Sign of differential reflection and transmission in pump-probe spectroscopy of graphene on dielectric substrate

Pump-probe differential reflection and transmission spectroscopy is a very effective tool to study the nonequilibrium carrier dynamics of graphene. The reported sign of differential reflection from graphene is not explicitly explained and not consistent. Here, we study the differential reflection and transmission signals of graphene on a dielectric substrate. The results reveal the sign of differential reflection changes with the incident direction of the probe beam with respect to the substrate. The obtained theory can be applied to predict the differential signals of other two-dimensional materials placed on various dielectric substrates.

NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES

We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.

A practical and effective method for reducing differential reflectance spectroscopy noise

Differential reflectance spectroscopy(DRS)is a powerful tool to study processes during thin-film growth,especially that of transition metal dichalcogenides and organic thin films.To satisfy the requirements for in situ and real-time monitoring of film growth,including spectral resolution and sensitivity at the level of monolayers and even sub-monolayers,the most challenging technical task in DRS is to reduce noise to an extremely low level so that the best possible signal-to-noise ratio can be achieved.In this paper,we present a simplified and cost-effective DRS apparatus,with which we show that the measurement noise is mainly composed of thermal drift noise and explore the temperature-dependence of the DRS signal.Based on the results obtained,we propose an easily realized and effective scheme aiming to reduce the noise.Experimental results demonstrate that this scheme is effective in stabilizing reliable signals for a long period of several hours.Significant noise reduction is achieved,with the typical average noise of the DRS system being decreased to 0.05%over several hours.The improved DRS system is applied to study the growth of an organic semiconductor layer for an organic field-effect transistor device.The results indicate that the apparatus proposed in this paper has potential applications in fabrication of devices on the nanoscale and even the sub-nanoscale.

Stochastic Differential Games with Reflection and Related Obstacle Problems for Isaacs Equations

In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations （RBSDEs）. We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bettman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of E1 Karoui, Kapoudjian, Pardoux, Peng and Quenez （1997）, which turns out to be very useful because it allows us to estimate the LP-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle.

Distribution dependent reflecting stochastic differential equations

To characterize the Neumann problem for nonlinear Fokker-Planck equations,we investigate distribution dependent reflecting stochastic differential equations(DDRSDEs)in a domain.We first prove the well-posedness and establish functional inequalities for reflecting stochastic differential equations with singular drifts,and then extend these results to DDRSDEs with singular or monotone coefficients,for which a general criterion deducing the well-posedness of DDRSDEs from that of reflecting stochastic differential equations is established.

Towards efficient strain engineering of 2D materials:A four-points bending approach for compressive strain

Strain engineering,as a powerful strategy to tune the optical and electrical properties of two-dimensional(2D)materials by deforming their crystal lattice,has attracted significant interest in recent years.2D materials can sustain ultra-high strains,even up to 10%,due to the lack of dangling bonds on their surface,making them ideal brittle solids.This remarkable mechanical resilience,together with a strong strain-tunable band structure,endows 2D materials with a broad optical and electrical response upon strain.However,strain engineering based on 2D materials is restricted by their nanoscale and strain quantification troubles.In this study,we have modified a homebuilt three-points bending apparatus to transform it into a four-points bending apparatus that allows for the application of both compressive and tensile strains on 2D materials.This approach allows for the efficient and reproducible construction of a strain system and minimizes the buckling effect caused by the van der Waals interaction by adamantane encapsulation strategy.Our results demonstrate the feasibility of introducing compressive strain on 2D materials and the potential for tuning their optical and physical properties through this approach.

Reflected solutions of backward stochastic differential equations driven by G-Brownian motion

In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion. The reflection keeps the solution above a given stochastic process. In order to derive the uniqueness of reflected G-BSDEs, we apply a "martingale condition" instead of the Skorohod condition. Similar to the classical case, we prove the existence by approximation via penalization. We then give some applications including a generalized Feynman-Kac formula of an obstacle problem for fully nonlinear partial differential equation and option pricing of American types under volatility uncertainty.

Reflected Backward Doubly Stochastic Differential Equations with Discontinuous Coefficients

In this paper, we study one-dimensional reflected backward doubly stochastic differential equations （RBDSDEs） with one continuous barrier and discontinuous （left or right continuous） genera- tor. We obtain an existence theorem and a comparison theorem for solutions of the class of RBDSDEs.

Hölder Continuity of Solutions of SPDEs with Reflection

In this paper,we obtain the Hölder continuity of the solutions of SPDEs with reflection,which have singular drifts(random measures).

STUDY ON RAINFALL MEASUREMENT AND RAINDROP SPECTRA WITH THE DIFFERENTIAL REFLECTIVITY Z_(DR)TECHNIQUE OF A DUAL LINEAR POLARIZATION RADAR

In this paper,it is shown that the differential reflectivity Z_(DR) is related to drop size distribution(DSD)and the spectral shape variation of different truncated diameters.Z_(DR) is a sensitive function to variation of DSD of the spectra.The effects of shape variation of DSD on rainfall can be deduced with a(Z_H,Z_(DR))dual-parameter technique,which is effective to improve the accuracy of rainfall measurement and is of the priority of identifying large particles of hydrometeors(especially hailstone)from the rain region.

CONTINUOUS DEPENDENCE ON THE TERMINAL CONDITION OF SOLUTIONS TO NONLINEAR REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper, we derive the continuous dependence on the terminal condition of solutions to nonlinear reflected backward stochastic differential equations involving the subdifferential operator convex function under non-Lipschitz of a lower semi-continuous, proper and condition by means of the corollary of Bihari inequality.

Laser trimming for lithography-free fabrications of MoS_(2)devices

Single-layer MoS_(2)produced by mechanical exfoliation is usually connected to thicker and multilayer regions.We show a facile laser trimming method to insulate single-layer MoS_(2)regions from thicker ones.We demonstrate,through electrical characterization,that the laser trimming method can be used to pattern single-layer MoS_(2)channels with regular geometry and electrically disconnected from the thicker areas.Scanning photocurrent microscope further confirms that in the as-deposited flake(connected to a multilayer area)most of the photocurrent is being generated in the thicker flake region.After laser trimming,scanning photocurrent microscopy shows how only the single-layer MoS_(2)region contributes to the photocurrent generation.The presented method is a direct-write and lithography-free(no need of resist or wet chemicals)alternative to reactive ion etching process to pattern the flakes that can be easily adopted by many research groups fabricating devices with MoS_(2) and similar twodimensional materials.

Strain engineering in single-,bi-and tri-layer MoS_(2),MoSe_(2),WS_(2)and WSe_(2)

Strain is a powerful tool to modify the optical properties of semiconducting transition metal dichalcogenides like MoS_(2),MoSe_(2),WS_(2) and WSe_(2).In this work we provide a thorough description of the technical details to perform uniaxial strain measurements on these two-dimensional semiconductors and we provide a straightforward calibration method to determine the amount of applied strain with high accuracy.We then employ reflectance spectroscopy to analyze the strain tunability of the electronic properties of single-,bi-and tri-layer MoS_(2),MoSe_(2),WS_(2) and WSe_(2).Finally,we quantify the flake-to-flake variability by analyzing 15 different single-layer MoS_(2) flakes.

PROPAGATION EFFECTS AND APPLICATION OF PHASE INFORMATION FOR C-BAND DUAL-POLARIZATION RADAR

As a study on exploiting and popularizing the advanced dual-polarization weather radar technique in China,the physical mechanism for the propagation effect of the radar wave is discussed by using the widely adapted extended boundary condition method,and some theoretic results are provided for improving rain measurement accuracy.Furthermore,phase information, another important characteristic quantity of microwave,is considered for tapping the potentialities of the new meteorological radar system.

RBSDEs with optional barriers:monotone approximation

In this short note we consider reflected backward stochastic differential equations(RBSDEs)with a Lipschitz driver and barrier processes that are optional and right lower semicontinuous.In this case,the barrier is represented as a nondecreasing limit of right continuous with left limit(RCLL)barriers.We combine some well-known existence results for RCLL barriers with comparison arguments for the control process to construct solutions.Finally,we highlight the connection of these RBSDEs with standard RCLL BSDEs.

Existence, Uniqueness and Approximation for Lp Solutions of Reflected BSDEs with Generators of One-sided Osgood Type

We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.

Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations

We consider in this paper random batch interacting particle methods forsolving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann(PB) equation as the equilibrium, in the external unbounded domain. To justify thesimulation in a truncated domain, an error estimate of the truncation is proved inthe symmetric cases for the PB equation. Then, the random batch interacting particle methods are introduced which are O(N) per time step. The particle methods cannot only be considered as a numerical method for solving the PNP and PB equations,but also can be used as a direct simulation approach for the dynamics of the chargedparticles in solution. The particle methods are preferable due to their simplicity andadaptivity to complicated geometry, and may be interesting in describing the dynamics of the physical process. Moreover, it is feasible to incorporate more physical effectsand interactions in the particle methods and to describe phenomena beyond the scopeof the mean-field equations.