stability analysis of particle methods with corrected derivatives abstract the stability of discretizations by particle methods with corrected derivatives is analyzed it is shown that the standard particle method which is equivalent to the element free galerkin method with an eulerian kernel and nodal quadrature has two sources of instability 1 rank deficiency of the discrete equations and 2 distortion of the material instability the latter leads to the so called tensile instability it is shown that a lagrangian kernel with the addition of stress points eliminates both instabilities examples that verify the stability of the new formulation are given

generalized multiple scale reproducing kernel particle methods abstract an approach to unify reproducing kernel methods under one large umbrella and an extension to include time and spatial shifting are proposed the study is divided into three major topics the groundwork is set by revisiting the fourier analysis of discrete systems the multiresolution concept and its significance in devising the reproducing kernel methods and its discrete counterpart reproducing kernel particle methods are explained an edge detection technique based on multiresolution analysis is developed this wavelet approach together with particle methods gives rise to a straightforward h adaptivity algorithm by using this framework a hermite reproducing kernel method is also proposed and its relation to wavelet methods is presented it is also shown that the new approach generalizes existing kernel methods and it can easily be degenerated into other widely used methods such as partition of unity moving least square interpolants smooth particle hydrodynamics scaling functions and wavelets and multiple scale analysis furthermore the hermite reproducing kernel particle method a particle based discrete version of the hermite reproducing kernel method is developed finally multiple scale methods based on frequency and wave number shifting techniques are presented a stability analysis is also presented for newmark time integration schemes for the low frequency equation numerical examples are presented throughout the paper to illustrate the flexibility and accuracy of this class of multiple scale methods

the dependency of timbre on fundamental frequency the dependency of the timbre of musical sounds on their fundamental frequency f0 was examined in three experiments in experiment i subjects compared the timbres of stimuli produced by a set of 12 musical instruments with equal f0 duration and loudness there were three sessions each at a different f0 in experiment ii the same stimuli were rearranged in pairs each with the same difference in f0 and subjects had to ignore the constant difference in pitch in experiment iii instruments were paired both with and without an f0 difference within the same session and subjects had to ignore the variable differences in pitch experiment i yielded dissimilarity matrices that were similar at different f0 s suggesting that instruments kept their relative positions within timbre space experiment ii found that subjects were able to ignore the salient pitch difference while rating timbre dissimilarity dissimilarity matrices were symmetrical suggesting further that the absolute displacement of the set of i

separate mechanisms govern the selection of spectral components for perceptual fusion and for the computation of global pitch the perceptual fusion of harmonics is often assumed to result from the operation of a template mechanism that is also responsible for computing global pitch this dual role hypothesis was tested using frequency shifted complexes these sounds are inharmonic but preserve a regular pattern of equal component spacing the stimuli had a nominal fundamental f0 frequency of 200 hz 20 and were frequency shifted either by 25 0 or 37 5 of f0 three consecutive components 6 8 were removed and replaced with a sinusoidal probe located at one of a set of positions spanning the gap on any trial subjects heard a complex tone followed by an adjustable pure tone in a continuous loop subjects were well able to match the pitch of the probe unless it corresponded with a position predicted by the spectral pattern of the complex peripheral factors could not account for this finding in contrast hit rates were not depressed for probes positioned at integer multiples of the f0 s corresponding to the global pit

symmetric interactions and interference between pitch and timbre variations in the spectral shape of harmonic tone complexes are perceived as timbre changes and can lead to poorer fundamental frequency f0 or pitch discrimination less is known about the effects of f0 variations on spectral shape discrimination the aims of the study were to determine whether the interactions between pitch and timbre are symmetric and to test whether musical training affects listeners ability to ignore variations in irrelevant perceptual dimensions difference limens dls for f0 were measured with and without random concurrent variations in spectral centroid and vice versa additionally sensitivity was measured as the target parameter and the interfering parameter varied by the same amount in terms of individual dls results showed significant and similar interference between pitch f0 and timbre spectral centroid dimensions with upward spectral motion often confused for upward f0 motion and vice versa musicians had better f0dls than non musicians on average but similar spectral centroid dls both groups showed similar interference effects in terms of decreased sensitivity in both dimensions results reveal symmetry in the interference effects between pitch and timbre once differences in sensitivity between dimensions and subjects are controlled musical training does not reliably help to overcome these effects

meshfree and finite element nodal integration methods nodal integration can be applied to the galerkin weak form to yield a particle type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions this particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods to a lesser degree nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods in this work aspects regarding stability consistency efficiency and explicit time integration are explored within the context of nodal integration both small and large deformation numerical examples are provided copyright 2007 john wiley sons ltd

a unitary model of pitch perception a model of the mechanism of residue pitch perception is revisited it is evaluated in the context of some new empirical results and it is proposed that the model is able to reconcile a number of differing approaches in the history of theories of pitch perception the model consists of four sequential processing stages peripheral frequency selectivity within channel half wave rectification and low pass filtering within channel periodicity extraction and cross channel aggregation of the output the pitch percept is represented by the aggregated periodicity function using autocorrelation as the periodicity extraction method and the summary autocorrelation function sacf as the method for representing pitch information it is shown that the model can simulate new experimental results that show how the quality of the pitch percept is influenced by the resolvability of the harmonic components of the stimulus complex these include i the pitch of harmonic stimuli whose components alternate in phase ii the increased frequency difference limen of tones consisting of higher harmonics and iii the influence of a mistuned harmonic on the pitch of the complex as a function of its harmonic number to accommodate these paradigms it was necessary to compare stimuli along the length of the sacf rather than relying upon the highest peak alone these new results demonstrate that the model responds differently to complexes consisting of low and high harmonics as a consequence it is not necessary to postulate two separate mechanisms to explain different pitch percepts associated with resolved and unresolved harmonics

extended finite element method coupled with face based strain smoothing technique for three dimensional fracture problems summary in this work the extended finite element method xfem is for the first time coupled with face based strain smoothing technique to solve three dimensional fracture problems this proposed method which is called face based smoothed xfem here is expected to combine both the advantages of xfem and strain smoothing technique in xfem arbitrary crack geometry can be modeled and crack advance can be simulated without remeshing strain smoothing technique can eliminate the integration of singular term over the volume around the crack front thanks to the transformation of volume integration into area integration special smoothing scheme is implemented in the crack front smoothing domain three examples are presented to test the accuracy efficiency and convergence rate of the face based smoothed xfem from the results it is clear that smoothing technique can improve the performance of xfem for three dimensional fracture problems copyright 2015 john wiley sons ltd

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

cracking node method for dynamic fracture with finite elements a new method for modeling discrete cracks based on the extended finite element method is described in the method the growth of the actual crack is tracked and approximated with contiguous discrete crack segments that lie on finite element nodes and span only two adjacent elements the method can deal with complicated fracture patterns because it needs no explicit representation of the topology of the actual crack path a set of effective rules for injection of crack segments is presented so that fracture behavior beginning from arbitrary crack nucleations to macroscopic crack propagation is seamlessly modeled the effectiveness of the method is demonstrated with several dynamic fracture problems that involve complicated crack patterns such as fragmentation and crack branching copyright 2008 john wiley sons ltd

embedded crack vs smeared crack models a comparison of elementwise discontinuous crack path approaches with emphasis on mesh bias this paper is concerned with an analysis of the mesh dependence of results from numerical failure analyses using the strong discontinuity approach sda based on an analytical and numerical comparison with a standard plasticity model pertaining to the classical fracture energy based smeared crack concept using a consistent characteristic length the sda is characterized by incorporating the kinematics of fractured solids locally within the finite element the resulting jumps in the displacement field are captured by their corresponding singularly distributed strains for the analytical and numerical study of the mesh dependence only mode i failure is considered analogies and differences of both finite element formulations are investigated and evaluated

spectral pattern harmonic relations and the perceptual grouping of low numbered components mistuning a harmonic increases its salience and produces an exaggerated change in its pitch the effects on component grouping of spectral pattern global pitch and local harmonicity were explored using these phenomena stimuli were either harmonic f0 200 hz or frequency shifted by 25 of f0 component 1 or 2 was replaced by one of a set of sinusoidal probes in the same spectral region listeners either matched the probe pitch by adjusting the frequency of a pure tone experiments 1 and 3 or matched the probe loudness by adjusting the level of a tone of identical frequency experiment 2 probe positions corresponding to greatest perceptual fusion were estimated from the variations in pitch shift and loudness across frequency both measures gave similar estimates for harmonic stimuli fusion was greatest at harmonic values for shifted stimuli fusion was greatest close to the suboctave 225 hz and the frequency 450 hz of component 2 the latter value moved downwards to near 433 hz 2 3 ratio with component 3 when component 1 was removed together these results indicate that the lowest component of a shifted complex is grouped by local harmonicity whereas the higher components are grouped by common spectral spacing global pitch did not influence component grouping

iterated rippled noise discrimination at long durations iterated rippled noise irn was used to study discrimination of irn stimuli with a lower number of iterations from irn stimuli with a higher number of iterations as a function of stimulus duration 100 2000 ms such irn stimuli differ in the strength of the repetition pitch in some cases the gain used to generate irn stimuli was adjusted so that both irn stimuli in the discrimination task had the same height of the first peak in the autocorrelation function or autocorrelogram in previous work involving short duration irn stimuli 500 ms listeners were not able to discriminate between irn stimuli that had different numbers of iterations but the same height of the first peak in the autocorrelation function in the current study irn discrimination performance improved with increases in duration even in cases when the height of the first peak in the autocorrelation was the same for the two irn stimuli thus future studies involving discrimination of irn stimuli may need to use longer durations 1 s or greater than those that have been used in the past

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

h adaptive finite element methods for dynamic problems with emphasis on localization various types of error criteria are examined and it is shown that for problems involving plastic response or localization an error criterion based on an l 2 projection of strains is the most effective for the constant strain elements considered here examples of one dimensional and two dimensional localization shear band formation problems are given

does fundamental frequency discrimination measure virtual pitch discrimination studies of pitch perception often involve measuring difference limens for complex tones dlcs that differ in fundamental frequency f0 these measures are thought to reflect f0 discrimination and to provide an indirect measure of subjective pitch strength however in many situations discrimination may be based on cues other than the pitch or the f0 such as differences in the frequencies of individual components or timbre brightness here dlcs were measured for harmonic and inharmonic tones under various conditions including a randomized or fixed lowest harmonic number with and without feedback the inharmonic tones were produced by shifting the frequencies of all harmonics upwards by 6 25 12 5 or 25 of f0 it was hypothesized that if dlcs reflect residue pitch discrimination these frequency shifted tones which produced a weaker and more ambiguous pitch than would yield larger dlcs than the harmonic tones however if dlcs reflect comparisons of component pitches or timbre they should no

moving least square reproducing kernel method part ii fourier analysis in part i of this work the moving least square reproducing kernel mlsrk method is formulated and implemented based on its generic construction an m consistency structure is discovered and the convergence theorems are established in this part of the work a systematic fourier analysis is employed to evaluate and further establish the method the preliminary fourier analysis reveals that the mlsrk method is stable for sufficiently dense non degenerated particle distribution in the sense that the kernel function family satisfies the riesz bound one of the novelties of the current approach is to treat the mlsrk method as a variant of the standard finite element method and depart from there to make a connection with the multiresolution approximation in the spirits of multiresolution analysis we propose the following mlsrk transformation fm k hu i 1npu k ik h x xi x w1 the highlight of this paper is to embrace the mlsrk formulation with the notion of the controlled fp approximation based on its characterization the strang fix condition for example a systematic procedure is proposed to design new window functions so they can enhance the computational performance of the mlsrk algorithm the main effort here is to obtain a constant correction function in the interior region of a general domain i e c h 1 this can create a leap in the approximation order of the mlsrk algorithm significantly if a highly smooth window function is embedded within the kernel one consequence of this development is the synchronized convergence phenomenon a unique convergence mechanism for the mlsrk method i e by properly tuning the dilation parameter the convergence rate of higher order error norms will approach the same order convergence rate of the l2 error norm they are synchronized

auditory intensity perception successive versus simultaneous across channel discriminations this study measures the ability of observers to compare the intensities of two stimuli occupying different frequency regions it includes three experiments each experiment having two conditions in one condition the two stimuli to be compared were presented simultaneously within each interval this condition has been called profile analysis in the other condition the two stimuli were presented successively within each interval because the overall level of the stimuli was randomized between intervals the observers were encouraged to compare the intensities of the two stimuli within each observation interval rather than between intervals the stimuli were two simple tones in experiment 1 and two tonal complexes in both experiments 2 and 3 the stimuli used in experiments 2 and 3 differed in frequency the results show that simultaneous comparisons are superior to successive comparisons for simple tones the difference in threshold is about 8 db for complexes with 10 to 11 components the difference

a central spectrum model a synthesis of auditory nerve timing and place cues in monaural communication of frequency spectrum a probabilistic psychophysical model for monaural communication from the auditory nerve to the brain is given in the form of a tonotopic display of stimulus spectrum termed central spectrum the model builds upon prior research demonstrating the potential of neural timing cues from the auditory nerve for conveying information on complex spectra and was designed to meet the quantified demands of the psychophysics of frequency measurement the central spectrum magnitude at each frequency is determined by the response of the auditory nerve fiber with characteristic frequency matching that frequency an interval histogram from each fiber is passed through a filter matched to the characteristic frequency of the fiber this output versus characteristic frequency defines the central spectrum detailed analysis demonstrates that efficient probabilistic processing of the central spectrum describes known psychophysical properties of frequency measurement in discrimination and periodicity pitch experiments psycho

a local homology theory for linearly compact modules abstract we introduce a local homology theory for linearly compact modules which is in some sense dual to the local cohomology theory of a grothendieck a grothendieck local cohomology lecture notes in math vol 20 springer verlag berlin tokyo new york 1967 10 some basic properties such as the noetherianness the vanishing and non vanishing of local homology modules of linearly compact modules are proved a duality theory between local homology and local cohomology modules of linearly compact modules is developed by using matlis duality and macdonald duality as consequences of the duality theorem we obtain some generalizations of well known results in the theory of local cohomology for semi discrete linearly compact modules

the relative strength of the tone and noise components in iterated rippled noise rippled noise is constructed by delaying a random noise and adding it back to the original iterated rippled noise irn is constructed by repeating the delay and add process irn produces a two component perception i e a buzzy tone with a pitch equal to the reciprocal of the delay and a background noise that sounds like the original random noise the perceived tone noise ratio increases with the number of iterations the effective tone noise ratio in irn sounds with 1 16 iterations was measured in a discrimination matching experiment each irn was paired with a range of standard sounds having varying proportions of a broadband noise and a complex tone to find the point where their perceived tone noise ratios are the same the experiment shows that the tone noise ratio of the matching standard increases 3 8 db per doubling of the number of iterations in the irn stimulus spectral models of auditory perception explain the pitch of irn in terms of peaks in the region of the first five to eight harmonic

an autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination fundamental frequency f0 difference limens dls were measured as a function of f0 for sine and random phase harmonic complexes bandpass filtered with 3 db cutoff frequencies of 2 5 and 3 5 khz low region or 5 and 7 khz high region and presented at an average 15 db sensation level approximately 48 db spl per component in a wideband background noise fundamental frequencies ranged from 50 to 300 hz and 100 to 600 hz in the low and high spectral regions respectively in each spectral region f0 dls improved dramatically with increasing f0 as approximately the tenth harmonic appeared in the passband generally f0 dls for complexes with similar harmonic numbers were similar in the two spectral regions the dependence of f0 discrimination on harmonic number presents a significant challenge to autocorrelation ac models of pitch in which predictions generally depend more on spectral region than harmonic number a modification involving a lag window is proposed and tested restricting the ac repr

pitch matching in bimodal cochlear implant patients effects of frequency spectral envelope and level this study systematically investigated the effects of frequency level and spectral envelope on pitch matching in twelve bimodal cochlear implant ci users the participants were asked to vary the frequency and level of a pure or complex tone adjustable sounds presented in the non implanted ear to match the pitch and loudness of different reference stimuli presented to the implanted ear three reference sounds were used single electrode pulse trains pure tones and piano notes the data showed a significant effect of the frequency and complexity of the reference sounds no significant effect of the level of the reference sounds was found the magnitude of effect of frequency was compressed in the implanted ear on average a difference of seven semitones in the non implanted ear induced the same pitch change as a difference of 19 to 24 semitones for a stimulus presented to the implanted ear the spectral envelope of the adjustable sound presented to the non implanted ear also had a significant effect the matched frequencies were higher by an average of six semitones for the pure tone compared to a complex tone overall the ci listeners might have matched the stimuli based on timbre characteristics such as brightness

the extended finite element method with new crack tip enrichment functions for an interface crack between two dissimilar piezoelectric materials summary this paper studies the static fracture problems of an interface crack in linear piezoelectric bimaterial by means of the extended finite element method x fem with new crack tip enrichment functions in the x fem crack modeling is facilitated by adding a discontinuous function and crack tip asymptotic functions to the classical finite element approximation within the framework of the partition of unity in this work the coupled effects of an elastic field and an electric field in piezoelectricity are considered corresponding to the two classes of singularities of the aforementioned interface crack problem namely class and class two classes of crack tip enrichment functions are newly derived and the former that exhibits oscillating feature at the crack tip is numerically investigated computation of the fracture parameter i e the j integral using the domain form of the contour integral is presented excellent accuracy of the proposed formulation is demonstrated on benchmark interface crack problems through comparisons with analytical solutions and numerical results obtained by the classical fem moreover it is shown that the geometrical enrichment combining the mesh with local refinement is substantially better in terms of accuracy and efficiency copyright 2015 john wiley sons ltd

adaptivity for structured meshfree particle methods in 2d and 3d the implementation of h adaptivity for meshfree particle methods within a structured framework is described in this framework the initial particle arrangement is structured along with a background mesh and outside boundaries and interior interfaces are described by implicit functions the advantage of meshfree approximations in this framework lies in the ease of implementing h adaptivity and the simplicity of the data structures particles can easily be added and removed without complications in the data structure although there are some issues in the quadrature an a posteriori error estimation is used for the adaptive refinement an adaptive refinement strategy is applied to several linear elastic problems with high stress and strain gradients and singularities several non linear examples are also given copyright 2005 john wiley sons ltd

the effect of fundamental frequency on the brightness dimension of timbre the dependency of the brightness dimension of timbre on fundamental frequency fo was examined experimentally subjects compared the timbres of 24 synthetic stimuli produced by the combination of six values of spectral centroid to obtain different values of expected brightness and four fo s ranging over 18 semitones subjects were instructed to ignore pitch differences dissimilarity scores were analyzed by both anova and multidimensional scaling mds results show that timbres can be compared between stimuli with different fo s over the range tested and that differences in fo affect timbre dissimilarity in two ways first dissimilarity scores reveal a term proportional to fo difference that shows up in the mds solution as a dimension correlated with fo and orthogonal to other timbre dimensions second fo affects systematically the timbre dimension brightness correlated with spectral centroid interestingly both terms covaried with differences in fo rather than chroma or consonance the first term probably corresponds to pitch the second can be eliminated if the formula for spectral centroid is modified by introducing a corrective factor dependent on fo

a unified stability analysis of meshless particle methods a uni ed stability analysis of meshless methods with eulerian and lagrangian kernels is presented three types of instabilities were identi ed in one dimension an instability due to rank de ciency a tensile instability and a material instability which is also found in continua the stability of particle methods with eulerian and lagrangian kernels is markedly di erent lagrangian kernels do not exhibit the tensile instability in both kernels the instability due to rank de ciency can be suppressed by stress points in two dimensions the stabilizing e ect of stress points is dependent on their locations it was found that the best approach to stable particle discretizations is to use lagrangian kernels with stress points the stability of the least squares stabilization was also studied copyright 2000 john wiley sons ltd

restricted homological dimensions and cohen macaulayness abstract the classical homological dimensions the projective flat and injective ones are usually defined in terms of resolutions and then proved to be computable in terms of vanishing of appropriate derived functors in this paper we define restricted homological dimensions in terms of vanishing of the same derived functors but over classes of test modules that are restricted to assure automatic finiteness over commutative noetherian rings of finite krull dimension when the ring is local we use a mixture of methods from classical commutative algebra and the theory of homological dimensions to show that vanishing of these functors reveals that the underlying ring is a cohen macaulay ring or at least close to being one

consistent pseudo derivatives in meshless methods a meshless petrov galerkin formulation is developed in which derivatives of the trial functions are obtained as a linear combination of derivatives of shepard functions a key contribution is the development of conditions on test functions and trial functions for nonintegrable pseudo derivatives for petrov galerkin method which pass the patch test numerical results show that the resulting method is substantially more accurate than the galerkin method with shepard approximants and exceeds the rate of convergence of linear finite elements

dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment summary a methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial dierential equation loses hyperbolicity the approach is limited to rate independent materials so that the transition occurs on a set of measure zero the discrete discontinuity is treated by the extendednite element method xfem whereby arbitrary discontinuities can be incorporated in the model without remeshing loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model a new method was developed for the case when the discontinuity ends within an element it facilitates the modelling of crack tips that occur within an element in a dynamic setting the method is applied to several dynamic crack growth problems including the branching of cracks copyright 2003 john wiley sons ltd

on generation of lumped mass matrices in partition of unity based methods summary the partition of unity based methods such as the extended finite element method and the numerical manifold method are able to construct global functions that accurately reflect local behaviors through introducing locally defined basis functions beyond polynomials in the dynamic analysis of cracked bodies using an explicit time integration algorithm as a result huge difficulties arise in deriving lumped mass matrices because of the presence of those physically meaningless degrees of freedom associated with those locally defined functions observing no spatial derivatives of trial or test functions exist in the virtual work of inertia force we approximate the virtual work of inertia force in a coarser manner than the virtual work of stresses where we inversely utilize the from local to global skill the proposed lumped mass matrix is strictly diagonal and can yield the results in agreement with the consistent mass matrix but has more excellent dynamic property than the latter meanwhile the critical time step of the numerical manifold method equipped with an explicit time integration scheme and the proposed mass lumping scheme does not decrease even if the crack in study approaches the mesh nodes a very excellent dynamic property copyright 2017 john wiley sons ltd

comparing f0 discrimination in sequential and simultaneous conditions in an influential study carlyon and shackleton j acoust soc am 95 3541 3554 1994 measured listeners performance d in fundamental frequency f0 discrimination between harmonic complex tones hcts presented simultaneously in different spectral regions and compared their performance with that found in a sequential comparison task in this letter it is suggested that carlyon and shackleton s analysis of the simultaneous comparison data did not adequately reflect their assumption that listeners were effectively comparing f0 s across regions a reanalysis consistent with this assumption is described the new results suggest that under the assumption that listeners were effectively comparing f0 across regions their performance in this task was substantially higher than originally estimated by carlyon and shackleton and in some conditions much higher than expected from the performances measured in a traditional f0 discrimination task with sequential hcts possible explanations for this outcome

element free galerkin methods for static and dynamic fracture abstract element free galerkin efg methods are presented and applied to static and dynamic fracture problems efg methods which are based on moving least square mls interpolants require only nodal data no element connectivity is needed the description of the geometry and numerical model of the problem consists only of a set of nodes and a description of exterior boundaries and interior boundaries from any cracks this makes the method particularly attractive for growing crack problems since only minimal remeshing is needed to follow crack growth in moving least square interpolants the dependent variable at any point is obtained by minimizing a function in terms of the nodal values of the dependent variable in the domain of influence of the point numerical examples involving fatigue crack growth and dynamic crack propagation are presented to illustrate the performance and potential of this method

an enriched finite element method and level sets for axisymmetric two phase flow with surface tension a finite element method for axisymmetric two phase flow problems is presented the method uses an enriched finite element formulation in which the interface can move arbitrarily through the mesh without remeshing the enrichment is implemented by the extended finite element method x fem which models the discontinuity in the velocity gradient at the interface by a local partition of unity it provides an accurate representation of the velocity field at interfaces on an eulerian grid that is not conformal to the weak discontinuity the interface is represented by a level set which is also used in the construction of the element enrichment surface tension effects are considered and the interface curvature is computed from the level set field the method is demonstrated by several examples copyright 2003 john wiley sons ltd

dynamic fracture using element free galerkin methods the element free galerkin method for dynamic crack propagation is described and applied to several problems this method is a gridless method which facilitates the modelling of growing crack problems because it does not require remeshing the growth of the crack is modelled by extending its surfaces the essential feature of the method is the use of moving least squares interpolants for the trial and test functions in these interpolants the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point the discrete equations are obtained by a galerkin method the procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described

pitch strength of iterated rippled noise when the pitch is ambiguous two versions of a cascade of delay gain following delay and add circuits were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit the repetition pitch of irn is different when the delayed noise is subtracted gain 0 to the undelayed noise in the case of subtraction irn pitch is often ambiguous having two or more pitches listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli generated with different gains different network circuits and different number of iterations for most conditions the gain was less than one the data were described by a description based on an exponential function of the largest peak of the autocorrelation function of irn stimuli w a yost j acoust soc am 100 511 518 1996 processed such that the spectral dominance region is emphasized these results suggest that the strength of the pitch of irn stimuli can be described by temporal processing mechanisms as might be revealed by autocorrelation

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

the generalized finite element method this paper describes a pilot design and implementation of the generalized finite element method gfem as a direct extension of the standard finite element method sfem or fem which makes possible the accurate solution of engineering problems in complex domains which may be practically impossible to solve using the fem the development of the gfem is illustrated for the laplacian in two space dimensions in domains which may include several hundreds of voids and or cracks for which the construction of meshes used by the fem is practically impossible the two main capabilities are 1 it can construct the approximation using meshes which may overlap part or all of the domain boundary 2 it can incorporate into the approximation handbook functions which are known analytically or are generated numerically and approximate well the solution of the boundary value problem in the neighborhood of corner points voids cracks etc the main tool is a special integration algorithm which we call the fast remeshing approach which is robust and works for any domain with arbitrary complexity the incorporation of the handbook functions into the gfem is done by employing the partition of unity method pum the presented formulations and implementations can be easily extended to the multi material medium where the voids are replaced by inclusions of various shapes and sizes and to the case of the elasticity problem this work can also be understood as a pilot study for the feasibility and demonstration of the capabilities of the gfem which is needed before analogous implementations are attempted in the three dmensional and nonlinear cases which are the cases of main interest for future work

perception of the pitch of unresolved harmonics by 3 and 7 month old human infants three month olds discriminate resolved harmonic complexes on the basis of missing fundamental mf pitch in view of reported difficulty in discriminating unresolved complexes at 7 months and striking changes in the organization of the auditory system during early infancy infants ability to discriminate unresolved complexes is of some interest this study investigated the ability of 3 month olds 7 month olds and adults to discriminate the pitch of unresolved harmonic complexes using an observer based method stimuli were mf complexes bandpass filtered with a 12 db octave slope combined in random phase presented at 70 db sound pressure level spl for 650 ms with a 50 ms rise fall with a pink noise at 65 db spl the conditions were 1 low unresolved harmonics 2500 4500 hz based on mfs of 160 and 200 hz and 2 high unresolved harmonics 4000 6000 hz based on mfs of 190 and 200 hz to demonstrate mf discrimination participants had to ignore spectral changes in complexes with the same fundamental and respond only when the fundamental changed nearly all infants tested categorized complexes by mf pitch suggesting discrimination of pitch extracted from unresolved harmonics by 3 months adults also categorized the complexes by mf pitch although musically trained adults were more successful than musically untrained adults

a sliding two alternative forced choice paradigm for pitch discrimination studies that measure frequency discrimination often use 2 3 or 4 tones per trial this paper shows an investigation of a two alternative forced choice 2afc task in which each tone of a series is judged relative to the previous tone sliding 2afc potential advantages are a greater yield number of responses per unit time and a more uniform history of stimulation for the study of context effects or to relate time varying performance to cortical activity the new task was evaluated relative to a classic 2 tone per trial 2afc task with similar stimulus parameters for each task conditions with different stimulus parameters were compared the main results were as follows 1 thresholds did not differ significantly between tasks when similar parameters were used 2 thresholds did differ between conditions for the new task showing a deleterious effect of inserting relatively large steps in the frequency sequence 3 thresholds also differed between conditions for the classic task showing an adv

pitch discrimination of harmonic complex signals residue pitch or multiple component discriminations two models for pitch discrimination of harmonic complex sounds are discussed a multiple band probability summation model using comparisons among component frequencies and a model in which residue pitches are compared the second model is based on goldstein s optimum processor pitch theory j acoust soc am 54 1496 1516 1973 and is distinguished from the multiple band model by an internal noise process pitch difference limens from 2i2afc tasks show that when the test signals comprise corresponding harmonics relative pitch difference limens are less than the smaller relative difference limens for the component frequencies which is consistent with the multiple band model the absence of corresponding harmonics significantly reduces relative pitch discriminability this effect supports the model on goldstein s theory it appears that residue pitch comparisons are not used for pitch discrimination between sounds with corresponding components rather comparisons based on residue pitch are only employed where there are no common resolved components in the signals to be discriminated

complete modules and torsion modules suppose that r is a ring and that a is a chain complex over r inside the derived category of differential graded a modules there are naturally defined subcategories of a torsion objects and of a complete objects under a finiteness condition on a we develop a morita theory for these subcat egories find conceptual interpretations for some associated algebraic functors and in appropriate commutative situations identify the associated functors as local homology or local cohomology some of the results are suprising even in the case r z and a z p 1 introduction let r be a ring and r mod the derived category of chain complexes of left modules see section 1 2 we choose a fixed complex a which is perfect in other words isomorphic in mod to a complex of finite length in which the entries are finitely generated projective modules we de clare another complex n to be a trivial if hom a a0 0 where hom denotes the chain complex of morphisms in r mod going further we say that x is a torsion if hom x at 0 for all a trivial n9 and that x is a complete if homr n9x 0 for all a trivial n we then study the category ators of a torsion complexes and the category acomp of a complete complexes both of these are triangulated full subcategories of r mod it turns out that these categories are equivalent to one another and also equivalent to the derived category of dif ferential graded modules over the endomorphism complex of a we construct approximation functors celu r mod at0rs and a r mod acomp for an object m of r mod9 the complex celu m is a kind of a cellular approxi mation to m in the sense that it is the best approximation to m which can be cobbled together from a and its suspensions the complex ma is the bousfield localization of m with respect to a homology theory on r mod derived from a we provide algebraic formulas for the functors and find that the functors are related in interesting ways one of which involves an arithmetic square we also show that if cciia r has certain finite dimensionality properties then an object m of r mod is a torsion or a complete if and only if the homology groups 77 m individually satisfy appropriate torsion or completeness conditions suppose now that r is a commutative ring that 7 c r is a finitely generated ideal that a r i9 and that k is the associated koszul complex the complex a

finite element analysis on implicitly defined domains an accurate representation based on arbitrary parametric surfaces in this paper we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis the novel contributions of this paper are threefold 1 describe and validate a method to represent arbitrary parametric surfaces implicitly 2 represent arbitrary solids implicitly including sharp features using level sets and boolean operations 3 impose arbitrary dirichlet and neumann boundary conditions on the resulting implicitly defined boundaries the methods proposed do not require local refinement of the finite element mesh in regions of high curvature ensure the independence of the domain s volume on the mesh do not rely on boundary regularization and are well suited to methods based on fixed grids such as the extended finite element method xfem numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries this approach is one step in the desired direction of tying numerical simulations to computer aided design cad similarly to the isogeometric analysis paradigm

perceptual fusion and fragmentation of complex tones made inharmonic by applying different degrees of frequency shift and spectral stretch global pitch depends on harmonic relations between components but the perceptual coherence of a complex tone cannot be explained in the same way instead it has been proposed that the auditory system responds to a common pattern of equal spacing between components but is only sensitive to deviations from this pattern over a limited range roberts and brunstrom j acoust soc am 104 2326 2338 1998 this hypothesis predicts that spectral fusion will be largely unaffected either by frequency shifting a harmonic stimulus because equal spacing is preserved or by small degrees of spectral stretch because significant deviations from equal spacing only cumulate over large spectral distances complex tones were either shifted by 0 50 of f0 200 hz 10 or stretched by 0 12 of f0 100 hz 10 subjects heard a complex followed by a pure tone in a continuous loop one of the components 2 11 was mistuned by 4 and subjects adjusted the pure tone to match its pitch broadly consistent with our hypothesis frequency shifts had relatively little effect on hit rates and only large degrees of stretch reduced them substantially the implications for simultaneous grouping are explored with reference to an autocorrelation model of auditory processing

effects of spectral pattern on the perceptual salience of partials in harmonic and frequency shifted complex tones a performance measure a single even harmonic added to an odd harmonic complex is often judged to be more salient than its odd neighbors in a clarity rating task roberts and bregman j acoust soc am 90 3050 3060 1991 this study used similar complexes in a two interval forced choice procedure each interval consisted of a complex tone followed by a pure tone whose frequency matched that of a harmonic in one interval but was changed by 0 5 x fundamental frequency in the other subjects were asked to identify the matching interval since the pure tone followed the complex tone it could not cue listening to a particular frequency region the possibility of cross interval cuing was reduced by changing the fundamental frequency between intervals 100 150 hz range the procedure was designed to maximize the effects on performance of differences in immediate perceptual salience between the partials the added even harmonic was typically judged with greater accuracy than its odd neighbors experiment 1 though this effect was greatly reduced for harmonics above 8 experiment 2 the even odd difference persisted when the original stimuli were made inharmonic by applying a frequency shift of 15 but was abolished for stimuli consisting of successive partials experiment 3

temporal dynamics of pitch strength in regular interval noises the pitch strength of rippled noise and iterated rippled noise has recently been fitted by an exponential function of the height of the first peak in the normalized autocorrelation function j acoust soc am 100 3329 3335 1996 the current study compares the pitch strengths and autocorrelation functions of rippled noise rn and another regular interval noise aabb rn is generated by delaying a copy of a noise sample and adding it to the undelayed version aabb with the same pitch is generated by taking a sample of noise a with the same duration as the rn delay and repeating it to produce aa and then concatenating many of these once repeated sequences to produce aabbccdd the height of the first peak h1 in the normalized autocorrelation function of aabb is 0 5 identical to that of rn the current experiments show the following 1 aabb and rn can be discriminated when the pitch is less than about 250 hz 2 for these low pitches the pitch strength of aabb is greater than that for rn

pitch of iterated rippled noise iterated rippled noise irn stimuli are generated by a cascade of delay d gain g and add networks the matched pitch of irn stimuli was determined as a function of the type of network used to generate irn stimuli the delay d 2 4 and 8 ms the number of iterations n 1 2 3 4 6 8 of the delay and add networks and whether the delayed noise was added g 1 to or subtracted g 1 from the undelayed noise the matched pitch of irn stimuli did not depend on the type of network when g 1 addition the matched pitch did not depend on the number of stages of iterations n and was always equal to the reciprocal of the delay 1 d when g 1 subtraction the match pitch depended on n when n 1 the matched pitch of irn stimuli was ambiguous having two pitches in the region of 1 d 10 when n 8 the match pitch was equal to 1 2d this change in the pitch occurred between n 2 and 6 the results are discussed in terms of spectral and temporal models of complex pitch processing a temporal model based on autocorrelation was able to provide quantitative predictions for the pitch of these irn stimuli however a spectral type of model can also account for the pitch of these irn stimuli

a cell based smoothed finite element method for multi body contact analysis using linear complementarity formulation abstract in this paper the cell based smoothed finite element using quadrilateral elements cs fem is used for 2d contact problems which are converted into linear complementarity problems lcps which can be solved efficiently using the lemke method the modified coulomb friction contact model with tangential strength and normal adhesion is considered which models sticking slipping contacting departing and bonding debonding processes in a unified formulation smoothed galerkin weak form with contact boundary is deduced in which the stiffness is implemented using the cs fem with 1 smoothing domain 1sd 2sd 3sd 4sd 8sd and 16sd for each element contact interface equations are discretized through contact point pairs that are constructed using a master slave surface algorithm intensive numerical examples are given to investigate the effects of contact parameters on contact behaviors and examine the effectiveness of the proposed approach the numerical results of cs fem models are compared with that of fem q4 model which demonstrates that all cs fem models are softer than fem q4 model the strain energy solutions obtained using several cs fem models are monotonically decreasing with the number of the sds for each element increasing the upper bound solutions in strain energy can be obtained using a cs fem 1sd model in our examples while the lower bound solutions are obtained using cs fem 16sd model or fem q4 with fem q4 solution being the lowest

further evidence that fundamental frequency difference limens measure pitch discrimination difference limens for complex tones dlcs that differ in f0 are widely regarded as a measure of periodicity pitch discrimination however because f0 changes are inevitably accompanied by changes in the frequencies of the harmonics dlcs may actually reflect the discriminability of individual components to test this hypothesis dlcs were measured for complex tones the component frequencies of which were shifted coherently upward or downward by f 0 25 37 5 or 50 of the f0 yielding fully harmonic f 0 strongly inharmonic f 25 37 5 or odd harmonic f 50 tones if dlcs truly reflect periodicity pitch discriminability they should be larger worse for inharmonic tones than for harmonic and odd harmonic tones because inharmonic tones have a weaker pitch consistent with this prediction the results of two experiments showed a non monotonic dependence of dlcs on f with larger dlcs for f s of 25 or 37 5 than for f s of 0 or 50 of f0 these findings are consistent with

pitch strength of iterated rippled noise two versions of a cascade add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds the number of iterations and the attenuation in the network a description based on an exponential function of the first peak of the autocorrelation function of irn stimuli is consistent with the results the discrimination data were well fit by a function based on the difference in the exponential functions of the first peak of the autocorrelation functions a magnitude estimation experiment indicated that pitch strength was an exponential function of the height of the first peak in the autocorrelation function these results suggest that the strength of the pitch of irn stimuli is based on temporal processing as might be revealed by autocorrelation

vanishing of local homology we study the vanishing properties of local homology of complexes of modules without assuming that its homology is artinian using vanishing results for local homology and cohomology we prove new vanishing results for ext and tor modules

depth for complexes and intersection theorems this paper introduces a new notion of depth for complexes it agrees with the classical definition for modules and coincides with earlier extensions to complexes whenever those are defined techniques are developed leading to a quick proof of an extension of the improved new intersection theorem this uses hochster s big cohen macaulay modules and also a generalization of the depth formula for tensor product of modules properties of depth for complexes are established extending the usual properties of depth for modules

a simple and robust three dimensional cracking particle method without enrichment abstract a new robust and efficient approach for modeling discrete cracks in meshfree methods is described the method is motivated by the cracking particle method rabczuk t belytschko t international journal for numerical methods in engineering 2004 where the crack is modeled by a set of cracked segments however in contrast to the above mentioned paper we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity instead the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics we apply this method to several two and three dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any mesh orientation bias

perception of missing fundamental pitch by 3 and 4 month old human infants a hallmark of complex pitch perception is that the pitch of a harmonic complex is the same whether or not the fundamental frequency is present by 7 months infants appear to discriminate on the basis of the pitch of the missing fundamental mf although electrophysiological cortical responses to mf pitch changes have been recorded in infants younger than 7 months no psychophysical studies have been published this study investigated the ability of 3 and 4 month olds to perceive the pitch of mf harmonic complexes based on fundamentals of 160 hz and 200 hz using an observer based method in experiment i to demonstrate mf pitch discrimination 3 and 4 month olds were required to ignore spectral changes in complexes with the same fundamental and to respond only when the fundamental changed in experiment ii a 60 260 hz noise was presented with complexes to mask combination tones at the fundamental frequency in experiment iii complexes were bandpass filtered with a 12 db octave slope to limit use of

a new weight function enrichment in meshless methods for multiple cracks in linear elasticity summary a new enriched weight function for meshless methods is proposed for the numerical treatment of multiple arbitrary cracks in two dimensions the main novelty consists in modifying the weight function with an intrinsic enrichment which is discontinuous over the finite length of the crack represented by a segment but continuous all around the crack tips an analytical function is used to introduce discontinuities that are incorporated in the kernel in a simple multiplicative manner the resulting method allows a more straightforward implementation and simulation of the presence of multiple cracks crack branching and crack propagation in a meshless framework without using any of the existing algorithms such as visibility transparency and diffraction and without using additional unknowns and additional equations for the evolution of the level sets as in extrinsic partition of unity based methods stress intensity factors calculated using the j integral demonstrate excellent agreement with analytical solutions for classical fracture mechanics benchmarks copyright 2011 john wiley sons ltd

the h p adaptive finite element method for the numerical simulation of compressible flow an h p adaptive finite element method is presented for the numerical simulation of compressible fluid flow in addition to refining the mesh in regions where the estimated error is large the polynomial degree of the elements is increased it is shown that by using high order polynomials highly accurate approximations are obtained to a regularized form of the equations governing viscous compressible flow

prediction of absolute thresholds and equal loudness contours using a modified loudness model the loudness model described by moore et al j audio eng soc 45 224 240 1997 forms the basis for a recent ansi standard for the calculation of the loudness of steady sounds however the model does not give accurate predictions of the absolute thresholds published in a recent iso standard here it is described how the assumed middle ear transfer function in the model can be modified to give more accurate absolute threshold predictions the modified model also gives reasonably accurate predictions of the equal loudness contours published in a recent iso standard

smoothing and accelerated computations in the element free galerkin method two topics in the formulation and implementation of meshless methods are considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximating functions and their derivatives these techniques are described in the context of the element free galerkin method but they are applicable to other meshless methods results are presented for some elastostatic problems which show a moderate improvement in the accuracy of the smoothed interpolant the speedup in calculating the shape functions is about a factor of two

on gorenstein projective injective and flat dimensions a functorial description with applications gorenstein homological dimensions are refinements of the classical homological dimensions and finiteness singles out modules with amenable properties reflecting those of modules over gorenstein rings as opposed to their classical counterparts these dimensions do not immediately come with practical and robust criteria for finiteness not even over commutative noetherian local rings in this paper we enlarge the class of rings known to admit good criteria for finiteness of gorenstein dimensions

dual horizon peridynamics a stable solution to varying horizons abstract in this paper we present a dual horizon peridynamics formulation which allows for simulations with dual horizon with minimal spurious wave reflection we prove the general dual property for dual horizon peridynamics based on which the balance of momentum and angular momentum in pd are naturally satisfied we also analyze the crack pattern of random point distribution and the multiple materials issue in peridynamics for selected benchmark problems we show that dh pd is less sensitive to the spatial than the original pd formulation

the perceptual tone noise ratio of merged iterated rippled noises iterated rippled noise irn is constructed by delaying a random noise by d ms adding it back to the same noise and repeating the process iteratively when two irns with the same power but slightly different delays are added together the perceptual tone noise ratio of the merged irn is markedly reduced with respect to that of either of the component irns in this paper the reduction in the perceptual tone noise ratio is measured for irns in which one of the delays is always 16 ms and the other is either 16 0 1 ms or 16 1 1 ms the component irns have the same number of iterations and the number varies across conditions from 4 to 256 the perceptual tone noise ratio is measured using a discrimination matching procedure developed for single irns each merged irn is compared with a range of standard stimuli having varying proportions of a complex tone and a broadband noise patterson et al j acoust soc am 100 3286 3294 1996 for single irns the function relating the signal to noise ratio of the matching standard to the number of iterations in the irn was found to be essentially straight this relationship was explained in terms of the height of the first peak in the autocorrelation of the stimulus wave or by the first peak in the summary autocorrelogram produced by a time domain auditory model for the merged irns in the current experiment the matching point functions are found to have pronounced downward curvature in addition to being well below the function for single irns to account for the reduction in the perceptual tone noise ratio of merged irns the autocorrelation model was extended to include a simple rule for combining adjacent peaks in the autocorrelation function of the wave and the autocorrelogram model was revised to improve the simulation of the loss of phase locking at higher frequencies in the autocorrelogram

stable particle methods based on lagrangian kernels abstract a large deformation particle method based on the krongauz belytschko corrected gradient meshfree method with lagrangian kernels is developed in this form the gradient is corrected by a linear transformation so that linear completeness is satisfied for the test functions shepard functions are used this guarantees that the patch test is met lagrangian kernels are introduced to eliminate spurious distortions of the domain of material stability a mass allocation scheme is developed that captures correct reflection of waves without any explicit application of traction boundary conditions in addition the lagrangian kernel versions of various forms of smooth particle methods sph including the standard forms and the randles libersky modification are presented and studied results are obtained for a variety of problems that compare this method to standard forms of sph the randles libersky correction and large deformation versions of the element free galerkin method

the generalized finite element method an example of its implementation and illustration of its performance the generalized finite element method gfem was introduced in reference 1 as a combination of the standard fem and the partition of unity method the standard mapped polynomial finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data the geometry of the domain the loads and the boundary conditions the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and are pasted to the existing finite element basis to construct a conforming approximation the essential boundary conditions can be imposed exactly as in the standard fem adaptive numerical quadrature is used to ensure that the errors in integration do not affect the accuracy of the approximation this paper gives an example of how the gfem can be developed for the laplacian in domains with multiple elliptical voids and illustrates implementation issues and the superior accuracy of the gfem versus the standard fem copyright 2000 john wiley sons ltd

perception of the low pitch of frequency shifted complexes when all of the components in a harmonic complex tone are shifted in frequency by f the pitch of the complex shifts roughly in proportion to f for tones with a small number of components the shift is usually somewhat larger than predicted from pitch theories which has been attributed to the influence of combination tones smoorenburg j acoust soc am 48 924 941 1970 experiment 1 assessed whether combination tones influence the pitch of complex tones with more than five harmonics by using noise to mask the combination tones the matching stimulus was a harmonic complex test complexes were bandpass filtered with passbands centered on harmonic numbers 5 resolved 11 intermediate or 16 unresolved and fundamental frequencies f0s were 100 200 or 400 hz for the intermediate and unresolved conditions the matching stimuli were filtered with the same passband to minimize differences in the excitation patterns of the test and matching stimuli for the resolved condition the matching st

moderate cochlear hearing loss leads to a reduced ability to use temporal fine structure information the ability of normally hearing and hearing impaired subjects to use temporal fine structure information in complex tones was measured subjects were required to discriminate a harmonic complex tone from a tone in which all components were shifted upwards by the same amount in hz in a three alternative forced choice task the tones either contained five equal amplitude components non shaped stimuli or contained many components but were passed through a fixed bandpass filter to reduce excitation pattern changes shaped stimuli components were centered at nominal harmonic numbers n 7 11 and 18 for the shaped stimuli hearing impaired subjects performed much more poorly than normally hearing subjects with most of the former scoring no better than chance when n 11 or 18 suggesting that they could not access the temporal fine structure information performance for the hearing impaired subjects was significantly improved for the non shaped stimuli presumably because they could benefit from spectral cues it is proposed that normal hearing subjects can use temporal fine structure information provided the spacing between fine structure peaks is not too small relative to the envelope period but subjects with moderate cochlear hearing loss make little use of temporal fine structure information for unresolved components

isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth abstract we present a novel numerical method to simulate crack growth in 3d directly from the computer aided design cad geometry of the component without any mesh generation the method is an isogeometric boundary element method igabem based on non uniform rational b splines nurbs nurbs basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations a stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements convergence studies in the crack opening displacement is performed for a penny shaped crack and an elliptical crack two approaches to extract stress intensity factors sifs the contour m integral and the virtual crack closure integral are compared using dual integral equations the results show remarkable accuracy in the computed sifs leading to smooth crack paths and reliable fatigue lives without requiring the generation of any mesh from the cad model of the component under consideration

a comparative study on finite elements for capturing strong discontinuities e fem vs x fem a comparative study on finite elements for capturing strong discontinuities by means of elemental e fem or nodal enrichments x fem is presented based on the same constitutive model continuum damage and linear elements triangles and tetrahedra optimized implementations of both types of enrichments in the same non linear code are tested for a representative set of 2d and 3d crack propagation examples it is shown that both methods provide the same qualitative and quantitative results for enough refined meshes for the performed tests e fem exhibited in general a higher accuracy mostly for coarse meshes whereas convergence rate with mesh refinement which is super linear showed slightly higher for x fem as for the computational costs for single crack modelling x fem showed depending on the case from 1 1 to about 2 5 times more expensive than e fem for multiple cracks the computational cost of e fem keeps constant whereas the cost associated to x fem increases linearly with the number of modelled cracks

a time domain description for the pitch strength of iterated rippled noise two versions of a cascaded add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose strength relative to the noise can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds or the number of iterations n 1 2 3 4 7 and 9 performance was determined for irn stimuli generated with delays of 2 4 and 8 ms and for four bandpass filter conditions 0 2000 250 2000 500 2000 and 750 2000 hz some irn stimuli were extremely difficult to discriminate despite relatively large spectral differences while other irn stimuli produced readily discriminable changes in perception despite small spectral differences these contrasting results are inconsistent with simple spectral explanations for the perception of irn stimuli an explanation based on the first peak of the autocorrelation function of irn stimuli is consistent with the results simulations of the processing performed by the peripheral auditory system i e interval histograms and correlograms produce results which are consistent with the involvement of these temporal processes in the perception of irn stimuli

pitch discrimination of diotic and dichotic tone complexes harmonic resolvability or harmonic number three experiments investigated the relationship between harmonic number harmonic resolvability and the perception of harmonic complexes complexes with successive equal amplitude sine or random phase harmonic components of a 100 or 200 hz fundamental frequency f0 were presented dichotically with even and odd components to opposite ears or diotically with all harmonics presented to both ears experiment 1 measured performance in discriminating a 3 5 5 frequency difference between a component of a harmonic complex and a pure tone in isolation listeners achieved at least 75 correct for approximately the first 10 and 20 individual harmonics in the diotic and dichotic conditions respectively verifying that only processes before the binaural combination of information limit frequency selectivity experiment 2 measured fundamental frequency difference limens f0 dls as a function of the average lowest harmonic number similar results at both f0 s provide further evidence that harmonic number not absolute frequency underlies the order of magnitude increase observed in f0 dls when only harmonics above about the 10th are presented similar results under diotic and dichotic conditions indicate that the auditory system in performing f0 discrimination is unable to utilize the additional peripherally resolved harmonics in the dichotic case in experiment 3 dichotic complexes containing harmonics below the 12th or only above the 15th elicited pitches of the f0 and twice the f0 respectively together experiments 2 and 3 suggest that harmonic number regardless of peripheral resolvability governs the transition between two different pitch percepts one based on the frequencies of individual resolved harmonics and the other based on the periodicity of the temporal envelope