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- Language: English
- Creators: Ira A. Fulton Schools of Engineering
First, studying persistent currents in confined chaotic Dirac fermion systems with a ring geometry and an applied Aharonov-Bohm flux, unusual whispering-gallery modes with edge-dependent currents and spin polarization are identified. They can survive for highly asymmetric rings that host fully developed classical chaos. By sustaining robust persistent currents, these modes can be utilized to form a robust relativistic quantum two-level system.
Second, the quantized topological edge states in confined massive Dirac fermion systems exhibiting a remarkable reverse Stark effect in response to an applied electric field, and an electrically or optically controllable spin switching behavior are uncovered.
Third, novel wave scattering and transport in Dirac-like pseudospin-1 systems are reported. (a), for small scatterer size, a surprising revival resonant scattering with a peculiar boundary trapping by forming unusual vortices is uncovered. Intriguingly, it can persist in arbitrarily weak scatterer strength regime, which underlies a superscattering behavior beyond the conventional scenario. (b), for larger size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect. (c), in the far-field, an unexpected isotropic transport emerges at low energies.
Fourth, a geometric valley Hall effect (gVHE) originated from fractional singular Berry flux is revealed. It is shown that gVHE possesses a nonlinear dependence on the Berry flux with asymmetrical resonance features and can be considerably enhanced by electrically controllable resonant valley skew scattering. With the gVHE, efficient valley filtering can arise and these phenomena are robust against thermal fluctuations and disorder averaging.
My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points.
Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized.
In this paper, we present a Bayesian analysis for the Weibull proportional hazard (PH) model used in step-stress accelerated life testings. The key mathematical and graphical difference between the Weibull cumulative exposure (CE) model and the PH model is illustrated. Compared with the CE model, the PH model provides more flexibility in fitting step-stress testing data and has the attractive mathematical properties of being desirable in the Bayesian framework. A Markov chain Monte Carlo algorithm with adaptive rejection sampling technique is used for posterior inference. We demonstrate the performance of this method on both simulated and real datasets.
We describe mechanical metamaterials created by folding flat sheets in the tradition of origami, the art of paper folding, and study them in terms of their basic geometric and stiffness properties, as well as load bearing capability. A periodic Miura-ori pattern and a non-periodic Ron Resch pattern were studied. Unexceptional coexistence of positive and negative Poisson's ratio was reported for Miura-ori pattern, which are consistent with the interesting shear behavior and infinity bulk modulus of the same pattern. Unusually strong load bearing capability of the Ron Resch pattern was found and attributed to the unique way of folding. This work paves the way to the study of intriguing properties of origami structures as mechanical metamaterials.
Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.
We develop a completely data-driven approach to reconstructing coupled neuronal networks that contain a small subset of chaotic neurons. Such chaotic elements can be the result of parameter shift in their individual dynamical systems and may lead to abnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the network to a normal state. However, due to couplings among the nodes, the measured time series, even from non-chaotic neurons, would appear random, rendering inapplicable traditional nonlinear time-series analysis, such as the delay-coordinate embedding method, which yields information about the global dynamics of the entire network. Our method is based on compressive sensing. In particular, we demonstrate that identifying chaotic elements can be formulated as a general problem of reconstructing the nodal dynamical systems, network connections and all coupling functions, as well as their weights. The working and efficiency of the method are illustrated by using networks of non-identical FitzHugh–Nagumo neurons with randomly-distributed coupling weights.
X-ray tomography has provided a non-destructive means for microstructure characterization in three and four dimensions. A stochastic procedure to accurately reconstruct material microstructure from limited-angle X-ray tomographic projections is presented and its utility is demonstrated by reconstructing a variety of distinct heterogeneous materials and elucidating the information content of different projection data sets. A small number of projections (e.g. 20–40) are necessary for accurate reconstructions via the stochastic procedure, indicating its high efficiency in using limited structural information.
Numerous recent investigations have been devoted to the determination of the equilibrium phase behavior and packing characteristics of hard nonspherical particles, including ellipsoids, superballs, and polyhedra, to name but just a few shapes. Systems of hard nonspherical particles exhibit a variety of stable phases with different degrees of translational and orientational order, including isotropic liquid, solid crystal, rotator and a variety of liquid crystal phases. In this paper, we employ a Monte Carlo implementation of the adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations to ascertain with high precision the equilibrium phase behavior of systems of congruent Archimedean truncated tetrahedra over the entire range of possible densities up to the maximal nearly space-filling density. In particular, we find that the system undergoes two first-order phase transitions as the density increases: first a liquid–solid transition and then a solid–solid transition. The isotropic liquid phase coexists with the Conway–Torquato (CT) crystal phase at intermediate densities, verifying the result of a previous qualitative study [J. Chem. Phys. 2011, 135, 151101]. The freezing- and melting-point packing fractions for this transition are respectively ϕF = 0.496 ± 0.006 and ϕM = 0.591 ± 0.005.
At higher densities, we find that the CT phase undergoes another first-order phase transition to one associated with the densest-known crystal, with coexistence densities in the range ϕ ∈ [0.780 ± 0.002, 0.802 ± 0.003]. We find no evidence for stable rotator (or plastic) or nematic phases. We also generate the maximally random jammed (MRJ) packings of truncated tetrahedra, which may be regarded to be the glassy end state of a rapid compression of the liquid. Specifically, we systematically study the structural characteristics of the MRJ packings, including the centroidal pair correlation function, structure factor and orientational pair correlation function. We find that such MRJ packings are hyperuniform with an average packing fraction of 0.770, which is considerably larger than the corresponding value for identical spheres (≈ 0.64). We conclude with some simple observations concerning what types of phase transitions might be expected in general hard-particle systems based on the particle shape and which would be good glass formers.
Background: Styrene is an important building-block petrochemical and monomer used to produce numerous plastics. Whereas styrene bioproduction by Escherichia coli was previously reported, the long-term potential of this approach will ultimately rely on the use of hosts with improved industrial phenotypes, such as the yeast Saccharomyces cerevisiae.
Results: Classical metabolic evolution was first applied to isolate a mutant capable of phenylalanine over-production to 357 mg/L. Transcription analysis revealed up-regulation of several phenylalanine biosynthesis pathway genes including ARO3, encoding the bottleneck enzyme DAHP synthase. To catalyze the first pathway step, phenylalanine ammonia lyase encoded by PAL2 from A. thaliana was constitutively expressed from a high copy plasmid. The final pathway step, phenylacrylate decarboxylase, was catalyzed by the native FDC1. Expression of FDC1 was naturally induced by trans-cinnamate, the pathway intermediate and its substrate, at levels sufficient for ensuring flux through the pathway. Deletion of ARO10 to eliminate the competing Ehrlich pathway and expression of a feedback-resistant DAHP synthase encoded by ARO4[subscript K229L] preserved and promoted the endogenous availability precursor phenylalanine, leading to improved pathway flux and styrene production. These systematic improvements allowed styrene titers to ultimately reach 29 mg/L at a glucose yield of 1.44 mg/g, a 60% improvement over the initial strain.
Conclusions: The potential of S. cerevisiae as a host for renewable styrene production has been demonstrated. Significant strain improvements, however, will ultimately be needed to achieve economical production levels.