For the observed line at 799.23 Å in tungsten EBIT experiment, which was assigned to be 3 F 4 o − 3 F 3 o ([Ar]4s24p54d) of W38+ ion, there were noticeable deviations for most calculated wavelengths from the meas...
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We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical *** demonstrate that conventional machine lea...
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We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical *** demonstrate that conventional machine learning models and algorithms,such as the random feature model,the two-layer neural network model and the residual neural network model,can all be recovered(in a scaled form)as particular discretizations of different continuous *** also present examples of new models,such as the flow-based random feature model,and new algorithms,such as the smoothed particle method and spectral method,that arise naturally from this continuous *** discuss how the issues of generalization error and implicit regularization can be studied under this framework.
High-resolution collinear laser spectroscopy of neutron-rich actinium has been performed at TRIUMF’s isotope separator and accelerator facility ISAC. By probing the 7s2 1S0 → 6d7p 1P1 ionic transition, the hyperfine...
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We demonstrate the constant feedback and the modified constant feedback method to the Hénon map. Using the convergence of the chaotic orbit in finite time, we can control the system from chaos to the stable fixed...
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We demonstrate the constant feedback and the modified constant feedback method to the Hénon map. Using the convergence of the chaotic orbit in finite time, we can control the system from chaos to the stable fixed point, and even to the stable period-2 orbit or higher periodic orbit by the action of a proper feedback strength and pulse interval. We also find that the multi-steady solutions appear with the same control strength and different initial conditions. The aim of this control method is explicit and the feedback strength is easy to determine. The method is robust under the presence of weak external noise.
A novel Eulerian Gaussian beam method was developed in[8]to compute the Schrödinger equation efficiently in the semiclassical *** this paper,we introduce an efficient semi-Eulerian implementation of this *** new ...
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A novel Eulerian Gaussian beam method was developed in[8]to compute the Schrödinger equation efficiently in the semiclassical *** this paper,we introduce an efficient semi-Eulerian implementation of this *** new algorithm inherits the essence of the Eulerian Gaussian beam method where the Hessian is computed through the derivatives of the complexified level set functions instead of solving the dynamic ray tracing *** difference lies in that,we solve the ray tracing equations to determine the centers of the beams and then compute quantities of interests only around these *** yields effectively a local level set implementation,and the beam summation can be carried out on the initial physical space instead of the phase *** a consequence,it reduces the computational cost and also avoids the delicate issue of beam summation around the caustics in the Eulerian Gaussian beam ***,the semi-Eulerian Gaussian beam method can be easily generalized to higher order Gaussian beam methods,which is the topic of the second part of this *** numerical examples are provided to verify the accuracy and efficiency of both the first order and higher order semi-Eulerian methods.
We introduce a numerical approach to perform the effective (coarse-scale) bifurcation analysis of solutions of dissipative evolution equations with spatially varying coefficients. The advantage of this approach is tha...
We introduce a numerical approach to perform the effective (coarse-scale) bifurcation analysis of solutions of dissipative evolution equations with spatially varying coefficients. The advantage of this approach is that the `coarse model' (the averaged, effective equation) need not be explicitly constructed. The method only uses a time-integrator code for the detailed problem and judicious choices of initial data and integration times; the bifurcation computations are based on the so-called recursive projection method (Shroff and Keller 1993 SIAM J. Numer. Anal. 30 1099-120).
Focuses on a study which discreted Ginzburg-Landau-BBM equations with periodic initial boundary value conditions by the finite difference method in spatial direction. Background on the discretization of the equations ...
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Focuses on a study which discreted Ginzburg-Landau-BBM equations with periodic initial boundary value conditions by the finite difference method in spatial direction. Background on the discretization of the equations and the priori estimates; Existence of the attractors for the discrete system; Estimates of the upper bounds of Hausdorff and fractal dimensions for the attractors.
Total and state-selective charge transfer,ionization and stripping cross sections due to the collision of Si^(2+)ion with atomic hydrogen are investigated using the classical-trajectory Monte-Carlo(CTMC)method in the ...
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Total and state-selective charge transfer,ionization and stripping cross sections due to the collision of Si^(2+)ion with atomic hydrogen are investigated using the classical-trajectory Monte-Carlo(CTMC)method in the collision energy from 1 keV/amu to 10 MeV/*** electron capture rate coefficient is obtained in the temperature range from 105 Ko to 108 *** with the data available shows that our CTMC results are *** behaviors for these cross sections varying with the projectile energy are analyzed.A classical physical picture is presented to explain the reason behind the behaviors.
Generation of the second harmonic initiated by Bell-Plesset effects in a cylindrical geometry is studied analytically. For an initial single-mode velocity perturSation, the second-order mode-coupling formula is obtain...
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Generation of the second harmonic initiated by Bell-Plesset effects in a cylindrical geometry is studied analytically. For an initial single-mode velocity perturSation, the second-order mode-coupling formula is obtained by expanding the perturbation displacement and velocity potential up to the second-order accuracy. It is found that the initially symmetric interface evolves into a significant bubble-spike asymmetric pattern. The second-order solutions clearly show that the amplitude of the spike grows faster than that of the buSble. The temporal evolutions of the amplitudes of the 5ubSie and spike are dependent on the interface velocity Vo. The larger interface velocity leads to the smaller amplitude of the perturbation at an arbitrary interface position in a cylindrically convergent geometry.
Under the development of society, the dissemination of information plays an increasingly significant role. How to achieve the goal of continually reducing the error rate and enhance the quality of communication and co...
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