•The dynamic liquid–ice equilibrium relationship considering the contribution of water seepage pressure is established.•The relationship between the decrease of water freezing point temperature and ...water seepage pressure is derived.•A thermal-hydraulic model is established for AGF under water seepage.•The temperature field evolution characteristics in the subway cross passages freezing are analyzed.
In the system of artificial ground freezing under water seepage, the dynamic liquid–ice phase equilibrium relationship considering the contribution of water seepage pressure was established based on the classical thermodynamics fundamentals. The freezing characteristic function was represented by combining the Young–Laplace law with van Genuchten model. A thermal-hydraulic model of saturated porous media considering dynamic liquid–ice phase equilibrium was established and validated thorough laboratory tests under various seepage velocities. The temperature field evolution laws of sand, silty and clay grounds were studied based on the thermal-hydraulic model. The temperature field development laws of primary side tunnel of subway cross passages in silty-clay layer were analyzed by applying the thermal-hydraulic model. The relationship between water seepage pressure and the decrease of water freezing point temperature was obtained according to the dynamic liquid–ice phase equilibrium. Compared with the simulation results of considering static liquid–ice phase equilibrium relationship, considering the dynamic liquid–ice phase equilibrium relationship changes the distribution of water-ice phase transition front and has significant influence on the temperature evolution in silty ground. However, that influence in sand ground and clay ground is insignificant because of the relatively lower water seepage pressure in sand ground and poor thermal conductivity in clay ground. Due to the cold energy accumulation bring by water seepage, the freezing rate in the downstream of freezing pipes is faster than that in the upstream of freezing pipes. This effects are exacerbated by lower decrease of water freezing point temperature caused by minor water seepage pressure in the downstream of freezing pipes. Four representative temperature measured points were selected to acquire the relationship between simulation and on-site temperatures. It was observed that the trends of simulation results reflect the tunnel freezing process well.
This paper focuses on the variance and volatility swaps pricing in the framework of a liquidity-adjusted underlying assets model. The pricing formulas of discretely-sampled variance and volatility ...swaps are obtained under the stochastic liquidity risk by deriving the characteristic function and solving the governing PDEs. The limiting properties for the pricing formulas of discretely-sampled variance and volatility swaps, namely the pricing formulas of continuous sampling, are also given. Finally, to illustrate the performance of the pricing formulas, some detailed numerical experiments are provided, including the comparisons with Monte Carlo (MC) simulations results, the effects of stochastic liquidity and parameters variation on derivative prices as well as the empirical studies from real-market data.
Let m be an integer with m≥2. For a given set S⊆Zm and n‾∈Zm, let RS(n‾) denote the number of solutions of the equation n‾=s‾+s′‾ with unordered pair (s‾,s′‾)∈S×S and s‾≠s′‾. In this paper, we ...determine the structure of sets A,B satisfying A∪B=Zm, |A∩B|=2 and RA(n‾)=RB(n‾) for all n‾∈Zm, where m is even.
This study focused on the low-occurrence wind events at pedestrian levels. The probability density functions (PDFs) are reliable statistical information. However, instantaneous velocity datasets are ...required to determine PDFs. In this study, theoretical methods were derived to model PDFs, based on the Gram–Charlier series (GCS methods) and higher-order statistics. The time-series data of the wind velocity components and speed at the pedestrian level around an isolated building from a large-eddy simulation (LES) database were used to validate GCS methods. Results showed that all GCS methods showed enhanced flexibility than the Gaussian distribution for modelling PDFs. For the low-occurrence values, the estimation accuracy of the GCS method gradually increased as the modelling order increased, at most probe points. The GCS-A method was developed to adaptively remove the large-error points based on thresholds of the fifth- and sixth-order moments. For global accuracy, the GCS-4th and GCS-A methods have higher estimation accuracy than other methods. The present model provides a new framework to estimate the low-occurrence wind events at pedestrian levels using only turbulence statistics, yielding to the expansion of the application of LESs for pedestrian-level wind assessments.
•Low-occurrence wind events at the pedestrian level were focused.•The methods based on the Gram–Charlier series were derived and applied.•The methods were validated for an isolated building case.•The methods showed enhanced flexibility than the Gaussian distribution.•The accuracy of the method generally increased as the modelling order increased.
The test of independence of two groups of variables is addressed in the case where the sample size N is considered randomly distributed. This assumption may lead to a more realist testing procedure ...since in many situations the sample size is not known in advance. Three sample schemes are considered where N may have a Poisson, Binomial or Hypergeometric distribution. For the case of two groups with p1 and p2 variables, it is shown that when either p1 or p2 (or both) are even the exact distribution corresponds to a finite or an infinite mixture of Exponentiated Generalized Integer Gamma distributions. In these cases a computational module is made available for the cumulative distribution function of the test statistic. When both p1 and p2 are odd, the exact distribution of the test statistic may be represented as a finite or an infinite mixture of products of independent Beta random variables whose density and cumulative distribution functions do not have a manageable closed form. Therefore, a computational approach for the evaluation of the cumulative distribution function is provided based on a numerical inversion formula originally developed for Laplace transforms. When the exact distribution is represented through infinite mixtures, an upper bound for the error of truncation of the cumulative distribution function is provided. Numerical studies are developed in order to analyze the precision of the results and the accuracy of the upper bounds proposed. A simulation study is provided in order to assess the power of the test when the sample size N is considered randomly distributed. The results are compared with the ones obtained for the fixed sample size case.
Many numerical models for simulating freezing and thawing phenomena of soil have been developed due to emerging geotechnical issues in cold regions. In particular, coupled thermo‐hydro‐mechanical ...(THM) analysis is used to evaluate complicated deformation, thermal, and moisture transport behavior of freezing–thawing soils. This study proposes a soil‐freezing characteristic curve (SFCC) that is robust and adaptive with various computational frameworks, including the THM approach. The proposed SFCC can also account for different soil types by incorporating the particle size distribution. Here an automatic regression scheme is adopted to update the SFCC associated with deformation and thermal changes. In addition, a smoothing algorithm is adopted to prevent a sharp change of the SFCC due to phase transition between the liquid water and crystal ice. Based on experimental works in the literature, the applicability of our model is demonstrated when the initial water contents and soil particle distribution differ. We further investigate the performance of the proposed SFCC as a constitutive model within a simplified THM framework. Our results show that the proposed model captures the desired behavior of different soil types in the freezing process, such as freezing temperature depreciation, the effect of compaction, and mechanical loading on unfrozen water content.
The Heston stochastic volatility model is a standard model for valuing financial derivatives, since it can be calibrated using semi-analytical formulas and captures the most basic structure of the ...market for financial derivatives with simple structure in time-direction. However, extending the model to the case of time-dependent parameters, which would allow for a parametrization of the market at multiple timepoints, proves more challenging. We present a simple and numerically efficient approach to the calibration of the Heston stochastic volatility model with piecewise constant parameters. We show that semi-analytical formulas can also be derived in this more complex case and combine them with recent advances in computational techniques for the Heston model. Our numerical scheme is based on the calculation of the characteristic function using Gauss–Kronrod quadrature with an additional control variate that stabilizes the numerical integrals. We use our method to calibrate the Heston model with piecewise constant parameters to the foreign exchange (FX) options market. Finally, we demonstrate improvements of the Heston model with piecewise constant parameters upon the standard Heston model in selected cases.
Domain adaptation has great values in unpaired cross-modality image segmentation, where the training images with gold standard segmentation are not available from the target image domain. The aim is ...to reduce the distribution discrepancy between the source and target domains. Hence, an effective measurement for this discrepancy is critical. In this work, we propose a new metric based on characteristic functions of distributions. This metric, referred to as CF distance, enables explicit domain adaptation, in contrast to the implicit manners minimizing domain discrepancy via adversarial training. Based on this CF distance, we propose an unsupervised domain adaptation framework for cross-modality cardiac segmentation, which consists of image reconstruction and prior distribution matching. We validated the method on two tasks, i.e., the CT-MR cross-modality segmentation and the multi-sequence cardiac MR segmentation. Results showed that the proposed explicit metric was effective in domain adaptation, and the segmentation method delivered promising and superior performance, compared to other state-of-the-art techniques. The data and source code of this work has been released via https://zmiclab.github.io/projects.html .
•The characteristic function of the grid-connected VSC is established.•The impacts of the system resistances on the system stability are studied analytically.•An analytical stability criterion for ...the grid-connected VSC is derived by neglecting the system resistances.•The power transmission limitation of the converter is obtained from the derived stability criterion.
This paper provides an analytical investigation of the small-signal stability of the grid-connected voltage source converter (VSC) as well as the impacts of the system resistances. The dynamic model of the studied system is first established, and the characteristic function is derived from the linearized model. Based on the characteristic function, the analytical relationships between the system resistances and the dominated pole are obtained utilizing the analytical sensitivity approach. It is found that the line resistance can provide positive damping for the oscillation mode, improving the system stability, while the converter resistance will worsen the system stability. Generally, the line resistance has an evident more substantial impact on the stability of the grid-connected VSC than the converter resistance. The stability analysis results of the grid-connected VSC conducted by ignoring the system resistances are conservative. Ulteriorly, the characteristic function is simplified by neglecting the system resistances, and a sufficient and analytical stability criterion is established from the simplified characteristic function using the Routh Judgement. It exhibits the constraint condition among controller parameters, electrical distance and operation conditions for ensuring system stability. Moreover, the power transmission limitation of the converter affected by the controller parameters and electrical distance is obtained from the derived stability criterion. The small perturbation analysis and electromagnetic transient simulation give a demonstration to the analysis.
We consider a problem of propagation of monochromatic electromagnetic waves in a circle cylindrical waveguide filled with nonlinear dielectric medium. The permittivity of the waveguide is described ...by the Kerr law, which is one of the most important nonlinear dependence in nonlinear optics. In order to find guided waves we develop an original mathematical approach that allows us to prove existence of infinitely many guided waves. In addition, we prove that only a finite number of the founded nonlinear guided waves have linear counterparts; the others are nonlinearizable solutions. Numerical results are also presented.
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