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Better energies for low-dimensional elastic systems under combined bending and stretching
We present new kinematic bending measures and quadratic energies for isotropic elastic plates and shells, with certain desirable features not present in commonly employed models in mechanics and soft matter. These are justified both by simple physical arguments related to the through-thickness variation in strain, and through a detailed reduction from a three-dimensional energy quadratic in stretch. The measure of plate bending is a dilation-invariant surface tensor that couples stretch and curvature in a natural extension of primitive generalized bending strains for straight rods. The extension to naturally-curved rods and shells, for which the pure stretching of a curved rest configuration is not a dilation, contrasts with previous ad hoc postulated forms. Our results provide a clean basis for simple models of low-dimensional elastic systems, and should enable more accurate probing of the structure of singularities in soft sheets and membranes.
NMC4 Short Talk: Stretching and squeezing of neuronal log firing rate distribution by psychedelic and intrinsic brain state transitions
How psychedelic drugs change the activity of cortical neuronal populations is not well understood. It is also not clear which changes are specific to transition into the psychedelic brain state and which are shared with other brain state transitions. Here, we used Neuropixels probes to record from large populations of neurons in prefrontal cortex of mice given the psychedelic drug TCB-2. The primary effect of drug ingestion was stretching of the distribution of log firing rates of the recorded population. This phenomenon was previously observed across transitions between sleep and wakefulness, which prompted us to examine how common it is. We found that modulation of the width of the log-rate distribution of a neuronal population occurred in multiple areas of the cortex and in the hippocampus even in awake drug-free mice, driven by intrinsic fluctuations in their arousal level. Arousal, however, did not explain the stretching of the log-rate distribution by TCB-2. In both psychedelic and intrinsically occurring brain state transitions, the stretching or squeezing of the log-rate distribution of an entire neuronal population were the result of a more close overlap between log-rate distributions of the upregulated and downregulated subpopulations in one brain state compared to the other brain state. Often, we also observed that the log-rate distribution of the downregulated subpopulation was stretched, whereas the log-rate distribution of the upregulated subpopulation was squeezed. In both subpopulations, the stretching and squeezing were a signature of a greater relative impact of the brain state transition on the rates of the slow-firing neurons. These findings reveal a generic pattern of reorganisation of neuronal firing rates by different kinds of brain state transitions.