Perturbations of time optimal control problems for a class of abstract parabolic systems

In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application to PDEs systems concerns the behavior of optimal time and of the associated optimal controls for parabolic equations with highly oscillating coefficients, as we encounter in homogenization theory. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the solutions of the time optimal control problems for the systems with oscillating coefficients converge, in the usual norms, to the solution of the corresponding problem for the homogenized system. In order to prove our main theorem, we provide several new results, which could be of a broader interest, on time and norm optimal control problems

Diffusion Dynamics, Moments, and Distribution of First Passage Time on the Protein-Folding Energy Landscape, with Applications to Single Molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We obtain information for the first passage-time (FPT) distribution and its moments. The results show a dynamic transition temperature below which the FPT distribution develops a power-law tail, a signature of the intermittency phenomena of the folding dynamics. We also discuss the possible application of the results to single-molecule dynamics experiments

A laser based differential power method for measuring the natural frequency of vibrations in a plastic string

The laser based non-contact and high bandwidth technique was developed to measure the natural frequency of vibrations in a thin string. The string, which is caused to vibrate by a piezoelectric actuator, was located in the middle of a beam of light from a laser. Changes in the power of the laser light resulting from micro-vibrations of the string were measured by a two-quadrant photo sensor. Tennis racket strings were selected for use in this experiment and vibrations were generated over a range of different frequencies to validate the laser measurement system. The results showed that the measured signals, which for analysis were subject to Fast Fourier Transformation, were coincident with the input frequency. Finally, the natural frequencies of strings subjected to different tension force were measured and analyzed to determine the validity of the method. The results showed a relative error of less than 0.6 %

Self-Supervised Ensemble Learning: A Universal Method for Phase Transition Classification of Many-Body Systems

We develop a self-supervised ensemble learning (SSEL) method to accurately classify distinct types of phase transitions by analyzing the fluctuation properties of machine learning outputs. Employing the 2D Potts model and the 2D Clock model as benchmarks, we demonstrate the capability of SSEL in discerning first-order, second-order, and Berezinskii-Kosterlitz-Thouless transitions, using in-situ spin configurations as the input features. Furthermore, we show that the SSEL approach can also be applied to investigate quantum phase transitions in 1D Ising and 1D XXZ models upon incorporating quantum sampling. We argue that the SSEL model simulates a special state function with higher-order correlations between physical quantities, and hence provides richer information than previous machine learning methods. Consequently, our SSEL method can be generally applied to the identification/classification of phase transitions even without explicit knowledge of the underlying theoretical models

New class of 3D topological insulator in double perovskite

We predict a new class of three-dimensional topological insulators (TIs) in which the spin-orbit coupling (SOC) can more effectively generate a large band gap at $\Gamma$ point. The band gap of conventional TI such as Bi$_2$Se$_3$ is mainly limited by two factors, the strength of SOC and, from electronic structure perspective, the band gap when SOC is absent. While the former is an atomic property, we find that the latter can be minimized in a generic rock-salt lattice model in which a stable crossing of bands {\it at} the Fermi level along with band character inversion occurs for a range of parameters in the absence of SOC. Thus, large-gap TI's or TI's comprised of lighter elements can be expected. In fact, we find by performing first-principle calculations that the model applies to a class of double perovskites A$_2$BiXO$_6$ (A = Ca, Sr, Ba; X = Br, I) and the band gap is predicted up to 0.55 eV. Besides, more detailed calculations considering realistic surface structure indicate that the Dirac cones are robust against the presence of dangling bond at the boundary with a specific termination.Comment: submitted; title changed and new references added; see DOI for published versio

A Comparative Study on Spin-Orbit Torque Efficiencies from W/ferromagnetic and W/ferrimagnetic Heterostructures

It has been shown that W in its resistive form possesses the largest spin-Hall ratio among all heavy transition metals, which makes it a good candidate for generating efficient dampinglike spin-orbit torque (DL-SOT) acting upon adjacent ferromagnetic or ferrimagnetic (FM) layer. Here we provide a systematic study on the spin transport properties of W/FM magnetic heterostructures with the FM layer being ferromagnetic Co$_{20}$Fe$_{60}$B$_{20}$ or ferrimagnetic Co$_{63}$Tb$_{37}$ with perpendicular magnetic anisotropy. The DL-SOT efficiency $|\xi_{DL}|$, which is characterized by a current-induced hysteresis loop shift method, is found to be correlated to the microstructure of W buffer layer in both W/Co$_{20}$Fe$_{60}$B$_{20}$ and W/Co$_{63}$Tb$_{37}$ systems. Maximum values of $|\xi_{DL}|\approx 0.144$ and $|\xi_{DL}|\approx 0.116$ are achieved when the W layer is partially amorphous in the W/Co$_{20}$Fe$_{60}$B$_{20}$ and W/Co$_{63}$Tb$_{37}$ heterostructures, respectively. Our results suggest that the spin Hall effect from resistive phase of W can be utilized to effectively control both ferromagnetic and ferrimagnetic layers through a DL-SOT mechanism