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The change in the phase, from quiescence to surge, may perturb the glacier’s dynamical behavior. To understand these changes through geospatial technique, the fastest moving tidewater Monacobreen Glacier, Svalbard, was studied for the year 2016–2019. It was elucidated that the surge had initiated during 2017–2018 before it the glacier was in quiescence since 2001. Initially, the glacier radar zones, namely percolation refreeze, lower percolation, and clean ice, were identified using the multi-temporal SAR data. These zones were utilized to delineate the equilibrium line altitude, and it was found that it is continuously moving down during surging, unlike the quiescence phase. The accumulation area ratio was always more than 0.67 throughout the analysis. The seasonal change in glacier surface velocity for both the phases was estimated, adapting the most appropriate Offset Tracking approach using the SAR data. The mean velocity over the main trunk was found to vary from 0.5 to 4 m/day. Thereafter, Glen's flow law equation was used to estimate the ice-thickness and found that the glacier has an average thickness range of 216–326 m in quiescence and 136–244 m during the surging. The analysis depicted that the basal shear stresses are increasing with surging, and the viscosity is decreasing. It can be said that the transition of the glacier from quiescent to surging phase has entirely changed its dynamic behavior and characteristics. Further, in the absence of field observations, the geospatial technique may provide reasonable estimates of the glacier’s physical and dynamical parameters.

The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of genuine nonlinearity, namely the ability for shocks and rarefactions to form instead of contact discontinuities. In the context of the Whitham modulation equations, this paper demonstrate that a loss of genuine nonlinearity leads to the appearance of a dispersive set of dynamics in the form of the modified Korteweg de-Vries equation governing the evolution of the waves instead. Its form is universal in the sense that its coefficients can be written entirely using linear properties of the underlying waves such as the conservation laws and linear dispersion relation. This insight is applied to two systems of physical interest, one an optical model and the other a stratified hydrodynamics experiment, to demonstrate how it can be used to provide insight into how waves in these systems evolve when genuine nonlinearity is lost.

In this paper, the compressible immiscible two-phase flow with relaxation is investigated, this model can be regarded as a natural modification of Jin-Xin relaxation scheme proposed and developed by S.Jin and Z.P.Xin([Comm.Pure Appl.Math., 48,1995]) in view of the numerical approximation of conservation laws. Given any entropy solution consists of two different families of shocks interacting at some positive time for the standard two-phase compressible Euler equations, it is proved that such entropy solution is the sharp interface limit for a family global strong solutions of the modified Jin-Xin relaxation scheme for Navier-Stokes/Allen-Cahn system, here the relaxation time is selected as the thickness of the interface, weighted estimation and improved antiderivative method are used in the proof. Moreover, the simulation results are given by this modified Jin-Xin relaxation scheme method. Both numerical and theoretical results show that, the interacting shock waves can pass through the interface without any effect., 25 pages, 9 figures

Using in situ methods to characterize the state of a system during reactions is critical to understanding and improving solvothermal syntheses. This work demonstrates the use of in situ energy-dispersive X-ray diffraction (EDXRD) to investigate the local dynamics during solvothermal formation of Cu4O3 using a general-purpose full-sized laboratory oven. This allows for direct comparison of in situ data with laboratory-based reactions. Using in situ EDXRD, changes in the local amounts of Cu4O3, Cu2O and CuO within approximately 100 × 100 × 700 µm gauge volumes during solvothermal Cu4O3 formation were recorded. Fast conversion between Cu2O and CuO was observed in the solvothermal environment, whereas Cu4O3 was found to be chemically stable against disturbances once formed. The observed differences in local dynamics give further support to the differences in formation mechanisms between Cu4O3 and Cu2O/CuO proposed here.

Methanol is one of the most abundant interstellar Complex Organic Molecules (iCOMs) and it represents a major building block for the synthesis of increasingly complex oxygen-containing molecules. The reaction between protonated methanol and its neutral counterpart, giving protonated dimethyl ether, (CH$_3$)$_2$OH$^+$, along with the ejection of a water molecule, has been proposed as a key reaction in the synthesis of dimethyl ether in space. Here, gas phase vibrational spectra of the (CH$_3$)$_2$OH$^+$ reaction product and of the [C$_2$H$_9$O$_2$]$^+$ intermediate complex(es), formed under different pressure and temperature conditions, are presented. The widely tunable free electron laser for infrared experiments, FELIX, was employed to record their vibrational fingerprint spectra using different types of infrared action spectroscopy in the $600-1700$ cm$^{-1}$ frequency range, complemented with measurements using an OPO/OPA system to cover the O-H stretching region $3400-3700$ cm$^{-1}$. The formation of protonated dimethyl ether as a product of the reaction is spectroscopically confirmed, providing the first gas-phase vibrational spectrum of this potentially relevant astrochemical ion., 15 pages, 6 figures, Molecular Physics, Published online: 22 Jun 2023, for associated data files see Zenodo repository at https://doi.org/10.5281/zenodo.7868559

A comprehensive study of the vortex phases and vortex dynamics is presented for a recently discovered high-temperature superconductor YH$_6$ with T$_C$ (onset) of 215 K under pressure of 200 GPa.Thermal activation energy (U$_0$) is derived in the framework of thermally activated flux flow (TAFF) theory. The activation energy yields a power law dependence U$_0$ $\propto$ H$^\alpha$ on magnetic field with a possible crossover at a field around 8-10 Tesla. Furthermore, we have depicted the vortex phase transition from vortex-glass to vortex-liquid state according to the vortex-glass theory. Finally, vortex phase diagram is constructed for the first time for superhydrides. Very high estimated values of flux flow barriers U$_0$(H) = 1.5-7*10$^4$ K together with high crossover fields makes YH$_6$ a rather outstanding superconductor as compared to most cuprates and iron-based systems. The Ginzburg number for YH$_6$ Gi = 3-7*10$^{-3}$ indicates that thermal fluctuations are not so strong and cannot broaden superconducting transitions in weak magnetic fields.

The phase of low-frequency, rhythmic cortical activity is essential for organizing brain processes because it provides a recurrent temporal frame for information coding. However, the low-frequency cortical phase exhibits great flexibility in response to external influences. Given that brain rhythms have been found to track respiratory inputs, we hypothesized that slow breathing, commonly associated with mental regulation, could reorganize the relationship between these two rhythmic systems through the adjustment of the cortical phase to such a slow train of inputs. Based on simultaneous magnetoencephalography and respiratory measurements, we report that while participants performed paced breathing, slow relative to normal breathing modulated cortical phase activity in the alpha range across widespread brain areas. Such modulation effects were specifically locked to the middle of the inspiration stage and exhibited a well-structured pattern. At the single-subject level, the phase angles underlying the effects became more likely to be diametrically opposed across breaths, indicating unique and consistent phase adjustment to slow inspiratory inputs. Neither cardiac fluctuations nor breathing-unrelated task effects could account for the findings. We suggest that slow-paced inspiration could organize the cortical phase in a regularized phase pattern, revealing a rhythmic but dynamic neural network integrated with different neurophysiological systems through volitional control. NEW & NOTEWORTHY Breathing is more complicated than a simple gas exchange, as it is integrated with numerous cognitive and emotional functions. Controlled slow breathing has often been used to regulate mental processes. This magnetoencephalography study demonstrates that slow-paced relative to normal-paced inspiration could organize the timing of alpha rhythmic activities across breathing cycles in a structured manner over widespread brain areas. Our results reveal how a volitionally controlled change in respiratory behavior could systematically modulate cortical activity.

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T∗ is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T∗ is also tuned by a magnetic flux., Physical Review Letters, 130 (8), ISSN:0031-9007, ISSN:1079-7114

We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phase-oscillators, we derive formulae which connect the responses with the system parameters including the time delay in interactions. We examine our method by applying it to two phase models, one of which describes a mean-field network of the Hodgkin--Huxley type neurons with a nonzero time delay. The method does not require much invasiveness nor microscopic observations, and these advantages highlight its broad applicability in various fields., Comment: 12 pages, 5 figures

Many learning algorithms used as normative models in neuroscience or as candidate approaches for learning on neuromorphic chips learn by contrasting one set of network states with another. These Contrastive Learning (CL) algorithms are traditionally implemented with rigid, temporally non-local, and periodic learning dynamics that could limit the range of physical systems capable of harnessing CL. In this study, we build on recent work exploring how CL might be implemented by biological or neurmorphic systems and show that this form of learning can be made temporally local, and can still function even if many of the dynamical requirements of standard training procedures are relaxed. Thanks to a set of general theorems corroborated by numerical experiments across several CL models, our results provide theoretical foundations for the study and development of CL methods for biological and neuromorphic neural networks., 23 pages, 4 figures

The CALPHAD system of fundamental phase-level databases, now known as the Materials Genome, has enabled a mature technology of computational materials design and qualification that has already met the acceleration goals of the national Materials Genome Initiative. As first commercialized by QuesTek Innovations, the methodology combines efficient genomic-level parametric design of new material composition and process specifications with multidisciplinary simulation-based forecasting of manufacturing variation, integrating efficient uncertainty management. Recent projects demonstrated under the multi-institutional CHiMaD Design Center notably include novel alloys designed specifically for the new technology of additive manufacturing. With the proven success of the CALPHAD-based Materials Genome technology, current university research emphasizes new methodologies for affordable accelerated expansion of more accurate CALPHAD databases. Rapid adoption of these new capabilities by US apex corporations has compressed the materials design and development cycle to under 2 years, enabling a new "materials concurrency" integrated into a new level of concurrent engineering supporting an unprecedented level of manufacturing innovation.

Methanol is one of the most abundant interstellar Complex Organic Molecules (iCOMs) and represents a major building block for the synthesis of increasingly complex oxygen-containing molecules. The reaction between protonated methanol and its neutral counterpart, giving protonated dimethyl ether, (CH3)2OH+, along with the ejection of a water molecule, has been proposed as a key reaction in the synthesis of dimethyl ether in space. Here, gas phase vibrational spectra of the (CH3)2OH+ reaction product and the [C2H9O2]+ intermediate complex(es), formed under different pressure and temperature conditions, are presented. The widely tunable free electron laser for infrared experiments, FELIX, was employed to record these vibrational fingerprint spectra using different types of infrared action spectroscopy in the 600-1700 cm−1 frequency range, complemented with measurements using an OPO/OPA system to cover the O−H stretching region 3400−3700cm−1. The formation of protonated dimethyl ether as a product of the reaction is spectroscopically confirmed, providing the first gas-phase vibrational spectrum of this potentially relevant astrochemical ion.

Nonlocally coupled oscillators with a phase lag self-organize into various patterns, such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, whereas it destroys coherence for a repulsive coupling. The transition behaviors are discussed in terms of the timescales of synchronization and diffusion of the oscillators. We also find a novel spatiotemporal pattern at the border between coherent and incoherent states.

Through its ability to image liquid-phase dynamics at nano/atomic-scale resolution, liquid-cell electron microscopy is essential for a wide range of applications, including wet-chemical synthesis, catalysis, and nanoparticle tracking, for which involved structural features are critical. However, statistical investigations by usual techniques remain challenging because of the difficulty in fabricating substantial liquid cells with appreciable efficiency. Here, we report a general approach for efficiently printing huge numbers of ready-to-use liquid cells (∼9000) within 30 s by electrospinning, with the unique feature of statistical liquid-phase studies requiring only one experimental time slot. Our solution efficiently resolves a complete transition picture of bubble evolution and also the induced nanoparticle motion. We statistically quantify the effect of the electron dose rate on the bubble variation and conclude that the bubble-driven nanoparticle motion is a ballistic-like behavior insignificant to morphological asymmetries. The versatile approach here is critical for statistical research, offering great opportunities in liquid-phase-associated dynamic studies.

The problem of directional coupling detection in ensembles of temporally evolving systems from observed time series is important in diverse fields. A small ensemble of three oscillators is a model of large ensembles which carry important features such as the distinction between direct and indirect influences and, therefore, allows the study of the methods for coupling detection in respect of their ability to distinguish between such influences and, hence, correctly identify directional couplings and provide their appropriate quantitative description. This work considers an ensemble of three exemplary oscillators as a test system to improve the coupling estimation method based on phase dynamics modeling and compare it to the spectral approach called Granger – Geweke spectrum. Possibilities of false conclusions about the structure of couplings are analyzed, sensitivity of both methods and interpretations of coupling characteristics are discussed.

Intrinsic optical signal (IOS) imaging promises a noninvasive method for objective assessment of retinal function. This study demonstrates concurrent optical coherence tomography (OCT) of amplitude-IOS and phase-IOS changes in human photoreceptors. A new procedure for differential-phase-mapping (DPM) is validated to enable depth-resolved phase-IOS imaging. Dynamic OCT revealed rapid amplitude-IOS and phase-IOS changes, which occur almost right away after the stimulus onset. These IOS changes were predominantly observed within the photoreceptor outer segment (OS), particularly two boundaries connecting to the inner segment and retinal pigment epithelium. The comparative analysis supports that both amplitude-IOS and phase-IOS attribute to transient OS morphological change associated with phototransduction activation in retinal photoreceptors. A simulation modeling is proposed to discuss the relationship between the photoreceptor OS length and phase-IOS changes.

Raw video files associated with the paper described as follows: The cellular cytoskeleton relies on diverse populations of motors, filaments, and binding proteins acting in concert to enable non-equilibrium processes ranging from mitosis to chemotaxis. The cytoskeleton’s versatile reconfigurability, programmed by interactions between its constituents, make it a foundational active matter platform. However, current active matter endeavors are limited largely to single force-generating components acting on a single substrate–far from the composite cytoskeleton in cells. Here, we engineer actin-microtubule composites, driven by kinesin and myosin motors and tuned by crosslinkers, to ballistically restructure and flow with speeds that span three orders of magnitude depending on the composite formulation and time relative to the onset of motor activity. Differential dynamic microscopy analyses reveal that kinesin and myosin compete to delay the onset of acceleration and suppress discrete restructuring events, while passive crosslinking of either actin or microtubules has an opposite effect. Our minimal advection-diffusion model and spatial correlation analyses correlate these dynamics to structure, with motor antagonism suppressing reconfiguration and de-mixing, while crosslinking enhances clustering. Despite the rich formulation space and emergent formulation-dependent structures, the non-equilibrium dynamics across all composites and timescales can be organized into three classes–slow isotropic reorientation, fast directional flow, and multimode restructuring. Moreover, our mathematical model demonstrates that diverse structural motifs can arise simply from the interplay between motor-driven advection and frictional drag. These general features of our platform facilitate applicability to other active matter systems, and shed light on diverse ways that cytoskeletal components can cooperate or compete to enable wide-ranging cellular processes.

The authors show that neural networks exhibiting noise-induced rhythms, also known as quasi-cycle oscillations, can synchronize through out-of-phase locking depending on the noise intensity and the size of the coupling delay

When a solute molecule is placed in solution, is it acceptable to presume that its electronic structure is essentially the same as that in the gas phase? In this paper, we address this question from a simulation perspective for the case of the sodium dimer cation (Na

The population and number dynamics of small mammals in the vicinity of the Torey lakes (Southeast Transbaikalia, Russia) were characterized between 2008 and 2017. The monitoring was carried out against the backdrop of the complete drying out of these largest lakes in the region. The stability of the fauna of small mammals was revealed over an 80-year period, although the structure of communities has changed significantly as a result of changes in moistening of the territory. Xerophilous species of mammals had an advantage in the period of studies in the dry climate phase. Correlation analysis showed a possible link between the population dynamics of some common species of small mammals with the precipitation amount of the current and previous years or with the precipitation amount of some spring (in one case, winter) months.

A transient metal Vanadium dioxide is known to have a coupled structural and electronic transition that can be accessed through light, thermal, or electrical excitation. Ultrafast optical studies of this insulator-to-metal transition indicate that it is mediated by the formation of a transient metallic phase that retains the structure of the original insulating phase. Sood et al. show that a similar sequence occurs when the material is electrically excited with a series of voltage pulses. Using ultrafast electron diffraction, the researchers monitored the structure of a vanadium dioxide sample after excitation and found evidence of a metastable metallic phase that appears during the transition. Science , abc0652, this issue p. 352

Although Mn-Ga alloys are discussed as novel permanent magnetic materials, there are several drawbacks, including the high price of Ga and the yet too small saturation magnetization to name a few. We used several guidelines to motivate the replacement of Ga by Sn to tackle these issues and explored the phase formation, structural and magnetic properties of a Mn 2.6 Ga 1− x Sn x alloy series. The structure of Sn-rich samples is dominated by the corresponding hexagonal and orthorhombic phases, while the structure of Ga-rich samples shows additional contributions from the tetragonal DO 22 structure. However, formation of the tetragonal phase happens only upon an appropriate annealing procedure. In contrast to the discussion in the literature, our experiments do not hint on the tetragonal DO 22 structure being metastable, but rather indicate the DO 22 structure being an equilibrium phase. In general, the experimentally found phase fractions impact on the magnetic properties and hard magnetic properties are downgraded very rapidly even if only a small amount of Ga is substituted by Sn. This indicates that the DO 22 phase found only in the Ga-rich samples is indeed the one which is most relevant for realization of high magnetic anisotropy.

The fragmentation of metals during megaplastic (severe) deformation is described in terms of a two-defect model. The process kinetics has been studied qualitatively. A general expression for the Lyapunov indices, which determine the stability of limiting (stationary) structures, is derived. Critical conditions for controlling parameters are found, and the diagrams that determine the stability of stationary states are constructed.

We investigate the unbiased model for money exchanges with collective debt limit: agents give at random time a dollar to one another as long as they have at least one dollar or they can borrow a dollar from a central bank if the bank is not empty. Surprisingly, this dynamics eventually leads to an asymmetric Laplace distribution of wealth (conjectured in [22] and shown formally in a recent work [18]). In this manuscript, we carry out a formal mean-field limit as the number of agents goes to infinity where we uncover a two-phase (ODE) dynamics. Convergence towards the unique equilibrium (two-sided geometric) distribution in the large time limit is also shown and the role played by the bank and debt (in terms of Gini index or wealth inequality) will be explored numerically as well., 25 pages, 7 figures

In the presence of an AC drive, multiterminal Josephson junctions exhibit the inverse AC Josephson effect, where the oscillations of the superconducting phase of each junction can lock onto one another or onto the external drive. The competition between these different phase locked states results in a complex array of quantized voltage plateaus whose stability strongly depend on the circuit parameters of the shunted junctions. This phase diagram cannot be explored with low temperature transport experiments alone, given the breadth of the parameter space, so we present an easily tunable analog circuit whose dynamical properties emulate those of a three terminal junction. We focus on the observation of the multiterminal inverse AC Josephson effect, and we discuss how to identify Shapiro steps associated with each of the three junctions as well as their quartet states. We only observe integer phase locked states in strongly overdamped networks, but fractional Shapiro steps appear as well when the quality factor of the junctions increases. Finally, we discuss the role of transverse coupling in the synchronization of the junctions., 11 pages, 7 figures

Bipedal walking is the most prevalent form of human locomotion — versatile, robust, and efficient. However, it is a form of motion few other animals share, and plantigrade bipedalism is fairly unique to our species. Plantigrade feet play an important role in shaping the fundamental gait dynamics, and understanding their role unlocks a huge potential for biomechanical insights for locomotion research, gait rehabilitation, and humanoid robotics. Still, a comprehensive functional model of the foot, which ties the fundamental dynamics of walking to the interaction of foot and ground, does not yet exist due to the inherent mechanical complexity. In this paper, we present a set of assumptions in detail to simplify the development of a mathematical description of the foot’s motion during stance phase in human walking. These assumptions are validated using experimental data. We can show that the complex motion of the foot can be ultimately reduced to a simple rotation, which allows the formulation of a single degree of freedom equation of motion that ties proximal dynamics and constraints into a planar foot model of dynamic interactions.

The study was carried out to evaluate the dynamics of monthly numbers of cases, deaths, tests and case fatality ratio worldwide during three phases of the COVID-19 pandemic. Material and methods: Twenty-three sets of databases, dated the 22nd of each month from January 2020 to November 2021, for 213 countries were collected from the Worldometer website. The number of cases, deaths, tests, case fatality ratio, infection fatality ratio, etc. were counted for various periods of time for each of the 213 countries, then the results related to different periods of time were compared. The analysis of main epidemiological parameters resulted in division of three phases of the global pandemic evolution. The first phase (23.01.20-22.07.20), the second phase (23.07.20-22.01.21) and the third phase (23.01.21-22.07.21) were different in terms of the number of tests performed, new cases and mortality due to COVID-19. By the end of second phase, the worldwide statistics indicated end of the pandemic, but the third phase was characterized by sudden rise in number of new cases and deaths. The most dramatic evolution of epidemic curve occurred in the countries where physicians had successfully confronted COVID-19 during the first two phases of the pandemic. Despite the decrease in the overall numbers deaths during the latest months analyzed, additional study is necessary to identify causes of new cases and deaths during the third phase of the pandemic. It can be suggested that preventive and therapeutic protocols should be changed from the 'standard' to 'personalized' types.

The Josephson equations predict remarkable effects concerning the phase state of a superconducting junction with an oscillating current induced by a static voltage. Whether the paradigm can be twisted by yielding an oscillating voltage without making use of harmonic drives is a fundamentally relevant problem yet not fully settled. Here, we demonstrate that a dynamical regime with an oscillating phase evolution is a general hallmark of driven Josephson systems exhibiting sign competition in the Josephson couplings. We show that in frustrated Josephson systems an oscillating phase dynamics gets switched on by driving the changeover among different ground states, which can be induced by varying the parameters that set the phase state. Remarkably, the character of the transitions in the Josephson phase space allows different types of dynamics, with few or several harmonics. This result sets out a characteristic mark of any superconducting system with frustrated Josephson couplings and can be exploited to disentangle the complexity of the underlying phases., 11 pages, 7 figures

Aneurysmal subarachnoid haemorrhage (SAH) is a devastating subset of stroke. One of the major determinates of morbidity is the development of delayed cerebral ischemia (DCI). Disruption of the nitric oxide (NO) pathway and consequently the control of cerebral blood flow (CBF), known as cerebral autoregulation, is believed to play a role in its pathophysiology. Through the pharmacological manipulation of in vivo NO levels using an exogenous NO donor we sought to explore this relationship.Phase synchronisation index (PSI), an expression of the interdependence between CBF and arterial blood pressure (ABP) and thus cerebral autoregulation, was calculated before and during sodium nitrite administration in 10 high-grade SAH patients acutely postrupture. In patients that did not develop DCI, there was a significant increase in PSI around 0.1 Hz during the administration of sodium nitrite (33%; p-value 0.006). In patients that developed DCI, PSI did not change significantly.Synchronisation between ABP and CBF at 0.1 Hz has been proposed as a mechanism by which organ perfusion is maintained, during periods of physiological stress. These findings suggest that functional NO depletion plays a role in impaired cerebral autoregulation following SAH, but the development of DCI may have a distinct pathophysiological aetiology.

Objective:We assessed the delay times in the interaction between the autonomic regulatory loop of Heart Rate Variability (HRV) and autonomic regulatory loop of photoplethysmographic waveform variability (PPGV), showing low-frequency oscillations.Material and Methods:In eight healthy subjects aged 25–30 years (3 male, 5 female), we studied at rest (in a supine position) the simultaneously recorded two-hour signals of RR intervals (RRIs) chain and finger photoplethysmogram (PPG). To extract the low-frequency components of RRIs and PPG signal, associated with the low-frequency oscillations in HRV and PPGV with a frequency of about 0.1 Hz, we filtered RRIs and PPG with a bandpass 0.05-0.15 Hz filter. We used a method for the detection of coupling between oscillatory systems, based on the construction of predictive models of instantaneous phase dynamics, for the estimation of delay times in the interaction between the studied regulatory loops.Results:Averaged value of delay time in coupling from the regulatory loop of HRV to the loop of PPGV was 0.9±0.4 seconds (mean ± standard error of the means) and averaged value of delay time in coupling from PPGV to HRV was 4.1±1.1 seconds.Conclusion:Analysis of two-hour experimental time series of healthy subjects revealed the presence of delay times in the interaction between regulatory loops of HRV and PPGV. Estimated delay time in coupling regulatory loops from HRV to PPGV was about one second or even less, while the delay time in coupling from PPGV to HRV was about several seconds. The difference in delay times is explained by the fact that PPGV to HRV response is mediated through the autonomic nervous system (baroreflex), while the HRV to PPGV response is mediated mechanically via cardiac output.

Purpose The ecological environment of the Loess Plateau, China, is extremely fragile under the context of global warming. Over the past two decades, the vegetation of the Loess Plateau has undergone great changes. This paper aims to clarify the response mechanisms of vegetation to climate change, to provide support for the restoration and environmental treatment of vegetation on the Loess Plateau. Design/methodology/approach The Savitsky–Golay (S-G) filtering algorithm was used to reconstruct time series of moderate resolution imaging spectroradiometer (MODIS) 13A2 data. Combined with trend analysis and partial correlation analysis, the influence of climate change on the phenology and enhanced vegetation index (EVI) during the growing season was described. Findings The S-G filtering algorithm is suitable for EVI reconstruction of the Loess Plateau. The date of start of growing season was found to gradually later along the Southeast–Northwest direction, whereas the date of the end of the growing season showed the opposite pattern and the length of the growing season gradually shortened. Vegetation EVI values decreased gradually from Southeast to Northwest. Vegetation changed significantly and showed clear differentiation according to different topographic factors. Vegetation correlated positively with precipitation from April to July and with temperature from August to November. Originality/value This study provides technical support for ecological environmental assessment, restoration of regional vegetation coverage and environmental governance of the Loess Plateau over the past two decades. It also provides theoretical support for the prediction model of vegetation phenology changes based on remote sensing data.

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase reduction of the hybrid system to derive an effective, dimensionality-reduced phase equation. We apply the reduced phase model to a periodically forced excitable system and two-coupled excitable systems, both undergoing noise-induced oscillations. The reduced phase model can quantitatively predict the entrainment of a single system to the periodic force and the mutual synchronization of two coupled systems, including the phase slipping behavior due to noise, as verified by Monte Carlo simulations. The derived phase model gives a simple and efficient description of noise-induced oscillations and can be applied to the analysis of more general cases.

Asymptotic AFM amplitude-phase dynamics is a powerful modeling tool for the development of AFM control systems and applications. We explain the model and demonstrate simple practical examples that can be easily programmed and analyzed using simulation tools such as Control and Simulation Loop (National Instruments) or Simulink (Mathworks). We first introduce asymptotic AFM models, then formulate their mathematical properties relevant to AFM, and provide examples of simulation for Hertz and Lennard-Jones tip-sample interaction forces. Material of this paper can be used to study and practice AFM dynamics in simulation, as well as for design of AFM model-based control modes and applications.

In this thesis, comprised of four publications, I investigated phase dynamics of visuomotor control in humans during upright stance in response to an oscillatory visual drive. For this purpose, I applied different versions of a ���moving room��� paradigm in virtual reality while stimulating human participants with anterior-posterior motion of their visual surround and analyzed their bodily responses. Human balance control constitutes a complex interplay of interdependent processes. The main sensory contributors include vision, vestibular input, and proprioception, with a dominant role attributed to vision. The purpose of the balance control system is to keep the body���s center of mass (COM) within a certain spatial range around the current base of support. Ever-changing environmental circumstances along with sensory noise cause the body to permanently sway around its point of equilibrium. Considering this sway, the human body can be modelled as a (multi-link) inverted pendulum. To maintain balance while being exposed to perturbations of the visual environment, humans adjust their sway to counteract the perceived motion of their bodies. Neurodegenerative diseases like Parkinson���s impair balance control and thus are likely to affect these mechanisms. Hence, investigation of bodily responses to a visual drive gives insight into visuomotor control in health and disease. In my first study, I introduced inter-trial phase coherence (ITPC) as a novel method to investigate postural responses to periodical visual stimulation. I found that human participants phase-locked the motion of their center of pressure (COP) to a 3-D dot cloud which oscillated in the anterior-posterior direction. This effect was equally strong for a low frequency of visual stimulation at 0.2 Hz and a high frequency of 1.5 Hz, the latter exceeding the previously assumed frequency range associated with coherent postural sway responses to periodical oscillations of the visual environment (moving room). Moreover, I was able to show that ITPC reliably captured responses in almost all participants, thereby addressing the common problem of inter-subject variability in body sway research. Based on the results of my first study, I concluded phase locking to be an essential feature in human postural control. For the second study, I introduced a mobile and cost-effective setup to apply a visual paradigm consisting of a virtual tunnel which stretched in the anterior-posterior direction and oscillated back and forth at three distinct frequencies (0.2 Hz, 0.8 Hz, and 1.2 Hz). Because tracking of the COP alone neglects crucial information about how COM shifts are arranged across the body, I included additional full-body motion tracking here to evaluate sway of individual body segments. Using a modified measure of phase locking, the phase locking value (PLV), allowed me to find participants phase-locking not only their COP, but also additional segments of their body to the visual drive. While their COP exhibited a strong phase locking to all frequencies of visual stimulation, distribution of phase locking across the body underwent a shift as the frequency of the visual stimulation increased. For the lowest frequency of 0.2 Hz, participants phase-locked almost their entire body to the stimulus. At higher frequencies, this phase locking shifted towards the lower torso and hip, with subjects almost exclusively phase-locking their hip to the visual drive at the highest frequency of 1.2 Hz. Having introduced a novel and reliable measurement along with a mobile setup, these results allowed me to empirically confirm shifts in postural strategies previously proposed in the literature. In the third study, a collaboration with the neurology department of the Universit��tsklinikum Gie��en und Marburg (UKGM), I used the same setup and paradigm as in the previous study and additionally derived the trajectory of the COM from a weighted combination of certain body segments. The aim was to investigate phase locking of body sway in a group of patients suffering from Parkinson���s disease (PD) to find potential means for an early diagnosis of the illness. For this purpose, I recruited a group of PD patients, an age-matched control group, and a group of young healthy adults. Even though the sway amplitude of PD patients was significantly larger than that of both other groups, they phase-locked their COP and COM in a similar manner as the control groups. However, considering individual body segments, the shift in PLV distribution differed between groups. While young healthy adults, analogous to the participants in the second study, exhibited a shift towards exclusive phase locking of their hips as frequency of the stimulation increased, both PD patients and age-matched controls maintained a rather homogeneous phase locking across their body. This suggested increased body stiffness, although being an effect of age rather than disease. Overall, I concluded that patients of early-to-mid stage PD exhibit impaired motor control, reflected in their increased sway amplitude, but intact visuomotor processing, indicated by their ability to phase-lock the motion of their body to a visual drive. The fourth study, to which I contributed as second author, used experimental data collected from an additional visual condition in the course of the third study. This condition consisted of unpredictable back and forward motion of the simulated tunnel. Here, we investigated the velocity profiles of the COP and COM in response to the unpredictable visual motion and a baseline condition at which the tunnel remained static. We found PD patients to exhibit larger velocities of their COP and COM under both conditions when compared to the control groups. When examining the net increase that unpredictable motion had on the velocity of both parameters, we found a significantly higher increase in COP velocity for both PD patients and age-matched controls, but no increase in COM velocity in any of the groups. These results suggested that all groups successfully maintained their balance under unpredictable visual perturbations, but that PD patients and older adults required more effort to accomplish this task, as reflected by the increased velocity of their COP. Again, these results indicated an effect of age rather than disease on the observed postural responses. In summary, using innovative phase-locking techniques and simultaneously tracking multiple body sway parameters, I was able to provide novel insight into visuomotor control in humans. First, I overcame previous issues of inconsistent sway parameters in groups of participants; Second, I found phase-locking to be an essential feature of visuomotor processing, which also allowed me to empirically confirm previously established theories of postural control; Third, through studies in collaboration with the neurology department of the UKGM, I was able to uncover new aspects of visuomotor processing in Parkinson���s, contributing to a better understanding of the sensorimotor aspects of the disease., Im Rahmen dieser Arbeit, welche sich aus vier experimentellen Studien zusammensetzt, habe ich das Phasenverhalten des menschlichen visuomotorischen Systems w��hrend des aufrechten Stands in Antwort auf visuelle Bewegungsreize untersucht. Hierf��r verwendete ich verschiedene Varianten des ���Moving Room���-Paradigmas, welches ich in virtueller Realit��t (VR) simulierte. W��hrend sich das visuelle Umfeld meiner Proband:innen in unterschiedlicher Weise in anterior-posteriorer (a-p) Richtung bewegte, zeichnete ich die K��rperbewegungen auf, mit denen sie darauf reagierten. Das Halten unseres Gleichgewichts w��hrend des aufrechten Stands bedarf eines komplexen Zusammenspiels vieler voneinander abh��ngiger Prozesse. Die wichtigsten Sinne, welche uns hierf��r zur Verf��gung stehen, sind unser Sehsinn, die Signale unseres Vestibularorgans (Gleichgewichtssinn) sowie unsere Propriozeption. Hierbei wird unserem Sehsinn eine dominante Rolle zugeschrieben. Die Aufgabe unseres sensomotorischen Systems ist es, unseren K��rperschwerpunkt (engl.: Center Of Mass, COM) in eine situationsabh��ngige Gleichgewichtsposition zu bringen und dort zu halten. Da sich unsere Umwelt fortlaufend ver��ndert und unsere Sinneseindr��cke mit einem Grundrauschen versehen sind, schwankt unser K��rper typischerweise kontinuierlich um diesen Gleichgewichtspunkt. In Bezug auf diese Bewegung kann der menschliche K��rper als umgedrehtes (mehrgliedriges) Pendel aufgefasst werden. Nehmen wir durch St��rungen unseres visuellen Umfelds eine Bewegung unseres K��rpers wahr, so regulieren wir besagtes Schwanken, um der wahrgenommenen Bewegung entgegenzuwirken. Neurodegenerative Krankheiten wie Morbus Parkinson beeintr��chtigen diese Mechanismen und somit einen stabilen aufrechten Stand. Aus diesem Grund erm��glichen Untersuchungen von K��rperbewegungen in Antwort auf visuelle Bewegungsreize Einblicke in die visuomotorische Verarbeitung in gesunden und neuropathologischen Populationen. In meiner ersten Studie f��hrte ich eine neue Methode der Datenanalyse ein, mit welcher ich die Phasenkoh��renz der k��rperlichen Antworten auf oszillatorische visuelle Bewegungsreize zwischen einzelnen Versuchsdurchl��ufen (engl.: Trials) untersuchte (engl.: Inter-trial Phase Coherence, ITPC). Ich fand heraus, dass menschliche Proband:innen die Phase der Bewegung ihres Druckschwerpunktes auf dem Boden (engl.: Center Of Pressure, COP) an den periodischen visuellen Reiz koppelten. Der Stimulus bestand aus einer 3-D Punktewolke, welche in a-p Richtung oszillierte. Diese Kopplung trat sowohl bei einer niedrigen Frequenz der visuellen Oszillation von 0,2 Hz als auch bei einer hohen Frequenz von 1,5 Hz auf. Dabei ��berstiegen die von mir gefundenen Kopplungen an die Frequenz von 1,5 Hz das bisher angenommene Spektrum koh��renter Antworten auf eine periodische Schwingung der Umwelt (���moving room���) bei menschlichen K��rperschwankungen. Ich konnte zeigen, dass ITPC als neue Analysemethode im Kontext von K��rperbewegungen erlaubt, verl��ssliche Antworten bei fast allen Proband:innen nachzuweisen, wodurch es mir zus��tzlich gelang, das in diesem Forschungsfeld g��ngige Problem einer hohen Varianz der Antworten ��ber Proband:innen hinweg zu adressieren. Meine Ergebnisse legen nahe, dass Phasenkopplung einen wichtigen Bestandteil der menschlichen Gleichgewichtskontrolle darstellt. Im Rahmen der zweiten Studie entwickelte ich einen neuen, mobilen und kosteng��nstigen Versuchsaufbau, um visuelle Bewegungsreize in virtueller Realit��t zu pr��sentieren und dabei K��rperbewegungen aufzuzeichnen. Das neue Versuchs-Paradigma bestand hier aus einem virtuellen Tunnel, welcher sich in die a-p Richtung erstreckte. Im Experiment oszillierte der Tunnel mit einer von drei verschiedenen Frequenzen (0,2 Hz; 0,8 Hz; 1,2 Hz) vor und zur��ck. Da ein alleiniges Aufzeichnen des COP unzureichende Informationen dazu liefert, wie Bewegungen des COM realisiert werden, implementierte ich zus��tzlich ein mit dem VR-Setup synchronisiertes video-basiertes Bewegungsmesssystem, welches mir erlaubte, die Bewegungsantworten des gesamten K��rpers aufzuzeichnen. In dieser Studie verwendete ich eine leicht modifizierte Analyse zu Phasenkopplungen, den sogenannten ���Phase-Coupling Value��� (PLV). Mithilfe dieser Analyse fand ich heraus, dass Proband:innen nicht nur die Bewegung ihres COP, sondern auch die Bewegung einzelner K��rpersegmente an die Phase des visuellen Reizes koppelten. W��hrend diese Kopplung im Falle des COP bei allen pr��sentierten Frequenzen deutlich vorhanden war, zeigten die Antworten bestimmter K��rperteile mit steigender Frequenz unterschiedlich starke Kopplungen. Bei der niedrigsten Frequenz von 0,2 Hz koppelten die Proband:innen die Phase der Bewegung ihres nahezu ganzen K��rpers an den visuellen Reiz. Mit steigender Frequenz konzentrierte sich die Phasenkopplung auf den unteren Torso und die H��fte, w��hrend die Proband:innen bei der h��chsten Frequenz von 1,2 Hz beinahe nur noch ausschlie��lich ihre H��ftbewegung an die Phase des Reizes koppelten. Mein neuartiger Versuchsaufbau und die Analysemethode der Phasenkopplung erm��glichten es mir somit, frequenzabh��ngige Bewegungsmuster als Antworten auf die visuellen Reize nachzuweisen, wodurch ich bestehende Theorien empirisch belegen konnte. In der dritten Studie, welche als Kollaboration mit der Klinik f��r Neurologie des Unversit��tsklinikums Gie��en und Marburg (UKGM) durchgef��hrt wurde, verwendete ich denselben Versuchsaufbau und das gleiche Paradigma wie in der vorherigen Studie. Zus��tzlich errechnete ich in dieser Studie die Trajektorie des COM als gewichtete Kombination bestimmter K��rpersegmente. Ziel dieser Studie war es, die Phasenkopplung von K��rperschwingungen in einer Gruppe von Parkinson-Patient:innen zu untersuchen, um langfristig dabei mitzuwirken, Methoden f��r eine m��gliche Fr��herkennung der Krankheit zu entwickeln. Zu diesem Zweck untersuchte ich eine Gruppe von Patient:innen, eine Gruppe von gleichaltrigen, gesunden Kontrollproband:innen sowie eine Gruppe von jungen, gesunden Erwachsenen. Patient:innen zeigten eine deutlich erh��hte Amplitude ihrer K��rperbewegungen, koppelten jedoch die Phase ihres COP und auch ihres COM in gleicher Weise an den Stimulus wie beide Kontrollgruppen. Eine Untersuchung der Bewegung einzelner K��rperteile ergab hier jedoch, dass die in der zweiten Studie beschriebenen Bewegungsmuster in Antwort auf h��here Frequenzen in den einzelnen Gruppen unterschiedlich waren. W��hrend die junge Kontrollgruppe, analog zu den Proband:innen meiner zweiten Studie, ihr Bewegungsmuster an die h��heren Frequenzen anpasste bzw. wechselte, behielten sowohl die Patient:innen als auch die gleichaltrige Kontrollgruppe ein eher homogenes Bewegungsmuster bei, auch bei den beiden h��heren Frequenzen des visuellen Reizes. Dies lie�� mich auf eine erh��hte k��rperliche Steifigkeit schlie��en, welche jedoch ein Effekt des Alters und nicht der Krankheit zu sein scheint. Generell folgerte ich aus den Ergebnissen dieser Studie, dass Parkinson-Patient:innen in fr��hen Stadien der Krankheit zwar eine beeintr��chtigte Motorik zeigen, was sich in ihrer erh��hten Bewegungsamplitude widerspiegelt, sie jedoch keine Beeintr��chtigung in ihrer visuomotorischen Verarbeitung aufweisen, da sie prinzipiell noch immer in der Lage sind, die Phase ihrer K��rperbewegung an den visuellen Reiz zu koppeln. In der vierten Studie, in welcher ich als Zweitautor mitwirkte, nutzten wir Daten, welche wir in einem in der dritten Studie zus��tzlich verwendeten Paradigma erhoben hatten. Dieses Paradigma bestand aus einer kontinuierlichen, aber unvorhersehbaren a-p Bewegung des virtuellen Tunnels. Anhand dieser Daten untersuchten wir die Geschwindigkeitsprofile des COP und COM in Antwort auf die unvorhersehbare Bewegung sowie auf eine Kontrollbedingung, w��hrend welcher der Tunnel stillstand. Patient:innen zeigten im Vergleich zu den Kontrollgruppen erh��hte Geschwindigkeiten beider Parameter (COP und COM) unter beiden visuellen Bedingungen. Untersuchungen der Geschwindigkeitserh��hung beider Parameter als Effekt der unvorhersehbaren Bewegung des Tunnels ergaben einen Anstieg der mittleren Geschwindigkeit des COP bei Patient:innen und der gleichaltrigen Kontrollgruppe, jedoch keine Ver��nderung bei der jungen Kontrollgruppe. Die mittlere Geschwindigkeit des COM ��nderte sich bei keiner der Gruppen. Dies lie�� uns schlussfolgern, dass alle Gruppen bei unvorhersehbaren St��rungen ihres visuellen Umfelds in der Lage waren, ihr Gleichgewicht zu halten. Jedoch mussten Patient:innen und ��ltere Kontrollproband:innen hierf��r einen gesteigerten Aufwand betreiben, was sich in der erh��hten mittleren Geschwindigkeit ihres COP zeigte. Die Ergebnisse dieser Studie zeigten erneut einen Alters-, jedoch keinen Krankheits-Effekt. Zusammenfassend kann gesagt werden, dass meine neu in der Forschung zu Stand- und Gangverhalten eingef��hrte Analysemethode der Phasenkopplung sowie das gleichzeitige Aufzeichnen mehrerer Bewegungsparameter es mir erlaubten, neue Erkenntnisse ��ber die visuomotorische Verarbeitung beim Menschen zu gewinnen. Zum einen konnte ich g��ngige Probleme von inkonsistenten Bewegungsantworten innerhalb von untersuchten Personengruppen ��berwinden. Zum anderen konnte ich zeigen, dass Phasenkopplung ein essenzieller Bestandteil der visuomotorischen Verarbeitung zu sein scheint, was mir zus��tzlich erm��glichte, bestehende Theorien der posturalen Kontrolle beim Menschen empirisch zu best��tigen. Zus��tzlich konnte ich durch Studien in Kollaboration mit der Klinik f��r Neurologie des UKGM neue Aspekte der visuomotorischen Verarbeitung bei Morbus Parkinson untersuchen, wodurch ich zu einem besseren Verst��ndnis von sensomotorischen Aspekten der Krankheit beitragen konnte.

In this thesis, comprised of four publications, I investigated phase dynamics of visuomotor control in humans during upright stance in response to an oscillatory visual drive. For this purpose, I applied different versions of a ‘moving room’ paradigm in virtual reality while stimulating human participants with anterior-posterior motion of their visual surround and analyzed their bodily responses. Human balance control constitutes a complex interplay of interdependent processes. The main sensory contributors include vision, vestibular input, and proprioception, with a dominant role attributed to vision. The purpose of the balance control system is to keep the body’s center of mass (COM) within a certain spatial range around the current base of support. Ever-changing environmental circumstances along with sensory noise cause the body to permanently sway around its point of equilibrium. Considering this sway, the human body can be modelled as a (multi-link) inverted pendulum. To maintain balance while being exposed to perturbations of the visual environment, humans adjust their sway to counteract the perceived motion of their bodies. Neurodegenerative diseases like Parkinson’s impair balance control and thus are likely to affect these mechanisms. Hence, investigation of bodily responses to a visual drive gives insight into visuomotor control in health and disease. In my first study, I introduced inter-trial phase coherence (ITPC) as a novel method to investigate postural responses to periodical visual stimulation. I found that human participants phase-locked the motion of their center of pressure (COP) to a 3-D dot cloud which oscillated in the anterior-posterior direction. This effect was equally strong for a low frequency of visual stimulation at 0.2 Hz and a high frequency of 1.5 Hz, the latter exceeding the previously assumed frequency range associated with coherent postural sway responses to periodical oscillations of the visual environment (moving room). Moreover, I was able to show that ITPC reliably captured responses in almost all participants, thereby addressing the common problem of inter-subject variability in body sway research. Based on the results of my first study, I concluded phase locking to be an essential feature in human postural control. For the second study, I introduced a mobile and cost-effective setup to apply a visual paradigm consisting of a virtual tunnel which stretched in the anterior-posterior direction and oscillated back and forth at three distinct frequencies (0.2 Hz, 0.8 Hz, and 1.2 Hz). Because tracking of the COP alone neglects crucial information about how COM shifts are arranged across the body, I included additional full-body motion tracking here to evaluate sway of individual body segments. Using a modified measure of phase locking, the phase locking value (PLV), allowed me to find participants phase-locking not only their COP, but also additional segments of their body to the visual drive. While their COP exhibited a strong phase locking to all frequencies of visual stimulation, distribution of phase locking across the body underwent a shift as the frequency of the visual stimulation increased. For the lowest frequency of 0.2 Hz, participants phase-locked almost their entire body to the stimulus. At higher frequencies, this phase locking shifted towards the lower torso and hip, with subjects almost exclusively phase-locking their hip to the visual drive at the highest frequency of 1.2 Hz. Having introduced a novel and reliable measurement along with a mobile setup, these results allowed me to empirically confirm shifts in postural strategies previously proposed in the literature. In the third study, a collaboration with the neurology department of the Universitätsklinikum Gießen und Marburg (UKGM), I used the same setup and paradigm as in the previous study and additionally derived the trajectory of the COM from a weighted combination of certain body segments. The aim was to investigate phase locking of body sway in a group of patients suffering from Parkinson’s disease (PD) to find potential means for an early diagnosis of the illness. For this purpose, I recruited a group of PD patients, an age-matched control group, and a group of young healthy adults. Even though the sway amplitude of PD patients was significantly larger than that of both other groups, they phase-locked their COP and COM in a similar manner as the control groups. However, considering individual body segments, the shift in PLV distribution differed between groups. While young healthy adults, analogous to the participants in the second study, exhibited a shift towards exclusive phase locking of their hips as frequency of the stimulation increased, both PD patients and age-matched controls maintained a rather homogeneous phase locking across their body. This suggested increased body stiffness, although being an effect of age rather than disease. Overall, I concluded that patients of early-to-mid stage PD exhibit impaired motor control, reflected in their increased sway amplitude, but intact visuomotor processing, indicated by their ability to phase-lock the motion of their body to a visual drive. The fourth study, to which I contributed as second author, used experimental data collected from an additional visual condition in the course of the third study. This condition consisted of unpredictable back and forward motion of the simulated tunnel. Here, we investigated the velocity profiles of the COP and COM in response to the unpredictable visual motion and a baseline condition at which the tunnel remained static. We found PD patients to exhibit larger velocities of their COP and COM under both conditions when compared to the control groups. When examining the net increase that unpredictable motion had on the velocity of both parameters, we found a significantly higher increase in COP velocity for both PD patients and age-matched controls, but no increase in COM velocity in any of the groups. These results suggested that all groups successfully maintained their balance under unpredictable visual perturbations, but that PD patients and older adults required more effort to accomplish this task, as reflected by the increased velocity of their COP. Again, these results indicated an effect of age rather than disease on the observed postural responses. In summary, using innovative phase-locking techniques and simultaneously tracking multiple body sway parameters, I was able to provide novel insight into visuomotor control in humans. First, I overcame previous issues of inconsistent sway parameters in groups of participants; Second, I found phase-locking to be an essential feature of visuomotor processing, which also allowed me to empirically confirm previously established theories of postural control; Third, through studies in collaboration with the neurology department of the UKGM, I was able to uncover new aspects of visuomotor processing in Parkinson’s, contributing to a better understanding of the sensorimotor aspects of the disease.

Under consideration is the system of partial differential equations describing the dynamics of a two-phase medium. Exact partially invariant solutions of rank 1 and defect 1 of this system are obtained with respect to some four-dimensional subalgebras. The phenomenon of collapse (an instantaneous source) in a two-phase medium is described.

The problem of interval estimation of the time delay of the coupling between oscillatory systems from observed time series is considered. It is shown that the known asymptotic estimates based on the empirical model in the form of a system of first-order phase oscillators and the maximum likelihood formalism can lead to false inferences of the value of the time delay in two typical situations: 1) nonlinear low-dimensional systems whose phases are well-determined but, as a result of significant amplitude fluctuations, the phase approximation is insufficient for describing the dynamics and 2) systems whose phases are defined not quite well because of too large amplitude fluctuations. A method for empirical diagnostics of problematic situations and its modification (coarse estimation) providing a low probability of false inferences in these situation are proposed. The efficiency of the diagnostic criterion and coarse estimation suggested is demonstrated on reference systems with different dynamic properties (linear stochastic oscillators, van der Pol oscillators, and Ressler and Lorenz chaotic systems).

We investigate nonlinear phase dynamics of an ideal kink mode, induced by E × B flow. Here the phase is the cross phase (θ c) between perturbed stream function of velocity ( ϕ ˜ ) and magnetic field ( ψ ˜ ), i.e. θ c = θ ϕ − θ ψ . A dimensionless parameter, analogous to the Richardson number, R i = 16 γ kink 2 / ω ˆ E 2 (γ kink: the normalized growth rate of the pure kink mode; ω ˆ E : normalized E × B shearing rate) is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear. When R i > 1, θ c is locked to a fixed value, corresponding to the conventional eigenmode solution. When R i ≤ 1, θ c enters a phase slipping or oscillating state, corresponding to a nonmodal solution. The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E × B shear flow.

Josephson junctions with weak-links of exotic materials allow the elucidation of the Josephson effect in previously unexplored regimes. Further, such devices offer a direct probe of novel material properties, for example in the search for Majorana fermions. In this work, we report on DC and AC Josephson effect of high-mobility, hexagonal boron nitride (h-BN) encapsulated graphene Josephson junctions. On the application of RF radiation, we measure phase-locked Shapiro steps. An unexpected bistability between $\pm 1$ steps is observed with switching times on the order of seconds. A critical scaling of a bistable state is measured directly from the switching time, allowing for direct comparison to numerical simulations. We show such intermittent chaotic behavior is a consequence of the nonlinear dynamics of the junction and has a sensitive dependence on the current-phase relation. This work draws connections between nonlinear phenomena in dynamical systems and their implications for ongoing condensed matter experiments exploring topology and exotic physics.

The cytoskeleton of biological cells relies on a diverse population of motors, filaments, and binding proteins acting in concert to enable non-equilibrium processes ranging from mitosis to chemotaxis. The cytoskeleton’s versatile reconfigurability, programmed by interactions between its constituents, make it a foundational active matter platform. However, current active matter endeavors are limited largely to single force-generating components acting on a single substrate – far from the composite cytoskeleton in live cells. Here, we engineer actin-microtubule composites, driven by kinesin and myosin motors and tuned by crosslinkers, that restructure into diverse morphologies from interpenetrating filamentous networks to de-mixed amorphous clusters. Our Fourier analyses reveal that kinesin and myosin compete to delay kinesin-driven restructuring and suppress de-mixing and flow, while crosslinking accelerates reorganization and promotes actin-microtubule correlations. The phase space of non-equilibrium dynamics falls into three broad classes– slow reconfiguration, fast advective flow, and multi-mode ballistic dynamics – with structure-dynamics relations described by the relative contributions of elastic and dissipative responses to motor-generated forces.

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two-dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopic techniques provide access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established, it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, centroid molecular dynamics, and Ring Polymer Molecular Dynamics (RPMD), naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

The study was carried out to evaluate the dynamics of monthly numbers of cases, deaths, tests and case fatality ratio worldwide during three phases of the COVID-19 pandemic. Material and methods: Twenty-three sets of databases, dated the 22nd of each month from January 2020 to November 2021, for 213 countries were collected from the Worldometer website. The number of cases, deaths, tests, case fatality ratio, infection fatality ratio, etc. were counted for various periods of time for each of the 213 countries, then the results related to different periods of time were compared. The analysis of main epidemiological parameters resulted in division of three phases of the global pandemic evolution. The first phase (23.01.20-22.07.20), the second phase (23.07.20-22.01.21) and the third phase (23.01.21-22.07.21) were different in terms of the number of tests performed, new cases and mortality due to COVID-19. By the end of second phase, the worldwide statistics indicated imminent end of the pandemic, but the third phase was characterized by sudden rise in the number of new cases and deaths that could not be explained rationally. The most dramatic evolution of epidemic curve occurred in the countries where physicians had successfully confronted COVID-19 during the first two phases of the pandemic. Despite the decrease in the overall numbers deaths during the latest months analyzed, additional study is necessary to identify the cause of increasing in the number of new cases and deaths during the third phase of the pandemic. Presumably, there are several causes of negative evolution of the current pandemic, including over-reliance on polymerase chain reaction tests, application of non-specialized premises for quarantine and treatment, non-professional management, following therapeutic protocols applied in countries with high number of deaths, ignoring preventive treatment, and decreasing in mass and individual immunity. It can be suggested that the use of drugs modulating T-cell immunity is necessary, and preventive and therapeutic protocols should be changed from the 'standard' to 'personalized' types.