跳扩散过程下的保险商偿债率模型研究

本文研究了在有金融困境成本的情况下,带有跳扩散过程的保险商偿债率(SR)模型的问题.利用Girsanov定理进行测度变换的方法以及跳扩散过程下的看涨期权定价公式,获得了保险商终期收益的现值的结果.推广了不带跳扩散过程的保险商偿债率模型的结果.     

带Markov状态转换的跳扩散方程的数值解

研究了一类带Markov状态转换的跳扩散方程的数值解的问题,为讨论这类方程精确解的数值计算问题,我们给出了一种基于Euler格式的方程解的跳适应算法,并在一定的条件下,证明了基于这种新的跳适应算法所得到的方程的数值解是收敛于它的精确解,同时还给出了数值解收敛到其精确解的收敛阶数.最后,本文通过两个例子说明了这种跳适应算法的计算有效性.     

Fast iterative solver for convection‐diffusion systems with spectral elements

We introduce a solver and preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection–diffusion equation. The method is based on a Robin–Robin interface preconditioner coupled to a fast diagonalization solver which is used to efficiently eliminate the interior degrees of freedom and perform subsidiary subdomain solves. Using a spectral element discretization, we first apply our technique to constant wind problems, and then propose a means for applying the technique as a preconditioner for variable wind problems. We demonstrate that iteration counts are mildly dependent on changes in mesh size and convection strength. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Iterative operator‐splitting methods for nonlinear differential equations and applications

In this article, we consider iterative operator‐splitting methods for nonlinear differential equations with bounded and unbounded operators. The main feature of the proposed idea is the embedding of Newton's method for solving the split parts of the nonlinear equation at each step. The convergence properties of such a mixed method are studied and demonstrated. We confirm with numerical applications the effectiveness of the proposed scheme in comparison with the standard operator‐splitting methods by providing improved results and convergence rates. We apply our results to deposition processes. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1026–1054, 2011     

Discrete maximum principles for FE solutions of nonstationary diffusion‐reaction problems with mixed boundary conditions

In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion‐reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Shrinking-core modeling of binary chromatographic breakthrough

Most chromatographic processes involve separation of two or more species, so development of a simple, accurate multicomponent chromatographic model can be valuable for improving process efficiency and yield. We consider the case of breakthrough chromatography, which has been considered in great depth for single-component modeling but to a much more limited degree for multicomponent breakthrough. We use the shrinking core model, which provides a reasonable approximation of particle uptake for proteins under strong binding conditions. Analytical column solutions for single-component systems are extended here to predict binary breakthrough chromatographic behavior for conditions under which the external transport resistance is negligible. Analytical results for the location and profile of displacement effects and expected breakthrough curves are derived for limiting cases. More generally, straightforward numerical results have also been obtained through simultaneous solution of a set of simple ordinary differential equations. Exploration of the model parameter space yields results consistent with theoretical expectations. Additionally, both analytical and numerical predictions compare favorably with experimental column breakthrough data for lysozyme-cytochrome c mixtures on the strong cation exchanger SP Sepharose FF. Especially significant is the ability of the model to predict experimentally observed displacement profiles of the more weakly adsorbed species (in this case cytochrome c). The ability to model displacement behavior using simple analytical and numerical techniques is a significant improvement over current methods.     

Kinetic investigation of narrow-bore columns packed with prototype sub-2 μm superficially porous particles with various shell thickness

The recent successful breakthrough of sub-3 μm shell particles in HPLC has triggered considerable research efforts toward the design of new brands of core-shell particles. We investigated the mass transfer mechanism of a few analytes in narrow-bore columns packed with prototype 1.7 μm shell particles, made of 1.0, 1.2, and 1.4 μm solid nonporous cores surrounded by porous shells 350, 250, and 150 nm thick, respectively. Three probe solutes, uracil, naphthalene, and insulin, were chosen to assess the kinetic performance of these columns. Inverse size exclusion chromatography, peak parking experiments, and the numerical integration of the experimental peak profiles were carried out in order to measure the external, internal, and total column porosities, the true bulk diffusion coefficients of these analytes, the height equivalent to a theoretical plate, the longitudinal diffusion term, and the trans-particle mass transfer resistance term. The residual eddy diffusion term was measured by difference. The results show the existence of important trans-column velocity biases (7%) possibly due to the presence of particle multiplets in the slurry mixture used during the packing process. Our results illustrates some of the difficulties encountered by scientists preparing and packing shell particles into narrow-bore columns.     

Description of the response of a fiber optic velocity sensor applied to capillary gas chromatography

This paper explores the response of a novel fiber optics sensor allowing real-time determination of the migration rate of vapor zones in capillary gas chromatography. The sensitivity is related to the gradient of the vapor zone distribution in the capillary and it is highest when vapor zones show steep variations in concentration. The expected linearity between the height of the velocity peaks and the response of a thermal conductivity detector is demonstrated experimentally. The sensor can be used to infer an approximate value of the analyte diffusion coefficient from the time response. Finally, the time evolution of the envelope of the optical signal is explained with experimental evidences.     

Experimental investigation of the difference in B-term dominated band broadening between fully porous and porous-shell particles for liquid chromatography using the Effective Medium Theory

The difference in B-term diffusion between fully porous and porous-shell particles is investigated using the physically sound diffusion equations originating from the Effective Medium Theory (EMT). Experimental data of the B-term diffusion obtained via peak parking measurements on six different commercial particle types have been analyzed (3 porous and 3 non porous). All particles were investigated using the same experimental design and test analytes, over a very broad range of retention factor values. First, the B-term reducing effect of the solid core (inducing an additional obstruction compared to fully porous particles) has been quantified using the Hashin-Shtrikman expression, showing that the presence of a solid core can account for a reduction of about 11% when the core diameter makes up 63% of the total particle diameter (Halo and Poroshell-particles) and a reduction of 16% when the core diameter makes up 73% (Kinetex). Remaining differences can be attributed to differences in the microscopic structure of the meso-porous material (meso-pore diameter, internal porosity or relative void volume). The much lower B-term diffusion of Halo and Kinetex particles compared to the fully porous Acquity particles (some 20-40% difference, of which about 10-15% can be attributed to the presence of the solid core) can hence largely be attributed to the much smaller internal porosity and the smaller pore size of the meso-porous material making up the shell of these particles.     

Molecular dynamics simulation of ionic transport on molten Li–KCl interface

A molecular dynamics study is performed to determine the dynamics and transport properties of the ions on the molten interface between anode metal Li and electrolyte KCl. Radial distribution function of the ionic pair and the behavior of the mean‐square displacement (MSD) as a function of time (t) indicate that KCl and metal Li are in the molten state at 2,200 K in the canonical ensemble. The dynamics of the ionic transport are characterized by studying MSD for the centers of mass of the ions at different temperatures. Diffusion coefficient is evaluated from the linear slope of the MSD (t) function in the range of 0–500 ps. The MSD and diffusion coefficient of the Li⁺ ions are much larger than those of the Cl^? and K⁺ ions due to the difference in ionic characteristic. The transport process has been dominated by the Li⁺ ions on the molten interface and the Li⁺ ions are main charge carriers. The energy barrier of the Li⁺ ions transporting into the molten KCl is fitted to be 5.28 kcal/mol in the light of the activation model. The electrical conductivity of the Li⁺ ions transporting into the molten KCl are calculated from the Nernst–Einstein formula to be in the range of 0.2–0.3 S cm^?1. The current density resulted from the Li⁺ ions through the interface are estimated to be an order of 10⁶ A cm^?2, which may be the value corresponding to a larger concentration gradient of the Li⁺ ions. Simulated results at different temperatures show that the diffusion coefficient, conductivity and current density have increased with the temperature. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011