Orbital stability analysis of trajectories of highly nonlinear dynamic systems with feedback coupling

Orbital stability and qualitative study of the oscillations of a highly nonlinear dynamic system with feedback coupling are considered. For a highly nonlinear dynamic system with feedback coupling that satisfies Liénard’s theorem (on the existence and uniqueness of a periodic solution), a complete study of the phase pattern of the system is conducted. Applying the Poincaré criterion, the conditions for the existence of limit cycles and their Lyapunov stability are determined. The diagrams of phase trajectories are constructed numerically using the Mathcad 15 software package. Limit cycles are established, which are consistent with the limit cycles obtained by the Poincaré method. The behavior of trajectories outside the limit cycles is investigated. Recurrent homogeneous Pfaff equations are obtained, which determine the behavior of the systems “at infinity”. It was determined that the infinitely distant point of the horizontal axis is the only singular point for these equations. Linear approximations of recurrent homogeneous equations are obtained, which make it possible to determine the nature of the singular points. It was found that the trajectories then wind like a spiral on the limit cycles. Images of trajectories on the phase plane outside the limit cycles for the cases of degrees of nonlinearity under consideration are constructed.

Quantum imaging of a polarisation sensitive phase pattern with hyper-entangled photons

A transparent polarisation sensitive phase pattern makes a polarisation dependent transformation of quantum state of photons without absorbing them. Such an invisible pattern can be imaged with quantum entangled photons by making joint quantum measurements on photons. This paper shows a long path experiment to quantum image a transparent polarisation sensitive phase pattern with hyper-entangled photon pairs involving momentum and polarisation degrees of freedom. In the imaging configuration, a single photon interacts with the pattern while the other photon, which has never interacted with the pattern, is measured jointly in a chosen polarisation basis and in a quantum superposition basis of its position which is equivalent to measure its momentum. Individual photons of each hyper-entangled pair cannot provide a complete image information. The image is constructed by measuring the polarisation state and position of the interacting photon corresponding to a measurement outcome of the non-interacting photon. This paper presents a detailed concept, theory and free space long path experiments on quantum imaging of polarisation sensitive phase patterns.

Development of the Relationships Among Dynamic Balance Control, Inter-limb Coordination, and Torso Coordination During Gait in Children Aged 3–10 Years

Knowledge about the developmental process of dynamic balance control comprised of upper arms and upper legs coordination and trunk and pelvis twist coordination is important to advance effective balance assessment for abnormal development. However, the mechanisms of these coordination and stability control during gait in childhood are unknown.This study examined the development of dynamic postural stability, upper arm and upper leg coordination, and trunk and pelvic twist coordination during gait, and investigated the potential mechanisms integrating the central nervous system with inter-limb coordination and trunk and pelvic twist coordination to control extrapolated center of the body mass (XCOM). This study included 77 healthy children aged 3–10 years and 15 young adults. The child cohort was divided into four groups by age: 3–4, 5–6, 7–8, and 9–10 years. Participants walked barefoot at a self-selected walking speed along an 8 m walkway. A three-dimensional motion capture system was used for calculating the XCOM, the spatial margin of stability (MoS), and phase coupling movements of the upper arms, upper legs, trunk, and pelvic segments. MoS in the mediolateral axis was significantly higher in the young adults than in all children groups. Contralateral coordination (ipsilateral upper arm and contralateral upper leg combination) gradually changed to an in-phase pattern with increasing age until age 9 years. Significant correlations of XCOMML with contralateral coordination and with trunk and pelvic twist coordination (trunk/pelvis coordination) were found. Significant correlations between contralateral coordination and trunk/pelvis coordination were observed only in the 5–6 years and at 7–8 years groups.Dynamic postural stability during gait was not fully mature at age 10. XCOM control is associated with the development of contralateral coordination and trunk and pelvic twist coordination. The closer to in-phase pattern of contralateral upper limb coordination improved the XCOM fluctuations. Conversely, the out-of-phase pattern (about 90 degrees) of the trunk/pelvis coordination increased theXCOM fluctuation. Additionally, a different control strategy was used among children 3–8 years of age and individuals over 9 years of age, which suggests that 3–4-year-old children showed a disorderly coordination strategy between limb swing and torso movement, and in children 5–8 years of age, limb swing depended on trunk/pelvis coordination.

"Fakes" in social networking media and modeling "fake infection"

The growth of dynamism, the complexity of relationships in social networks requires a systematic approach, the development of mathematical models for forecasting and the identification of fake news in social networks. Otherwise, it is difficult to resist media misinformation, fake news. The problem is urgent, there are more and more opportunities for exchanging "viral" and fake messages in social networks, and we poorly implement monitoring, identifying fake risks. Social networks so far do not allow reliably distinguishing lies from news from aggregator. The purpose of the work is to predict and analyze the system-phase pattern of the spread of fakes in the space of social interactions. "Fakes" are deliberately false, intended for manipulation. In recent years, they are easily distributed in social networks. In the work by methods of the theory of ordinary differential equations, their qualitative analysis, the above problem was full investigated. The study was conducted under assumptions: remote distributors are not allowed to participate in the transmission of fakes; an adult population susceptible to fakes has a constant birth rate; propagation can occur "vertically," wherein the transmission mechanism is introduced into the model by appropriate assumptions about the proportion of susceptible and distributors. The problem is fully investigated (solvability, unambiguity, phase patterns of stable behavior). The work will be useful in the practical identification and prediction of the influence of fake news.

Interdecadal Change in the Effect of Tibetan Plateau Snow Cover on Spring Precipitation over Eastern China around the Early 1990s

Previous works extensively investigated the influences of the winter-spring Tibetan Plateau snow cover (TP, TPSC) on climate variability over the East Asia. The present work documents an interdecadal-changed impacts of different spring TPSC anomaly (TPSCA) patterns on spring precipitation over eastern China (SPEC) around the early 1990s. It is found that the correlation of eastern and western TPSCA shifts from negative to positive around 1990. The empirical orthogonal function (EOF) analysis applying onto the spring TPSCA during 1970–1989 (P1) and during 1991–2017 (P2) adds additional support for such interdecadal change in the relationship between the eastern and western TPSCA. Specifically, the leading EOF (EOF1) mode in P1 shows an out-of-phase pattern with opposite signals lying over the eastern and western TP, while the counterpart in P2 is characterized by an in-phase pattern over the entire TP. Corresponding to more (less) snow cover in the eastern (western) TP in P1, a significant TP cold cyclone (TPCC) and a downstream anticyclone over the western North Pacific are observed. Anomalous southerly flow prevailing east to TPCC could bring the warm-wet air from tropics to the coast of East Asian, which largely enhances the spring precipitation south to Yangtze River Valley (YRV). By contrast, regarding more snow cover both in the eastern and western TP in P2, a relatively northward-displaced and wider TPCC sweeps over the entire TP compared with the TPSC-induced TPCC in P1. Moreover, there are significant sinking anomalies observed in the downstream YRV-HRV region, which leads to suppressed spring precipitation over there via the dry-cold advection process. Hence, these discrepancies of local and downstream atmospheric circulation induced by the out-of-phase and in-phase TPSCA patterns in two epochs play an important role in resulting in the interdecadal shift of the SPEC anomaly pattern around 1990.

Respiratory–Swallow Coordination in Healthy Adults During Drinking of Thin to Extremely Thick Liquids: A Research Note

Purpose Respiratory–swallow coordination is vital for airway protection, preventing aspiration, or penetration of foreign material into the airway. With the implementation of the International Dysphagia Diet Standardization Initiative definitions for different liquid consistencies used in dysphagia management, it is important to establish whether respiratory–swallow coordination patterns differ across these consistencies. This study aimed to evaluate respiratory behaviors during swallowing across the spectrum from thin to extremely thick liquids in healthy adults less than 60 years of age. Method Thirty healthy adults, aged 21–55 years, each consumed 54 naturally sized cup sips or spoonfuls of liquid stimuli prepared in thin, slightly thick, mildly thick, moderately thick, and extremely thick consistencies. Half of the stimuli were prepared using barium and half with a lemon-flavored water. Concurrent respiratory and swallowing pressure signals were collected to evaluate the respiratory phase pattern and pause duration associated with the swallow. Results An expiration–swallow–expiration pattern was the dominant respiratory phase pattern, observed in 92.7% of the trials, with no significant effect of consistency. Respiratory pause duration was found to be significantly shorter with barium stimuli (0.73 s) compared to nonbarium stimuli (0.78 s) ( p < .001, Cohen's d = .2), with no notable effects based on the factors of sex or liquid consistency. Conclusions In a convenience sample of healthy adults under the age of 60 years, consistent respiratory–swallow phasing and stable timing across the spectrum from thin to extremely thick liquids was observed. The data from this study can serve as preliminary reference data to which assessment information for individuals with dysphagia or respiratory challenges can be compared.

The water path in plasma-treated Leucaena seeds

The effects of cold atmospheric plasma (CAP) of dielectric barrier discharges on the wettability, imbibition and germination of Leucaena leucocephala were investigated. It was established that CAP treatment markedly hydrophilized the seed coat, especially at longer treatment times. From the profile of the imbibition curve and visual observation, it was possible to verify that there are two resistance barriers to water penetration: integument surface and region of the macrosclereid cell wall (light line). Although the plasma interacts only in the integument, increasing the density of hydrophilic sites increases the capacity of water absorption, producing enough driving force to overcome the second resistance barrier. The existence of these two barriers changes the three-phase pattern generally observed during seed germination. Despite an increase in imbibition, the plasma treatment conditions used in this work, were not enough to overcome completely the dormancy barrier.