Data-driven Efficient Solvers and Predictions of Conformational Transitions for Langevin Dynamics on Manifold in High Dimensions

We work on dynamic problems with collected data $\{\mathsf{x}_i\}$ that distributed on a manifold $\mathcal{M}\subset\mathbb{R}^p$. Through the diffusion map, we first learn the reaction coordinates $\{\mathsf{y}_i\}\subset \mathcal{N}$ where $\mathcal{N}$ is a manifold isometrically embedded into an Euclidean space $\mathbb{R}^\ell$ for $\ell \ll p$. The reaction coordinates enable us to obtain an efficient approximation for the dynamics described by a Fokker-Planck equation on the manifold $\mathcal{N}$. By using the reaction coordinates, we propose an implementable, unconditionally stable, data-driven upwind scheme which automatically incorporates the manifold structure of $\mathcal{N}$. Furthermore, we provide a weighted $L^2$ convergence analysis of the upwind scheme to the Fokker-Planck equation. The proposed upwind scheme leads to a Markov chain with transition probability between the nearest neighbor points. We can benefit from such property to directly conduct manifold-related computations such as finding the optimal coarse-grained network and the minimal energy path that represents chemical reactions or conformational changes. To establish the Fokker-Planck equation, we need to acquire information about the equilibrium potential of the physical system on $\mathcal{N}$. Hence, we apply a Gaussian Process regression algorithm to generate equilibrium potential for a new physical system with new parameters. Combining with the proposed upwind scheme, we can calculate the trajectory of the Fokker-Planck equation on $\mathcal{N}$ based on the generated equilibrium potential. Finally, we develop an algorithm to pullback the trajectory to the original high dimensional space as a generative data for the new physical system.Comment: 59 pages, 16 figure

Quantum Computer Using Coupled Quantum Dot Molecules

We propose a method for implementation of a quantum computer using artificial molecules. The artificial molecule consists of two coupled quantum dots stacked along z direction and one single electron. One-qubit and two-qubit gates are constructed by one molecule and two coupled molecules, respectively.The ground state and the first excited state of the molecule are used to encode the |0> and |1> states of a qubit. The qubit is manipulated by a resonant electromagnetic wave that is applied directly to the qubit through a microstrip line. The coupling between two qubits in a quantum controlled NOT gate is switched on (off) by floating (grounding) the metal film electrodes. We study the operations of the gates by using a box-shaped quantum dot model and numerically solving a time-dependent Schridinger equation, and demonstrate that the quantum gates can perform the quantum computation. The operating speed of the gates is about one operation per 4ps. The reading operation of the output of the quantum computer can be performed by detecting the polarization of the qubits.Comment: 18 pages, 7 figures, submitted to Jpn. J. Appl. Phys, please send your e-mail to Nan-Jian Wu <[email protected]

Possible hard X-ray shortages in bursts from KS 1731-260 and 4U 1705-44

Aims: A hard X-ray shortage, implying the cooling of the corona, was observed during bursts of IGR J17473-272, 4U 1636-536, Aql X-1, and GS 1826-238. Apart from these four sources, we investigate here an atoll sample, in which the number of bursts for each source is larger than 5, to explore the possible additional hard X-ray shortage during {\it Rossi X-ray timing explorer (RXTE)} era. Methods: According to the source catalog that shows type-I bursts, we analyzed all the available pointing observations of these sources carried out by the {\it RXTE} proportional counter array (PCA). We grouped and combined the bursts according to their outburst states and searched for the possible hard X-ray shortage while bursting. Results: We found that the island states of KS 1731-260 and 4U 1705-44 show a hard X-ray shortage at significant levels of 4.5 and 4.7 $\sigma$ and a systematic time lag of $0.9 \pm 2.1$ s and $2.5 \pm 2.0$ s with respect to the soft X-rays, respectively. While in their banana branches and other sources, we did not find any consistent shortage.Comment: 5 pages, 4 figures, accepted by A&A as a research not

In-situ TEM Study of Dislocation-Interface Interactions

In this chapter, we highlighted the in situ transmission electron microscope (TEM) observation of the interactions of dislocations with three types of interfaces: (i) twin boundaries in Cu; (ii) metallic interphase boundaries; and (iii) metal/ceramic interfaces. Interface structures, interface properties, and dislocation-interface interactions are characterized in a high-resolution TEM. These knowledge provided insights into the understanding of the physical properties of materials, developing materials modeling tools incorporating interface deformation physics, and designing materials with desired properties