Design of Band Gap Formation in Periodic Rotors via Optimization

Rotors are usually composed of rotating elements (e.g. disks, impellers, blade stages) which add mass and rotational inertia to the system. When this additional inertia of the rotating elements is evenly distributed along the rotor, inertia periodicity appears and the system presents considerably large band gaps in its frequency response, where no resonances appear. The present work shows that we can change the central frequency of these band gaps, without significantly affecting its bandwidth, by changing the distribution of the inertia along the rotor to a quasi-periodic condition. Such designing of the rotor, and consequently of the band gap, is achieved by an optimization procedure.

Separate functional subnetworks of excitatory neurons show preference to periodic and random sound structures

ABSTRACTAuditory cortex (ACX) neurons are sensitive to spectro-temporal sound patterns and violations in patterns induced by rare stimuli embedded within streams of sounds. We investigate the auditory cortical representation of repeated presentations of sequences of sounds with standard stimuli (common) with an embedded deviant (rare) stimulus in two conditions – Periodic (Fixed deviant position) or Random (Random deviant position), using extracellular single-unit and 2-photon Ca+2 imaging recordings in Layer 2/3 neurons of the mouse ACX. In the population average, responses increased over repetitions in the Random-condition and were suppressed or did not change in the Periodic-condition, showing irregularity preference. A subset of neurons also showed the opposite behavior, indicating regularity preference. Pairwise noise correlations were higher in Random-condition over Periodic-condition, suggesting the role of recurrent connections. 2-photon Ca+2 imaging of excitatory (EX) and parvalbumin-positive (PV) and somatostatin-positive (SOM) inhibitory neurons, showed different categories of adaptation or change in response over repetitions (categorized by the sign of the slope of change) as observed with single units. However, the examination of functional connectivity between pairs of neurons of different categories showed that EX-PV connections behaved opposite to the EX-EX and EX-SOM pairs that show more functional connections outside category in Random-condition than Periodic-condition. Finally considering Regularity preference, Irregularity preference and no preference categories, showed that EX-EX and EX-SOM connections to be in largely separate functional subnetworks with the different preferences, while EX-PV connections were more spread. Thus separate subnetworks could underly the coding of periodic and random sound sequences.Significance StatementStudying how the ACX neurons respond to streams of sound sequences help us understand the importance of changes in dynamic acoustic noisy scenes around us. Humans and animals are sensitive to regularity and its violations in sound sequences. Psychophysical tasks in humans show that auditory brain differentially responds to periodic and random structures, independent of the listener’s attentional states. Here we show that mouse ACX L2/3 neurons detect a change and respond differentially to changing patterns over long-time scales. The differential functional connectivity profile obtained in response to two different sound contexts, suggest the stronger role of recurrent connections in the auditory cortical network. Furthermore, the excitatory-inhibitory neuronal interactions can contribute to detecting the changing sound patterns.

Bifurcation Analysis and Pattern Selection of Solutions for the Modified Swift–Hohenberg Equation

In this paper, motivated by [Peletier & Rottschäfer, 2004; Peletier & Williams, 2007], we study the dynamical bifurcation of the modified Swift–Hohenberg equation endowed with an evenly periodic condition on the interval [Formula: see text]. As [Formula: see text] crosses over the critical points, the trivial solution bifurcates to an attractor and some new patterns of solutions emerge. We provide detailed descriptions of all possible final patterns of solutions on the overlapped intervals of [Formula: see text], which emerge after a gap collapses to a point. We also compute all critical values of [Formula: see text], [Formula: see text] and [Formula: see text] precisely, which are responsible for bifurcation and pattern formations. We finally provide numerical results that explain the main theorems.

THE STRONG-NORM CONVERGENCE OF A PROJECTION-DIFFERENCE METHOD OF SOLUTION OF A PARABOLIC EQUATION WITH THE PERIODIC CONDITION ON THE SOLUTION

A smooth soluble abstract linear parabolic equation with the periodic condition on the solution is treated in a separable Hilbert space. This problem is solved approximately by a projection-difference method using the Galerkin method in space and the implicit Euler scheme in time. Effective both in time and in space strong-norm error estimates for approximate solutions, which imply convergence of approximate solutions to the exact solution and order of convergence rate depending of the smoothness of the exact solution, are obtained.