We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independen...
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We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independent compensated Poisson random measure. A semi-discrete scheme is developed for discrete time approximation, which is constituted by a classic scheme for the forward SDE [20, 28] and a novel scheme for the backward SDE. Under some reasonable regularity conditions, we prove that the semi-discrete scheme can achieve second-order convergence in approximating the FBSDEs of interest; and such convergence rate does not require jump-adapted temporal discretization. Next, to add in spatial discretization, a fully discrete scheme is developed by designing accurate quadrature rules for estimating the involved conditional mathematical expectations. Several numerical examples are given to illustrate the effectiveness and the high accuracy of the proposed schemes.
A simplified relativistic configuration interaction method is used to study the dielectronic satellite transition processes,in which the whole high-n dielectronic satellite transition processes can be treated convenie...
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A simplified relativistic configuration interaction method is used to study the dielectronic satellite transition processes,in which the whole high-n dielectronic satellite transition processes can be treated conveniently in the frame of quantum defect *** theoretical results for heliumlike iron are in good agreement with the experimental measurements.
The Chahine-Twomey relaxation method for inversion of the atmospheric radiative transfer equation is extended to provide an inverse solution to Barrick's equation describing second order scatter of high frequency ...
The Chahine-Twomey relaxation method for inversion of the atmospheric radiative transfer equation is extended to provide an inverse solution to Barrick's equation describing second order scatter of high frequency (HF) radio waves from the ocean surface. The success of the method is demonstrated here using synthesised radar Doppler spectra obtained by solving the direct problem with wave buoy directional spectrum measurements. Wave buoy measurements are limited in the range of directional characteristics that can be measured. The results presented here suggest that HF radar is capable of providing a more general measurement of the directional spectrum.
Theoretically describing feature learning in neural networks is crucial for understanding their expressive power and inductive biases, motivating various approaches. Some approaches describe network behavior after tra...
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High frequency radar measurements of significant waveheight during two experiments in the Celtic Sea are discussed. A new algorithm has been developed which can be used to provide measurements of significant waveheigh...
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High frequency radar measurements of significant waveheight during two experiments in the Celtic Sea are discussed. A new algorithm has been developed which can be used to provide measurements of significant waveheight with accuracies of about 12 per cent relative to wave-buoy measurements. A dual-radar system is required for this measurement. For use with a single-radar system, some additional information on the directional properties of the wave spectrum are required.
A comparative study is made of five methods for calculating the optimal control function for a linear parabolic tracking problem with boundary control. Questions of computational instability, numerical accuracy and ec...
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A comparative study is made of five methods for calculating the optimal control function for a linear parabolic tracking problem with boundary control. Questions of computational instability, numerical accuracy and economic computer usage are investigated. Open-loop methods based upon the variational equations are shown to have the advantages of efficiency, accuracy and ease of programming. Methods based on the method of lines and the Riccati equation are shown to be less straightforward in use. The fourth-order explicit Runge-Kutta algorithm has little scope for application because of its restricted stability range. The Kalman-Englar algorithm is much more robust but a Crank-Nicholson algorithm for the associated auxiliary equation is not very satisfactory in some cases. The auxiliary variable method may then confer some benefits.
The University College London Global Thermospheric Model and the Sheffield University High-Latitude Ionospheric Convection Model have been integrated and improved to simulate the self-consistent interaction of the the...
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The University College London Global Thermospheric Model and the Sheffield University High-Latitude Ionospheric Convection Model have been integrated and improved to simulate the self-consistent interaction of the thermosphere and ionosphere at high latitudes. For mid- and low-latitudes, equatorward of 65 degrees geomagnetic, the neutral thermospheric code maintains the use of an empirical description of plasma densities. The neutral thermospheric wind velocity, composition, density, and energy budget are computed, including their full interactions with the high-latitude ion drift and the evolution of the plasma densities of O+, H+, NO+, N2
+, and O2
+. Two 24 hr Universal Time (UT) simulations have been performed at high solar activity, for a level of moderate geomagnetic activity, at the June and December solstices, to investigate the UT and seasonal response of the coupled system. During winter, the diurnal migration of the polar convection pattern into and out of sunlight, together with ion transport, plays a major role in the plasma density structure at F-region altitudes. Only during those UT periods, when the entire geomagnetic polar region is in total darkness, is the effect of auroral oval precipitation imprinted on the F-region. In summer, the increase in the proportion of molecular to atomic species, created by the global seasonal circulation and augmented by the geomagnetic forcing, is effective in controlling the plasma densities at all Universal Times. The increased destruction of atomic oxygen ions in summer reduces the mean level of F-region ionization to similar mean levels seen in winter, despite the increased level of solar insolation. The UT variation exceeds the seasonal differences, implying a longitudinal dependency in what can be described as a high-latitude winter ionospheric anomaly. Below 200 km summer plasma densities exceed winter values at all times, and are responsible for the larger summer conductivities, Joule heating, and consequent
The short-time behavior of the turbulent viscosity is inferred from the immediate response of the Reynolds stress deduced by Crow [1] for the problem of isotropic turbulence subjected to a mean strain at time t=0. The...
We report the determination of the Landé gJ factor and Zeeman coefficients for the ground-state of 171Yb+, relevant to microwave quantum frequency standards (QFSs). The gJ factor is obtained by using two independ...
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We report the determination of the Landé gJ factor and Zeeman coefficients for the ground-state of 171Yb+, relevant to microwave quantum frequency standards (QFSs). The gJ factor is obtained by using two independent methods, the multiconfiguration Dirac-Hartree-Fock and multireference configuration-interaction methods, yielding a consistent value of 2.002615(70). The first- and second-order Zeeman coefficients are determined as 14010.78(49)Hz/µT and 31.0869(22)mHz/µT2, respectively, based on the calculated gJ factor. These coefficients enable reduced magnetic-field-induced uncertainties, improving the accuracy of the 171Yb+ microwave QFSs. The results reported in this work also offer potential for improved constraints on variations in fundamental constants through frequency comparisons and advancing trapped-ion quantum computers based on the ground-state hyperfine splitting of 171Yb+.
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