And\^o dilations for a pair of commuting contractions: two explicit constructions and functional models

One of the most important results in operator theory is And\^o's \cite{ando} generalization of dilation theory for a single contraction to a pair of commuting contractions acting on a Hilbert space. While there are two explicit constructions (Sch\"affer \cite{sfr} and Douglas \cite{Doug-Dilation}) of the minimal isometric dilation of a single contraction, there was no such explicit construction of an And\^o dilation for a commuting pair $(T_1,T_2)$ of contractions, except in some special cases \cite{A-M-Dist-Var, D-S, D-S-S}. In this paper, we give two new proofs of And\^o's dilation theorem by giving both Sch\"affer-type and Douglas-type explicit constructions of an And\^o dilation with function-theoretic interpretation, for the general case. The results, in particular, give a complete description of all possible factorizations of a given contraction $T$ into the product of two commuting contractions. Unlike the one-variable case, two minimal And\^o dilations need not be unitarily equivalent. However, we show that the compressions of the two And\^o dilations constructed in this paper to the minimal dilation spaces of the contraction $T_1T_2$, are unitarily equivalent. In the special case when the product $T=T_1T_2$ is pure, i.e., if $T^{* n}\to 0$ strongly, an And\^o dilation was constructed recently in \cite{D-S-S}, which, as this paper will show, is a corollary to the Douglas-type construction. We define a notion of characteristic triple for a pair of commuting contractions and a notion of coincidence for such triples. We prove that two pairs of commuting contractions with their products being pure contractions are unitarily equivalent if and only if their characteristic triples coincide. We also characterize triples which qualify as the characteristic triple for some pair $(T_1,T_2)$ of commuting contractions such that $T_1T_2$ is a pure contraction.Comment: 24 page

Vibrational relaxation dynamics in layered perovskite quantum wells

Organic-inorganic layered perovskites are two-dimensional quantum wells with layers of lead-halide octahedra stacked between organic ligand barriers. The combination of their dielectric confinement and ionic sublattice results in excitonic excitations with substantial binding energies that are strongly coupled to the surrounding soft, polar lattice. However, the ligand environment in layered perovskites can significantly alter their optical properties due to the complex dynamic disorder of soft perovskite lattice. Here, we observe the dynamic disorder through phonon dephasing lifetimes initiated by ultrafast photoexcitation employing high-resolution resonant impulsive stimulated Raman spectroscopy of a variety of ligand substitutions. We demonstrate that vibrational relaxation in layered perovskite formed from flexible alkyl-amines as organic barriers is fast and relatively independent of the lattice temperature. Relaxation in aromatic amine based layered perovskite is slower, though still fast relative to pure inorganic lead bromide lattices, with a rate that is temperature dependent. Using molecular dynamics simulations, we explain the fast rates of relaxation by quantifying the large anharmonic coupling of the optical modes with the ligand layers and rationalize the temperature independence due to their amorphous packing. This work provides a molecular and time-domain depiction of the relaxation of nascent optical excitations and opens opportunities to understand how they couple to the complex layered perovskite lattice, elucidating design principles for optoelectronic devices.Comment: 7 pages, 4 figures, S

The Chinese Open Science Network (COSN): Building an Open Science Community From Scratch

Open Science is becoming a mainstream scientific ideology in psychology and related fields. However, researchers, especially early-career researchers (ECRs) in developing countries, are facing significant hurdles in engaging in Open Science and moving it forward. In China, various societal and cultural factors discourage ECRs from participating in Open Science, such as the lack of dedicated communication channels and the norm of modesty. To make the voice of Open Science heard by Chinese-speaking ECRs and scholars at large, the Chinese Open Science Network (COSN) was initiated in 2016. With its core values being grassroots-oriented, diversity, and inclusivity, COSN has grown from a small Open Science interest group to a recognized network both in the Chinese-speaking research community and the international Open Science community. So far, COSN has organized three in-person workshops, 12 tutorials, 48 talks, and 55 journal club sessions and translated 15 Open Science-related articles and blogs from English to Chinese. Currently, the main social media account of COSN (i.e., the WeChat Official Account) has more than 23,000 subscribers, and more than 1,000 researchers/students actively participate in the discussions on Open Science. In this article, we share our experience in building such a network to encourage ECRs in developing countries to start their own Open Science initiatives and engage in the global Open Science movement. We foresee great collaborative efforts of COSN together with all other local and international networks to further accelerate the Open Science movement

Applications of Metabolic Modelling: Understanding Energy Production in Electricity-Producing Shewanella oneidensis MR-1 and Lipid-Producing Nannochloropsis gaditana

With the improvement of computational technology in recent years, new research fields such as systems biology have been developed thanks to the interdisciplinary interface between computer science and traditional biology. Distinct from traditional biology, systems biology focuses on cellular activity at a systematic level rather than individual molecular scales. A new technique called ‘Omics’ data analysis has been introduced to systems biology to help understand bio-activities on a greater scale. For instance, proteomics is the study of various protein levels simultaneously. This type of research provides an overall picture of the organism, helping us understand how cellular activities interact with each other. To further understand subcellular activities, computational modelling was developed with techniques including elementary mode analysis, flux balance analysis, metabolic flux analysis, et cetera. In this report, two projects related to systems biology have been carried out. The first project is a model-driven metabolic analysis of electron-producing bacteria, called Shewanella oneidensis MR-1. In this project, the aerobic and anaerobic respiration was studied. The relation between electron productivity and carbon source has been described. A gene-knockout simulation was also carried out. It was found that the knockout of two ubiquinone-8 related reactions increased the total electron productivity by about 31%. This increase may be because with two knockouts, the flux through the tricarboxylic acid cycle (TCA) cycle maintains a low level, reducing cell growth. Thus, more energy can be converted into electricity. The main electron donor in the electron transport chain is nicotinamide adenine dinucleotide + hydrogen (NADH). The second project is a metabolic reconstruction of Nannochloropsis gaditana. As a result, over 300 reactions were included in the model reconstruction of Nannochloropsis gaditana and the biomass reaction is needed for further predictions. Together with the biomass reaction, this model can be further used for prediction via flux balance analysis (FBA). In the FBA model of S. oneidensis, it was found that the model had a better performance under carbon-limited conditions rather than oxygen-limited conditions. The theoretical electron transfer efficiency to the anode was found to be extremely low (less than 0.01% in direct electron transfer (DET) mode or 20% in mediated electron transfer (MET) mode)

Structural and Carrier Dynamics in Low-dimensional Halide Perovskites

Halide perovskites are emerging new semiconductors that have excellent optoelectronic performance. The great optical efficiency has triggered research in all fields of physical sciences, including electronic property studies, chemical synthesis, electrical engineering, and structural characterization. Different from traditional covalent semiconductors such as silicon or II-VI semiconductors, halide perovskites resemble ionic crystals to have lower mechanical strength, solution processability, and dynamical lattices. The uniqueness of halide perovskites evades conventional categorization so that renewed conceptual frameworks are necessary. Generally speaking, in the field of physical chemistry of halide perovskites, both the structural and electronic properties of this class of material are of great interest. The coupling between structural dynamics and electronic behaviors contributes to the intriguing carrier dynamical phenomena, such as the formation of polaron, delayed photoluminescence, dynamical screening of hot carriers, etc. The major obstacle to unravel the unprecedented properties of halide perovskites has been the lack of control over the atomic configuration of perovskite microstructures, which requires both synthetic and characterization advancement. Therefore, this Dissertation centers around the structural and carrier Dynamics of low-dimensional halide perovskites by making use of atomically defined nanostructures and advanced spectroscopic/microscopic tools. After a brief background introduction to halide perovskites, I discuss the scientific questions to be addressed in this Dissertation. In Chapter 2 and 3, I focus on a material platform composed of one-dimensional halide perovskite nanowires. With this material platform, an optical scaling law is observed and explained with Monte Carlo simulation. In these two chapters, I demonstrate the power of well-defined perovskite nanostructures and how to use these nanostructures to resolve intriguing carrier dynamics of halide perovskites in general. In Chapter 4, I introduce synthesis of atomically thin halide perovskite nanostructures. Both one-dimensional atomically thin nanowires and two-dimensional atomically thin nanosheets are used as case studies to demonstrate the advanced synthetic control over the atomic structure of halide perovskites. Electron microscopy is used to resolve the structure of atomic resolution. In Chapter 5, I select the atomically thin nanowires as a material platform to study the transient structural dynamics of halide perovskite nanostructures. Ultrafast electron camera is used to resolve the structural dynamics with millisecond resolution while atomic spatial resolution is maintained. I thoroughly investigate the structural behaviors of one-dimensional halide perovskites under electron beams and demonstrate the resilient while mobile lattice dynamics as a unique character of halide perovskites. Finally, in Chapter 6, I summarize the Dissertation by providing an outlook and new perspectives on the study of halide perovskites. Overall, this Dissertation is aimed to address the structural and electronic properties of halide perovskite with an emphasis on the synthetic control. The research logic of this Dissertation can be used as a new paradigmatic framework for the future exploration and investigation of this emerging new material