Stability of braneworlds with non-minimally coupled multi-scalar fields

Linear stability of braneworld models constructed with multi-scalar fields is very different from that of single-scalar field models. It is well known that both the tensor and scalar perturbation equations of the later can always be written as a supersymmetric Schr\"{o}dinger equation, so it can be shown that the perturbations are stable at linear level. However, in general it is not true for multi-scalar field models and especially there is no effective method to deal with the stability problem of the scalar perturbations for braneworld models constructed with non-minimally coupled multi-scalar fields. In this paper we present a method to investigate the stability of such braneworld models. It is easy to find that the tensor perturbations are stable. For the stability problem of the scalar perturbations, we present a systematic covariant approach. The covariant quadratic order action and the corresponding first-order perturbed equations are derived. By introducing the orthonormal bases in field space and making the Kaluza-Klein decomposition, we show that the Kaluza-Klein modes of the scalar perturbations satisfy a set of coupled Schr\"{o}dinger-like equations, with which the stability of the scalar perturbations and localization of the scalar zero modes can be analyzed according to nodal theorem. The result depends on the explicit models. For superpotential derived barane models, the scalar perturbations are stable, but there exist normalizable scalar zero modes, which will result in unaccepted fifth force on the brane. We also use this method to analyze the $f(R)$ braneworld model with an explicit solution and find that the scalar perturbations are stable and the scalar zero modes can not be localized on the brane, which ensure that there is no extra long-range force and the Newtonian potential on the brane can be recovered.Comment: 13 pages, 3 figure

Unilateral CVA for CDS in Contagion model: With volatilities and correlation of spread and interest

The price of financial derivative with unilateral counterparty credit risk can be expressed as the price of an otherwise risk-free derivative minus a credit value adjustment(CVA) component that can be seen as shorting a call option, which is exercised upon default of counterparty, on MtM of the derivative. Therefore, modeling volatility of MtM and default time of counterparty is key to quantification of counterparty risk. This paper models default times of counterparty and reference with a particular contagion model with stochastic intensities that is proposed by Bao et al. 2010. Stochastic interest rate is incorporated as well to account for positive correlation between spread and interest. Survival measure approach is adopted to calculate MtM of risk-free CDS and conditional survival probability of counterparty in defaultable environment. Semi-analytical solution for CVA is attained. Affine specification of intensities and interest rate concludes analytical expression for pre-default value of MtM. Numerical experiments at the last of this paper analyze the impact of contagion, volatility and correlation on CVA.Credit Value Adjustment, Contagion Model, Stochastic Intensities and Interest, Survival Measure, Affine Specification

Response of hydrological processes to input data in high alpine catchment : an assessment of the Yarkant River basin in China

Most studies of input data used in hydrological models have focused on flow; however, point discharge data negligibly reflect deviations in spatial input data. To study the effects of different input data sources on hydrological processes at the catchment scale, eight MIKE SHE models driven by station-based data (SBD) and remote sensing data (RSD) were implemented. The significant influences of input variables on water components were examined using an analysis of the variance model (ANOVA) with the hydrologic catchment response quantified based on different water components. The results suggest that compared with SBD, RSD precipitation resulted in greater differences in snow storage in the different elevation bands and RSD temperatures led to more snowpack areas with thinner depths. These changes in snowpack provided an appropriate interpretation of precipitation and temperature distinctions between RSD and SBD. For potential evapotranspiration (PET), the larger RSD value caused less plant transpiration because parameters were adjusted to satisfy the outflow. At the catchment scale, the spatiotemporal distributions of sensitive water components, which can be defined by the ANOVA model, indicate that this approach is rational for assessing the impacts of input data on hydrological processes