ASU Scholarship Showcase

Dexterous manipulation relies on modulation of digit forces as a function of digit placement. However, little is known about the sense of position of the vertical distance between finger pads relative to each other. We quantified subjects' ability to match perceived vertical distance between the thumb and index finger pads (d_y) of the right hand (“reference” hand) using the same or opposite hand (“test” hand) after a 10-second delay without vision of the hands. The reference hand digits were passively placed non-collinearly so that the thumb was higher or lower than the index finger (d_y = 30 or –30 mm, respectively) or collinearly (d_y = 0 mm). Subjects reproduced reference hand d_y by using a congruent or inverse test hand posture while exerting negligible digit forces onto a handle. We hypothesized that matching error (reference hand d_y minus test hand d_y) would be greater (a) for collinear than non-collinear d_ys, (b) when reference and test hand postures were not congruent, and (c) when subjects reproduced dy using the opposite hand. Our results confirmed our hypotheses. Under-estimation errors were produced when the postures of reference and test hand were not congruent, and when test hand was the opposite hand. These findings indicate that perceived finger pad distance is reproduced less accurately (1) with the opposite than the same hand and (2) when higher-level processing of the somatosensory feedback is required for non-congruent hand postures. We propose that erroneous sensing of finger pad distance, if not compensated for during contact and onset of manipulation, might lead to manipulation performance errors as digit forces have to be modulated to perceived digit placement.

Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems.

The phenomenon of Fano resonance is ubiquitous in a large variety of wave scattering systems, where the resonance profile is typically asymmetric. Whether the parameter characterizing the asymmetry should be complex or real is an issue of great experimental interest. Using coherent quantum transport as a paradigm and taking into account of the collective contribution from all available scattering channels, we derive a universal formula for the Fano-resonance profile. We show that our formula bridges naturally the traditional Fano formulas with complex and real asymmetry parameters, indicating that the two types of formulas are fundamentally equivalent (except for an offset). The connection also reveals a clear footprint for the conductance resonance during a dephasing process. Therefore, the emergence of complex asymmetric parameter when fitting with experimental data needs to be properly interpreted. Furthermore, we have provided a theory for the width of the resonance, which relates explicitly the width to the degree of localization of the close-by eigenstates and the corresponding coupling matrices or the self-energies caused by the leads. Our work not only resolves the issue about the nature of the asymmetry parameter, but also provides deeper physical insights into the origin of Fano resonance. Since the only assumption in our treatment is that the transport can be described by the Green’s function formalism, our results are also valid for broad disciplines including scattering problems of electromagnetic waves, acoustics, and seismology.

We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.

Most previous works on complete synchronization of chaotic oscillators focused on the one-channel interaction scheme where the oscillators are coupled through only one variable or a symmetric set of variables. Using the standard framework of master-stability function (MSF), we investigate the emergence of complex synchronization behaviors under all possible configurations of two-channel coupling, which include, for example, all possible cross coupling schemes among the dynamical variables. Utilizing the classic Rössler and Lorenz oscillators, we find a rich variety of synchronization phenomena not present in any previously extensively studied, single-channel coupling configurations. For example, in many cases two coupling channels can enhance or even generate synchronization where there is only weak or no synchronization under only one coupling channel, which has been verified in a coupled neuron system. There are also cases where the oscillators are originally synchronized under one coupling channel, but an additional synchronizable coupling channel can, however, destroy synchronization. Direct numerical simulations of actual synchronization dynamics verify the MSF-based predictions. Our extensive computation and heuristic analysis provide an atlas for synchronization of chaotic oscillators coupled through two channels, which can be used as a systematic reference to facilitate further research in this area.

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns the relativistic quantum manifestations of nonhyperbolic dynamics. We choose the mushroom billiard that has been mathematically proven to be nonhyperbolic, and study the resonant tunneling dynamics of a massless Dirac fermion. We find that the tunneling rate as a function of the energy exhibits a striking "clustering" phenomenon, where the majority of the values of the rate concentrate on a narrow region, as a result of the chaos component in the classical phase space. Relatively few values of the tunneling rate, however, spread outside the clustering region due to the integrable component. Resonant tunneling of electrons in nonhyperbolic chaotic graphene systems exhibits a similar behavior. To understand these numerical results, we develop a theoretical framework by combining analytic solutions of the Dirac equation in certain integrable domains and physical intuitions gained from current understanding of the quantum manifestations of chaos. In particular, we employ a theoretical formalism based on the concept of self-energies to calculate the tunneling rate and analytically solve the Dirac equation in one dimension as well as in two dimensions for a circular-ring-type of tunneling systems exhibiting integrable dynamics in the classical limit. Because relatively few and distinct classical periodic orbits are present in the integrable component, the corresponding relativistic quantum states can have drastically different behaviors, leading to a wide spread in the values of the tunneling rate in the energy-rate plane. In contrast, the chaotic component has embedded within itself an infinite number of unstable periodic orbits, which provide far more quantum states for tunneling. Due to the nature of chaos, these states are characteristically similar, leading to clustering of the values of the tunneling rate in a narrow band. The appealing characteristic of our work is a demonstration and physical understanding of the "mixed" role played by chaos and regular dynamics in shaping relativistic quantum tunneling dynamics.

The delicate tuning of digit forces to object properties can be disrupted by a number of neurological and musculoskeletal diseases. One such condition is Carpal Tunnel Syndrome (CTS), a compression neuropathy of the median nerve that causes sensory and motor deficits in a subset of digits in the hand. Whereas the effects of CTS on median nerve physiology are well understood, the extent to which it affects whole-hand manipulation remains to be addressed. CTS affects only the lateral three and a half digits, which raises the question of how the central nervous system integrates sensory feedback from affected and unaffected digits to plan and execute whole-hand object manipulation. We addressed this question by asking CTS patients and healthy controls to grasp, lift, and hold a grip device (445, 545, or 745 g) for several consecutive trials. We found that CTS patients were able to successfully adapt grip force to object weight. However, multi-digit force coordination in patients was characterized by lower discrimination of force modulation to lighter object weights, higher across-trial digit force variability, the consistent use of excessively large digit forces across consecutive trials, and a lower ability to minimize net moments on the object. Importantly, the mechanical requirement of attaining equilibrium of forces and torques caused CTS patients to exert excessive forces at both CTS-affected digits and digits with intact sensorimotor capabilities. These findings suggest that CTS-induced deficits in tactile sensitivity interfere with the formation of accurate sensorimotor memories of previous manipulations. Consequently, CTS patients use compensatory strategies to maximize grasp stability at the expense of exerting consistently larger multi-digit forces than controls. These behavioral deficits might be particularly detrimental for tasks that require fine regulation of fingertip forces for manipulating light or fragile objects.

Carpal tunnel syndrome (CTS) impairs sensation of a subset of digits. Although the effects of CTS on manipulation performed with CTS-affected digits have been studied using precision grip tasks, the extent to which CTS affects multi-digit force coordination has only recently been studied. Whole-hand manipulation studies have shown that CTS patients retain the ability to modulate multi-digit forces to object mass, mass distribution, and texture. However, CTS results in sensorimotor deficits relative to healthy controls, including significantly larger grip force and lower ability to balance the torques generated by the digits. Here we investigated the effects of CTS on multi-digit force modulation to object weight when manipulating an object with a variable number of fingers. We hypothesized that CTS patients would be able to modulate digit forces to object weight. However, as different grip types involve the exclusive use of CTS-affected digits (‘uniform’ grips) or a combination of CTS-affected and non-affected digits (‘mixed’ grips), we addressed the question of whether ‘mixed’ grips would reduce or worsen CTS-induced force coordination deficits. The former scenario would be due to adding digits with intact tactile feedback, whereas the latter scenario might occur due to a potentially greater challenge for the central nervous system of integrating ‘noisy’ and intact tactile feedback. CTS patients learned multi-digit force modulation to object weight regardless of grip type. Although controls exerted the same total grip force across all grip types, patients exerted significantly larger grip force than controls but only for manipulations with four and five digits. Importantly, this effect was due to CTS patients’ inability to change the finger force distribution when adding the ring and little fingers. These findings suggest that CTS primarily challenges sensorimotor integration processes for dexterous manipulation underlying the coordination of CTS-affected and non-affected digits.

Tactile perception is typically considered the result of cortical interpretation of afferent signals from a network of mechanical sensors underneath the skin. Yet, tactile illusion studies suggest that tactile perception can be elicited without afferent signals from mechanoceptors. Therefore, the extent that tactile perception arises from isomorphic mapping of tactile afferents onto the somatosensory cortex remains controversial. We tested whether isomorphic mapping of tactile afferent fibers onto the cortex leads directly to tactile perception by examining whether it is independent from proprioceptive input by evaluating the impact of different hand postures on the perception of a tactile illusion across fingertips. Using the Cutaneous Rabbit Effect, a well studied illusion evoking the perception that a stimulus occurs at a location where none has been delivered, we found that hand posture has a significant effect on the perception of the illusion across the fingertips. This finding emphasizes that tactile perception arises from integration of perceived mechanical and proprioceptive input and not purely from tactile interaction with the external environment.

Anticipatory force planning during grasping is based on visual cues about the object’s physical properties and sensorimotor memories of previous actions with grasped objects. Vision can be used to estimate object mass based on the object size to identify and recall sensorimotor memories of previously manipulated objects. It is not known whether subjects can use density cues to identify the object’s center of mass (CM) and create compensatory moments in an anticipatory fashion during initial object lifts to prevent tilt. We asked subjects (n = 8) to estimate CM location of visually symmetric objects of uniform densities (plastic or brass, symmetric CM) and non-uniform densities (mixture of plastic and brass, asymmetric CM). We then asked whether subjects can use density cues to scale fingertip forces when lifting the visually symmetric objects of uniform and non-uniform densities. Subjects were able to accurately estimate an object’s center of mass based on visual density cues. When the mass distribution was uniform, subjects could scale their fingertip forces in an anticipatory fashion based on the estimation. However, despite their ability to explicitly estimate CM location when object density was non-uniform, subjects were unable to scale their fingertip forces to create a compensatory moment and prevent tilt on initial lifts. Hefting object parts in the hand before the experiment did not affect this ability. This suggests a dichotomy between the ability to accurately identify the object’s CM location for objects with non-uniform density cues and the ability to utilize this information to correctly scale their fingertip forces. These results are discussed in the context of possible neural mechanisms underlying sensorimotor integration linking visual cues and anticipatory control of grasping.