dpoae group delays versus electrophysiological measures of cochlear delay in normal human ears group delays of 2 f1 f2 distortion product otoacoustic emissions dpoaes were determined using both f1 and f2 sweep paradigms in 24 normal hearing subjects these dpoae group delays were studied in comparison with cochlear delays estimated from derived band viiith nerve compound action potentials caps and auditory brainstem responses abrs in the same subjects the center frequencies of the derived bands in the electrophysiological experiment were matched with the f2 frequencies in the dpoae recording to ensure that dpoaes and derived caps and abrs were generated at the same places along the cochlear partition thus allowing for a direct comparison the degree to which dpoae group delays are larger in the f2 than in the f1 sweep paradigm is consistent with a theoretical analysis of the so called wave fixed model both dpoae group delays are highly correlated with cap and abr derived measures of cochlear delay the principal result of this study is that roundtrip dpoae group delay in the f1 sweep

high resolution schemes for conservation laws with locally varying time steps we develop upwind methods which use limited high resolution corrections in the spatial discretization and local time stepping for forward euler and second order time discretizations l infty stability is proven for both time stepping schemes for problems in one space dimension these methods are restricted by a local cfl condition rather than the traditional global cfl condition allowing local time refinement to be coupled with local spatial refinement numerical evidence demonstrates the stability and accuracy of the methods for problems in both one and two space dimensions

local time stepping in runge kutta discontinuous galerkin finite element methods applied to the shallow water equations abstract large geophysical flows often encompass both coarse and highly resolved regions approximating these flows using shock capturing methods with explicit time stepping gives rise to a courant friedrichs lewy cfl time step constraint even if the refined regions are sparse they can restrict the global cfl condition to very small time steps vastly increasing computational effort over the whole domain one method to cope with this problem is to use locally varying time steps over the domain these are also referred to as multi rate methods in the ode literature ideally such methods must be conservative accurate and easy to implement in this study we derive a second order local time stepping procedure within a runge kutta discontinuous galerkin rkdg framework to solve the shallow water equations this procedure is based on previous first order work of the second author and collaborator kirby 1 2 3 as we are interested in both coastal and overland flows due to e g rainfall wetting and drying is incorporated into the model numerical results are shown which verify the accuracy and efficiency of the approach compared to using a globally defined cfl time step and the application of the method to rainfall runoff scenarios

connection between orthogonal polynomials on the unit circle and bounded interval in this paper we establish the connection between measures on a bounded interval and on the unit circle by a transformation related with the szego classical transformation we transform a measure on the interval 1 1 into a measure on 0 2 in the same form in which the orthogonality measure of the chebyshev polynomials of fourth kind becomes the lebesgue measure we relate the sequences of orthogonal polynomials with respect to both measures and we also relate the coefficients of the three term recurrence relation with the schur parameters when the measures belong to the szego class we study the asymptotic behavior of the orthogonal polynomials on the interval outside the support of the measure as well as inside we also transform the generalized polynomials and we study the orthogonality properties of the new polynomials obtaining new interesting results and finally we solve two inverse problems connected with the transformation studied

on conservation at grid interfaces this paper considers the solution of hyperbolic systems of conservation laws on discontinuous grids in particular we consider what happens to conservation at grid interfaces a procedure is presented to derive conservative difference approximations at the grid interfaces for two dimensional grids which overlap in an arbitrary configuration the same procedures are applied to compute interface formulas for grids which are refined in space and or time and for continuous grids where a switch in the scheme causes the discontinuity

multicomponent acoustic distortion product otoacoustic emission phase in humans ii implications for distortion product otoacoustic emissions generation phase characteristics and latency of 2f1 f2 3f1 2f2 and 2f2 f1 acoustic distortion product otoacoustic emissions dpoaes recorded in normally hearing adults have been described in a companion paper moulin and kemp multicomponent acoustic distortion product otoacoustic emission phase in humans i general characteristics j acoust soc am 100 1617 1639 1996 phase versus frequency functions pff have been recorded using two methods depending whether f1 or f2 was swept in frequency defining respectively an f1 sweep and an f2 sweep method the present study compares 2f1 f2 3f1 2f2 4f1 3f2 and 2f2 f1 dpoaes phase characteristics and latencies obtained by these two methods for lower sideband dpoaes the f2 sweep gave consistently longer latencies than the f1 sweep method whereas no difference was obtained for the 2f2 f1 dpoae this suggests that the lower sideband dpoaes and the 2f2 f1 dpoae do not come from the same aspect of the traveling wave the longer delay obtained with an f2 sweep is suggested to be due to an additional delay added by the proximity of the peak of the f2 traveling wave the place fixed and the wave fixed models of dpoae generation are discussed and an intermediate model of dpoae generation is introduced to explain such additional delay and the existence of phase irregularities which were observed in the pff the ratio of the latencies obtained by the two sweep methods is frequency dependent and a relation to cochlear frequency selectivity is suggested finally analysis of the differences in latency of the different lower sideband dpoae components allowed an estimation of the return latency of dpoaes

temporal adaptive euler navier stokes algorithm involving unstructured dynamic meshes a temporal adaptive algorithm for the time integration of the two dimensional euler or navier stokes equations is presented the flow solver involves an upwind flux split spatial discretization for the convective terms and central differencing for the shear stress and heat flux terms on an unstructured mesh of triangles the temporal adaptive algorithm is a time accurate integration procedure that allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step

space time adaptive wavelet methods for parabolic evolution problems with respect to space time tensor product wavelet bases parabolic initial boundary value problems are equivalently formulated as bi infinite matrix problems adaptive wavelet methods are shown to yield sequences of approximate solutions which converge at the optimal rate in case the spatial domain is of product type the use of spatial tensor product wavelet bases is proved to overcome the so called curse of dimensionality i e the reduction of the convergence rate with increasing spatial dimension

a posteriori analysis of a multirate numerical method for ordinary differential equations in this paper we analyze a multirate time integration method for systems of ordinary differential equations that present significantly different scales within the components of the model the main purpose of this paper is to present a hybrid a priori a posteriori error analysis that accounts for the effects of projections between the coarse and fine scale discretizations the use of only a finite number of iterations in the iterative solution of the discrete equations the numerical error arising in the solution of each component and the effects on stability arising from the multirate solution the hybrid estimate has the form of a computable a posteriori leading order expression and a provably higher order a priori expression we support this estimate by an a priori convergence analysis we present several examples illustrating the accuracy of multirate integration schemes and the accuracy of the a posteriori estimate

approximations for viscosity solutions of hamilton jacobi equations with locally varying time and space grids a new monotone finite difference scheme is introduced that approximates viscosity solutions of first order nonlinear hamilton jacobi equations the main feature of the scheme is that it allows for locally varying time and space grids making it ideal for use with adaptive algorithms explicit a priori error estimates are given to establish convergence numerical examples including adaptive mesh refinement examples demonstrate the effectiveness of the proposed scheme

numerical experiments with the osher upwind scheme for the euler equations the osher algorithm for solving the euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations a first order accurate version of the numerical method was derived by osher circa 1980 for the one dimensional non isentropic euler equations in cartesian coordinates in this paper the extension of the scheme to arbitrary two dimensional geometries is explained results are then presented for several example problems in one and two dimensions future work will include extension of the method to second order accuracy and the development of implicit time differencing for the osher algorithm

an error estimate for finite volume methods for multidimensional conservation laws in this paper an l ll error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained these methods can be formally high order accurate and are defined on general triangulations the error is proven to be of order ft 4 where h represents the size of the mesh via an extension of kuznetsov approximation theory for which no estimate of the total variation and of the modulus of con tinuity in time are needed the result is new even for the finite volume method constructed from monotone numerical flux functions

convergence of the finite volume method for multidimensional conservation laws we establish the convergence of the finite volume method applied to multidimensional hyperbolic conservation laws and based on monotone numerical flux functions our technique applies with a fairly unrestrictive assumption on the triangulations flat elements are allowed and to lipschitz continuous flux functions we treat the initial and boundary value problem and obtain the strong convergence of the scheme to the unique entropy discontinuous solution in the sense of kruzkov the proof of convergence is based on a convergence framework coquel and lefloch math comp 57 1991 pp 169 210 and j numer anal 30 1993 pp 675 700 from a convex decomposition of the scheme we derive a new estimate for the rate of entropy dissipation and a new formulation of the discrete entropy inequalities these estimates are shown to be sufficient for the passage to the limit in the discrete equation convergence follows from diperna s uniqueness result in the class of entropy measure valued solutions

a moving mesh numerical method for hyperbolic conservation laws we show that the possibly discontinuous solution of a scalar conservation law in one space dimension may be approximated in l1 r to within o n 2 by a piecewise linear function with o fn nodes the nodes are moved according to the method of characteristics we also show that a previous method of dafermos which uses piecewise constant approxima tions is accurate to o n 1 these numerical methods for conservation laws are the first to have proven convergence rates of greater than o fn 1 2 1 introduction it is well known that the solution of the hyperbolic conservation law

sequences of orthogonal laurent polynomials bi orthogonality and quadrature formulas on the unit circle in this paper the construction of orthogonal bases in the space of laurent polynomials on the unit circle is considered as an application a connection with the so called bi orthogonal systems of trigonometric polynomials is established and quadrature formulas on the unit circle based on laurent polynomials are studied

solving the advection diffusion equation on unstructured meshes with discontinuous mixed finite elements and a local time stepping procedure explicit schemes are known to provide less numerical diffusion in solving the advection diffusion equation especially for advection dominated problems traditional explicit schemes use fixed time steps restricted by the global cfl condition in order to guarantee stability this is known to slow down the computation especially for heterogeneous domains and or unstructured meshes to avoid this problem local time stepping procedures where the time step is allowed to vary spatially in order to satisfy a local cfl condition have been developed in this paper a local time stepping approach is used with a numerical model based on discontinuous galerkin mixed finite element methods to solve the advection diffusion equation the developments are detailed for general unstructured triangular meshes numerical experiments are performed to show the efficiency of the numerical model for the simulation of i the transport of a solute on highly unstructured meshes and ii density driven flow where the velocity field changes at each time step the model gives stable results with significant reduction of the computational cost especially for the non linear problem moreover numerical diffusion is also reduced for highly advective problems copyright 2009 john wiley sons ltd

an efficient local time stepping scheme for solution of nonlinear conservation laws we develop an efficient local time stepping algorithm for the method of lines approach to numerical solution of transient partial differential equations the need for local time stepping arises when adaptive mesh refinement results in a mesh containing cells of greatly different sizes the global cfl number and hence the global time step are defined by the smallest cell size this can be inefficient as a few small cells may impose a restrictive time step on the whole mesh a local time stepping scheme allows us to use the local cfl number which reduces the total number of function evaluations the algorithm is based on a second order runge kutta time integration its important features are a small stencil and the second order accuracy in the l 2 and l norms

grid adaptive algorithms for the solution of the euler equations on irregular grids abstract the effect of grid irregularity on the accuracy of algorithms for one dimensional unsteady flow is investigated it is shown how standard second order accurate algorithms for equally spaced grids may be extended to act as first order accurate algorithms on an irregular grid the loss of accuracy on irregular grids is found to cause a significant reduction in the quality of the results to obtain solutions comparable in quality with second order accurate algorithms on equally spaced grids a class of second order accurate algorithms is derived which are conservative and compatible on randomly spaced grids they are shown to give solutions to the equations similar in quality to those obtainable on equally spaced grids

the moving grid method for nonlinear hyperbolic conservation laws numerically moving grids are often found to improve the resolution of approximate solutions to nonlinear hyperbolic conservation laws in this paper we show how to modify many standard numerical flux functions to incorporate this idea a generalized godunov type scheme is shown in the scalar case to converge to the entropy satisfying solution as the mesh size tends to zero a courant number of one half is found necessary in general and proved to be sufficient to obtain convergence convergence for methods based upon any two point conservative and monotone numerical flux function is also shown in the scalar case

a time accurate explicit multi scale technique for gas dynamics abstract we present a new time accurate algorithm for the explicit numerical integration of the compressible euler equations of gas dynamics this technique is based on the discrete event simulation des methodology for nonlinear flux conservative pdes y a omelchenko h karimabadi self adaptive time integration of flux conservative equations with sources j comput phys 216 1 2006 179 194 des enables adaptive distribution of cpu resources in accordance with local time scales of the underlying numerical solution it distinctly stands apart from multiple local time stepping algorithms in that it requires neither selecting a global synchronization time step nor pre determining a sequence of time integration operations for individual parts of a heterogeneous numerical system in this paper we extend the des methodology in three important directions i we apply des to a system of coupled gas dynamics equations discretized via a central upwind scheme a kurganov e tadmor new high resolution central schemes for nonlinear conservation laws and convection diffusion equations j comput phys 160 2000 241 282 a kurganov s noelle g petrova semidiscrete central upwind schemes for hyperbolic conservation laws and hamilton jacobi equations siam j sci comput 23 3 2001 707 740 ii we introduce a new preemptive event processing pep technique which automatically enforces synchronous execution of events with sufficiently close update times iii we significantly improve the accuracy of the previous algorithm y a omelchenko h karimabadi self adaptive time integration of flux conservative equations with sources j comput phys 216 1 2006 179 194 by applying locally second order in time flux conserving corrections to the solution obtained with the forward euler scheme the performance of the new technique is demonstrated in a series of one dimensional gas dynamics test problems by comparing numerical solutions obtained in event driven and equivalent time stepping simulations

local a posteriori error estimates for time dependent hamilton jacobi equations university of minnesota ph d dissertation may 2010 major mathematics advisor prof bernardo cockburn 1 computer file pdf viii 67 pages ill some col

measuring human cochlear traveling wave delay using distortion product emission phase responses a method is presented here in which cochlear traveling wave delays are estimated through the measurement of distortion product emission phase dpe responses this method assumes that the site of generation of dpes is at the f2 place eighteen adult female and 18 adult male human ears all with normal hearing underwent dpe testing for each ear dpe phase responses were computed for eight values of f2 varying from 10 to 0 78 khz linear dpe phase versus dpe frequency relationships were found estimates of traveling wave delay from the ear canal to the f2 place varied from about 1 ms for the 10 khz place to 3 5 ms for the 0 78 khz place these estimates agree well with previous traveling wave delay estimates using electrocochleography test retest comparisons of delay estimates were generally within 0 25 ms in addition within subject interaural delay differences were smaller than between subject interaural differences within subject interaural delay differences were generally less than 0 5 ms male ear

runge kutta based explicit local time stepping methods for wave propagation locally refined meshes severely impede the efficiency of explicit runge kutta rk methods for the simulation of time dependent wave phenomena by taking smaller time steps precisely where the smallest elements are located local time stepping lts methods overcome the bottleneck caused by the stringent stability constraint of but a few small elements in the mesh starting from classical or low storage explicit rk methods explicit lts methods of arbitrarily high accuracy are derived when combined with an essentially diagonal finite element mass matrix the resulting time marching schemes retain the high accuracy stability and efficiency of the original rk methods while circumventing the geometry induced stiffness numerical experiments with continuous and discontinuous galerkin finite element discretizations corroborate the expected rates of convergence and illustrate the usefulness of these lts rk methods

multi adaptive galerkin methods for odes i we present multi adaptive versions of the standard continuous and discontinuous galerkin methods for odes taking adaptivity one step further we allow for individual time steps order and quadrature so that in particular each individual component has its own time step sequence this paper contains a description of the methods an analysis of their basic properties and a posteriori error analysis in the accompanying paper a logg siam j sci comput submitted we present adaptive algorithms for time stepping and global error control based on the results of the current paper

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

simultaneous latency estimations for distortion product otoacoustic emissions and envelope following responses the purpose of this research was to simultaneously estimate processing delays in the cochlea and brainstem using the same acoustic stimuli apparent latencies were estimated from ear canal measurements of 2f1 f2 distortion product otoacoustic emissions dpoaes and scalp recordings of the f2 f1 envelope following response efr the stimuli were equal level tone pairs 65db spl with the upper tone f2 set at either 900 or 1800hz to fix the initiation site of the dpoae and efr the frequency of f1 was swept continuously between frequency limits chosen to keep the efr response between 150 and 170hz the average dpoae latencies were 9 6 and 6 2ms for f2 900 and 1800hz and the corresponding efr latencies were 12 4 and 8 8ms in a control condition a third suppressor tone was added near the dpoae response frequency to evaluate whether the potential source at fdp was contributing significantly to the measured emission dpoae latency is the sum of both inward and outward cochlear delays the efr apparent la

about a system of anti periodic trigonometric functions in this paper we introduce the so called second kind trigonometric system which is a useful tool for the representation of 2 p anti periodic functions using these functions we study a sequence of trigonometric polynomials which are bi orthogonal in the szego s sense we study the usual topics in the theory of fourier series and we present a new connection with the orthogonal polynomials op on the unit circle and some useful properties like recurrence relations kernel representations and a favard s type theorem

group delays of distortion product otoacoustic emissions relating delays measured with f1 and f2 sweep paradigms a theoretical analysis is presented of group delays of distortion product otoacoustic emissions dpoaes measured with the phase gradient method the aim of the analysis is to clarify the differences in group delays d1 and d2 obtained using the f1 and the f2 sweep paradigms respectively and the dependence of group delays on the order of the dpoae two models are considered the place fixed and the wave fixed models while in the former model the generation place is assumed to be invariant with both f1 and f2 sweeps in the latter model the shift of generation place is fully accounted for by making a simple local approximation of the cochlear scale invariance a mathematical conversion from phase place to phase frequency gradients is incorporated in the wave fixed model under the assumption that the dpoae as recorded at the best f2 f1 ratio is dominated by the contribution from the generation site and not by e g reflection components the analysis leads to simple expressions for the ratio and difference between d1 and d2 validation of the models against experimental data indicates that lower sideband dpoaes 2f1 f2 3f1 2f2 4f1 3f2 are most consistent with the wave fixed model upper sideband components 2f2 f1 in contrast are not properly described by either the place fixed or the wave fixed model independent whether dpoae generation is assumed to originate at the f2 or at the more basally located f dp characteristic place

an adaptive multiresolution scheme with local time stepping for evolutionary pdes we present a fully adaptive numerical scheme for evolutionary pdes in cartesian geometry based on a second order finite volume discretization a multiresolution strategy allows local grid refinement while controlling the approximation error in space for time discretization we use an explicit runge kutta scheme of second order with a scale dependent time step on the finest scale the size of the time step is imposed by the stability condition of the explicit scheme on larger scales the time step can be increased without violating the stability requirement of the explicit scheme the implementation uses a dynamic tree data structure numerical validations for test problems in one space dimension demonstrate the efficiency and accuracy of the local time stepping scheme with respect to both multiresolution scheme with global time stepping and finite volume scheme on a regular grid fully adaptive three dimensional computations for reaction diffusion equations illustrate the additional speed up of the local time stepping for a thermo diffusive flame instability

distortion product otoacoustic emission delay measurement in human ears the measurement of distortion product otoacoustic emission dpoae delay using the phase gradient method is discussed a short f2 sweep paradigm is described its merits are discussed and comparisons made with other methods using sweeps of less than 4 consistent and reliable measurements were obtained from 12 normal ears except for a few isolated measurements investigation of these apparent anomalies indicated that the short f2 sweep method was sensitive to the localized effects of narrow distortion product intensity notches and spontaneous emissions it is possible that middle ear pressure instability or some local change in the cochlea sometimes compounded the situation the intersubject range 63 of the mean of dpoae delay values was greater than the range of values observed due to measurement variability 5 6 of the mean or intrasubject variability 8 5 of the mean demonstrating that the method can detect real differences between ears however comparison with previous work shows that caution is needed in interpreting these data as all dpoae phase methods provide only partial latency values the physical interpretation depends on both the stimulus sweep used and the origin of dpoaes our data shows that f1 sweep derived latency is lower than f2 sweep data by more than 20 caution also needs to be exercised when comparing cochlear traveling wave delay as inferred from electrophysiological data with that obtained from dpoae delay measurements

space time adaptive wavelet methods for optimal control problems constrained by parabolic evolution equations an adaptive algorithm based on wavelets is proposed for the efficient numerical solution of a control problem governed by a linear parabolic evolution equation first the constraints are represented by means of a full weak space time formulation as a linear system in ell 2 in wavelet coordinates following a recent approach by schwab and stevenson second a quadratic cost functional involving a tracking type term for the state and a regularization term for the distributed control is also formulated in terms of ell 2 sequence norms of wavelet coordinates this functional serves as a representer for a functional involving different sobolev norms with possibly nonintegral smoothness parameter standard techniques from optimization are then used to derive the first order necessary conditions as a coupled system in ell 2 coordinates for this purpose an adaptive method is proposed which can be interpreted as an inexact gradient method for the control in each iteration step the primal and adjoint systems are solved up to a prescribed accuracy by the adaptive algorithm it is shown that the adaptive algorithm converges moreover the algorithm is proved to be asymptotically optimal the convergence rate achieved for computing each of the components of the solution state adjoint state and control up to a desired target tolerance is asymptotically the same as the wavelet best n term approximation of each solution component and the total computational work is proportional to the number of computational unknowns

self adaptive time integration of flux conservative equations with sources we present a novel flux conserving asynchronous method for the explicit time integration of multi scale flux conservative partial differential equations with source terms unlike the conventional explicit and implicit integration schemes it is based on a discrete event simulation paradigm which describes time advance in terms of increments to physical quantities and causality rules rather than time stepping this method exerts self adaptive control over local update rates of solution by predicting and correcting changes to simulation variables in accordance with local physical scales the discrete event simulation paradigm is independent of the underlying spatial mesh and thus can be incorporated into block structured and unstructured mesh refinement techniques the effectiveness and robustness of the new method is demonstrated on a number of one dimensional uniform mesh models based on diffusion convection reaction equations the event driven integration reduces numerical approximation errors due to large local time derivatives prevents explosive numerical instabilities in locally super courant calculations and automatically reduces the cpu overhead associated with stiff terms and inactive regions in computation space

one sided difference approximations for nonlinear conservation laws we analyze one sided or upwind finite difference approximations to hyperbolic partial differential equations and in particular nonlinear conservation laws second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions we show that no such stable approximation of order higher than two is possible these one sided schemes have desirable properties for shock calculations we show that the proper switch used to change the direction in the upwind differencing across a shock is of great importance new and simple schemes are developed for which we prove qualitative properties such as sharp monotone shock profiles existence uniqueness and stability of discrete shocks numerical examples are given

interpolation finite difference schemes on grids locally refined in time numerical methods in which the mesh is locally refined are widely used for problems with singularities in the solution in this case approaches with refining the grid in both space and time are being developed in this paper we consider a class of finite difference schemes with local refinement of the grid in time to solve the problems numerically here we compute the numerical solution on a finer time grid in a part of the domain we consider a model dirichlet problem for a second order parabolic equation on a rectangle we analyze the accuracy of completely implicit schemes with the simplest interpolated interface conditions on the boundary of the adaptation domain on the basis of the maximum principle the unconditional convergence of these schemes in the uniform norm is shown and the rate of convergence is analyzed

interrelations among distortion product phase gradient delays their connection to scaling symmetry and its breaking distortion product otoacoustic emission dpoae phase versus frequency functions and corresponding phase gradient delays have received considerable attention because of their potential for providing information about mechanisms of emission generation cochlear wave latencies and characteristics of cochlear tuning the three measurement paradigms in common use fixed f1 fixed f2 and fixed f2 f1 yield significantly different delays suggesting that they depend on qualitatively different aspects of cochlear mechanics in this paper theory and experiment are combined to demonstrate that simple phenomenological arguments which make no detailed mechanistic assumptions concerning the underlying cochlear mechanics predict relationships among the delays that are in good quantitative agreement with experimental data obtained in guinea pigs to understand deviations between the simple theory and experiment a general equation is found that relates the three delays for any deterministic model of dpoae generation both model independent and exact the general relation provides a powerful consistency check on the measurements and a useful tool for organizing and understanding the structure in dpoae phase data e g for interpreting the relative magnitudes and intensity dependencies of the three delays analysis of the general relation demonstrates that the success of the simple phenomenological approach can be understood as a consequence of the mechanisms of emission generation and the approximate local scaling symmetry of cochlear mechanics the general relation is used to quantify deviations from scaling manifest in the measured phase gradient delays the results indicate that deviations from scaling are typically small and that both linear and nonlinear mechanisms contribute significantly to these deviations intensity dependent mechanisms contributing to deviations from scaling include cochlear reflection and wave interference effects associated with the mixing of distortion and reflection source emissions as in dpoae fine structure finally the ratio of the fixed f1 and fixed f2 phase gradient delays is shown to follow from the choice of experimental paradigm and in the scaling limit contains no information about cochlear physiology whatsoever these results cast considerable doubt on the theoretical basis of recent attempts to use relative dpoae phase gradient delays to estimate the bandwidths of peripheral auditory filters

a lax wendroff type theorem for unstructured quasi uniform grids a well known theorem of lax and wendroff states that if the sequence of approximate solutions to a system of hyperbolic conservation laws generated by a conservative consistent numerical scheme converges boundedly a e as the mesh parameter goes to zero then the limit is a weak solution of the system moreover if the scheme satisfies a discrete entropy inequality as well the limit is an entropy solution the original theorem applies to uniform cartesian grids this article presents a generalization for quasi uniform grids with lipschitz boundary cells uniformly continuous inhomogeneous numerical fluxes and nonlinear inhomogeneous sources the added generality allows a discussion of novel applications like local time stepping grids with moving vertices and conservative remapping a counterexample demonstrates that the theorem is not valid for arbitrary non quasi uniform grids

numerical approximations to nonlinear conservation laws with locally varying time and space grids an explicit time differencing technique is introduced to approximate nonlinear conservation laws this differencing technique links together an arbitrary number of space regimes containing fine and coarse time increments previous stability requirements i e the cfl condition placed a global bound on the size of the time increments for scalar monotone approximations in one space dimension using this variable step time differencing convergence to the correct physical solution is proven given only a local cfl condition

on convergence of a domain decomposition method for a scalar conservation law in this paper we prove convergence of a domain decomposition method for one dimensional scalar conservation laws by dealing carefully with nonconservative terms at the interface of subdomains the method consists of an explicit scheme in some subdomains and an implicit scheme in other subdomains with a numerical flux being the same as the one used in the explicit scheme although such a multidomain algorithm is not strictly conservative the conservation error ce 0 n delta t is equal to mathcal o delta t regardless of the smoothness of the solution finally two test examples are given to validate convergence and the computational efficiency of the present method

group delays of distortion product otoacoustic emissions in the guinea pig this paper presents a comprehensive set of experimental data on group delays of distortion product otoacoustic emissions dpoaes in the guinea pig group delays of the dpoaes with frequencies 2f1 f2 3f1 2f2 4f1 3f2 and 2f2 f1 were measured with the phase gradient method both the f1 and the f2 sweep paradigm were used differences between the two sweep paradigms were investigated for the four dpoaes as well as the group delay differences between the dpoaes analysis revealed larger group delays with the f2 sweep paradigm but only for the lower sideband dpoaes with fdp f1 f2 for the lower sideband cubic distortion product 2f1 f2 the f2 sweep delays were a factor of 1 17 1 54 larger than the f1 sweep delays depending on frequency the upper sideband dpoae 2f2 f1 showed no significant difference between f1 and f2 sweep group delays except for the highest and lowest f2 frequencies comparing the group delays of the dpoaes for each sweep paradigm separately equal group delays were found for all four dpoaes measured with the f1 sweep with the f2 sweep paradigm on the other hand the group delays of the three lower sideband dpoaes occurred to be larger than the group delays of the upper sideband dpoae 2f2 f1 a tentative interpretation of the data in the context of proposed explanatory hypotheses on dpoae group delays is given

time asynchronous relative dimension in space method for multi scale problems in fluid dynamics a novel computational method is presented for solving fluid dynamics equations in the multi scale framework when the system size is an important parameter of the governing equations the method tardis is based on a concurrent transformation of the governing equations in space and time and solving the transformed equations on a uniform cartesian grid with the corresponding causality conditions at the grid interfaces for implementation in the framework of tardis the second order cabaret scheme of karabasov and goloviznin 1 is selected for it provides a good combination of numerical accuracy computational efficiency and simplicity of realisation numerical examples are first provided for several isothermal gas dynamics test problems and then for modelling of molecular fluctuations inside a microscopic flow channel and ultrasound wave propagation through a nano scale region of molecular fluctuations

an error analysis of conservative space time mesh refinement methods for the one dimensional wave equation we study two space time mesh refinement methods as the one introduced in f collino t fouquet and p joly numer math 95 2003 pp 197 221 the stability of such methods is guaranteed by construction through the conservation of a discrete energy in this paper we show the l2 convergence of these schemes and provide optimal error estimates the proof is based on energy techniques and bootstrap arguments our results are validated with numerical simulations and compared with results from plane wave analysis f collino t fouquet and p joly numer math 95 2003 pp 223 251

a parallel local timestepping runge kutta discontinuous galerkin method with applications to coastal ocean modeling abstract geophysical flows over complex domains often encompass both coarse and highly resolved regions approximating these flows using shock capturing methods with explicit timestepping gives rise to a courant friedrichs lewy cfl timestep constraint this approach can result in small global timesteps often dictated by flows in small regions vastly increasing computational effort over the whole domain one approach for coping with this problem is to use locally varying timesteps in previous work we formulated a local timestepping lts method within a runge kutta discontinuous galerkin framework and demonstrated the accuracy and efficiency of this method on serial machines for relatively small scale shallow water applications for more realistic models involving large domains and highly complex physics the lts method must be parallelized for multi core parallel computers furthermore additional physics such as strong wind forcing can effect the choice of local timesteps in this paper we describe a parallel lts method parallelized using domain decomposition and mpi we demonstrate the method on tidal flows and hurricane storm surge applications in the coastal regions of the western north atlantic ocean

application of implicit explicit high order runge kutta methods to discontinuous galerkin schemes despite the popularity of high order explicit runge kutta erk methods for integrating semi discrete systems of equations erk methods suffer from severe stability based time step restrictions for very stiff problems we implement a discontinuous galerkin finite element method dgfem along with recently introduced high order implicit explicit runge kutta imex rk schemes to overcome geometry induced stiffness in fluid flow problems the imex algorithms solve the non stiff portions of the domain using explicit methods and isolate and solve the more expensive stiff portions using an l stable stiffly accurate explicit singly diagonally implicit runge kutta method esdirk furthermore we apply adaptive time step controllers based on the embedded temporal error predictors we demonstrate in a number of numerical test problems that imex methods in conjunction with efficient preconditioning become more efficient than explicit methods for systems exhibiting high levels of grid induced stiffness

multirate runge kutta schemes for advection equations explicit time integration methods can be employed to simulate a broad spectrum of physical phenomena the wide range of scales encountered lead to the problem that the fastest cell of the simulation dictates the global time step multirate time integration methods can be employed to alter the time step locally so that slower components take longer and fewer time steps resulting in a moderate to substantial reduction of the computational cost depending on the scenario to simulate s osher r sanders numerical approximations to nonlinear conservation laws with locally varying time and space grids math comput 41 1983 321 336 h tang g warnecke a class of high resolution schemes for hyperbolic conservation laws and convection diffusion equations with varying time and pace grids siam j sci comput 26 4 2005 1415 1431 e constantinescu a sandu multirate timestepping methods for hyperbolic conservation laws siam j sci comput 33 3 2007 239 278 in air pollution modeling the advection part is usually integrated explicitly in time where the time step is constrained by a locally varying courant friedrichs lewy cfl number multirate schemes are a useful tool to decouple different physical regions so that this constraint becomes a local instead of a global restriction therefore it is of major interest to apply multirate schemes to the advection equation we introduce a generic recursive multirate runge kutta scheme that can be easily adapted to an arbitrary number of refinement levels it preserves the linear invariants of the system and is of third order accuracy when applied to certain explicit runge kutta methods as base method

an asynchronous scheme with local time stepping for multi scale transport problems application to gas discharges this paper presents an asynchronous integration scheme with local time stepping for transport problems the concept consists in associating refresh time tags to the interface fluxes between cells and to the source terms within the cells rather than to the cell themselves this scheme is less diffusive numerically than its synchronous equivalent this method is very effective in terms of computation time for problems with localized sharp minima in the cfl condition the method is then applied to dielectric barrier discharges for aerodynamic flow control

sources of dpoaes revealed by suppression experiments inverse fast fourier transforms and sfoaes in impaired ears dpoae sources are modeled by intermodulation distortion generated near the f2 place and a reflection of this distortion near the dp place in a previous paper inverse fast fourier transforms iffts of dpoae filter functions in normal ears were consistent with this model konrad martin et al j acoust soc am 109 2862 2879 2001 in the present article similar measurements were made in ears with specific hearing loss configurations it was hypothesized that hearing loss at f2 or dp frequencies would influence the relative contributions to the dpoae from the corresponding basilar membrane places and would affect the relative magnitudes of sfoaes at frequencies equal to f2 and fdp dpoaes were measured with f2 4 khz f1 varied and a suppressor near fdp l2 was 25 55 db spl l1 l2 10 db sfoaes were measured at f2 and at 2 7 khz the average fdp produced by the f1 sweep for stimulus levels of 20 60 db spl sfoae results supported predictions of the pattern of amplitude differences between sfoaes

moving mesh method with local time step refinement for blow up problems abstract in this paper the dynamical moving mesh method is merged with the local time stepping technique and the new method is applied for blow up problems it has some benefit in approximating an accurate blow up time by starting at any positive initial time t 0 0 our numerical experiment shows that without applying the local time stepping method wrong blow up time will be obtained if the equation integrates from t 0 0

optimal numerical parameterization of discontinuous galerkin method applied to wave propagation problems this paper deals with the high order discontinuous galerkin dg method for solving wave propagation problems first we develop a one dimensional dg scheme and numerically compute dissipation and dispersion errors for various polynomial orders an optimal combination of time stepping scheme together with the high order dg spatial scheme is presented it is shown that using a time stepping scheme with the same formal accuracy as the dg scheme is too expensive for the range of wave numbers that is relevant for practical applications an efficient implementation of a high order dg method in three dimensions is presented using 1d convergence results we further show how to adequately choose elementary polynomial orders in order to equi distribute a priori the discretization error we also show a straightforward manner to allow variable polynomial orders in a dg scheme we finally propose some numerical examples in the field of aero acoustics

interpretation of distortion product otoacoustic emission measurements i two stimulus tones the interpretation of common but poorly understood observed characteristics of distortion product emissions is assisted by the development of a simple model this model essentially includes only saturation of the cochlear amplifier with emissions arising naturally from the same nonlinear processes which cause the saturation the model provides useful physical explanations of emission behavior particularly considered as a function of the stimulus intensities of the two primaries i e behavior with fixed stimulus frequencies it is assumed that emission generation consists of two main components which are always present in the total emission but which most often have approximately opposite i e canceling phases one component arises in a small region centered about the peak of the emission generation function while the other arises from the region basal to this peak at low stimulus levels with normal cochlear amplifier operation the peak of the emission generation function is sharp so the emission from the peak region dominates the total emission this peak emission has typically been characterized as the active emission at high stimulus levels where saturation is important or at all levels when the gain of the cochlear amplifier is reduced the summed basal component dominates the total emission the characteristics of this basal emission are similar to and continuous with the characteristics of the truly passive emission i e the emission observed when the cochlear amplifier gain is identically zero under circumstances when the emissions from the peak and basal components are approximately equal there is seen a sharp notch characteristic of phase cancellation the simple model produces emission distributions as a function of independent variation of the two stimulus amplitudes which are in good agreement with observation it is shown that the furosemide assay provides a good estimate of cochlear amplifier gain when a correction factor of about 10 db is added however when using two stimulus tones neither absolute emission amplitudes or emission input output functions or the furosemide assay can adequately distinguish between cases of moderate versus poor cochlear amplifier dysfunction when the cochlear amplifier gains are in the range from about half normal to zero

moving mesh methods with locally varying time steps the time steps associated with moving mesh methods are proportional to the smallest mesh size in space and as a result they are very small at each time level for some practical problems the physical phenomena develop dynamically singular or nearly singular solutions in fairly localized regions and therefore the smallest time step at each time level occurs only in these localized regions in this work we will develop a local time stepping algorithm for the moving mesh methods the principal idea will be demonstrated by investigating the nonlinear hyperbolic conservation laws numerical experiments are carried out to demonstrate the efficiency and robustness of the proposed methods

multiadaptive galerkin methods for odes iii a priori error estimates the multiadaptive continuous discontinuous galerkin methods mcgq and mdgq for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with time steps which may vary for different components of the computed solution in this paper we prove general order a priori error estimates for the mcgq and mdgq methods to prove the error estimates we represent the error in terms of a discrete dual solution and the residual of an interpolant of the exact solution the estimates then follow from interpolation estimates together with stability estimates for the discrete dual solution

distortion product otoacoustic emission test performance when both 2 f1 f2 and 2 f2 f1 are used to predict auditory status the objective of this study was to determine whether distortion product otoacoustic emission dpoae test performance defined as its ability to distinguish normal hearing ears from those with hearing loss can be improved by examining response and noise amplitudes at 2 f1 f2 and 2 f2 f1 simultaneously in addition there was interest in knowing whether measurements at both dps and for several primary frequency pairs can be used in a multivariate analysis to further optimize test performance dpoae and noise amplitudes were measured at 2 f1 f2 and 2 f2 f1 for 12 primary levels l2 from 10 to 65 db spl in 5 db steps and 9 pairs of primary frequencies 0 5 to 8 khz in 1 2 octave steps all data were collected in a sound treated room from 70 subjects with normal hearing and 80 subjects with hearing loss subjects had normal middle ear function at the time of the dpoae test based on standard tympanometric measurements measurement based stopping rules were used such that the test terminated when the noise