Classical and sequential limit analysis revisited

Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic–plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity – in the absence of hardening and within a linearized geometrical framework –, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity – although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic–plastic coupling in the specific case considered.     

Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems

We study the growth with time of (the coefficients of the asymptoticexpansion of) the error in the numerical integration with linearmultistep methods of periodic solutions of systems of ordinarydifferential equations. Particular attention is devoted to reversiblesystems. It turns out that symmetric linear multistep methodscannot be recommended in spite of the fact that they mimic thereversibility of the true flow. For reversible second-ordersystems, linear multistep methods without parasitic double rootsare useful.     

Asymmetrical hippocampal connectivity in mesial temporal lobe epilepsy: evidence from resting state fMRI

Background

Recent studies have shown that the human right-hemispheric auditory cortex is particularly sensitive to reduction in sound quality, with an increase in distortion resulting in an amplification of the auditory N1m response measured in the magnetoencephalography (MEG). Here, we examined whether this sensitivity is specific to the processing of acoustic properties of speech or whether it can be observed also in the processing of sounds with a simple spectral structure. We degraded speech stimuli (vowel /a/), complex non-speech stimuli (a composite of five sinusoidals), and sinusoidal tones by decreasing the amplitude resolution of the signal waveform. The amplitude resolution was impoverished by reducing the number of bits to represent the signal samples. Auditory evoked magnetic fields (AEFs) were measured in the left and right hemisphere of sixteen healthy subjects.

Results

We found that the AEF amplitudes increased significantly with stimulus distortion for all stimulus types, which indicates that the right-hemispheric N1m sensitivity is not related exclusively to degradation of acoustic properties of speech. In addition, the P1m and P2m responses were amplified with increasing distortion similarly in both hemispheres. The AEF latencies were not systematically affected by the distortion.

Conclusions

We propose that the increased activity of AEFs reflects cortical processing of acoustic properties common to both speech and non-speech stimuli. More specifically, the enhancement is most likely caused by spectral changes brought about by the decrease of amplitude resolution, in particular the introduction of periodic, signal-dependent distortion to the original sound. Converging evidence suggests that the observed AEF amplification could reflect cortical sensitivity to periodic sounds.     

The stress field near the front of an arbitrarily shaped crack in a three-dimensional elastic body

The problem stated in the title is investigated with special emphasis on the first three terms of the stress expansion, proportional to r ^-1/2, r ⁰=1 and r ^1/2 respectively, where r denotes the distance to the crack front. The particular case of a plane crack with a straight front and of stresses independent of the distance along the latter is studied first. It is shown that the classical plane strain and antiplane solutions must be supplemented by a few additional particular solutions to obtain the full stress expansion. The general case is then considered. The stress expansion is studied by writing the field equations (equilibrium, strain compatibility and boundary conditions) in a system of suitable curvilinear coordinates. It is shown that the number of independent constants in the stress expansion is the same as in the particular case considered previously but that the curvatures of the crack and its front and the non-uniformity of the stresses along the latter induce the appearance of corrective terms in this expansion.