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Functional autonomous systems often realize complex tasks by utilizing state machines comprised of discrete primitive behaviors and transitions between these behaviors. This architecture has been widely studied in the context of…
We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and…
It has been a long-standing materials science challenge to establish structure-property relations in amorphous solids. Here we introduce a rotation-variant local structure representation that enables different predictions for different…
The dynamics of soft mechanical metamaterials provides opportunities for many exciting engineering applications. Previous studies often use discrete systems, composed of rigid elements and nonlinear springs, to model the nonlinear dynamic…
Transition waves are common in multistable mechanical metamaterials, and the dynamics of weakly discrete transition waves under driving forces have been extensively discussed. However, as lattice effects become more pronounced, strongly…
With extensive variational simulations, dissipative quantum phase transitions in the sub-Ohmic spin-boson model are numerically studied in a dense limit of environmental modes. By employing a generalized trial wave function composed of…
Reverse engineering (RE) of user interfaces (UIs) plays an important role in software evolution. However, the large diversity of UI technologies and the need for UIs to be resizable make this challenging. We propose ReverseORC, a novel RE…
In this paper, non-orthogonal multiple access (NOMA) networks assisted by multiple intelligent reflecting surfaces (IRSs) with discrete phase shifts are investigated, in which each user device (UD) is served by an IRS to improve the quality…
Out-of-Time-Order Correlators (OTOCs) quantify quantum information scrambling, but their connection to localized phase-space structures, such as chemical transition states, requires formal development. We derive a leading-order…
Despite the fundamental importance of solid--solid transitions for metallurgy, ceramics, earth science, reconfigurable materials, and colloidal matter, the details of how materials transform between two solid structures are poorly…
Origami has recently emerged as a platform for building functional engineering systems with versatile characteristics that targeted niche applications. One widely utilized origami-based structure is known as the Kresling origami spring…
Structured State Space Models (SSMs), which are at the heart of the recently popular Mamba architecture, are powerful tools for sequence modeling. However, their theoretical foundation relies on a complex, multi-stage process of…
This paper focuses on the construction of differential-cascaded structures for control of nonlinear robot manipulators subjected to disturbances and unavailability of partial information of the desired trajectory. The proposed…
Legged robots have the potential to leverage obstacles to climb steep sand slopes. However, efficiently repositioning these obstacles to desired locations is challenging. Here we present DiffusiveGRAIN, a learning-based method that enables…
This paper investigates the nonlinear dynamics of stepping flexible frames under seismic excitation. The conventional iterative method of solution of peak quasi-dynamic displacement of stepping frames is not guaranteed to converge. To…
Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up…
Solid-solid phase transitions are ubiquitous in nature, but the kinetic pathway of anisotropic particle systems remains elusive, where the coupling between translational and rotational motions plays a critical role in various kinetic…
Many engineered physical processes exhibit nonlinear but asymptotically stable dynamics that converge to a finite set of equilibria determined by control inputs. Identifying such systems from data is challenging: stable dynamics provide…
Explicit Runge-Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial semidiscretisations can be used to obtain systems…
Turbulence transition often arises from a subcritical transition between bistable states characterized by invariant sets of deterministic dynamical systems, and such transitions can be triggered by system noise as rare events. In this…