transient aging in fractional brownian and langevin equation motion stochastic processes driven by stationary fractional gaussian noise that is fractional brownian motion and fractional langevin equation motion are usually considered to be ergodic in the sense that after an algebraic relaxation time and ensemble averages of physical observables coincide recently it was demonstrated that fractional brownian motion and fractional langevin equation motion under external confinement are transiently nonergodic char22 time and ensemble averages behave differently char22 from the moment when the particle starts to sense the confinement here we show that these processes also exhibit transient aging that is physical observables such as the time averaged mean squared displacement depend on the time lag between the initiation of the system at time t 0 and the start of the measurement at the aging time t a in particular it turns out that for fractional langevin equation motion the aging dependence on t a is different between the cases of free and confined motion we obtain explicit analytical expressions for the aged moments of the particle position as well as the time averaged mean squared displacement and present a numerical analysis of this transient aging phenomenon

an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

a scheme for conservative interpolation on overlapping grids this paper describes how to interpolate in a conservative manner when solving systems of conservative laws on overlapping grids overlapping grids are a flexible and efficient way to create grids for complicated regions before now however no general method had been developed for conservative interpolation the basic idea consists of assuming that the interpolation coefficients are free parameters and then deriving constraints to ensure that the interpolation is conservative a system of equations is then solved to determine the coefficients a two dimensional viscous burger s equation is solved to demonstrate the conservative nature of the scheme

memory effects in the asymptotic diffusive behavior of a classical oscillator described by a generalized langevin equation we investigate the memory effects present in the asymptotic dynamics of a classical harmonic oscillator governed by a generalized langevin equation using laplace analysis together with tauberian theorems we derive asymptotic expressions for the mean values variances and velocity autocorrelation function in terms of the long time behavior of the memory kernel and the correlation function of the random force the internal and external noise cases are analyzed a simple criterion to determine if the diffusion process is normal or anomalous is established

on anomalous diffusion and the fractional generalized langevin equation for a harmonic oscillator the fractional generalized langevin equation fgle is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two parameter mittag leffler noise the solution of this fgle is discussed by means of the laplace transform methodology and the kernels are presented in terms of the three parameter mittag leffler functions recent results associated with a generalized langevin equation are recovered

the immersed boundary lattice boltzmann method for solving fluid particles interaction problems a new computational method the immersed boundary lattice boltzmann method is presented this method is a combination and utilizes the most desirable features of the lattice boltzmann and the immersed boundary methods the method uses a regular eulerian grid for the flow domain and a lagrangian grid to follow particles that are contained in the flow field the rigid body conditions for the fluid and the particles are enforced by a penalty method which assumes that the particle boundary is deformable with a high stiffness constant the velocity field of the fluid and particles is solved by adding a force density term into the lattice boltzmann equation this novel method preserves the advantages of lbm in tracking a group of particles and at the same time provides an alternative and better approach to treating the solid fluid boundary conditions the method also solves the problems of fluctuation of the forces and velocities on the particles when the bounce back boundary conditions are applied this method enables one to simulate problems with particle deformation and fluid structure deformation its results are validated by comparison with results from other methods

bimodality of the interspike interval distributions for subordinated diffusion models of integrate and fire neurons abstract a subordinated langevin process with a random operational time in the form of an inverse strictly increasing levy type subordinator is considered as a generalization of the conventional perfect and leaky integrate and fire neuron models the parent process is given by standard brownian motion the effect of the random activity of synaptic inputs which arises from other neurons forming local and distant networks is modeled via a levy exponent of the subordinator using a first passage time formulation in an external force field we find exact expressions for the laplace transform of the output interspike interval isi density more detailed analysis is presented on the properties of the isi distribution in the case of the levy exponent which corresponds to the truncated double order time fractional diffusion equation for the probability density of the membrane potential particularly it is shown that at some parameter regimes the isi density exhibits a bimodal structure moreover it is demonstrated that the isis regularity is maximized at an intermediate value of the mean input current

generalized langevin equation with a three parameter mittag leffler noise abstract the relaxation functions for a given generalized langevin equation in the presence of a three parameter mittag leffler noise are studied analytically the results are represented by three parameter mittag leffler functions exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the laplace transform method the asymptotic behavior of the particle in the short and long time limits are found by using the tauberian theorems it is shown that for large times the particle motion is subdiffusive for 1 and superdiffusive for many previously obtained results are recovered due to the many parameters contained in the noise term the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media

relaxation time distributions for an anomalously diffusing particle abstract as well known the generalized langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle here we focus attention on some new aspects of the dynamics successively considering the memory kernel the particle s mean velocity and the scattering function all these quantities are studied from a unique angle namely the discussion of the possible existence of a distribution of relaxation times characterizing their time decay although a very popular concept a relaxation time distribution cannot be associated with any time decreasing quantity from a mathematical point of view the decay has to be described by a completely monotonic function technically we use a memory kernel decaying as a mittag leffler function the mittag leffler functions interpolate between stretched or compressed exponential behaviour at short times and inverse power law behaviour at large times we show that in the case of a subdiffusive motion relaxation time distributions can be defined for the memory kernel and for the scattering function but not for the particle s mean velocity the situation is opposite in the superdiffusive case

markovian embedding of non markovian superdiffusion we consider different markovian embedding schemes of non markovian stochastic processes that are described by generalized langevin equations and obey thermal detailed balance under equilibrium conditions at thermal equilibrium superdiffusive behavior can emerge if the total integral of the memory kernel vanishes such a situation of vanishing static friction is caused by a super ohmic thermal bath one of the simplest models of ballistic superdiffusion is determined by a biexponential memory kernel that was proposed by bao j stat phys 114 503 2004 we show that this non markovian model has infinitely many different four dimensional markovian embeddings implementing numerically the simplest one we demonstrate that i the presence of a periodic potential with arbitrarily low barriers changes the asymptotic large time behavior from free ballistic superdiffusion into normal diffusion ii an additional biasing force renders the asymptotic dynamics superdiffusive again the development of transients that display a qualitatively different behavior compared to the true large time asymptotics presents a general feature of this non markovian dynamics these transients though may be extremely long as a consequence they can be even mistaken as the true asymptotics we find that such intermediate asymptotics exhibit a giant enhancement of superdiffusion in tilted washboard potentials and it is accompanied by a giant transient superballistic current growing proportional to t ensuremath alpha text eff with an exponent ensuremath alpha text eff that can exceed the ballistic value of 2

fractional brownian motion and motion governed by the fractional langevin equation in confined geometries motivated by subdiffusive motion of biomolecules observed in living cells we study the stochastic properties of a non brownian particle whose motion is governed by either fractional brownian motion or the fractional langevin equation and restricted to a finite domain we investigate by analytic calculations and simulations how time averaged observables e g the time averaged mean squared displacement and displacement correlation are affected by spatial confinement and dimensionality in particular we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain the general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality we define the displacement correlation function and find that this quantity shows distinct features for fractional brownian motion fractional langevin equation and continuous time subdiffusion such that it appears an efficient measure to distinguish these different processes based on single particle trajectory data

a sharp interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations a method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp interface immersed boundary methods ibms is proposed by first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary we adopt a cut cell based approach to strictly enforce geometric conservation in order to limit the complexity associated with the cut cell method the cut cell based discretization is limited only to the pressure poisson and velocity correction equations in the fractional step method and the small cell problem tackled by introducing a virtual cell merging technique the method is shown to retain all the desirable properties of the original finite difference based ibm while at the same time reducing pressure oscillations for moving boundaries by roughly an order of magnitude

a simple and efficient direct forcing immersed boundary framework for fluid structure interactions a direct forcing immersed boundary framework is presented for the simple and efficient simulation of strongly coupled fluid structure interactions the immersed boundary method developed by yang and balaras j yang e balaras an embedded boundary formulation for large eddy simulation of turbulent flows interacting with moving boundaries j comput phys 215 1 2006 12 40 is greatly simplified by eliminating several complicated geometric procedures without sacrificing the overall accuracy the fluid structure coupling scheme of yang et al j yang s preidikman e balaras a strongly coupled embedded boundary method for fluid structure interactions of elastically mounted rigid bodies j fluids struct 24 2008 167 182 is also significantly expedited by moving the fluid solver out of the predictor corrector iterative loop without altering the strong coupling property central to these improvements are the reformulation of the field extension strategy and the evaluation of fluid force and moment exerted on the immersed bodies by taking advantage of the direct forcing idea in a fractional step method several cases with prescribed motions are examined first to validate the simplified field extension approach then a variety of strongly coupled fluid structure interaction problems including vortex induced vibrations of a circular cylinder transverse and rotational galloping of rectangular bodies and fluttering and tumbling of rectangular plates are computed the excellent agreement between the present results and the reference data from experiments and other simulations demonstrates the accuracy simplicity and efficiency of the new method and its applicability in a wide range of complicated fluid structure interaction problems

strongly coupled dynamics of fluids and rigid body systems with the immersed boundary projection method a strong coupling algorithm is presented for simulating the dynamic interactions between incompressible viscous flows and rigid body systems in both two and three dimensional problems in this work the navier stokes equations for incompressible flow are solved on a uniform cartesian grid by the vorticity based immersed boundary projection method of colonius and taira dynamical equations for arbitrary rigid body systems are also developed the proposed coupling method attempts to unify the treatment of constraints in the fluid and structure the incompressibility of the fluid the linkages in the rigid body system and the conditions at the interface through the use of lagrange multipliers the resulting partitioned system of equations is solved with a simple relaxation scheme based on an identification of virtual inertia from the fluid the scheme achieves convergence in only 2 to 5 iterations per time step for a wide variety of mass ratios the formulation requires that only a subset of the discrete fluid equations be solved in each iteration several two and three dimensional numerical tests are conducted to validate and demonstrate the method including a falling cylinder flapping of flexible wings self excited oscillations of a system of many linked plates in a free stream and passive pivoting of a finite aspect ratio plate under the influence of gravity in a free stream the results from the current method are compared with previous experimental and numerical results and good agreement is achieved

correlation functions for the fractional generalized langevin equation in the presence of internal and external noise we study generalized fractional langevin equations in the presence of a harmonic potential general expressions for the mean velocity and particle displacement the mean squared displacement position and velocity correlation functions as well as normalized displacement correlation function are derived we report exact results for the cases of internal and external friction that is when the driving noise is either internal and thus the fluctuation dissipation relation is fulfilled or when the noise is external the asymptotic behavior of the generalized stochastic oscillator is investigated and the case of high viscous damping overdamped limit is considered additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed in addition the cases of a constant external force and the force free case are obtained the validity of the generalized einstein relation for this process is discussed the considered fractional generalized langevin equation may be used to model anomalous diffusive processes including single file type diffusion

anomalous diffusion exact solution of the generalized langevin equation for harmonically bounded particle we study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator starting from a generalized langevin equation and using laplace analysis we derive exact expressions for the mean values variances and velocity autocorrelation function of the particle in terms of generalized mittag leffler functions the long time behaviors of these quantities are obtained and the presence of a whip back effect is analyzed

a stable fluid structure interaction solver for low density rigid bodies using the immersed boundary projection method dispersion of low density rigid particles with complex geometries is ubiquitous in both natural and industrial environments we show that while explicit methods for coupling the incompressible navier stokes equations and newton s equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios for more complex particles such as a body with a protrusion they become unstable we present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method similarly to previous work on this method the resulting matrix equation in the present approach is solved using a block lu decomposition each step of the block lu decomposition is modified to incorporate the rigid body dynamics we show that our method achieves second order accuracy in space and first order in time third order for practical settings only with a small additional computational cost to the original method our implicit coupling yields stable solution for density ratios as low as 10 4 we also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method

lie point symmetries and poincare normal forms for dynamical systems the problem of finding the extended lie point time independent symmetries of autonomous systems of ordinary differential equations is compared with the poincare procedure of reducing the system to linear or normal form showing a close relationship between the two problems some special situations including the classical hopf bifurcation problem are also examined from this point of view

aging effects in free quantum brownian motion the two time correlation function cxx t t 0 of the displacement x t x t0 of a free quantum brownian particle with respect to its position at a given time t0 is calculated analytically in the framework of the caldeira and leggett ohmic dissipation model as a result at any temperature t cxx t t 0 exhibits aging i e it depends explicitly on both times t and t 0 and not only on the time dierence t t 0 even in the limit of large age t 0 t06t 0 6t in contrast with a dynamic variable in equilibrium such as the particle velocity the equilibrium quantum uctuation dissipation theorem qfdt has to be modied in order to relate the response function xx t t 0 t ocxx t t 0 since this latter quantity takes into account even those uctuations of the displacement which take place during the waiting time tw t 0 t0 we describe the deviation from qfdt in terms of an eective inverse temperature e tw the behaviour of this quantity as a function of for given values of t and tw is analysed in the classical limit it is shown that e tw d d d tw where d t denotes the time dependent diusion coecient c 2000 elsevier science b v all rights reserved

a fourth order accurate method for the incompressible navier stokes equations on overlapping grids a method is described to solve the time dependent incompressible navier stokes equations with finite differences on curvilinear overlapping grids in two or three space dimensions the scheme is fourth order accurate in space and uses the momentum equations for the velocity coupled to a poisson equation for the pressure the boundary condition for the pressure is taken as u 0 extra numerical boundary conditions are chosen to make the scheme accurate and stable the velocity is advanced explicitly in time any standard time stepping scheme such as runge kutta can be used the poisson equation is solved using direct or iterative sparse matrix solvers or by the multigrid algorithm computational results in two and three space dimensions are given

stability of pressure boundary conditions for stokes and navier stokes equations abstract the stability of a finite difference discretization of the time dependent incompressible navier stokes equations in velocity pressure formulation is studied in paticular we compare the stability for different pressure boundary conditions in a semiimplicit time integration scheme where only the viscous term is treated implicitly the stability is studied in three different ways by a normal mode analysis by numerical computation of the amplification factors and by direct numerical simulation of the governing equations all three approaches identify the same pressure boundary condition as the best alternative this condition implicitly enforces the normal derivative of the divergence to be zero on the boundary by coupling the normal derivative of the pressure to the normal component of the curl of the vorticity using this boundary condition we demonstrate that the time step is determined only by the convective term

ageing properties of critical systems in the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest ageing phenomena are observed during this everlasting non equilibrium evolution a simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high temperature phase to the critical point the aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case particular emphasis is put on the field theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities fluctuation dissipation relations are discussed and in particular the concept of fluctuation dissipation ratio fdr is reviewed emphasizing its connection with the definition of a possible effective temperature the renormalization group approach to critical dynamics is summarized and the scaling forms of the time dependent non equilibrium correlation and response functions of a generic observable are discussed from them the universality of the associated fdr follows as an amplitude ratio it is then possible to provide predictions for ageing quantities in a variety of different models in particular the results for models a b and c dynamics of the o n ginzburg landau hamiltonian and model a dynamics of the weakly dilute ising magnet and of the 3 theory are reviewed and compared with the available numerical results and exact solutions the effect of a planar surface on the ageing behaviour of model a dynamics is also addressed within the mean field approximation

an analysis of a new stable partitioned algorithm for fsi problems part ii incompressible flow and structural shells stable partitioned algorithms for fluid structure interaction fsi problems are developed and analyzed in this two part paper part i describes an algorithm for incompressible flow coupled with compressible elastic solids while part ii discusses an algorithm for incompressible flow coupled with structural shells the numerical approach described here for structural shells uses robin mixed interface conditions for the pressure and velocity in the fluid which are derived directly from the governing equations the resulting added mass partitioned amp algorithm is stable even for very light structures requires no sub iterations per time step and is second order accurate the stability and accuracy of the amp algorithm is evaluated for linearized fsi model problems a normal mode analysis is performed to show that the new amp algorithm is stable even for the case of very light structures when added mass effects are large exact traveling wave solutions are derived for the fsi model problems and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the amp algorithm for the cases of light medium and heavy structures a summary comparison of the amp algorithm developed here and the one in part i is provided

moving overlapping grids with adaptive mesh refinement for high speed reactive and non reactive flow we consider the solution of the reactive and non reactive euler equations on two dimensional domains that evolve in time the domains are discretized using moving overlapping grids in a typical grid construction boundary fitted grids are used to represent moving boundaries and these grids overlap with stationary background cartesian grids block structured adaptive mesh refinement amr is used to resolve fine scale features in the flow such as shocks and detonations refinement grids are added to base level grids according to an estimate of the error and these refinement grids move with their corresponding base level grids the numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from fixed parameter space to moving physical space the mapped equations are solved numerically using a second order extension of godunov s method the stiff source term in the reactive case is handled using a runge kutta error control scheme we consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid in the latter case the newton euler equations describe the motion of the center of mass of the each body and the rotation about it and these equations are integrated numerically using a second order predictor corrector scheme numerical boundary conditions at slip walls are described and numerical results are presented for both reactive and non reactive flows that demonstrate the use and accuracy of the numerical approach

fokker planck description for a linear delayed langevin equation with additive gaussian noise we construct an equivalent probability description of linear multi delay langevin equations subject to additive gaussian white noise by exploiting the time convolutionless transform and a time variable transformation we are able to write a fokker planck equation fpe for the 1 time and for the 2 time probability distributions valid irrespective of the regime of stability of the langevin equations we solve exactly the derived fpes and analyze the aging dynamics by studying analytically the conditional probability distribution we discuss explicitly why the initially conditioned distribution is not sufficient to describe fully out a non markov process as both preparation and observation times have bearing on its dynamics as our analytic procedure can also be applied to linear langevin equations with memory kernels we compare the non markov dynamics of a one delay system with that of a generalized langevin equation with an exponential as well as a power law memory application to a generalization of the green kubo formula is also presented

a non iterative direct forcing immersed boundary method for strongly coupled fluid solid interactions a non iterative direct forcing immersed boundary method is presented for the strongly coupled simulations of fluid solid interactions while it retains many advantages of the immersed boundary framework by yang and stern 2012 30 especially the simplified field extension strategy for moving boundary treatment and the pointwise integration of hydrodynamic force using the momentum forcing term the present approach improves upon the previous method in several aspects including optimized computational cost for a strong coupling scheme reduced algorithm complexity for a straightforward implementation and enhanced numerical stability for low density ratio problems central to these improvements is a simple intermediate step in which the velocity fields around solid bodies are predicted on temporary non inertial reference frames attached to moving solid bodies in a one to one manner this step enables the explicit inverse of the implicit equations for rigid body dynamics thus rendering unnecessary the previous predictor corrector scheme for iteratively adjusting the displacements and velocities of the immersed bodies until reaching a convergence in addition a simple generalized procedure is developed to obtain the interpolation coefficients in a local reconstruction stencil explicitly from the geometric relationship for verification and validation the vortex induced vibration of a circular cylinder and the rotational galloping of a rectangular body are considered first then several particulate flow problems including settling and buoyant particles of low density ratios a settling particle in a small container and the kissing drafting tumbling problem of two settling particles are studied the agreement between the present results and the reference data in the literature is excellent an overall second order accuracy of the algorithm is verified in two systematic grid convergence tests the present idea can be easily applied to similar methods for achieving a strong coupling scheme on top of a weak one with a nominal increase in the computational cost details of the algorithm are provided to facilitate its implementation in other solvers using non boundary conforming grids

a fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies application to particulate flow abstract in this article we discuss a methodology that allows the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies the simulation methods rest essentially on the combination of a lagrange multiplier based fictitious domain methods which allow the fluid flow computations to be done in a fixed flow region b finite element approximations of the navier stokes equations occurring in the global model c time discretizations by operator splitting schemes in order to treat optimally the various operators present in the model the above methodology is particularly well suited to the direct numerical simulation of particulate flow such as the flow of mixtures of rigid solid particles and incompressible viscous fluids possibly non newtonian we conclude this article with the presentation of the results of various numerical experiments including the simulation of store separation for rigid airfoils and of sedimentation and fluidization phenomena in two and three dimensions

immersed finite element method for rigid body motions in the incompressible navier stokes flow abstract the immersed finite element method ifem takes places as a method developed for the purpose of solving effectively fluid structure interaction problems including multi physics ones in the original ifem the reproducing kernel particle method rkpm playing a role of discrete dirac delta function is employed to distribute the interacting force on the structure to the surrounding fluid and calculate the velocity on the structure induced from the background fluid in this paper fluid structure interaction fsi problems in 2d between the incompressible navier stokes flow and rigid structure are considered and we make use of the transformed finite element basis functions to replace discrete dirac delta functions such as rkpm this replacement makes the numerical support of fsi force distributed to the fluid smaller than that in case where the discrete dirac delta function is used in the finite element formulation reducing the support size of distributed fsi force affects the accuracy of numerical solutions near the structure the comparison of our numerical solution for particulate flows shows this fact well we calculate particulate flows of rigid circular and rod type disks and compare them with the preceding results of reliability to show a good agreement to them moreover the interaction motion for rod type of rigid structure in the fluid is traced

aging and rejuvenation with fractional derivatives we discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non poisson processes we find that two state fluctuations with an inverse power law distribution of waiting times finite first moment and divergent second moment namely with the power indexm in the interval 2 m 3 yield a generalized master equation equivalent to the sum of an ordinary markov contribution and a fractional derivative term we show that the order of the fractional derivative depends on the age of the process under study if the system is infinitely old the order of the fractional derivative o is given by o 3 m a brand new system is characterized by the degree o m 2 if the system is prepared at time ta 0 and the observation begins at time t 0 we derive the following scenario for times 0 t ta the system is satisfactorily described by the fractional derivative with o 3 m upon time increase the system undergoes a rejuvenation process that in the time limit t ta yields o m 2 the intermediate time regime is probably incompatible with a picture based on fractional derivatives or at least with a mono order fractional derivative

a second order accurate immersed boundary method for fully resolved simulations of particle laden flows an immersed boundary method ibm with second order spatial accuracy is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles the method is based on the computationally efficient direct forcing method of uhlmann m uhlmann an immersed boundary method with direct forcing for simulation of particulate flows j comput phys 209 2005 448 476 that is embedded in a finite volume pressure correction method the ibm consists of two grids a fixed uniform eulerian grid for the fluid phase and a uniform lagrangian grid attached to and moving with the particles a regularized delta function is used to communicate between the two grids and proved to be effective in suppressing grid locking without significant loss of efficiency the original method is improved by 1 a better approximation of the no slip no penetration ns np condition on the surface of the particles by a multidirect forcing scheme 2 a correction for the excess in the effective particle diameter by a slight retraction of the lagrangian grid from the surface towards the interior of the particles with a fraction of the eulerian grid spacing and 3 an enhancement of the numerical stability for particle fluid mass density ratios near unity by a direct account of the inertia of the fluid contained within the particles the new ibm contains two new parameters the number of iterations n s of the multidirect forcing scheme and the retraction distance r d the effect of n s and r d on the accuracy is investigated for five different flows the results show that r d has a strong influence on the effective particle diameter and little influence on the error in the ns np condition while exactly the opposite holds for n s a novel finding of this study is the demonstration that r d has a strong influence on the order of grid convergence it is found that for spheres the choice of r d 0 3 dx yields second order accuracy compared to first order accuracy of the original method that corresponds to r d 0 finally n s 2 appears optimal for reducing the error in the ns np condition and maintaining the computational efficiency of the method

a distributed lagrange multiplier fictitious domain method for the simulation of flow around moving rigid bodies application to particulate flow in this article we discuss the application of a lagrange multiplier based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by the navier stokes equations around moving rigid bodies the rigid body motion is due to hydrodynamical forces and gravity the solution method combines finite element approximations time discretization by operators splitting and conjugate gradient algorithms for the solution of the linearly constrained quadratic minimization problems coming from the splitting method we conclude this article by the presentation of numerical results concerning the simulation of an incompressible viscous flow around a naca0012 airfoil with a fixed center but free to rotate then the sedimentation of circular cylinders in 2 d channels and finally the sedimentation of spherical balls in cylinders with square cross sections 2000 elsevier science s a all rights reserved

an embedded boundary formulation for large eddy simulation of turbulent flows interacting with moving boundaries a non boundary conforming formulation for simulating complex turbulent flows with dynamically moving boundaries on fixed cartesian grids is proposed the underlying finite difference solver for the filtered incompressible navier stokes equations is based on a second order fractional step method on a staggered grid to satisfy the boundary conditions on an arbitrary immersed interface the velocity field at the grid points near the interface is reconstructed using momentum forcing without smearing the sharp interface the concept of field extension is also introduced to treat the points emerging from a moving solid body to the fluid laminar flow cases and large eddy simulations les are presented to demonstrate the formal accuracy and range of applicability of the method in particular simulations of laminar flow induced by the harmonic in line oscillation of a circular cylinder in quiescent fluid and from a transversely oscillating cylinder in a free stream are presented and compared to reference simulations and experiments les of turbulent flow over a traveling wavy wall and transitional flow through a bileaflet prosthetic heart valve are also shown all results are in very good agreement with reference results in the literature

effects of transient subordinators on the firing statistics of a neuron model driven by dichotomous noise the behavior of a stochastic perfect integrate and fire pif model of neurons is considered the effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing levy type subordinator using a first passage time formulation we find exact expressions for the output interspike interval isi statistics particularly it is shown that at some parameter regimes the isi density exhibits a multimodal structure moreover it is demonstrated that the coefficient of variation the serial correlation coefficient and the fano factor display a nonmonotonic dependence on the mean input current i e the isi s regularity is maximized at an intermediate value of the features of spike statistics analytically revealed in our study are compared with previously obtained results for a perfect integrate and fire neuron model driven by dichotomous noise without subordination

an improved immersed boundary method with direct forcing for the simulation of particle laden flows an efficient approach for the simulation of finite size particles with interface resolution was presented by uhlmann m uhlmann an immersed boundary method with direct forcing for the simulation of particulate flows j comput phys 209 2005 448 476 the present paper proposes several enhancements of this method which considerably improve the results and extend the range of applicability an important step is a simple low cost iterative procedure for the euler lagrange coupling yielding a substantially better imposition of boundary conditions at the interface even for large time steps furthermore it is known that the basic method is restricted to ratios of particle density and fluid density larger than some critical value above 1 hence excluding for example non buoyant particles this can be remedied by an efficient integration step for the artificial flow field inside the particles to extend the accessible density range down to 0 3 this paper also shows that the basic scheme is inconsistent when moving surfaces are allowed to approach closer than twice the step size a remedy is developed based on excluding from the force computation all surface markers whose stencil overlaps with the stencil of a marker located on the surface of a collision partner the resulting algorithm is throughly validated and is demonstrated to substantially improve upon the original method

immersed boundary method for flow around an arbitrarily moving body for the simulation of flow around an arbitrarily moving body an immersed boundary method is developed in a non inertial reference frame that is fixed to the body the navier stokes equation is formulated in a conservative form such that the force terms due to the rotation and the translational and rotational accelerations are included in the nonlinear term in order to satisfy the no slip condition on the body surface momentum forcing and mass source sink are applied on the body surface or inside the body the numerical method is based on a finite volume approach on a staggered mesh together with a fractional step method the present numerical method is applied to both the forced motion and fluid structure interaction problems in the latter we solve fully coupled navier stokes and dynamic equations for the moving body without introducing any iteration four different flow problems are tested and the results are in excellent agreements with previous numerical and experimental ones

time averaged quadratic functionals of a gaussian process the characterization of a stochastic process from its single random realization is a challenging problem for most single particle tracking techniques which survey an individual trajectory of a tracer in a complex or viscoelastic medium we consider two quadratic functionals of the trajectory the time averaged mean square displacement msd and the time averaged squared root mean square displacement srms for a large class of stochastic processes governed by the generalized langevin equation with arbitrary frictional memory kernel and harmonic potential the exact formulas for the mean and covariance of these functionals are derived the formula for the mean value can be directly used for fitting experimental data e g in optical tweezers microrheology the formula for the variance and covariance allows one to estimate the intrinsic fluctuations of measured or simulated time averaged msd or srms for choosing the experimental setup appropriately we show that the time averaged srms has smaller fluctuations than the time averaged msd in spite of much broader applications of the latter one the theoretical results are successfully confirmed by monte carlo simulations of the langevin dynamics we conclude that the use of the time averaged srms would result in a more accurate statistical analysis of individual trajectories and more reliable interpretation of experimental data

aging properties of an anomalously diffusing particule we report new results about the two time dynamics of an anomalously diffusing classical particle as described by the generalized langevin equation with a frequency dependent noise and the associated friction the noise is defined by its spectral density proportional to 1 at low frequencies with 0 1 subdiffusion or 1 2 superdiffusion using laplace analysis we derive analytic expressions in terms of mittag leffler functions for the correlation functions of the velocity and of the displacement while the velocity thermalizes at large times slowly in contrast to the standard brownian motion case 1 the displacement never attains equilibrium it ages we thus show that this feature of normal diffusion is shared by a subdiffusive or superdiffusive motion we provide a closed form analytic expression for the fluctuation dissipation ratio characterizing aging

composite overlapping meshes for the solution of partial differential equations abstract we discuss the generation of curvilinear composite overlapping grids and the numerical solution of partial differential equations on them a composite overlapping grid consists of a set of curvilinear component grids that cover a region and overlap where they meet continuity conditions interpolation are imposed at the overlapping boundaries the principal advantage of composite grids is in the generation of grids for regions with complicated geometries the grid construction program cmpgrd is used to create composite grids with any number of component grids we describe some techniques for the solution of elliptic and time dependent pdes on composite meshes applications to the solution of the compressible navier stokes equations are presented

an added mass partition algorithm for fluid structure interactions of compressible fluids and nonlinear solids we describe an added mass partitioned amp algorithm for solving fluid structure interaction fsi problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements the computational approach is a mixed eulerian lagrangian scheme that makes use of deforming composite grids dcg to treat large changes in the geometry in an accurate flexible and robust manner the current work extends the amp algorithm developed in banks et al 1 for linearly elasticity to the case of nonlinear solids to ensure stability for the case of light solids the new amp algorithm embeds an approximate solution of a nonlinear fluid solid riemann fsr problem into the interface treatment the solution to the fsr problem is derived and shown to be of a similar form to that derived for linear solids the state on the interface being fundamentally an impedance weighted average of the fluid and solid states numerical simulations demonstrate that the amp algorithm is stable even for light solids when added mass effects are large the accuracy and stability of the amp scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi analytical solution that is obtained for a rotating solid disk immersed in a fluid the scheme is applied to the simulation of a planar shock impacting a light elliptical shaped solid and comparisons are made between solutions of the fsi problem for a neo hookean solid a linearly elastic solid and a rigid solid the ability of the approach to handle large deformations is demonstrated for a problem of a high speed flow past a light thin and flexible solid beam

direct numerical simulation of particulate flows with an overset grid method abstract we evaluate an efficient overset grid method for two dimensional and three dimensional particulate flows for small numbers of particles at finite reynolds number the rigid particles are discretised using moving overset grids overlaid on a cartesian background grid this allows for strongly enforced boundary conditions and local grid refinement at particle surfaces thereby accurately capturing the viscous boundary layer at modest computational cost the incompressible navier stokes equations are solved with a fractional step scheme which is second order accurate in space and time while the fluid solid coupling is achieved with a partitioned approach including multiple sub iterations to increase stability for light rigid bodies through a series of benchmark studies we demonstrate the accuracy and efficiency of this approach compared to other boundary conformal and static grid methods in the literature in particular we find that fully resolving boundary layers at particle surfaces is crucial to obtain accurate solutions to many common test cases with our approach we are able to compute accurate solutions using as little as one third the number of grid points as uniform grid computations in the literature a detailed convergence study shows a 13 fold decrease in cpu time over a uniform grid test case whilst maintaining comparable solution accuracy

fractional diffusion equation with a generalized riemann liouville time fractional derivative in this paper the solution of a fractional diffusion equation with a hilfer generalized riemann liouville time fractional derivative is obtained in terms of mittag leffler type functions and fox s h function the considered equation represents a quite general extension of the classical diffusion heat conduction equation the methods of separation of variables laplace transform and analysis of the sturm liouville problem are used to solve the fractional diffusion equation defined in a bounded domain by using the fourier laplace transform method it is shown that the fundamental solution of the fractional diffusion equation with a generalized riemann liouville time fractional derivative defined in the infinite domain can be expressed via fox s h function it is shown that the corresponding solutions of the diffusion equations with time fractional derivative in the caputo and riemann liouville sense are special cases of those diffusion equations with the hilfer generalized riemann liouville time fractional derivative the asymptotic behaviour of the solutions are found for large values of the spatial variable the fractional moments of the fundamental solution of the fractional diffusion equation are obtained the obtained results are relevant in the context of glass relaxation and aquifer problems

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

fractional langevin equation overdamped underdamped and critical behaviors the dynamical phase diagram of the fractional langevin equation is investigated for a harmonically bound particle it is shown that critical exponents mark dynamical transitions in the behavior of the system four different critical exponents are found i ensuremath alpha c 0 402 ifmmode pm else textpm fi 0 002 marks a transition to a nonmonotonic underdamped phase ii ensuremath alpha r 0 441 dots marks a transition to a resonance phase when an external oscillating field drives the system and iii ensuremath alpha ensuremath chi 1 0 527 dots and iv ensuremath alpha ensuremath chi 2 0 707 dots mark transitions to a double peak phase of the loss when such an oscillating field present as a physical explanation we present a cage effect where the medium induces an elastic type of friction phase diagrams describing over and underdamped regimes with or without resonances show behaviors different from normal

a unified mathematical framework and an adaptive numerical method for fluid structure interaction with rigid deforming and elastic bodies many problems of interest in biological fluid mechanics involve interactions between fluids and solids that require the coupled solution of momentum equations for both the fluid and the solid in this work we develop a mathematical framework and an adaptive numerical method for such fluid structure interaction fsi problems in which the structure may be rigid deforming or elastic we employ an immersed boundary ib formulation of the problem that permits us to avoid body conforming discretizations and to use fast cartesian grid solvers rigidity and deformational kinematic constraints are imposed using a formulation based on distributed lagrange multipliers and a conventional ib method is used to describe the elasticity of the immersed body we use cartesian grid adaptive mesh refinement amr to discretize the equations of motion and thereby obtain a solution methodology that efficiently captures thin boundary layers at fluid solid interfaces as well as flow structures shed from such interfaces this adaptive methodology is validated for several benchmark problems in two and three spatial dimensions in addition we use this scheme to simulate free swimming including the maneuvering of a two dimensional model eel and a three dimensional model of the weakly electric black ghost knifefish

generalized langevin equation with tempered memory kernel abstract we study a generalized langevin equation for a free particle in presence of a truncated power law and mittag leffler memory kernel it is shown that in presence of truncation the particle from subdiffusive behavior in the short time limit turns to normal diffusion in the long time limit the case of harmonic oscillator is considered as well and the relaxation functions and the normalized displacement correlation function are represented in an exact form by considering external time dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement additionally the double peak phenomenon in the imaginary part of the complex susceptibility is observed it is obtained that the truncation parameter has a huge influence on the behavior of these quantities and it is shown how the truncation parameter changes the critical frequencies the normalized displacement correlation function for a fractional generalized langevin equation is investigated as well all the results are exact and given in terms of the three parameter mittag leffler function and the prabhakar generalized integral operator which in the kernel contains a three parameter mittag leffler function such kind of truncated langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes

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

fractional langevin equation we investigate fractional brownian motion with a microscopic random matrix model and introduce a fractional langevin equation we use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath we further compare fractional brownian motion with the fractal time process the respective mean square displacements of these two forms of anomalous diffusion exhibit the same power law behavior here we show that their lowest moments are actually all identical except the second moment of the velocity this provides a simple criterion that enable us to distinguish these two non markovian processes

on multigrid for overlapping grids the solution of elliptic partial differential equations on composite overlapping grids using multigrid is discussed an approach is described that provides a fast and memory efficient scheme for the solution of boundary value problems in complex geometries the key aspects of the new scheme are an automatic coarse grid generation algorithm an adaptive smoothing technique for adjusting residuals on different component grids and the use of local smoothing near interpolation boundaries other important features include optimizations for cartesian component grids the use of over relaxed red black smoothers and the generation of coarse grid operators through galerkin averaging numerical results in two and three dimensions show that very good multigrid convergence rates can be obtained for dirichlet neumann and mixed boundary conditions a comparison to krylov based solvers shows that the multigrid solver can be much faster and require significantly less memory

an analysis of a new stable partitioned algorithm for fsi problems part i incompressible flow and elastic solids stable partitioned algorithms for fluid structure interaction fsi problems are developed and analyzed in this two part paper part i describes an algorithm for incompressible flow coupled with compressible elastic solids while part ii discusses an algorithm for incompressible flow coupled with structural shells importantly these new added mass partitioned amp schemes are stable and retain full accuracy with no sub iterations per time step even in the presence of strong added mass effects e g for light solids the numerical approach described here for bulk compressible solids extends the scheme of banks et al 1 2 for inviscid compressible flow and uses robin mixed boundary conditions with the fluid and solid solvers at the interface the basic amp robin conditions involving a linear combination of velocity and stress are determined from the outgoing solid characteristic relation normal to the fluid solid interface combined with the matching conditions on the velocity and traction two alternative forms of the amp conditions are then derived depending on whether the fluid equations are advanced with a fractional step method or not the stability and accuracy of the amp algorithm is evaluated for linearized fsi model problems the full nonlinear case being left for future consideration a normal mode analysis is performed to show that the new amp algorithm is stable for any ratio of the solid and fluid densities including the case of very light solids when added mass effects are large in contrast it is shown that a traditional partitioned algorithm involving a dirichlet neumann coupling for the same fsi problem is formally unconditionally unstable for any ratio of densities exact traveling wave solutions are derived for the fsi model problems and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the amp algorithm for the cases of light medium and heavy solids