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The heart rate in humans is regulated by the autonomic nervous system, which modulates the frequency of heart contractions, resulting in heart rate variability (HRV). Therefore, to assess the activity of the autonomic nervous system, which contains important information for medical diagnostics, methods based on the analysis of interbeat interval variability are often used. This approach does not require the use of invasive methods for measuring the signals of the autonomic nervous system, but its accuracy is an open question. click here Using mathematical modeling, we investigate the possibility of extracting the signal of frequency modulation of the heartbeats from the electrocardiogram (ECG) signal and conduct a detailed comparison of the extracted signal with the real modulating signal. Since the quality of extraction of the signal of frequency modulation from the ECG depends on the method of demodulation, we compare two different approaches. One is based on the detection of the main oscillation rhythm and its bandpass filtering, and the other on the heterodyning technique. It is shown that low-frequency (LF) and high-frequency (HF) oscillations in HRV associated, respectively, with sympathetic and parasympathetic modulation by the autonomic nervous system, in the general case, significantly differ from the signals of frequency modulation of the heart rate in shape, but have close similarity with them in the frequency domain. We find that in model systems, the similarity of the LF component of HRV with sympathetic modulation of the heart rate is higher than the similarity of the HF component of HRV with parasympathetic modulation.In this work, we show how "chimera states," namely, the dynamical situation when synchronized and desynchronized domains coexist in an oscillator ensemble, can be controlled through a linear augmentation (LA) technique. Specifically, in the networks of coupled chaotic oscillators, we obtain chimera states through induced multistability and demonstrate how LA can be used to control the size and spatial location of the incoherent and coherent populations in the ensemble. We examine basins of attraction of the system to analyze the effects of LA on its multistable behavior and thus on chimera states. Stability of the synchronized dynamics is analyzed through a master stability function. We find that these results are independent of a system's initial conditions and the strategy is applicable to the networks of globally, locally as well as nonlocally coupled oscillators. Our results suggest that LA control can be an effective method to control chimera states and to realize a desired collective dynamics in such ensembles.Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of a driven suspension consisting of many particles. We consider a pair of particles which, to linear order in the force, do not interact hydrodynamically. If the system possesses an intrinsic property (such as the shape of the particles, their position with respect to a boundary, or the shape of the boundary) which is affected by the external forcing, hydrodynamic interactions that depend nonlinearly on the force may emerge. We study the general properties of such nonlinear response. Analysis of the symmetries under particle exchange and under force reversal leads to general conclusions concerning the appearance of relative translation and the motion's time reversibility. We demonstrate the applicability of the conclusions in three specific examples (a) two spheres driven parallel to a wall; (b) two deformable objects driven parallel to their connecting line; and (c) two spheres driven along a curved path. The breaking of time reversibility suggests a possible use of nonlinear hydrodynamic interactions to disperse or assemble particles by an alternating force.Using hydrodynamic simulations, we study the single polymers flowing through model porous media (close-packed colloidal crystal). In good solvent or high flow rates, the polymer transport is similar to gel electrophoresis, with size-dependent sieving for L_c/L≲1 and size-independent biased reptation for L_c/L≳1 (L_c is the polymer contour length and L is the diameter of colloids forming the porous media). Importantly, in bad solvent and low flow rates, the polymers show an extra window of size-dependent velocity for 1≲L_c/L≲2, where the polymer transport is controlled by a globule-stretch transition at pore throats, and the transport velocity is much slower than reptation.The internal flow and mixing properties inside deformable droplets, after reaching the steady state within two types of passive droplet traps, are visualized and analyzed as dynamical systems. The first droplet trap (constriction) is formed by three spheres arranged in an equilateral triangle, while the second consists of two parallel spherocylinders (capsules). The systems are assumed to be embedded in a uniform far-field flow at low Reynolds number, and the steady shapes and interfacial velocities on the drops are generated using the boundary-integral method. The internal velocity field is recovered by solving the internal Dirichlet problem, also via a desingularized boundary-integral method. Calculation of 2D streamlines within planes of symmetry reveals the internal equilibria of the flow. The type of each equilibrium is classified in 3D and their interactions probed using passive tracers and their Poincaré maps. For the two-capsule droplet, saddle points located on orthogonal symmetry planes influence the regular flow within the drop. For the three-sphere droplet, large regions of chaos are observed, embedded with simple periodic orbits. Flow is visualized via passive dyes, using material lines and surfaces. In 2D, solely the interface between two passive interior fluids is advected using an adaptive number of linked tracer particles. The reduction in dimension decreases the number of required tracer points, and also resolves arbitrarily thin filaments, in contrast to backward cell-mapping methods. In 3D, the advection of a material surface, bounded by the droplet interface, is enabled using an adaptive mesh scheme. Off-lattice 3D contour advection allows for highly resolved visualizations of the internal flow and quantification of the associated degree of mixing. Analysis of the time-dependent growth of material surfaces and 3D mixing numbers suggests the three-sphere droplet exhibits superior mixing properties compared to the two-capsule droplet.
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