Gradient estimates and coupling property for semilinear SDEs driven by jump processes

Let L be a L′evy process with characteristic measureν,which has an absolutely continuous lower bound w.r.t.the Lebesgue measure on Rn.By using Malliavin calculus for jump processes,we investigate Bismut formula,gradient estimates and coupling property for the semigroups associated to semilinear SDEs forced by L′evy process L.

Derivative Formula and Coupling Property for Linear SDEs Driven by Lévy Processes

In this paper we investigate an integration by parts formula for Lévy processes by using lower bound conditions of the corresponding Lévy measure. As applications, derivative formula and coupling property are derived for transition semigroups of linear SDEs driven by Lévy processes.

Fluid-solid coupling model for studying wellbore instability in drilling of gas hydrate bearing sediments

As the oil or gas exploration and development activities in deep and ultra- deep waters become more and more, encountering gas hydrate bearing sediments （HBS） is almost inevitable. The variation in temperature and pressure can destabilize gas hydrate in nearby formation around the borehole, which may reduce the strength of the formation and result in wellbore instability. A non-isothermal, transient, two-phase, and fluid-solid coupling mathematical model is proposed to simulate the complex stability performance of a wellbore drilled in HBS. In the model, the phase transition of hydrate dissociation, the heat exchange between drilling fluid and formation, the change of mechanical and petrophysical properties, the gas-water two-phase seepage, and its interaction with rock deformation are considered. A finite element simulator is developed, and the impact of drilling mud on wellbore instability in HBS is simulated. Results indicate that the re- duction in pressure and the increase in temperature of the drilling fluid can accelerate hydrate decomposition and lead to mechanical properties getting worse tremendously. The cohesion decreases by 25% when the hydrate totally dissociates in HBS. This easily causes the wellbore instability accordingly. In the first two hours after the formation is drilled, the regions of hydrate dissociation and wellbore instability extend quickly. Then, with the soaking time of drilling fluid increasing, the regions enlarge little. Choosing the low temperature drilling fluid and increasing the drilling mud pressure appropriately can benefit the wellbore stability of HBS. The established model turns out to be an efficient tool in numerical studies of the hydrate dissociation behavior and wellbore stability of HBS.

Theoretical Study on the Spectroscopic Parameters and Transition Properties of MgH Radical Including Spin-orbit Coupling

An accurate theoretical study on the MgH radical is reported by adopting the high-level relativistic MRCI＋Q method with a quintuple-zeta quality basis set. The reliable potential energy curves of the five A-S states of MgH are derived. Then the associated spectroscopic parameters are determined and found to be in good accordance with the available experimental results. The permanent dipole moments （PDMs） and the spin-orbit （SO） matrix elements of A-S states are computed. The results show that the abrupt changes of PDMs and SO matrix elements are attributed to the variations of electronic configurations at the avoided crossing point. The SOC effect leads to the five A-S states split into ten Ω states and results in the double potential well of （2）1//2 state. Finally, the transition properties from the （2）1//2, （1）3//2 and （3）1//2 states to the ground state X2∑＋1//2 transitions are obtained, including the transition dipole moments, Franck-Condon factors and radiative lifetimes.

Calibration of coupled hydro-mechanical properties of grain-based model for simulating fracture process and associated pore pressure evolution in excavation damage zone around deep tunnels

The objective of this paper is to develop a methodology for calibration of a discrete element grain-based model(GBM)to replicate the hydro-mechanical properties of a brittle rock measured in the laboratory,and to apply the calibrated model to simulating the formation of excavation damage zone(EDZ)around underground excavations.Firstly,a new cohesive crack model is implemented into the universal distinct element code(UDEC)to control the fracturing behaviour of materials under various loading modes.Next,a methodology for calibration of the components of the UDEC-Voronoi model is discussed.The role of connectivity of induced microcracks on increasing the permeability of laboratory-scale samples is investigated.The calibrated samples are used to investigate the influence of pore fluid pressure on weakening the drained strength of the laboratory-scale rock.The validity of the Terzaghi’s effective stress law for the drained peak strength of low-porosity rock is tested by performing a series of biaxial compression test simulations.Finally,the evolution of damage and pore pressure around two unsupported circular tunnels in crystalline granitic rock is studied.

Phase Control of Transient Optical Properties of Double Coupled Quantum-Dot Nanostructure via Gaussian Laser Beams

We theoretically analyze the transient properties of a probe field absorption and dispersion in a coupled semiconductor double-quantum-dot nanostructure.We show that in the presence of the Gaussian laser beams,absorption and dispersion of the probe field can be dramatically influenced by the relative phase between applied fields and intensity of the Gaussian laser beams.Transient and steady-state behaviors of the probe field absorption and dispersion are discussed to estimate the required switching time.The estimated range is between 5-8 ps for subluminal to superluminal light propagation.

Forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by CNTs based on MCST with temperature-variable material properties

In this study, free and forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by carbon nanotubes （CNTs） under magnetic field based on modify couple stress theory （MCST） with temperature-variable material propertiesis presented. Also, the boundary conditions at two ends of nano-composite rotating pressurized microbeam reinforced by CNTs are considered as simply supported. The governing equations are obtained based on the Hamilton＇s principle and then computed these equations by using Navier＇s solution. The magnetic field is inserted in the thickness direction of the nano-composite microbeam. The effects of various parameters such as angular velocity, temperature changes, and pressure between of the inside and outside, the magnetic field, material length scale parameter, and volume fraction of nanocomposite microbeam on the natural frequency and response systemare studied. The results show that with increasing volume fraction of nano-composite microbeam, thickness, material length scale parameter, and magnetic fields, the natural frequency increases. The results of this research can be used for optimization of micro-structures and manufacturing sensors, displacement fluid, and drug delivery.

Investigation of Thermal Losses in a Soft Magnetic Composite Using Multiphysics Modelling and Coupled Material Properties in an Induction Heating Cell

The complex interaction between material properties in an induction heating circuit was studied by multi physics simulation and by experimental verification in a full-scale laboratory heater. The work aims to illustrate the complexity of the system of interacting materials, but also to propose a method to verify properties of soft magnetic composite materials in an integrated system and to identify which properties are the most critical under different circumstances and load cases. Heat losses at different loads were primarily studied, from DC currents to AC currents at 15, 20 and 25 kHz, respectively. A FE model for magnetic simulation was correlated with a corresponding model for heat simulation. The numerical model, as well as the established input material data, could be verified through the experimental measurements. In this particular study, the current loss in the litz wire was the dominant heat source, thus making the thermal conductivity of the SMC the most important property in this material.

Successful couplings for a class of stochastic differential equations driven by Lvy processes

By constructing proper coupling operators for the integro-differential type Markov generator, we establish the existence of a successful coupling for a class of stochastic differential equations driven by Levy processes. Our result implies a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying Markov semigroups, and it is sharp for Ornstein-Uhlenbeck processes driven by s-stable Levy processes.

Effects of calendering state on coupled electrochemical-mechanical performance of silicon based composite electrodes

The super volume changes and severe mechanical degradation have been a hindrance in the wide application of silicon based composite electrodes in commercial lithium-ion batteries(LIBs).Calendering,one procedure in producing LIBs'electrodes,is indispensable to ensure low porosity and energy density.However,the repercussions of the calendering process on the physical characteristics related to the behavior of silicon(Si)based electrodes during the electrochemical reaction have not been well understood.Thus,on account of the deformation characteristic of cantilever electrodes,an in-situ technique is employed to analyze the repercussions of calendering status on the coupled electro-chemo-mechanical performances.During the electrochemical cycling,Young's modulus and diffusion-induced stress in composite electrodes are quantified.The results show that the swelling strain,the stress and the modulus of the Si-based electrode and the calendering degree are positively correlated.Meanwhile,the stress induced by diffusion in the active layer tends to increase in the stage of lithiation and reverses during the delithiation process.Accompany with the SEM analysis,we conclude that the calendering process can induce larger stress,driving the formation of cracks in electrodes.These findings can help understand how the calendering process could affect the capacity dissipating and lifetime of Si based electrodes.

A novel coupled quantum well structure and its excellent electro-optical properties

A novel InGaAs/InAlAs coupled quantum well structure is proposed for large field-induced refractive index change with low absorption loss. In the case of low applied electric field of 15 kV/cm and low absorption loss （α≤100 cm^-1）, a large field-induced refractive index change （for transverse electric （TE） mode, △n= 0.012; for transverse magnetic （TM） mode, △n = 0.0126） is obtained in the structure at the operation wavelength of 1.55 μm. The value is larger by over one order of magnitude than that in a rectangular quantum well. The result is very attractive for semiconductor optical switching devices.