Solutions to a cubic Schrödinger system with mixed attractive and repulsive forces in a critical regime

<abstract><p>We study the existence of solutions to the cubic Schrödinger system</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ -\Delta u_i = \sum\limits_{j = 1}^m \beta_{ij} u_j^2u_i + \lambda_i u_i\ \hbox{in}\ \Omega,\ u_i = 0\ \hbox{on}\ \partial\Omega,\ i = 1,\dots,m, $\end{document} </tex-math></disp-formula></p> <p>when $ \Omega $ is a bounded domain in $ \mathbb R^4, $ $ \lambda_i $ are positive small numbers, $ \beta_{ij} $ are real numbers so that $ \beta_{ii} &gt; 0 $ and $ \beta_{ij} = \beta_{ji} $, $ i\neq j $. We assemble the components $ u_i $ in groups so that all the interaction forces $ \beta_{ij} $ among components of the same group are attractive, i.e., $ \beta_{ij} &gt; 0 $, while forces among components of different groups are repulsive or weakly attractive, i.e., $ \beta_{ij} &lt; \overline\beta $ for some $ \overline\beta $ small. We find solutions such that each component within a given group blows-up around the same point and the different groups blow-up around different points, as all the parameters $ \lambda_i $'s approach zero.</p></abstract>

Robust Walking Control of a Lower Limb Rehabilitation Exoskeleton Coupled with a Musculoskeletal Model via Deep Reinforcement Learning

Background: Few studies have systematically investigated robust controllers for lower limb rehabilitation exoskeletons (LLREs) that can safely and effectively assist users with a variety of neuromuscular disorders to walk with full autonomy. One of the key challenges for developing such a robust controller is to handle different degrees of uncertain human-exoskeleton interaction forces from the patients. Consequently, conventional walking controllers either are patient-condition specific or involve tuning of many control parameters, which could behave unreliably and even fail to maintain balance. Methods: We present a novel and robust controller for a LLRE based on a decoupled deep reinforcement learning framework with three independent networks, which aims to provide reliable walking assistance against various and uncertain human-exoskeleton interaction forces. The exoskeleton controller is driven by a neural network control policy that acts on a stream of the LLRE’s proprioceptive signals, including joint kinematic states, and subsequently predicts real-time position control targets for the actuated joints. To handle uncertain human-interaction forces, the control policy is trained intentionally with an integrated human musculoskeletal model and realistic human-exoskeleton interaction forces. Two other neural networks are connected with the control policy network to predict the interaction forces and muscle coordination. To further increase the robustness of the control policy, we employ domain randomization during training that includes not only randomization of exoskeleton dynamics properties but, more importantly, randomization of human muscle strength to simulate the variability of the patient’s disability. Through this decoupled deep reinforcement learning framework, the trained controller of LLREs is able to provide reliable walking assistance to the human with different degrees of neuromuscular disorders. Results and Conclusion: A universal, RL-based walking controller is trained and virtually tested on a LLRE system to verify its effectiveness and robustness in assisting users with different disabilities such as passive muscles (quadriplegic), muscle weakness, or hemiplegic conditions. An ablation study demonstrates strong robustness of the control policy under large exoskeleton dynamic property ranges and various human-exoskeleton interaction forces. The decoupled network structure allows us to isolate the LLRE control policy network for testing and sim-to-real transfer since it uses only proprioception information of the LLRE (joint sensory state) as the input. Furthermore, the controller is shown to be able to handle different patient conditions without the need for patient-specific control parameters tuning.

Efficient time–frequency approach for prediction of subway train-induced tunnel and ground vibrations

In this paper, an efficient time–frequency approach is presented for the prediction of subway train-induced tunnel and ground vibrations. The proposed approach involves two steps. In the first step, a time domain simulation of the vehicle–track subsystem is used to determine the track–tunnel interaction forces and, in the second step, the resulting forces are then applied to a 2.5 D FEM–PML model of the tunnel–soil system. There are two main aspects to the novelty and contribution of this work: First, the errors of the linearized Hertzian wheel–rail contact models in the calculation of the track–tunnel interaction forces are quantified by a comparison with the nonlinear Hertzian contact model. The results show that the relative errors are less than 2%. Second, an efficient time–frequency analysis framework is proposed, including the use of a strongly coupled model in the time domain solution and a 2.5 D FEM–PML model in the frequency–wavenumber domain solution. Finally, the accuracy and efficiency of the proposed approach are verified by comparison with a time-dependent 3 D approach, where three types of soil, i.e. soft, medium, and hard, are considered.

Analysis of Light Grip Influence on Standing Posture

Upright posture control and gait are essential for achieving autonomous daily living activities. Postural control of upright posture relies, among others, on the integration of various sensory information. In this context, light touch (LT) and light grip (LG) of a stationary object provide an additional haptic sensory input that helps to reduce postural sway. When LG was studied through the grasp of a cane, the sensory role of this assistive tool was often limited to a mediation interface. Its role was restricted to transmit the interaction forces between its tip and the ground to the hand. While most studies involve participants standing in an unstable way, such as the tandem stance, in this paper we study LG from a different perspective. We attached a handle of a cane firmly to a stationary support. Thus, we can focus on the role of the hand receptors in the LG mechanism. LG condition was ensured through the tactile information gathered by FSR sensors placed on the handle surface. Moreover, participants involved in our study stood in a usual way. The study involved twelve participants in an experiment composed of two conditions: standing relaxed while lightly gripping an equipped handle attached to the ground, and standing in the same way without gripping the handle. Spatial and frequency analyses confirmed the results reported in the literature with other approaches.

Conducting Medium Electrical Conductivity at High Current Density

The experimental research example of electrical characteristics of structurally heterogeneous thinlayer conductors (nickel, copper) at high current density (108--109 А/m2) is shown. This current density in conditions of the samples intensive cooling is sufficient for the process of irreversible, nonthermally activated deformation. The experiment results show that the conducting medium at high current density has essential nonlinearities expressed in nonlinear dependence of the samples electrical resistance from current density. With repeated current treatments of the samples the conductors' electrical resistivity decreases. The number of defects removed from the volume of material as a result of nickel foil treatment by electric current is estimated. It is shown that under conditions of highdensity direct electric current flow in microvolumes of homogeneous and inhomogeneous conducting media a volume charge can appear. The appearance of the volume charge in a conducting medium can be caused by interaction forces during the motion of electrons and ions. Due to the interaction forces between ions and electrons of basic material and impurities, additional local ionization occurs which is realized in nano-volumes of a conductor. In the case of heterogeneous medium, the volume charge depends on the nature of the specific conductivity distribution. In a homogeneous conductor the volume charge is proportional to the square of the current density in the sample

Adaptive Admittance Control Scheme with Virtual Reality Interaction for Robot-Assisted Lower Limb Strength Training

Muscle weakness is the primary impairment causing mobility difficulty among stroke survivors. Millions of people are unable to live normally because of mobility difficulty every year. Strength training is an effective method to improve lower extremity ability but is limited by the shortage of medical staff. Thus, this paper proposes a robot-assisted active training (RAAT) by an adaptive admittance control scheme with virtual reality interaction (AACVRI). AACVRI consists of a stiffness variable admittance controller, an adaptive controller, and virtual reality (VR) interactions. In order to provide human-robot reality interactions corresponding to virtual scenes, an admittance control law with variable stiffness term was developed to define the mechanics property of the end effector. The adaptive controller improves tracking performances by compensating interaction forces and dynamics model deviations. A virtual training environment including action following, event feedback, and competition mechanism is utilized for improving boring training experience and engaging users to maintain active state in cycling training. To verify controller performances and the feasibility of RAAT, experiments were conducted with eight subjects. Admittance control provides desired variable interactions along the trajectory. The robot responds to different virtual events by changing admittance parameters according to trigger feedbacks. Adaptive control ensures tracking errors at a low level. Subjects were maintained in active state during this strength training. Their physiological signals significantly increased, and interaction forces were at a high level. RAAT is a feasible approach for lower limb strength training, and users can independently complete high-quality active strength training under RAAT.