a block triple relaxation time lattice boltzmann model for nonlinear anisotropic convection diffusion equations abstract a block triple relaxation time b trirt lattice boltzmann model for general nonlinear anisotropic convection diffusion equations nacdes is proposed and the chapman enskog analysis shows that the present b trirt model can recover the nacdes correctly there are some striking features of the present b trirt model firstly the relaxation matrix of b trirt model is partitioned into three relaxation parameter blocks rather than a diagonal matrix in general multiple relaxation time mrt model secondly based on the analysis of half way bounce back hbb scheme for dirichlet boundary conditions we obtain an expression to determine the relaxation parameters thirdly the anisotropic diffusion tensor can be recovered by the relaxation parameter block that corresponds to the first order moment of non equilibrium distribution function a number of simulations of isotropic and anisotropic convection diffusion equations are conducted to validate the present b trirt model the results indicate that the present model has a second order accuracy in space and is also more accurate and more stable than some available lattice boltzmann models

numerical method for solving stochastic differential equations with poissonian white shot noise we propose a numerical integration scheme to solve stochastic differential equations driven by poissonian white shot noise our formula which is based on an integral equation which is equivalent to the stochastic differential equation utilizes a discrete time approximation with fixed integration time step we show that our integration formula approaches the euler formula if the poissonian noise approaches the gaussian white noise the accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by poissonian white shot noise in a spatially periodic potential we find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the poissonian white shot noise this holds true even if the limit of gaussian white noise is approached

simulating time harmonic flows with the lattice boltzmann method we simulate time harmonic flows by the lattice boltzmann method we propose a general scheme to choose simulation parameters under the constraints of fixed reynolds and womersley numbers and with a specified simulation error under these constraints parameters are chosen to minimize the execution time numerical stability is studied in a range of reynolds and womersley numbers as an example of time harmonic flow simulations results of blood flow in a human abdominal aorta are presented

numerical solution of differential equations with colored noise using the general theory of numerical integration of stochastic differential equations a constructive approach to numerical methods for a system with colored noise is proposed efficient methods up to the 5 2 strong order and up to the third weak order including runge kutta and implicit schemes are presented the algorithms are tested on the kubo oscillator

numerical simulations of stochastic differential equations a simple very accurate algorithm for numerical simulation of stochastic differential equations is described its relationship to colored noise is elucidated and exhibited by explicit results the especially delicate problem of mean first passage times is highlighted and highly accurate agreement between the numerical simulations and analytic results are shown

optimal design for non newtonian flows using a topology optimization approach we study non newtonian effects on the layout and geometry of flow channels using a material distribution based topology optimization approach the flow is modeled with the single relaxation hydrodynamic lattice boltzmann method and the shear dependence of viscosity is included through the carreau yasuda model for non newtonian fluids to represent the viscosity of blood in this model we use non newtonian similarity further we introduce a scaling to decrease the effects of the non newtonian model in porous regions in order to stabilize the coupling of the lbm porosity and non newtonian flow models for the resulting flow model we derive the non newtonian sensitivity analysis for steady state conditions and illustrate the non newtonian effect on channel layouts for a 2d dual pipe design problem at different reynolds numbers

escape rates in periodically driven markov processes we present an approximate analytical expression for the escape rate of time dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrateand fire model for neural spiking the novel approximation i s based on a discrete state markovian modeling of the full long time dynamics with time dependent rates it is valid in a wide parameter regime beyond the restraining limits of weak driving linear response and or weak noise the scheme is carefully tested and yields excellent agreement with three different numerical methods based on the langevin equation the fokker planck equation and an integral equation

preconditioning multichannel adaptive filtering algorithms using evd and svd based signal prewhitening and system decoupling abstract it is well known that the convergence rate of multichannel lms based algorithms is limited by the correlation properties of the reference signals and the cross coupling within the plant dynamics these factors give rise to excessive eigenvalue spread and slow convergence rate of a gradient descent algorithm a preconditioning technique is developed in this study for the multichannel lms algorithm so as to improve its convergence rate signal prewhitening and system decoupling are the two key elements of the proposed techniques preconditioning filters are first formulated in the frequency domain by using eigenvalue decomposition and singular value decomposition these filters are then transformed into the time domain with causality taken into account the preconditioning filters are incorporated into a multichannel lms algorithm where the reference signals are prewhitened and the plants are decoupled prior to the adaptation process simulations for a two channel one listener cross talk cancellation problem illustrate the effectiveness of the preconditioning technique in improving the convergence rate of the adaptive algorithms

persistent diffusion on a line we consider solutions to the telegraph equation describing persistent diffusion on a line under various initial conditions the first passage time distribution is evaluated in closed form biased persistent diffusion is also considered a direct derivation of the telegraph equation from the stochastic equation for the displacement is presented in an appendix

contact angle measurement in lattice boltzmann method abstract contact angle is an essential characteristic in wetting capillarity and moving contact line however although contact angle phenomena are effectively simulated an accurate and real time measurement for contact angle has not been well studied in computational fluid dynamics especially in dynamic environments here we design a geometry based mesoscopic scheme for on the spot measurement of the contact angle in the lattice boltzmann method the measuring results without gravity effect are in good agreement with the benchmarks from the spherical cap method the performances of the scheme are further verified in gravitational environments by simulating sessile and pendent droplets on smooth solid surfaces and dynamic contact angle hysteresis on chemically heterogeneous surfaces this scheme is simple and computationally efficient it requires only the local data and is independent of multiphase models

stochastic giant resonance the model of an electric circuit with dichotomous resistance is investigated it is shown that the dichotomous resistance can induce a phenomenon of stochastic giant resonance for the signal to noise ratio snr as a function of input signal frequency this phenomenon is a direct consequence of the existence of a zero noise power spectrum with a nonzero signal power spectrum for the same parameters in addition two kinds of the usual stochastic resonance phenomena have been obtained for the snr one is as a function of the correlation time of the asymmetric dichotomous resistance the other is as a function of the input signal frequency

on the relation between white shot noise gaussian white noise and the dichotomic markov process it is shown that the dichotomic markov process converges to a white shot noise interpreted according to the stratonovich integration rule in the joint limit in which the average duration of one of the states goes to zero and the value at this state goes to infinity a further limit procedure allows us to obtain gaussian white noise from white shot noise these results are applied to the problem of noise induced transitions it is shown that white shot noise can give rise to transitions which do not occur for gaussian white noise the above results are finally generalized in introducing compound dichotomic markov processes

the lms algorithm with delayed coefficient adaptation the behavior of the delayed least mean square dlms algorithm is studied it is found that the step size in the coefficient update plays a key role in the convergence and stability of the algorithm an upper bound for the step size is derived that ensures the stability of the dlms the relationship between the step size and the convergence speed and the effect of the delay on the convergence speed are also studied the analytical results are supported by computer simulations

model selection for convolutive ica with an application to spatiotemporal analysis of eeg we present a new algorithm for maximum likelihood convolutive independent component analysis ica in which components are unmixed using stable autoregressive filters determined implicitly by estimating a convolutive model of the mixing process by introducing a convolutive mixing model for the components we show how the order of the filters in the model can be correctly detected using bayesian model selection we demonstrate a framework for deconvolving a subspace of independent components in electroencephalography eeg initial results suggest that in some cases convolutive mixing may be a more realistic model for eeg signals than the instantaneous ica model

designing correct fluid hydrodynamics on a rectangular grid using mrt lattice boltzmann approach while the lattice boltzmann method lbm has become a powerful numerical approach for solving complex flows the standard lattice boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions for inhomogeneous and anisotropic flows it is desirable to have a lbm model that utilizes a rectangular grid there were two previous attempts to extend the multiple relaxation time mrt lbm to a rectangular lattice grid in 2d however the resulting hydrodynamic momentum equation was not fully consistent with the navier stokes equation due to anisotropy of the transport coefficients in the present work a new mrt model with an additional degree of freedom is developed in order to match precisely the navier stokes equation when a rectangular lattice grid is used we first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the chapman enskog procedure then an additional adjustable parameter that governs the relative orientation in the energy normal stress subspace is introduced it is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients thus the exact navier stokes equation can be derived on a rectangular grid our theoretical findings are confirmed by numerical solutions using three two dimension benchmark problems i e the channel flow the cavity flow and the decaying taylor green vortex flow the numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters

a partitioned scheme for fluid composite structure interaction problems we present a benchmark problem and a loosely coupled partitioned scheme for fluid structure interaction with composite structures the benchmark problem consists of an incompressible viscous fluid interacting with a structure composed of two layers a thin elastic layer with mass which is in contact with the fluid and modeled by the koiter membrane shell equations and a thick elastic layer with mass modeled by the equations of linear elasticity an efficient modular partitioned operator splitting scheme is proposed to simulate solutions to the coupled nonlinear fsi problem without the need for sub iterations at every time step an energy estimate associated with unconditional stability is derived for the fully nonlinear fsi problem defined on moving domains two instructive numerical benchmark problems are presented to test the performance of numerical fsi schemes involving composite structures it is shown numerically that the proposed scheme is at least first order accurate both in time and space this work reveals a new physical property of fsi problems involving thin interfaces with mass the inertia of the thin fluid structure interface regularizes solutions to the full fsi problem

response to a periodic stimulus in a perfect integrate and fire neuron model driven by colored noise the output interspike interval statistics of a stochastic perfect integrate and fire neuron model driven by an additive exogenous periodic stimulus is considered the effect of temporally correlated random activity of synaptic inputs is modeled by an additive symmetric dichotomous noise using a first passage time formulation exact expressions for the output interspike interval density and for the serial correlation coefficient are derived in the nonsteady regime and their dependence on input parameters e g the noise correlation time and amplitude as well as the frequency of an input current is analyzed it is shown that an interplay of a periodic forcing and colored noise can cause a variety of nonequilibrium cooperation effects such as sign reversals of the interspike interval correlations versus noise switching rate as well as versus the frequency of periodic forcing a power law like decay of oscillations of the serial correlation coefficients in the long lag limit amplification of the output signal modulation in the instantaneous firing rate of the neural response etc the features of spike statistics in the limits of slow and fast noises are also discussed

computing a non maxwellian velocity distribution from first principles we investigate a family of single particle anomalous velocity distribution by solving a particular class of stochastic liouville equations the stationary state is obtained analytically and the maxwell boltzmann distribution is reobtained in a particular limit we discuss the comparison with other different methods to obtain the stationary state extensions when the models cannot be solved in an exact way are also pointed out in connection with the one ficton approximation

stochastic calculus in physics the relationship of the ito stratonovich stochastic calculus to studies of weakly colored noise is explained a functional calculus approach is used to obtain an effective fokker planck equation for the weakly colored noise regime in a smooth limit this representation produces the stratonovich version of the ito stratonovich calculus for white noise it also provides an approach to steady state behavior for strongly colored noise numerical simulation algorithms are explored and a novel suggestion is made for efficient and accurate simulation of white noise equations

numerical integration of multiplicative noise stochastic differential equations a two stage runge kutta algorithm for vector ito and by transform also stratonovich stochastic differential equations with multiplicative noise has been developed the method is second order accurate but for vanishing drift the algorithm yields a martingale independent of step size several examples are included to illustrate our method a discussion of errors shows that sample size can be as important as truncation

fluid structure interaction in blood flow capturing non zero longitudinal structure displacement we present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid structure interaction fsi in blood flow allowing non zero longitudinal displacement arterial walls are modeled by a linearly viscoelastic cylindrical koiter shell model capturing both radial and longitudinal displacement fluid flow is modeled by the navier stokes equations for an incompressible viscous fluid the two are fully coupled via kinematic and dynamic coupling conditions our numerical scheme is based on a new modified lie operator splitting that decouples the fluid and structure sub problems in a way that leads to a loosely coupled scheme which is unconditionally stable this was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub problems leading to an implicit coupling between the fluid and structure velocities the proposed scheme is a modification of the recently introduced kinematically coupled scheme for which the newly proposed modified lie splitting significantly increases the accuracy the performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme it was shown that the accuracy of our scheme was comparable to that of the monolithic scheme while our scheme retains all the main advantages of partitioned schemes such as modularity simple implementation and low computational costs

lattice boltzmann method for simulating the viscous flow in large distensible blood vessels a lattice boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries the mass conservation for the boundary condition is tested in detail the viscous flow in elastic vessels is simulated with a pressure radius relationship similar to that of the pulmonary blood vessels the numerical results for steady flow agree with the analytical prediction to very high accuracy and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally the model is expected to find many applications for studying blood flows in large distensible arteries especially in those suffering from atherosclerosis stenosis aneurysm etc

an integral algorithm for numerical integration of one dimensional additive colored noise problems we present an integral closed algorithm for solving a langevin equation driven by an additive colored noise both the mean first passage time in a bistable system and the diffusion current in a titled periodic potential are calculated and the comparison with existing algorithms is carried out the dependence of the numerical results on the time steps is studied our algorithm is shown to have high accuracy and stability

ito versus stratonovich a survey is given of the facts and fancies concerning the nonlinear langevin or ito equation actually it is merely a pre equation which becomes an equation when an interpretation rule is added the rules of ito and stratonovich differ but both are mathematically consistent and therefore equally admissible conventions the reason why they seem to lead to physical differences is that the langevin approach used to arrive at the equation involves a tacit assumption for systems with external noise this assumption can be justified and it is then clear that the stratonovich rule applies systems with internal noise however can only be properly described by a master equation and the ito stratonovich controversy never enters afterward one is free to model the resulting fluctuations either with an ito or a stratonovich scheme but that does not lead to any new information

a haar like construction for the ornstein uhlenbeck process the classical haar construction of brownian motion uses a binary tree of triangular wedge shaped functions this basis has compactness properties which make it especially suited for certain classes of numerical algorithms we present a similar basis for the ornstein uhlenbeck process in which the basis elements approach asymptotically the haar functions as the index increases and preserve the following properties of the haar basis all basis elements have compact support on an open interval with dyadic rational endpoints these intervals are nested and become smaller for larger indices of the basis element and for any dyadic rational only a finite number of basis elements is nonzero at that number thus the expansion in our basis when evaluated at a dyadic rational terminates in a finite number of steps we prove the covariance formulae for our expansion and discuss its statistical interpretation

accurate monte carlo tests of the stochastic ginzburg landau model with multiplicative colored noise an accurate and fast monte carlo algorithm is proposed for solving the ginzburg landau equation with multiplicative colored noise the stable cases of solution for choosing time steps and trajectory numbers are discussed

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

stochastic resonance reverse resonance and resonant activation induced by a multi state noise abstract in this paper we investigate the periodic response for a linear system driven by a multiplicative multi state noise which is composed of the multiplication of two dichotomous noises to an input temporal oscillatory signal and the escape of brownian particles over the fluctuating potential barrier for a system with a piece wise linear potential and driven by an additive multi state noise which is also composed of the multiplication of two dichotomous noises for the first system we get the stochastic resonance phenomenon for the amplitude of the periodic response vs the two dichotomous noise strengths and the phenomenon of reverse resonance for the amplitude of the periodic response vs k which represents the asymmetry degree of the dichotomous noises for the second system we obtain the resonant activation phenomenon for which the mean first passage time of the brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi state noise

brief regularization networks for inverse problems a state space approach linear inverse problems with discrete data are equivalent to the estimation of the continuous time input of a linear dynamical system from samples of its output the solution obtained by means of regularization theory has the structure of a neural network similar to classical rbf networks however the basis functions depend in a nontrivial way on the specific linear operator to be inverted and the adopted regularization strategy by resorting to the bayesian interpretation of regularization we show that such networks can be implemented rigorously and efficiently whenever the linear operator admits a state space representation an analytic expression is provided for the basis functions as well as for the entries of the matrix of the linear system used to compute the weights the results are illustrated through a deconvolution problem where the spontaneous secretory rate of luteinizing hormone lh of the hypophisis is reconstructed from measurements of plasma lh concentrations

numerical method for solving stochastic differential equations with dichotomous noise we propose a numerical method for solving stochastic differential equations with dichotomous markov noise the numerical scheme is formulated such that i the stochastic formula used follows the stratonovichtaylor form over the entire range of noise correlation times including the gaussian white noise limit and ii the method is readily applicable to dynamical systems driven by arbitrary types of noise provided there exists a way to describe the random increment of the stochastic process expressed in the stratonovich taylor form we further propose a simplified taylor scheme that significantly reduces the computation time while still satisfying the moment properties up to the required order the accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions

second order algorithm for simulating stochastic differential equations with white noises abstract the second order algorithm for simulating stochastic differential equations with gaussian white noises is presented these stochastic differential equations are universal type among these gaussian white noises come from different sources specifically the proposed algorithm extends previous first order algorithm for stochastic differential equations with different white noises and second order algorithm for stochastic differential equations with same white noise in practice it is proved that this algorithm is scientific

the availability of logical operation induced by dichotomous noise for a nonlinear bistable system instead of a continuous system driven by gaussian white noise logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise which shows a phenomenon different from gaussian white noise we can realize two parallel logical operations by simply adjusting the values of these two thresholds besides to quantify the reliability of obtaining the correct logic output we numerically calculate the success probability and effects of dichotomous noise on the success probability are observed these observations show that the reliability of realizing logical operation in the bistable system can be improved through optimizing parameters of dichotomous noise

stochastic processes driven by dichotomous markov noise some exact dynamical results stochastic processes defined by a general langevin equation of motion where the noise is the non gaussian dichotomous markov noise are studied a non fokker planck master differential equation is deduced for the probability density of these processes two different models are exactly solved in the second one a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time critical slowing down does not appear in this point but in another one

lattice boltzmann simulations of blood flow non newtonian rheology and clotting processes the numerical simulation of thrombosis in stented aneurysms is an important issue to estimate the efficiency of a stent in this paper we consider a lattice boltzmann lb approach to bloodflow modeling and we implement a non newtonian correction in order to reproduce more realistic flow profiles we obtain a good agreement between simulations and casson s model of blood rheology in a simple geometry finally we discuss how by using a passive scalar suspension model with aggregation on top of the lb dynamics we can describe the clotting processes in the aneurysm

a second order accurate lattice boltzmann non newtonian flow model a second order accurate lattice boltzmann model is presented for non newtonian flow the non newtonian nature of the flow is implemented using a power law model this is used to enable the accuracy of the model to be assessed and is not a limitation of the model the second order accuracy is demonstrated for a range of power law model parameter values representing shear thinning and shear thickening fluids these results are compared with those of gabbanelli et al 2006 phys rev e 72 046312 and it is noted that a higher order of accuracy and greater computational efficiency are achieved these results demonstrate the suitability of the lbm for shear dependent non newtonian flow simulations

computation of lyapunov spectra effect of interactive noise and application to a chemical oscillator abstract a refined version of the sano sawada algorithm to compute lyapunov spectra has been implemented and tested with several models which include periodic chaotic and hyperchaotic attractors under conditions designed to mimic experimental situations it was found that reliable lyapunov exponents can be obtained for time series of moderate length and point density also in the presence of interactive noise as long as its amplitude does not exceed 1 of the oscillation amplitude the algorithm was then applied to experimental data from the co oxidation on pt 110 clearly showing the occurrence of chaos as well as hyperchaos

numerical simulations of generalized langevin equations with deeply asymptotic parameters a unified algorithm for solving langevin equations with deeply asymptotic parameters is proposed and tested the method consists of identifying solvable linear friction and implementing the force evaluations by use of the runge kutta method we apply the present scheme to the periodic motion of an overdamped particle subjected to a multiplicative white noise the accurate calculations for the temporal velocity of the particle and its correlation function can be realized by introducing an inertial term it is shown that the fluctuation around the steady quantity increases with decreasing time step in the overdamped white noise algorithm however a massive white noise technique greatly reduces this spurious drift and the result can converge to the correct value if the added inertia approaches zero the other application is the simulation of generalized langevin equation with an exponential memory friction this allows us to treat a weak non markovian process

self whitening algorithms for adaptive equalization and deconvolution in equalization and deconvolution tasks the correlated nature of the input signal slows the convergence speeds of stochastic gradient adaptive filters prewhitening techniques have been proposed to improve the convergence performance but the additional coefficient memory and updates for the prewhitening filter can be prohibitive in some applications we present two simple algorithms that employ the equalizer as a prewhitening filter within the gradient updates these self whitening algorithms provide quasi newton convergence locally about the optimum coefficient solution for deconvolution and equalization tasks multichannel extensions of the techniques are also described

solvability of the master equation for dichotomous flow we consider the one dimensional stochastic flow mathrm x ifmmode dot else fi f x g x ensuremath xi t where ensuremath xi t is a dichotomous markov noise and use a simple procedure to identify the conditions under which the integro differential equation satisfied by the total probability density p x t of the driven variable can be reduced to a differential equation of finite order this generalizes the enumeration of the solvable cases

stochastic algorithms for discontinuous multiplicative white noise stochastic differential equations with multiplicative noise need a mathematical prescription due to different interpretations of the stochastic integral this fact implies specific algorithms to perform numerical integrations or simulations of the stochastic trajectories moreover if the multiplicative noise function is not continuous then the standard algorithms cannot be used we present an explicit algorithm to avoid this problem and we apply it to a well controlled example finally we discuss on the existence of higher order algorithms for this specific situation

statistics of a leaky integrate and fire model of neurons driven by dichotomous noise the behavior of a stochastic leaky integrate and fire model of neurons is considered the effect of temporally correlated random neuronal input is modeled as a colored two level dichotomous markovian noise relying on the riemann method exact expressions for the output interspike interval density and for the serial correlation coefficient are derived and their dependence on noise parameters such as correlation time and amplitude is analyzed particularly noise induced sign reversal and a resonancelike amplification of the kurtosis of the interspike interval distribution are established the features of spike statistics analytically revealed in our study are compared with recently obtained results for a perfect integrate and fire neuron model

effect of correlated dichotomous noises on stochastic resonance in a linear system a linear system driven by correlated asymmetric dichotomous noises and periodic signal was investigated in the overdamped case the exact expressions of output signal amplitude and signal to noise ratio snr of the system were derived by means of numerical calculations we found that i at some fixed multiplicative noise intensities the output signal amplitude with frequency exhibits the structure of a weak peak even no peak as the dichotomous noise is asymmetric ii in the case of asymmetric dichotomous noise the signal frequency can cause non monotonous behavior of the output signal amplitude with respect to multiplicative noise intensity iii the curve of snr with frequency has a weak peak and a trough in the case of symmetric dichotomous noise but no peak with asymmetric iv whether the multiplicative noise is symmetric or asymmetric the noise can enhance response of the system v the snr increases with the correlation strength between the two noises decreasing in addition the plane of multiplicative noise intensity versus noise symmetric parameter was plotted

a fast algorithm for the first passage times of gauss markov processes with holder continuous boundaries even for simple diffusion processes treating first passage problems analytically proves intractable for generic barriers and existing numerical methods are inaccurate and computationally costly here we present a novel numerical method that is faster and has more tightly controlled accuracy our algorithm is a probabilistic variant of dichotomic search for the computation of first passage times through non negative homogeneously holder continuous boundaries by gauss markov processes these include the ornstein uhlenbeck process underlying the ubiquitous leaky integrate and fire model of neuronal excitation our method evaluates discrete points in a sample path exactly and refines this representation recursively only in regions where a passage is rigorously estimated to be probable e g when close to the boundary

stable loosely coupled type algorithm for fluid structure interaction in blood flow we introduce a novel loosely coupled type algorithm for fluid structure interaction between blood flow and thin vascular walls this algorithm successfully deals with the difficulties associated with the added mass effect which is known to be the cause of numerical instabilities in fluid structure interaction problems involving fluid and structure of comparable densities our algorithm is based on a time discretization via operator splitting which is applied in a novel way to separate the fluid sub problem from the structure elastodynamics sub problem in contrast with traditional loosely coupled schemes no iterations are necessary between the fluid and structure sub problems this is due to the fact that our novel splitting strategy uses the added mass effect to stabilize rather than to destabilize the numerical algorithm this stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub problem the stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable due to the crucial role played by the kinematic lateral boundary condition the proposed algorithm is named the kinematically coupled scheme