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This paper focuses on the motion planning problem for the systems exhibiting both continuous and discrete behaviors, which we refer to as hybrid dynamical systems. First, the motion planning problem for hybrid systems is formulated using the hybrid equation framework, which is general to capture most hybrid systems. Second, a propagation algorithm template is proposed that describes a general framework to solve the motion planning problem for hybrid systems. Third, a rapidly-exploring random trees (RRT) implementation of the proposed algorithm template is designed to solve the motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HyRRT, randomly picks a state sample and extends the search tree by flow or jump, which is also chosen randomly when both regimes are possible. Through a definition of concatenation of functions defined on hybrid time domains, we show that HyRRT is probabilistically complete, namely, the probability of failing to find a motion plan approaches zero as the number of iterations of the algorithm increases. This property is guaranteed under mild conditions on the data defining the motion plan, which include a relaxation of the usual positive clearance assumption imposed in the literature of classical systems. The motion plan is computed through the solution of two optimization problems, one associated with the flow and the other with the jumps of the system. The proposed algorithm is applied to an actuated bouncing ball system and a walking robot system so as to highlight its generality and computational features. 

Abstract Laser ablation is a process that bears both fundamental physics interest and has wide industrial applications. For decades, the lack of probes on the relevant time and length scales has prevented access to the highly nonequilibrium phase decomposition processes triggered by laser excitation. In this study, a close integration of time-resolved probing by intense femtosecond X-ray pulses with large-scale atomistic modeling has yielded unique insights into the ablation dynamics of thin gold films irradiated by femtosecond laser pulses. The emergence and growth of nanoscale density heterogeneities in the expanding ablation plume, predicted in the simulations, are mapped to the rapid evolution of distinct small angle diffraction features. This mapping enables identification of the characteristic signatures of different phase decomposition processes occurring simultaneously in the plume, which are driven by photomechanical and thermodynamic driving forces. Beyond the specific insights into the ablation phenomenon, this study demonstrates the power of joint X-ray probing and atomistic modeling of material dynamics under extreme conditions of thermal and mechanical nonequilibrium. 

Climate change leads to frequent extreme temperature events, making cities vulnerable to severe heatwaves. Therefore, this study aims to provide a systematic and overarching review of the urban planning and design policy interventions for heatwave management. This study used a series of key terms to search for relevant studies in three databases, including Web of Science, ScienceDirect, and Wiley, and then identified 28 articles published between 2007 and 2023 after several inclusion and exclusion criteria. After a systematic review, 15 policy interventions for heatwave management were summarized from the built environment level and building level. Cooling mechanisms and the scope of application were discussed. The results of this study provide policymakers with comprehensive guidance on sustainable urban design and planning for heatwave management. 

Abstract Phase change materials, which show different electrical characteristics across the phase transitions, have attracted considerable research attention for their potential electronic device applications. Materials with metal‐to‐insulator or charge density wave (CDW) transitions such as VO₂and 1T‐TaS₂have demonstrated voltage oscillations due to their robust bi‐state resistive switching behavior with some basic neuronal characteristics. BaTiS₃is a small bandgap ternary chalcogenide that has recently reported the emergence of CDW order below 245 K. Here, the discovery of DC voltage / current‐induced reversible threshold switching in BaTiS₃devices between a CDW phase and a room temperature semiconducting phase is reported. The resistive switching behavior is consistent with a Joule heating scheme and sustained voltage oscillations with a frequency of up to 1 kHz are demonstrated by leveraging the CDW phase transition and the associated negative differential resistance. Strategies of reducing channel sizes and improving thermal management may further improve the device's performance. The findings establish BaTiS₃as a promising CDW material for future electronic device applications, especially for energy‐efficient neuromorphic computing.