation based on the previous mesh in this paper attention is focused on the poisson s equation the optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing when the estimated error exceeds the tolerance in only a small part of the domain the adaptive procedure is switched automatically to an adaptive refinement

finite element navier stokes calculation of three dimensional turbulent flow near a propeller les equations de navier stokes sont resolues par une methode d elements finis a fonction de penalite l helice est modelisee par un disque actuateur et le transport turbulent par une equation d energie cinetique turbulente

arbitrary lagrangian eulerian finite element analysis of free surface flow an arbitrary lagrangian eulerian ale description of newtonian fluid flow is presented it allows the simulation of free surfaces with the finite element method fem we develop a robust node repositioning algorithm which consists of two parts an energy minimization principle controls the positions of the internal nodes a good approximation of the boundaries is ensured by explicitly enforcing the free surface conditions numerical examples are done employing the mini element

stieltjes moment problem via fractional moments stieltjes moment problem is considered to recover a probability density function from the knowledge of its infinite sequence of ordinary moments the approximate density is obtained through maximum entropy technique under the constraint of few fractional moments the latter are numerically obtained from the infinite sequence of ordinary moments and are chosen in such a way as to convey the maximum information content carried by the ordinary moments as a consequence a model with few parameters is obtained and intrinsic numerical instability is avoided it is proved that the approximate density is useful for calculating expected values and some other interesting probabilistic quantities

exponential basis functions in solution of incompressible fluid problems with moving free surfaces in this paper a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries a lagrangian formulation established on pressure as a potential equation is employed in this method the approximate solution is expressed by a linear combination of exponential basis functions ebfs with complex valued exponents satisfying the governing equation constant coefficients of the solution series are evaluated through point collocation on the domain boundaries via a complex discrete transformation technique the numerical solution is performed in a time marching approach using an implicit algorithm in each time step the governing equation is solved at the beginning and the end of the step with the aid of an intermediate geometry the use of ebfs helps to find boundary velocities with high accuracy leading to a precise geometry updating the developed lagrangian meshless algorithm is applied to variety of linear and nonlinear benchmark problems non linear sloshing fluids in rigid rectangular two dimensional basins are particularly addressed

a completely explicit scheme of cauchy problem in bslm for solving the navier stokes equations abstract this paper presents a backward semi lagrangian method bslm with third order convergence in both time and space for solving incompressible navier stokes equations the third order backward differentiation formula for the total time derivative and the projection method for the steady state stokes equation are used a fourth order difference scheme together with a local bi cubic interpolation is used to solve the resulted two governing equations for the velocity and pressure this paper mainly focuses on the development of an efficient scheme for solving the nonlinear cauchy problem of the characteristic curve we employ a modified linear multi step method of the implicit type based on the error correction strategy a novel contribution of this paper is the design of a completely explicit formula for the three foot points the proposed method is superior to existing methods in terms of computational costs and accuracy allowing the use of a large time step size the fully explicit formula for the foot points significantly improves the performance of a common bslm for a wide range of practical applications

adaptive mesh refinement in strain localization problems an adaptive meshing method tailored to problems of strain localization is given the adaption strategy consists of equi distributing the variation of the velocity field over the elements of the mesh a heuristic justification for the use of variations as indicators is advanced and possible connections with interpolation error bounds are discussed meshes are constructed by delaunay triangulation it is shown how the hu washizu principle determines a consistent transfer operator for the state variables examples of application are given which demonstrate the versatility of the method

a mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method a multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study we call this procedure the mesoscopic bridging scale mbs method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models g j wagner w k liu coupling of atomistic and continuum simulations using a bridging scale decomposition j comput phys 190 2003 249 274 we derive the governing equations of the mbs method and show that the differential equations of motion of the mesoscale discrete particle model and finite element fe model are only coupled through the force terms based on this coupling we express the finite element equations which rely on the navier stokes and continuity equations in a way that the internal nodal fe forces are evaluated using viscous stresses from the mesoscale model the dissipative particle dynamics dpd method for the discrete particle mesoscale model is employed the entire fluid domain is divided into a local domain and a global domain fluid flow in the local domain is modeled with both dpd and fe method while fluid flow in the global domain is modeled by the fe method only the mbs method is suitable for modeling complex colloidal fluid flows where continuum methods are sufficiently accurate only in the large fluid domain while small local regions of particular interest require detailed modeling by mesoscopic discrete particles solved examples simple poiseuille and driven cavity flows illustrate the applicability of the proposed mbs method

adaptive remeshing for three dimensional compressible flow computations an adaptive mesh procedure for computing steady state solutions of the compressible euler equations in three dimensions is presented the method is an extension of previous work in two dimensions the approach requires the coupling of a surface triangulator an automatic tetrahedral mesh generator a finite element flow solver and an error estimation procedure an example involving flow at high mach number is included to demonstrate the numerical performance of the proposed approach the example shows that the use of this form of adaptivity in three dimensions offers the potential of even greater computational savings than those attained in the corresponding two dimensional implementation

robust geometrically based automatic two dimensional mesh generation a technical description of the algorithms employed in the modified quadtree mesh generator is given although the basis of the mesh generator is the same as the original version developed by yerry and shephard 1 2 the actual algorithms on which it is built have been entirely changed for the purpose of ensuring the robustness of the technique as demonstrated in the paper the algorithmic changes made do ensure the robustness of the approach but introduce additional algorithmic difficulties the solutions of which are also presented in addition to examples showing the capability of the mesh generator the linear computational growth rate of the mesh generator is demonstrated

fluid structure interaction using the particle finite element method abstract in the present work a new approach to solve fluid structure interaction problems is described both the equations of motion for fluids and for solids have been approximated using a material lagrangian formulation to approximate the partial differential equations representing the fluid motion the shape functions introduced by the meshless finite element method mfem have been used thus the continuum is discretized into particles that move under body forces gravity and surface forces due to the interaction with neighboring particles all the physical properties such as density viscosity conductivity etc as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion the so called particle finite element method pfem provides a very advantageous and efficient way for solving contact and free surface problems highly simplifying the treatment of fluid structure interactions

finite element analysis of oscillatory flow with heat transfer inside a square cavity in this work a semi implicit projection type finite element method is applied to solve the incompressible oscillatory cavity flow with heat transfer the two dimensional time dependent navier stokes and energy equations are numerically integrated by a time split galerkin finite element method using direct matrix solvers the time accuracy of the method was tested by calculating the transient buoyancy driven flow in a square cavity with differentially heated vertical walls the oscillatory cavity flow is then studied considering the effects of heat transfer reynolds number and oscillatory stokes number to measure the stability of the scheme for such a high singularity phenomenon the proposed scheme is found to be stable and convergent for high rayleigh numbers and will be applicable to general problems involving flow and heat transfer especially in three dimensions

fluid structure algorithms based on steklov poincare operators in this paper we review some classical algorithms for fluid structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory this approach yields preconditioned richardson iterations on the steklov poincare nonlinear equation at the fluid structure interface

a finite element formulation to solve a non local constitutive model with stresses and strains due to slip gradients solving constitutive models that incorporate the effects of plasticity and slip gradients is often complicated by the non local nature of the models this work presents a finite element solution to a crystal plasticity constitutive model that includes kinematic and stress effects due to slip gradients the foundation of the model is a three term multiplicative decomposition of the deformation gradient that results in a second order differential equation in terms of the stress that drives slip converting the equation into a weak form results in an integral equation that includes first order derivatives of the stress as well as boundary conditions for the stress and gradients of slip rate for each slip system using this weak form an incremental finite element method is developed to solve the constitutive model within a finite element solution to the equilibrium equation results for the compression of a two dimensional plate show the effects of including slip gradient effects in the constitutive model and indicate the tendency for localization of the slip and dislocation density into narrow bands separating regions of nearly constant dislocation density and long range strain

maxentropic solution of fractional moment problems the problem of reconstructing a function from the knowledge of a few of its moments is a special case of the problem inverting an integral transform when there are finitely many data points the classical method of maximum entropy and the method of maximum entropy in the mean are well suited to attack these problems what is interesting is that when we are free to choose the data points the choice can be made to improve the quality of the reconstruction when the method of maximum entropy is used too in this note we review how to apply these methods and compare them in a couple of examples

three dimensional adaptive meshing by subdivision and edge collapse in finite deformation dynamic plasticity problems with application to adiabatic shear banding this paper is concerned with the development of a general framework for adaptive mesh refinement and coarsening in three dimensional finite deformation dynamic plasticity problems mesh adaption is driven by a posteriori global error bounds derived on the basis of a variational formulation of the incremental problem the particular mesh refinement strategy adopted is based on rivara s longest edge propagation path lepp bisection algorithm our strategy for mesh coarsening or unrefinement is based on the elimination of elements by edge collapse the convergence characteristics of the method in the presence of strong elastic singularities are tested numerically an application to the three dimensional simulation of adiabatic shear bands in dynamically loaded tantalum is also presented which demonstrates the robustness and versatility of the method copyright c 2001 john wiley sons ltd

hamiltonian moving particle semi implicit hmps method for incompressible fluid flows particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles and thus have a great degree of flexibility for instance in dealing with the complex motion of surfaces or boundaries in this paper a particle method is developed from a direct discretization of the lagrangian for inviscid incompressible fluid flows the discretized lagrangian is transformed into a hamiltonian with holonomic constraints that stem from the incompressibility condition the rattle algorithm that is a symplectic scheme for holonomically constrained hamiltonian systems is adopted so that the resulting particle method inherits structures possessed by the partial differential equations that govern inviscid incompressible flows the algorithm of the particle method is semi implicit so we call it the hamiltonian moving particle semi implicit hmps method some numerical tests indicate the excellence of the hmps method in conservation of mechanical energy as well as linear and angular momenta

bifurcation and nonlinear dynamic analysis of united gas lubricated bearing system this paper studies the bifurcation and nonlinear behaviors of a united gas lubricated bearing ugb system by a hybrid numerical method combining the differential transformation method and the finite difference method the analytical results reveal a complex dynamic behavior comprising periodic sub harmonic quasi periodic and chaotic responses of the rotor center furthermore the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass and bearing number are increased the current analytical results are found to be in good agreement with those of other numerical methods therefore the proposed method provides an effective means of gaining insights into the nonlinear dynamics of ugb systems

a second order time accurate ale lagrange galerkin method applied to wind engineering and control of bridge profiles abstract in this paper we propose a second order time accurate ale formulation of lagrange galerkin methods for the transient solution of navier stokes equations for an incompressible fluid in a moving domain following a previous work rev europeenne elem finis 8 1999 659 we show that this time discretization based on a backward differentiation formula and the construction of characteristic paths in a grid relative velocity field leads to second order time accuracy numerical results are compared with those given by a first order approach the numerical diffusion is dramatically reduced which makes the use of turbulence model quasi mandatory for realistic wind engineering applications the software developed was also used to solve elementary control problems the solution method is based on the linearization of the discretized problem including the method of characteristics the formulation and implementation were successfully completed and will be detailed elsewhere

on the roles of minimization and linearization in least squares finite element models of nonlinear boundary value problems in this paper we examine the roles of minimization and linearization in the least squares finite element formulations of nonlinear boundary values problems the least squares principle is based upon the minimization of the least squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations in the present case we consider l 2 norms since the least squares method is independent of the discretization procedure and the solution scheme the least squares principle suggests that minimization should be performed prior to linearization where linearization is employed in the context of either the picard or newton iterative solution procedures however in the least squares finite element analysis of nonlinear boundary value problems it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations the main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged the assessment is performed mathematically through an examination of the variational setting for the least squares formulation of an abstract nonlinear boundary value problem and also computationally through the numerical simulation of the least squares finite element solutions of both a nonlinear form of the poisson equation and also the incompressible navier stokes equations the assessment suggests that although the least squares principle indicates that minimization should be performed prior to linearization such an approach is often impractical and not necessary

a novel exact representation of stationary colored gaussian processes fractional differential approach a novel representation of functions called generalized taylor form is applied to the filtering of white noise processes it is shown that every gaussian colored noise can be expressed as the output of a set of linear fractional stochastic differential equations whose solution is a weighted sum of fractional brownian motions the exact form of the weighting coefficients is given and it is shown that it is related to the fractional moments of the target spectral density of the colored noise

the particle finite element method a powerful tool to solve incompressible flows with free surfaces and breaking waves summary particle methods are those in which the problem is represented by a discrete number of particles each particle moves accordingly with its own mass and the external internal forces applied to it particle methods may be used for both discrete and continuous problems in this paper a particle method is used to solve the continuous fluid mechanics equations to evaluate the external applied forces on each particle the incompressible navier stokes equations using a lagrangian formulation are solved at each time step the interpolation functions are those used in the meshless finite element method and the time integration is introduced by an implicit fractional step method in this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the lagrangian formulation once the forces are evaluated the particles move independently of the mesh all the information is transmitted by the particles fluid structure interaction problems including free fluid surfaces breaking waves and fluid particle separation may be easily solved with this methodology copyright 2004 john wiley sons ltd

optimal transportation meshfree approximation schemes for fluid and plastic flows we develop an optimal transportation meshfree otm method for simulating general solid and fluid flows including fluid structure interaction the method combines concepts from optimal transportation theory with material point sampling and max ent meshfree interpolation the proposed otm method generalizes the benamou brenier differential formulation of optimal mass transportation problems to problems including arbitrary geometries and constitutive behavior the otm method enforces mass transport and essential boundary conditions exactly and is free from tension instabilities the otm method exactly conserves linear and angular momentum and its convergence characteristics are verified in standard benchmark problems we illustrate the range and scope of the method by means of two examples of application the bouncing of a gas filled balloon off a rigid wall and the classical taylor anvil benchmark test extended to the hypervelocity range

multistep characteristic method for incompressible flow in porous media in this paper we present a multistep difference scheme for the problem of miscible displacement of incompressible fluid flow in porous media the discretization involves a three level time scheme based on the characteristic method and a five point finite difference scheme for space discretization we prove that the convergence is of order o h 2 dt 2 which is in contrast to the convergence of order o h dt proved for a singlestep characteristic with the same space discretization numerical experiments demonstrate the stability and second order convergence of the scheme

bifurcation and chaos analysis of the porous squeeze film damper mounted gear bearing system porous squeeze film damper psfd has been widely used in the industry and the advantages are very abundant this study presents a systematic analysis of the dynamic behavior of a gear bearing system with psfd under nonlinear suspension nonlinear oil film force and nonlinear gear meshing force effect it can be found that the system exhibits very rich forms of nt periodic and chaotic vibrations the bifurcation diagrams also reveal that greater values of permeability may not only improve non periodic motions effectively but also suppress dynamic amplitudes of the system therefore we may conclude that psfd can improve dynamic stability of gear bearing systems the results presented in this study provide some useful insights into the design and development of a gear bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes

fractional calculus approach to the statistical characterization of random variables and vectors fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts fractional moments are indeed important when the density of the random variable has inverse power law tails and consequently it lacks integer order moments in this paper starting from the mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables introducing the class of complex moments that include both integer and fractional moments we show that every random variable can be represented within this approach even if its integer moments diverge applications to the statistical characterization of raw data and in the representation of both random variables and vectors are provided showing that the good numerical convergence makes the proposed approach a good and reliable tool also for practical data analysis

application of the differential transformation method to bifurcation and chaotic analysis of an afm probe tip the afm atomic force microscope has become a popular and useful instrument for measuring intermolecular forces with atomic resolution that can be applied in electronics biological analysis and studying materials semiconductors etc this paper conducts a systematic investigation into the bifurcation and chaotic behavior of the probe tip of an afm using the differential transformation dt method the validity of the analytical method is confirmed by comparing the dt solutions for the displacement and velocity of the probe tip at various values of the vibrational amplitude with those obtained using the runge kutta rk method the behavior of the probe tip is then characterized utilizing bifurcation diagrams phase portraits power spectra poincare maps and maximum lyapunov exponent plots the results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude specifically the tip motion changes first from subharmonic to chaotic motion then from chaotic to multi periodic motion and finally from multi periodic motion to subharmonic motion with windows of chaotic behavior as the non dimensional vibrational amplitude is increased from 1 0 to 5 0

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

lagrangian finite element analysis of newtonian fluid flows a fully lagrangian nite element method for the analysis of newtonian ows is developed the approach furnishes in eect a lagrangian implementation of the compressible navier stokes equations as the ow proceeds the mesh is maintained undistorted through continuous and adaptive remeshing of the uid mass the principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries uid uid or uid solid interfaces in contrast to eulerian approaches boundary conditions are enforced at material surfaces ab initio and therefore require no special attention consistent tangents are obtained for lagrangian implicit analysis of a newtonian uid ow which may exhibit compressibility eects the accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results and its versatility demonstrated through a simulation of wave breaking the nite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing 1998 john wiley sons ltd

hausdorff moment problem via fractional moments we outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments the approximate density is obtained resorting to maximum entropy technique under the constraint of some fractional moments the latter ones are obtained explicitly in terms of the infinite sequence of given ordinary moments it is proved that the approximate density converges in entropy to underlying density so that it turns out to be useful for calculating expected values

a lagrangian finite element approach for the analysis of fluid structure interaction problems a lagrangian finite element method for the analysis of incompressible newtonian fluid flows based on a continuous re triangulation of the domain in the spirit of the so called particle finite element method is here revisited and applied to the analysis of the fluid phase in fluid structure interaction problems a new approach for the tracking of the interfaces between fluids and structures is proposed special attention is devoted to the mass conservation problem it is shown that despite its lagrangian nature the proposed combined finite element particle method is well suited for large deformation fluid structure interaction problems with evolving free surfaces and breaking waves the method is validated against the available analytical and numerical benchmarks copyright 2010 john wiley sons ltd

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner