Return Map Research Articles

Assessment of Autonomic Nervous System Dysfunction in the Early Phase of Infection With SARS-CoV-2 Virus.

BackgroundWe are facing the outburst of coronavirus disease 2019 (COVID-19) defined as a serious, multisystem, disorder, including various neurological manifestations in its presentation. So far, autonomic dysfunction (AD) has not been reported in patients with COVID-19 infection.AimAssessment of AD in the early phase of infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2 virus).Patients and methodsWe analyzed 116 PCR positive COVID-19 patients. After the exclusion of 41 patients with associate diseases (CADG), partitioned to patients with diabetes mellitus, hypertension, and syncope, the remaining patients were included into a severe group (45 patients with confirmed interstitial pneumonia) and mild group (30 patients). Basic cardiovascular autonomic reflex tests (CART) were performed, followed by beat-to-beat heart rate variability (HRV) and systolic and diastolic blood pressure variability (BPV) analysis, along with baroreceptor sensitivity (BRS). Non-linear analysis of HRV was provided by Poincare Plot. Results were compared to 77 sex and age-matched controls.ResultsAD (sympathetic, parasympathetic, or both) in our study has been revealed in 51.5% of severe, 78.0% of mild COVID-19 patients, and the difference compared to healthy controls was significant (p = 0.018). Orthostatic hypotension has been established in 33.0% COVID-19 patients compared to 2.6% controls (p = 0.001). Most of the spectral parameters of HRV and BPV confirmed AD, most prominent in the severe COVID-19 group. BRS was significantly lower in all patients (severe, mild, CADG), indicating significant sudden cardiac death risk.ConclusionCardiovascular autonomic neuropathy should be taken into account in COVID-19 patients’ assessment. It can be an explanation for a variety of registered manifestations, enabling a comprehensive diagnostic approach and further treatment.

Classification of Fetal Heart Rate Based on Poincare Plot and LSTM

Fetal heart rate plays an essential role in maternal and fetal monitoring and fetal health detection. In this study, a method based on Poincare Plot and LSTM is proposed to realize the high performance classification of abnormal fetal heart rate. Firstly, the original fetal heart rate signal of CTU-UHB database is preprocessed via interpolation, then the sequential fetal heart rate signal is converted into Poincare Plot to obtain nonlinear characteristics of the signals, and then SquenzeNet is used to extract the features of Poincare Plot. Finally, the features extracted by SqueezeNet are classified by LSTM. And the accuracy, the true positive rate and the false positive rate are 98.00%, 100.00%, 92.30% respectively on 2 000 test set data. Compared with the traditional fetal heart rate classification method, all respects are improved. The method proposed in this study has good performance in CTU-UHB fetal monitoring database and has certain practical value in the clinical diagnosis of auxiliary fetal heart rate detection.

Analytic moduli for parabolic Dulac germs

This paper gives moduli of analytic classification for parabolic Dulac germs (that is, almost regular germs). Dulac germs appear as first return maps of hyperbolic polycycles. Their moduli are given by a sequence of Écalle–Voronin-type germs of analytic diffeomorphisms. The result is stated in a broader class of parabolic generalized Dulac germs having power- logarithmic asymptotic expansions. Bibliography: 23 titles.

Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law

Two numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a form adapted to the fixed-point method. The second algorithm relates to the computation of the elastoplastic consistent tangent matrix using a simple finite difference scheme. A first validation is performed on a nonlinear bar problem. The results obtained show that both numerical algorithms are very efficient and yield the exact solution. The proposed algorithms are applied to a two-dimensional rockfill dam loaded in plane strain. The elastoplastic tangent matrix is calculated by using the finite difference scheme for Mohr–Coulomb’s constitutive law. The results obtained with the developed algorithms are very close to those obtained via the commercial software PLAXIS. It should be noted that the algorithm’s code, developed under the Matlab environment, offers the possibility of modeling the construction phases (i.e., building layer by layer) by activating the different layers according to the imposed loading. This algorithmic and implementation framework allows to easily integrate other laws of nonlinear behaviors, including the Hardening Soil Model.

A variational minimization formulation for hydraulically induced fracturing in elastic-plastic solids

A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is modeled by means of a phase-field approach to fracture, plastic effects are taken into account by using a Drucker–Prager-type yield-criterion function. This yield-criterion function governs the plastic evolution of the fluid-solid mixture. Fluid storage and transport are described by a Darcy–Biot-type formulation. Thereby the fluid storage is decomposed into a contribution due to the elastic deformations and one due to the plastic deformations. A local return mapping scheme is used for the update of the plastic quantities. The global minimization structure demands a $$H(\mathrm{div})$$ -conforming finite-element formulation. Furthermore this is combined with an enhanced-assumed-strain formulation in order to overcome locking phenomena arising from the plastic deformations. The robustness and capabilities of the presented framework will be shown in a sequence of numerical examples.

Non‐linear behaviour of electron acoustic wave dynamics in a magnetized plasma with non‐thermal hot electrons

AbstractNon‐linear dynamical behaviour of electron acoustic waves (EAWs) is studied in a magnetized non‐thermal plasma (containing inertial cold electrons, inertialess hot electrons following non‐thermal distribution function, and static ions) via a fluid dynamical approach. A linear dispersion relation is derived and the propagation of two possible modes and their evolution are studied through the different plasma configuration parameters, such as non‐thermality and external magnetic field strength. In a non‐linear perturbation regime, a reductive perturbation technique is employed to derive the non‐linear evolution equation and the analysis is executed for travelling plane waves in terms of a non‐linear dynamical system to enlighten the numerous aspects of the phase space dynamics. The results of numerical simulation predict the existence of a wide class of non‐linear structures, namely solitonic, periodic, quasiperiodic, and chaotic depending upon different controlling plasma parameters. Also, Poincaré return map analysis confirms these non‐linear structures of the EAWs.

Mesh-independent damage model for trabecular bone fracture simulation and experimental validation.

We propose in this study a two-dimensional constitutive model for trabecular bone combining continuum damage with embedded strong discontinuity. The model is capable of describing the three failure phases of trabecular bone tissue which is considered herein as a quasi-brittle material with strains and rotations assumed to be small and without viscous, thermal or other non-mechanical effects. The finite element implementation of the present model uses constant strain triangle (CST) elements. The displacement jump vector is implicitly solved through a return mapping algorithm at the local (finite element) level, while the global equilibrium equations are dealt with by Newton-Raphson method. The performance, accuracy and applicability of the proposed model for trabecular bone fracture are evaluated and validated against experimental measurements. These comparisons include both global and local aspects through numerical simulations of three-point bending tests performed on 10 single bovine trabeculae in the quasi-static regime.

Heart Rate Variability is Altered in College‐Aged Chronic Cannabis Users versus Non‐Users

Cannabis is an increasingly popular recreational drug among college students. Prior investigations have shown that acute cannabis use alters heart rate variability via increased sympathetic activation. However, the effects of chronic cannabis use on heart rate variability (HRV) have not been reported. PURPOSE We tested the hypothesis that HRV would be lower in chronic cannabis users (THC) compared to non-users (CON). METHODS Eleven cannabis users (age: 21±2 y, 2 females) and six controls (age: 20±2 y; 4 females) completed one study visit. Participants in the THC group self-reported using cannabis at least once per week for the past year or more. Participants in the CON reported to not use for 6 months prior to enrollment. Participants were instructed to abstain from alcohol for 24 h and cannabis for 72 h prior to the study visit. After 10 minutes of supine rest, heart rate (5-lead electrocardiogram) was continuously recorded at 1 kHz for 5 minutes of supine rest while participants breathed spontaneously. HRV was assessed using linear analysis via Fast Fourier transformation and non-linear analysis via Poincare plots. The root mean square of successive differences (RMSSD), percent of R-R intervals that differ by more than 50 ms (pRR50), and the standard deviation of R-R intervals (SDRR) were calculated to assess HRV in the time-domain. Fast Fourier transformation was used to assess HRV in the frequency domain (low-frequency (LF) and high-frequency (HF) power). Non-linear HRV analysis was performed using Poincare plots to calculate standard deviation 1 (SD1) and 2 (SD2). We used one-tailed unpaired t-tests to determine if the main outcome variables were different between groups. Values are reported as mean ± SD. RESULTS RRI was lower in THC (THC: 917±109 vs. CON: 1018±141 ms; P=0.06). RMSSD was lower in THC (THC: 57±21 vs. CON: 74±24 ms; P=0.07). There was no difference between groups for pRR50 (THC: 36±20 vs. CON: 47±21 %; P=0.12) or SDRR (THC: 68±16 vs. CON: 78±24 ms; P=0.15). LF power was not different between groups (THC: 1105±850 vs. CON: 1321±852 ms2; P=0.31), but HF power was lower in THC (THC: 1353±925 vs. CON: 2256±1195 ms2; P=0.05). SD1 was lower in THC (THC: 40±15 vs. CON: 53±17 ms; P=0.07). SD2 was not different between groups (THC: 86±19 vs. CON: 96±33 ms; P=0.23). CONCLUSION These preliminary data indicate that college-aged adults who regularly use cannabis have lower heart rate variability than their non-cannabis user counterparts. Based on linear and non-linear analyses, it appears that cannabis users have altered cardiac vagal activity at rest. However, more research is warranted to determine if cannabis use alters autonomic function and reactivity.

A division method for shallow tunnels and deep tunnels considering soil stress path dependency

Critical burial depth plays an important role in tunnel design and analysis. So, the division method for deep tunnels and shallow tunnels is perceived as a main concern. Considering the soil stress path dependency, this paper investigates the construction mechanical behavior of soil mass at different burial depths, and aims to explore a method for identifying critical burial depth. Firstly, using the Eulerian method and stress return mapping scheme, an elastoplastic algorithm applicable to double loading criteria was developed for a soil constitutive model considering complex stress paths. Then, the developed algorithm was implemented into a user-defined material subroutine (UMAT) and validated through numerical triaxial tests under different stress paths. Subsequently, the UMAT was used to model tunnel excavation in soils. The simulated results were compared with the results that from practical engineering, which shows that the UMAT could accurately predict the ground surface settlement. On the basis of this, the stress distribution and deformation performance in soil during tunneling at different burial depths were explored. Finally, the division method for differentiating shallow tunnels and deep tunnels in soil was discussed and a method for determining the critical depth was proposed.

Increased High Frequency Compared to Low Frequency Power in Heart Rate Variability in Parkinsonism

Heart rate variability (HRV) decreases in Parkinson’s disease which could be a consequence of reduced motor activity besides being a marker of cardiovascular dysautonomia. The diurnal low frequency power and high frequency power decrease in advanced Parkinsonism. In this case, there is decreased low frequency (LF) but high frequency (HF) is found to be very high compared to LF, which needs explanation. Multiple lobed pattern on Poincare plot in this case increases SD1, which has an analogy to HF, therefore HF is increased. If we remove premature beats from the recording while analysing, and then frame Poincare plot, it would be a normal torpedo pattern and HF value will be decreased in this case like LF, as is normally found in Parkinsonism, which would truly reflect the HRV values due to autonomic effects. HRV report should be interpreted for autonomic dysfunction when Poincare plot is torpedo pattern as other patterns may signify some intrinsic disease of heart.

Sliding homoclinic bifurcations in a Lorenz-type system: Analytic proofs.

Non-smooth systems can generate dynamics and bifurcations that are drastically different from their smooth counterparts. In this paper, we study such homoclinic bifurcations in a piecewise-smooth analytically tractable Lorenz-type system that was recently introduced by Belykh et al. [Chaos 29, 103108 (2019)]. Through a rigorous analysis, we demonstrate that the emergence of sliding motions leads to novel bifurcation scenarios in which bifurcations of unstable homoclinic orbits of a saddle can yield stable limit cycles. These bifurcations are in sharp contrast with their smooth analogs that can generate only unstable (saddle) dynamics. We construct a Poincaré return map that accounts for the presence of sliding motions, thereby rigorously characterizing sliding homoclinic bifurcations that destroy a chaotic Lorenz-type attractor. In particular, we derive an explicit scaling factor for period-doubling bifurcations associated with sliding multi-loop homoclinic orbits and the formation of a quasi-attractor. Our analytical results lay the foundation for the development of non-classical global bifurcation theory in non-smooth flow systems.

Virtual Field Characterization for Ratcheting Effect Under Cyclic Loading

Ratcheting is an important mechanical behavior of metals and alloys, which is caused by the repeated accumulations of tensile and compressive strain in circle load. However, the current characterization methods of ratcheting effect are mostly based on standardized testing and uniform data, and more comprehensive field measurement data cannot be used. This paper focuses on how to make full use of field measurement data to characterize ratcheting effect and identify the corresponding kinematic constitutive. A nonlinear virtual field method that can invert the parameters of Chaboche constitutive from strain field data is proposed. And a return mapping strategy driven by iteration of internal variables is used to reconstruct the stress field, which ensures the convergence speed and global convergence in the black box search of the nonlinear virtual field method. By using the finite-element model to generate the strain field data, the numerical experiment shows that the ratchet path identified by the nonlinear virtual field algorithm is basically consistent with the prior ratchet path generated by the finite-element simulation. The adaptability of the algorithm to data density and noise amplitude was also verified: under lower data noise interference, more strain field training data makes the inversion results more accurate; but in the case of high sound amplitude, it is necessary to reduce the data size to obtain accurate fitting results of the ratchet path. By training the measured field data from 3D-digital image correlation, it is shown that the algorithm can also run effectively under the complex working conditions of non-uniform deformation.

Biped Walking Based on Stiffness Optimization and Hierarchical Quadratic Programming.

The spring-loaded inverted pendulum model is similar to human walking in terms of the center of mass (CoM) trajectory and the ground reaction force. It is thus widely used in humanoid robot motion planning. A method that uses a velocity feedback controller to adjust the landing point of a robot leg is inaccurate in the presence of disturbances and a nonlinear optimization method with multiple variables is complicated and thus unsuitable for real-time control. In this paper, to achieve real-time optimization, a CoM-velocity feedback controller is used to calculate the virtual landing point. We construct a touchdown return map based on a virtual landing point and use nonlinear least squares to optimize spring stiffness. For robot whole-body control, hierarchical quadratic programming optimization is used to achieve strict task priority. The dynamic equation is given the highest priority and inverse dynamics are directly used to solve it, reducing the number of optimizations. Simulation and experimental results show that a force-controlled biped robot with the proposed method can stably walk on unknown uneven ground with a maximum obstacle height of 5 cm. The robot can recover from a 5 Nm disturbance during walking without falling.

A THERMODYNAMIC CONSISTENT ELASTOPLASTIC FRACTIONAL TIME-DEPENDENT DAMAGE MODEL FOR ROCK-LIKE MATERIALS

This paper aims at presenting a thermodynamically consistent elastoplastic fractional time-dependent damage model for describing short- and long-term behaviors of rock-like materials. The model utilizes generalized potential theory with a yield criterion, a non-associated flow rule and an isotropic plastic hardening function for describing the evolution of plasticity. A time-dependent Lemaitre-type damage is introduced through fractional derivative considering the short- and long-term evolution of microstructure, which leads to progressive degradation of elastic modulus and failure strength of material. In this context, both instantaneous and delayed deformations shall be well described within the unique constitutive model. For practical application, an efficient and convergent semi-implicit return mapping (SRM) algorithm involving a plasticity-damage decoupling corrector is developed. The proposed model is finally adopted to predict the mechanical and deformation behavior of several types of rocks under different loading conditions in conventional or quasi-static (different loading strain rate) triaxial compression tests, creep tests and relaxation tests. Comparisons between model predictions and experimental data demonstrate that the proposed model has the capability to reproduce main features of short and long-term behaviors of rock-like materials.

Enhancement of Drucker-Prager yield model by adding corner points for pressure-dependent materials

To flexibly describe the pressure-dependent behaviors of materials, Drucker-Prager yield model is enhanced by introducing corner points. We call it piecewise Drucker-Prager (pDP) yield model. Constitutive model is derived by considering strain hardening with non-associative yield flows. Integration algorithm includes the return mapping to corner point. Consistent tangent operator is also formulated, and user material subroutine is written. It is demonstrated that the pDP model is effective in describing the pressure-dependent yield behavior of polymers.

Simultaneously iterative procedure based on block Newton method for elastoplastic problems

AbstractIn this article, the authors formulate elastoplastic problems as a coupled problem of the equilibrium equation and the yield condition at each material point, and develop a numerical procedure based on the block Newton method to solve the overall structure using the finite element discretization. For the integration of stress, the backward difference scheme is employed. In the conventional return mapping algorithm, the algorithmic tangent moduli are derived analytically so that it is consistent with local iterative calculation to determine internal variables. On the other hand, in the proposed block Newton method, the tangent moduli can be obtained algebraically by eliminating the internal variables, and the internal variables are also updated algebraically without local iterative calculation. The residual of the yield condition is incorporated into the linearized equilibrium equation. The proposed approach enables the errors of the equilibrium equation and the yield condition to decrease simultaneously. Some numerical examples show the validity and effectiveness of the proposed approach by comparing the results of the proposed approach with those of the conventional return mapping algorithm.

Study of heart rate recovery and cardiovascular autonomic modulation in healthy participants after submaximal exercise

Heart rate variability (HRV), blood pressure variability (BPV), and baroreflex sensitivity (BRS) provide important information on cardiovascular autonomic control. However, little is known about the reorganization of HRV, BPV, and BRS after aerobic exercise. While there is a positive relationship between heart rate (HR) recovery rate and cardiorespiratory fitness, it is unclear whether there is a relationship between cardiorespiratory fitness and reorganization of cardiovascular autonomic modulation during recovery. Thus, this study aimed to investigate whether cardiorespiratory fitness influences the cardiovascular autonomic modulation recovery, after a cardiopulmonary exercise test. Sixty men were assigned into groups according to their cardiorespiratory fitness: low cardiorespiratory fitness (LCF = VO2: 22–38 mL kg−1 min−1), moderate (MCF = VO2: 38–48 mL kg−1 min−1), and high (HCF = VO2 > 48 mL kg−1 min−1). HRV (linear and non-linear analysis) and BPV (spectral analysis), and BRS (sequence method) were performed before and after a cardiopulmonary exercise test. The groups with higher cardiorespiratory fitness had lower baseline HR values and HR recovery time after the cardiopulmonary exercise test. On comparing rest and recovery periods, the spectral analysis of HRV showed a decrease in low-frequency (LF) oscillations in absolute units and high frequency (HF) in absolute and normalized units. It also showed increases in LF oscillations of blood pressure. Nonlinear analysis showed a reduction in approximate entropy (ApEn) and in Poincare Plot parameters (SD1 and SD2), accompanied by increases in detrended fluctuation analysis (DFA) parameters α1 and α2. However, we did not find differences in cardiovascular autonomic modulation parameters and BRS in relation to cardiorespiratory fitness neither before nor after the cardiopulmonary test. We concluded that cardiorespiratory fitness does not affect cardiovascular autonomic modulations after cardiopulmonary exercise test, unlike HR recovery.

First Return Time to the contact hyperplane for $ N $-degree-of-freedom vibro-impact systems

<p style='text-indent:20px;'>The paper deals with the dynamics of conservative <inline-formula><tex-math id="M2">\begin{document}$ N $\end{document}</tex-math></inline-formula>-degree-of-freedom vibro-impact systems involving one unilateral contact condition and a linear free flow. Among all possible trajectories, grazing orbits exhibit a contact occurrence with vanishing incoming velocity which generates mathematical difficulties. Such problems are commonly tackled through the definition of a Poincaré section and the attendant First Return Map. It is known that the First Return Time to the Poincaré section features a square-root singularity near grazing. In this work, a non-orthodox yet natural and intrinsic Poincaré section is chosen to revisit the square-root singularity. It is based on the unilateral condition but is not transverse to the grazing orbits. A detailed investigation of the proposed Poincaré section is provided. Higher-order singularities in the First Return Time are exhibited. Also, activation coefficients of the square-root singularity for the First Return Map are defined. For the linear and periodic grazing orbits from which bifurcate nonlinear modes, one of these coefficients is necessarily non-vanishing. The present work is a step towards the stability analysis of grazing orbits, which still stands as an open problem.</p>

A thermomechanical constitutive model for porous SMAs accounting for the influence of void evolution

A new thermomechanical constitutive model is proposed for shape memory alloys (SMAs) with randomly distributed microscopic porosity. The influence of the microscopic voids on SMA behavior is accounted for by means of two scalar variables representing damage due to porosity and inelastic dilatation due to the expansion or shrinking of voids. Starting with a newly formulated expression of the Helmholtz free energy density, a general stress-strain relation is derived for porous SMAs. The relation features internal dissipative variables for which thermodynamically consistent flow rules are proposed. In particular, loading functions are obtained for variables representing the volume fraction of martensite, inelastic strain due to martensite detwinning and reorientation, as well as damage and inelastic dilatation caused by the presence and evolution of voids. Appropriate loading conditions and flow rules are then introduced in a way that satisfies the principles of thermodynamics. The model is numerically integrated using a multi-surface return mapping algorithm implemented in a finite element software. The integration procedure, including the formulation of the required time-discrete equations and the derivation of the material Jacobian are presented in detail. The developed model is validated by two sets of experimental results and one modeling work to good agreement. The model is then used for simulating reference stress-strain data taken from the literature, in addition to test cases showcasing the ability of the model to simulate complex structures in presence of non-proportional loading and strong stress gradients.

A time-stepping method for multibody systems with frictional impacts based on a return map and boundary layer theory

This work presents a new numerical integration method for determining dynamics of a class of multibody systems involving impact and friction. Specifically, these systems are subject to a set of equality constraints and can exhibit single frictional impact events. Such events are associated to significant numerical stiffness, appearing in the equations of motion. The new method is a time-stepping scheme, involving proper incorporation of a novel return mapping into an augmented Lagrangian formulation, developed recently for systems with bilateral constraints only. Namely, when an impact is detected during a time step, this map is applied at the end of the step in order to bring the system position back to the configuration manifold with the allowable motions. The construction of this map is based on the concept of Jacobi fields on non-flat manifolds. Moreover, once an impact event is detected, the post-impact state is determined by employing a combination of analytical and numerical tools. First, a proper coordinate transformation is performed, bringing the system into a new set of coordinates, which are suitable for describing the impact dynamics. In these coordinates, the dominant dynamics is described by a system of three equations of motion only, which are valid during the short contact interval. In addition, these equations are geometrically discretized by using appropriate cubic splines on the configuration manifold. In this way, the inherent numerical stiffness of the class of systems examined is properly addressed, since it is restricted to a space with a much smaller dimension and a much shorter time scale. Finally, the accuracy and efficiency of the new method is demonstrated by applying it to a selected set of mechanical examples.