Bifurcation and Patterns Analysis for a Spatiotemporal Discrete Gierer-Meinhardt System

The Gierer-Meinhardt system is one of the prototypical pattern formation models. The bifurcation and pattern dynamics of a spatiotemporal discrete Gierer-Meinhardt system are investigated via the couple map lattice model (CML) method in this paper. The linear stability of the fixed points to such spatiotemporal discrete system is analyzed by stability theory. By using the bifurcation theory, the center manifold theory and the Turing instability theory, the Turing instability conditions in flip bifurcation and Neimark–Sacker bifurcation are considered, respectively. To illustrate the above theoretical results, numerical simulations are carried out, such as bifurcation diagram, maximum Lyapunov exponents, phase orbits, and pattern formations.

Spontaneous emergence of topologically robust grid cell modules: A multiscale instability theory

Modular structures in the brain play a central role in compositionality and intelligence, however the general mechanisms driving module emergence have remained elusive. Studying entorhinal grid cells as paradigmatic examples of modular architecture and function, we demonstrate the spontaneous emergence of a small number of discrete spatial and functional modules from an interplay between continuously varying lateral interactions generated by smooth cortical gradients. We derive a comprehensive analytic theory of modularization, revealing that the process is highly generic with its robustness deriving from topological origins. The theory generates universal predictions for the sequence of grid period ratios, furnishing the most accurate explanation of grid cell data to date. Altogether, this work reveals novel principles by which simple bottom-up dynamical interactions lead to macroscopic modular organization.

Suppression of Baroclinic Eddies by Strong Jets

The midlatitude storm tracks are of the most prominent features of extratropical climate. Despite the theoretical expectation, based on baroclinic instability theory, that baroclinic eddies strengthen with jet intensification, there is evidence that this relation breaks when the jet is particularly strong. The most known case is the Pacific midwinter minimum in storm track activity. To isolate the effect of jet strength on storm activity, we conduct a series of GCM experiments systematically varying jet intensity. The simulations are analyzed using Lagrangian tracking to understand the response from a single-eddy perspective. The Lagrangian analysis shows that while the response of upper-level eddies is dominated by a reduction in the amount of tracked features, the lower-level eddies’ response is also affected by a reduction in their lifetime. Analyzing the jet strength effect on the pairing between the upper- and lower-level eddies, we find that the jet intensification increases the relative speed of the upper-level eddies, breaking the baroclinic wave structure and limiting its growth. We show that the Lagrangian response correlates with a shift in the midlatitude spectrum to low wavenumbers. The shift settles these results with linear baroclinic instability theory, as under the stronger jet conditions synoptic-scale eddies are predicted to have a sub-optimal growth rate. These results can potentially explain the midwinter suppression of storm activity over the Pacific and the difference from the Atlantic response.

Direct validation of dune instability theory

Modern dune fields are valuable sources of information for the large-scale analysis of terrestrial and planetary environments and atmospheres, but their study relies on understanding the small-scale dynamics that constantly generate new dunes and reshape older ones. Here, we designed a landscape-scale experiment at the edge of the Gobi desert, China, to quantify the development of incipient dunes under the natural action of winds. High-resolution topographic data documenting 42 mo of bedform dynamics are examined to provide a spectral analysis of dune pattern formation. We identified two successive phases in the process of dune growth, from the initial flat sand bed to a meter-high periodic pattern. We focus on the initial phase, when the linear regime of dune instability applies, and measure the growth rate of dunes of different wavelengths. We identify the existence of a maximum growth rate, which readily explains the mechanism by which dunes select their size, leading to the prevalence of a 15-m wavelength pattern. We quantitatively compare our experimental results with the prediction of the dune instability theory using transport and flow parameters independently measured in the field. The remarkable agreement between theory and observations demonstrates that the linear regime of dune growth is permanently expressed on low-amplitude bed topography, before larger regular patterns and slip faces eventually emerge. Our experiment underpins existing theoretical models for the early development of eolian dunes, which can now be used to provide reliable insights into atmospheric and surface processes on Earth and other planetary bodies.

Two-point radiation statistics from large-scale turbulent structures within supersonic jets

The noise from large-scale coherent turbulent structures within jets remains the dominant source. For the purpose of developing future control systems for the large-scale noise source, we investigate the statistics between upstream and downstream radiating waves. We investigate two off-design supersonic jet flows with instability theory and associated noise radiation, large-eddy simulation (LES), and experiments. We compare the auto-correlation, cross-correlation, coherence, and other statistics predicted by aeroacoustic instability theory. As instability waves are closely connected with the formation of large-scale turbulent structures, they yield insight into large-scale noise statistics. We investigate two nozzles at two supersonic off-design conditions. The first is a biconic nozzle operating at an unheated condition, and the second is a NASA nozzle operating at a heated condition. We find that for these jets, the noise from instability waves is coherent between 0.40 to 0.70 at large-scale radiation frequencies between the downstream and upstream radiation directions.

Static Rest Frame to Improve Postural Stability in Virtual and Augmented Reality

Many users have shown increased postural instability while using Head-Mounted Displays (HMDs) as HMDs block their real-world vision. People with balance impairments are especially more affected by this as they depend more on their visual cues to maintain their balance. In addition, balance is a good indication of cybersickness according to postural instability theory. In this research, we have investigated how to use additional visual cues to improve postural stability. Through conducting one user study in Virtual Reality (VR) and Augmented Reality (AR), we have studied the effect of a Static Rest Frame (SRF) on postural stability in persons with balance impairments due to Multiple Sclerosis (MS). Results indicate that an SRF significantly improves postural stability in VR and AR for users with MS. Based on these results, we propose guidelines for designing more accessible VR and AR systems for persons with balance impairments.

Postural Instability and Seasickness in a Motion-Based Shooting Simulation

BACKGROUND: Motion sickness is a problem for many; however, it is especially pressing for military personnel who need to operate in life and death environments. The current study investigated the underlying cause of motion sickness by testing postural instability theory.METHODS: Subjects experienced realistic motion profiles while performing a virtual reality shooting task and reporting any motion sickness symptoms. Postural instability was manipulated within 20 subjects across 2 conditions. In one condition, subjects could readily adapt their posture to the motion profile by adjusting their feet on the platform (Free), and in the other condition, their feet were fixed in place on the moving platform (Fixed). This Free condition decreased postural instability by allowing adjustment, while the Fixed condition increased postural instability by restricting adjustment. The same subjects completed both conditions to control for individual differences in motion sickness susceptibility.RESULTS: Overall, motion sickness was mild as measured by SSQ (M 14.41, Free; M 18.89, Fixed), and no statistically significant differences were observed between the conditions. Performance on the shooting task was reduced in accuracy by approximately 40%, although this result did not differ between conditions.DISCUSSION: The results do not support postural instability as a contributing factor in motion sickness symptomology. They also demonstrate the importance of accounting for motion when conducting training.Pettijohn KA, Pistone DV, Warner AL, Roush GJ, Biggs AT. Postural instability and seasickness in a motion-based shooting simulation. Aerosp Med Hum Perform. 2020; 91(9):703709.

Motion Sickness Manifestations and Prevention

Motion sickness is an ancient problem associated with transportation (ships and other vehicles), which is affecting humans since ages. Motion sickness is characteristically occurring during abnormal movements induced by the motion and when there is a conflict between various senses such as visual, vestibular and motor system. Depending on the type of motion, various kinds of sicknesses, such as air sickness, car sickness, train sickness, seasickness, etc. may occur. A very less per cent of individuals are highly susceptible to motion sickness and very less per cent of individuals are highly insusceptible for motion sickness. However, most of the population comes in between. The primary symptoms of motion sickness include nausea, vomiting, wanes, and cold sweating. Varieties of drugs are available to reduce susceptibility to motion sickness. However, nausea, pallor, sweating, headache, dizziness, malaise, increased salivation, apathy, drowsiness, belching, hyperventilation and stomach awareness are the other symptoms of motion sickness. Anti-cholinergics and anti-histamines are the most effective motion sickness prophylactics with apparent side effects such as dry mouth, drowsiness, and depression. There are theories and mechanisms which include intra-vestibular (Canal-Otolith) mismatch theory, sensory conflict theory, visual-vestibular mismatch theory, the poison theory, the postural instability theory, and the movement program theory. Benzodiazepines, anticholinergics, anti-histamines and monoamine antagonists have commonly used treatment regimes. The traditional way of tackling the problem is the consumption of ginger, peppermint, lemon, fennel, marjoram, rosemary, basil. This review summarizes prediction and evaluation, behavioural strategies to prevent or minimize symptoms of motion sickness and available countermeasures of motion sickness.