Transient dynamics of a one-dimensional Holstein polaron under the influence of an external electric field

Following the Dirac-Frenkel time-dependent variational principle, transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal exciton-phonon coupling in an external electric field is studied by employing the multi-D$_2$ {\it Ansatz}, also known as a superposition of the usual Davydov D$_2$ trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exciton-phonon coupling leads to a broadened exciton wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare exciton oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non-zero exciton current. For both scenarios, temporal periodicity is unchanged by exciton-phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite-sized ring within the anti-adiabatic regime. For strong diagonal coupling, the multi-$\rm D_2$ {\it Anstaz} is found to be highly accurate, and the phonon confinement gives rise to exciton localization and decay of the Bloch oscillations

Matricial Wasserstein-1 Distance

In this note, we propose an extension of the Wasserstein 1-metric ($W_1$) for matrix probability densities, matrix-valued density measures, and an unbalanced interpretation of mass transport. The key is using duality theory, in particular, a "dual of the dual" formulation of $W_1$. This matrix analogue of the Earth Mover's Distance has several attractive features including ease of computation.Comment: 8 page

Manipulation Planning for Forceful Human-Robot-Collaboration

This thesis addresses the problem of manipulation planning for forceful human-robot collaboration. Particularly, the focus is on the scenario where a human applies a sequence of changing external forces through forceful operations (e.g. cutting a circular piece off a board) on an object that is grasped by a cooperative robot. We present a range of planners that 1) enable the robot to stabilize and position the object under the human applied forces by exploiting supports from both the object-robot and object-environment contacts; 2) improve task efficiency by minimizing the need of configuration and grasp changes required by the changing external forces; 3) improve human comfort during the forceful interaction by optimizing the defined comfort criteria. We first focus on the instance of using only robotic grasps, where the robot is supposed to grasp/regrasp the object multiple times to keep it stable under the changing external forces. We introduce a planner that can generate an efficient manipulation plan by intelligently deciding when the robot should change its grasp on the object as the human applies the forces, and choosing subsequent grasps such that they minimize the number of regrasps required in the long-term. The planner searches for such an efficient plan by first finding a minimal sequence of grasp configurations that are able to keep the object stable under the changing forces, and then generating connecting trajectories to switch between the planned configurations, i.e. planning regrasps. We perform the search for such a grasp (configuration) sequence by sampling stable configurations for the external forces, building an operation graph using these stable configurations and then searching the operation graph to minimize the number of regrasps. We solve the problem of bimanual regrasp planning under the assumption of no support surface, enabling the robot to regrasp an object in the air by finding intermediate configurations at which both the bimanual and unimanual grasps can hold the object stable under gravity. We present a variety of experiments to show the performance of our planner, particularly in minimizing the number of regrasps for forceful manipulation tasks and planning stable regrasps. We then explore the problem of using both the object-environment contacts and object-robot contacts, which enlarges the set of stable configurations and thus boosts the robot’s capability in stabilizing the object under external forces. We present a planner that can intelligently exploit the environment’s and robot’s stabilization capabilities within a unified planning framework to search for a minimal number of stable contact configurations. A big computational bottleneck in this planner is due to the static stability analysis of a large number of candidate configurations. We introduce a containment relation between different contact configurations, to efficiently prune the stability checking process. We present a set of real-robot and simulated experiments illustrating the effectiveness of the proposed framework. We present a detailed analysis of the proposed containment relationship, particularly in improving the planning efficiency. We present a planning algorithm to further improve the cooperative robot behaviour concerning human comfort during the forceful human-robot interaction. Particularly, we are interested in empowering the robot with the capability of grasping and positioning the object not only to ensure the object stability against the human applied forces, but also to improve human experience and comfort during the interaction. We address human comfort as the muscular activation level required to apply a desired external force, together with the human spatial perception, i.e. the so-called peripersonal-space comfort during the interaction. We propose to maximize both comfort metrics to optimize the robot and object configuration such that the human can apply a forceful operation comfortably. We present a set of human-robot drilling and cutting experiments which verify the efficiency of the proposed metrics in improving the overall comfort and HRI experience, without compromising the force stability. In addition to the above planning work, we present a conic formulation to approximate the distribution of a forceful operation in the wrench space with a polyhedral cone, which enables the planner to efficiently assess the stability of a system configuration even in the presence of force uncertainties that are inherent in the human applied forceful operations. We also develop a graphical user interface, which human users can easily use to specify various forceful tasks, i.e. sequences of forceful operations on selected objects, in an interactive manner. The user interface ties in human task specification, on-demand manipulation planning and robot-assisted fabrication together. We present a set of human-robot experiments using the interface demonstrating the feasibility of our system. In short, in this thesis we present a series of planners for object manipulation under changing external forces. We show the object contacts with the robot and the environment enable the robot to manipulate an object under external forces, while making the most of the object contacts has the potential to eliminate redundant changes during manipulation, e.g. regrasp, and thus improve task efficiency and smoothness. We also show the necessity of optimizing human comfort in planning for forceful human-robot manipulation tasks. We believe the work presented here can be a key component in a human-robot collaboration framework

Finite-temperature time-dependent variation with multiple Davydov states

The Dirac-Frenkel time-dependent variational approach with Davydov Ans\"atze is a sophisticated, yet efficient technique to obtain an acuurate solution to many-body Schr\"odinger equations for energy and charge transfer dy- namics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperatures dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In or- der to demonstrate the applicability of this approach, we compare real-time quantum dynamics of the spin-boson model calculated with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ans\"atze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.Comment: 8 pages, 3 figure

Effect of microstructure on fatigue properties of hyperelastic materials

Homogenization is a technique for the analysis of complex materials by replacing them with equivalent homogeneous materials that exhibit similar properties. By constructing a three-dimensional (3D) porous material model and employing homogenization technique, effective properties of the hydrogel pore structure were calculated. It is found that the microstructure of hyperelastic materials has considerable influence on their macroscopic mechanical properties, pores with a radius of up to 65 microns at a small strain can significantly reinforce material structure and improve its fatigue resistance. This work highlights the potential of engineering pore structures for the enhancement of mchanical properties and durability of hydrogels

Hierarchical Equations-of-Motion Method for Momentum System-Bath Coupling

[Image: see text] For a broad class of quantum models of practical interest, we demonstrate that the Hamiltonian of the system nonlinearly coupled to a harmonic bath through the system and bath coordinates can be equivalently mapped into the Hamiltonian of the system bilinearly coupled to the bath through the system and bath momenta. We show that the Hamiltonian with bilinear system–bath momentum coupling can be treated by the hierarchical equations-of-motion (HEOM) method and present the corresponding proof-of-principle simulations. The developed methodology creates the opportunity to scrutinize a new family of nonlinear quantum systems by the numerically accurate HEOM method

Atomic-scale control of magnetic anisotropy via novel spin-orbit coupling effect in La2/3Sr1/3MnO3/SrIrO3 superlattices

Magnetic anisotropy (MA) is one of the most important material properties for modern spintronic devices. Conventional manipulation of the intrinsic MA, i.e. magnetocrystalline anisotropy (MCA), typically depends upon crystal symmetry. Extrinsic control over the MA is usually achieved by introducing shape anisotropy or exchange bias from another magnetically ordered material. Here we demonstrate a pathway to manipulate MA of 3d transition metal oxides (TMOs) by digitally inserting non-magnetic 5d TMOs with pronounced spin-orbit coupling (SOC). High quality superlattices comprised of ferromagnetic La2/3Sr1/3MnO3 (LSMO) and paramagnetic SrIrO3 (SIO) are synthesized with the precise control of thickness at atomic scale. Magnetic easy axis reorientation is observed by controlling the dimensionality of SIO, mediated through the emergence of a novel spin-orbit state within the nominally paramagnetic SIO.Comment: Proceedings of the National Academy of Sciences, May 201

An Information Perception-Based Emotion Contagion Model for Fire Evacuation

In fires, people are easier to lose their mind. Panic will lead to irrational behavior and irreparable tragedy. It has great practical significance to make contingency plans for crowd evacuation in fires. However, existing studies about crowd simulation always paid much attention on the crowd density, but little attention on emotional contagion that may cause a panic. Based on settings about information space and information sharing, this paper proposes an emotional contagion model for crowd in panic situations. With the proposed model, a behavior mechanism is constructed for agents in the crowd and a prototype of system is developed for crowd simulation. Experiments are carried out to verify the proposed model. The results showed that the spread of panic not only related to the crowd density and the individual comfort level, but also related to people’s prior knowledge of fire evacuation. The model provides a new way for safety education and evacuation management. It is possible to avoid and reduce unsafe factors in the crowd with the lowest cost