General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian

Combination of deep learning and ab initio calculation has shown great promise in revolutionizing future scientific research, but how to design neural network models incorporating a priori knowledge and symmetry requirements is a key challenging subject. Here we propose an E(3)-equivariant deep-learning framework to represent density functional theory (DFT) Hamiltonian as a function of material structure, which can naturally preserve the Euclidean symmetry even in the presence of spin-orbit coupling. Our DeepH-E3 method enables very efficient electronic-structure calculation at ab initio accuracy by learning from DFT data of small-sized structures, making routine study of large-scale supercells ($> 10^4$ atoms) feasible. Remarkably, the method can reach sub-meV prediction accuracy at high training efficiency, showing state-of-the-art performance in our experiments. The work is not only of general significance to deep-learning method development, but also creates new opportunities for materials research, such as building Moir\'e-twisted material database

Global existence of solutions for 1-D nonlinear wave equation of sixth order at high initial energy level

Abstract This paper considers the Cauchy problem of solutions for a class of sixth order 1-D nonlinear wave equations at high initial energy level. By introducing a new stable set we derive the result that certain solutions with arbitrarily positive initial energy exist globally.</jats:p

Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations

Global well-posedness and finite time blow up issues for some strongly damped nonlinear wave equation are investigated in the present paper. For subcritical initial energy by employing the concavity method we show a finite time blow up result of the solution. And for critical initial energy we present the global existence, asymptotic behavior and finite time blow up of the solution in the framework of the potential well. Further for supercritical initial energy we give a sufficient condition on the initial data such that the solution blows up in finite time

Modulating Electronic Structure of Monolayer Transition Metal Dichalcogenides by Substitutional Nb-Doping

Modulating electronic structure of monolayer transition metal dichalcogenides (TMDCs) is important for many applications and doping is an effective way towards this goal, yet is challenging to control. Here we report the in-situ substitutional doping of niobium (Nb) into TMDCs with tunable concentrations during chemical vapour deposition. Taking monolayer WS2 as an example, doping Nb into its lattice leads to bandgap changes in the range 1.98 eV to 1.65 eV. Noteworthy, electrical transport measurements and density functional theory calculations show that the 4d electron orbitals of the Nb dopants contribute to the density of states of Nb-doped WS2 around the Fermi level, resulting in an n to p-type conversion. Nb-doping also reduces the energy barrier of hydrogen absorption in WS2, leading to an improved electrocatalytic hydrogen evolution performance. These results highlight the effectiveness of controlled doping in modulating the electronic structure of TMDCs and their use in electronic related applications.Comment: 20 pages, 5 figure

Liquid–Liquid Phase‐Separated Systems from Reversible Gel–Sol Transition of Protein Microgels

Funder: Wellcome Trust; Id: http://dx.doi.org/10.13039/100010269Funder: Newman FoundationFunder: BBSRC; Id: http://dx.doi.org/10.13039/501100000268Funder: Cambridge Trust; Id: http://dx.doi.org/10.13039/501100003343Funder: Jardine FoundationFunder: Trinity College CambridgeFunder: Trinity College Krishnan‐Ang StudentshipFunder: Honorary Trinity‐Henry Barlow ScholarshipFunder: China Scholarship Council; Id: http://dx.doi.org/10.13039/501100004543Funder: Herchel Smith FundsFunder: Wolfson College Cambridge Junior Research FellowshipAbstract: Liquid–liquid phase‐separated biomolecular systems are increasingly recognized as key components in the intracellular milieu where they provide spatial organization to the cytoplasm and the nucleoplasm. The widespread use of phase‐separated systems by nature has given rise to the inspiration of engineering such functional systems in the laboratory. In particular, reversible gelation of liquid–liquid phase‐separated systems could confer functional advantages to the generation of new soft materials. Such gelation processes of biomolecular condensates have been extensively studied due to their links with disease. However, the inverse process, the gel–sol transition, has been less explored. Here, a thermoresponsive gel–sol transition of an extracellular protein in microgel form is explored, resulting in an all‐aqueous liquid–liquid phase‐separated system with high homogeneity. During this gel–sol transition, elongated gelatin microgels are demonstrated to be converted to a spherical geometry due to interfacial tension becoming the dominant energetic contribution as elasticity diminishes. The phase‐separated system is further explored with respect to the diffusion of small particles for drug‐release scenarios. Together, this all‐aqueous system opens up a route toward size‐tunable and monodisperse synthetic biomolecular condensates and controlled liquid–liquid interfaces, offering possibilities for applications in bioengineering and biomedicine

AFM measurement of self-propulsion forces generated by a Janus particle

The behavior of Pt-coated Janus particle in an aqueous solution of hydrogen peroxide is studied using atomic force microscopy (AFM). The catalytic chemical reaction between the platinum and hydrogen peroxide generates a propulsion force to propel the Janus particle in the liquid. To characterize the self-propelling nature of the Janus particle, we designed and assembled a new AFM probe with a Janus particle glued on the free end of the hanging fiber. The self-propulsion force generated by the Janus particle is then measured by recording and analyzing the capillary-force-versus-travel-distance curve and the power spectrum ∣z(w)∣2 of the modified hanging fiber probe at an optimal immersion depth of the liquid-air interface. Meanwhile, theoretical attempts were made to determine the physical origin of the propulsion force. A new propulsion peak was found in the measured power spectrum ∣z(w)∣2 in the low frequency range of 100 - 300 Hz. The concentration dependence of the propulsion peak location and height were analyzed to find the catalytic chemical reaction rates between Pt and hydrogen peroxide and the height fluctuation of the contact line near the Janus particle equator. The obtained values of the production rate k1 of the intermediate product Pt(H2O2) and the production rate k2 of the solute molecule O2 for the catalytic reaction are found in reasonable agreement with those obtained from previous experiments by particle tracking. The fluctuating height h of the contact line is analyzed theoretically. Compared to the traditional method of particle tracking, the AFM measurement is faster and more accurate, and provides a new reliable way of determining the chemical reaction rate. The newly developed AFM method will become a useful tool for the study of dynamic properties of various micro- or nano-scale systems.</p

Asymptotic behavior and blow-up of solutions for the viscous diffusion equation

AbstractWe study the initial–boundary value problem of the viscous diffusion equations which include GBBM equations, Sobolov–Galpern equations and some standard nonlinear diffusion equations as special cases. By using the integral estimate method and the eigenfunction method we prove that when the nonlinear terms satisfy some conditions the solutions of the problem decay to zero according to the exponent of t. And when the nonlinear terms of the equation satisfy some other conditions the solutions blow up in finite time. Then the known results are improved and generalized