A new dimensional analysis for high Rayleigh number thermal convection is proposed to give an alternative interpretation of the scaling laws observed recently by Castaing et al. [J. Fluid Mech. (in press)]. The key as...
A new dimensional analysis for high Rayleigh number thermal convection is proposed to give an alternative interpretation of the scaling laws observed recently by Castaing et al. [J. Fluid Mech. (in press)]. The key assumption in the present approach is that the central fluctuating temperature field actively interacts with the turbulent velocity field, and this interaction leads to a velocity inertial subrange that deviates significantly from Kolmogorov’s freely cascading inertial range.
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...
详细信息
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.
This article is concerned with the well-posedness as well as long-term dynamics of a wide class of non-autonomous,non-local,fractional,stochastic Fitz Hugh-Nagumo systems driven by nonlinear noise defined on the entir...
详细信息
This article is concerned with the well-posedness as well as long-term dynamics of a wide class of non-autonomous,non-local,fractional,stochastic Fitz Hugh-Nagumo systems driven by nonlinear noise defined on the entire space *** well-posedness is proved for the systems with polynomial drift terms of arbitrary order as well as locally Lipschitz nonlinear diffusion terms by utilizing the pathwise and mean square uniform *** mean random dynamical system generated by the solution operators is proved to possess a unique weak pullback mean random attractor in a Bochner *** existence of invariant measures is also established for the autonomous systems with globally Lipschitz continuous diffusion *** idea of uniform tail-estimates of the solutions in the appropriate spaces is employed to derive the tightness of a family of probability distributions of the solutions in order to overcome the non-compactness of the standard Sobolev embeddings on RNas well as the lack of smoothing effect on one component of the *** results of this paper are new even when the fractional Laplacian is replaced by the standard Laplacian.
Three models are considered for single component, single phase flow in naturally fractured porous media. The microscopic model holds on the Darcy scale, and it is considered to govern the system. The macroscopic, dual...
详细信息
Three models are considered for single component, single phase flow in naturally fractured porous media. The microscopic model holds on the Darcy scale, and it is considered to govern the system. The macroscopic, dual-porosity model was derived in Part I of this work from the microscopic model by two-scale mathematical homogenization. In this paper, we show that the dual-porosity model predicts well the behavior of the microscopic model by comparing their computed solutions in certain reasonable test cases. Homogenization gives a complex formula for a key parameter in the dual-porosity model;herein a simple approximation to this formula is presented. The third model considered is a single-porosity model with averaged parameters. It is shown that this type of model cannot predict the behavior of the microscopic flow.
The nuclear data of n+^(240;242;244)Pu reactions for incident energy below 200 MeV are calculated and evaluated to meet the requirement in the design of an accelerator-driven subcritical system. The optical model is u...
详细信息
The nuclear data of n+^(240;242;244)Pu reactions for incident energy below 200 MeV are calculated and evaluated to meet the requirement in the design of an accelerator-driven subcritical system. The optical model is used to calculate the total, nonelastic, shape elastic cross sections, shape elastic scattering angular distributions, and transmission coefficients. The distorted-wave Born approximation is applied to calculate the direct inelastic scatterings to the discrete excited states. The nuclear reaction statistical models and fission theory are applied to describe neutron, proton, deuteron, triton, helium-3, alpha and c emissions, and fission consistently. The results thus obtained are compared with experimental data and the evaluated data obtained from ENDF/B-VII.1 and JENDL-4.0.
A frequency-stepping algorithm for solving multifrequency (acoustic) wave propagation is considered. A two-grid method is employed for the problems of single frequency. For high frequency applications, the coarse grid...
详细信息
A frequency-stepping algorithm for solving multifrequency (acoustic) wave propagation is considered. A two-grid method is employed for the problems of single frequency. For high frequency applications, the coarse grid problem is still huge, since one has to choose at least six to eight grid points per wavelength for a stability reason. The coarse grid problem is solved by a nonoverlapping domain decomposition (DD) method. The solution of the former frequency problem is used as the initial guess for the solution of the next larger frequency problem. Such an algorithm turns out to be efficient for multifrequency, as well as single-frequency problems, as shown in numerical results. Also, it is easily parallelizable with a high efficiency.
In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.
In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.
We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove tha...
详细信息
We study the initial value problem of the Davey-Stewartson systems for the elliptic-elliptic and hyperbolic-elliptic cases. The local and global existence and uniqueness of solutions in Hs is shown. Also, we prove that the scattering operator carries a band in Hs into Hs.
We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effec...
详细信息
We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish this through the mathematical technique of formal two-scale homogenization. This technique enables us to average the single-porosity, Darcy equations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We consider three flow situations, the flow of a single component in a single phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.
An FFT method is described for the solution of Poisson's equation over a rectangular region with Robbins boundary conditions on either one or two sides of the region, together with suitable conditions on the rest ...
详细信息
An FFT method is described for the solution of Poisson's equation over a rectangular region with Robbins boundary conditions on either one or two sides of the region, together with suitable conditions on the rest of the boundary. In contrast to earlier applications of the FFT technique, the equations for the Fourier harmonic amplitudes do not decouple into simpler independent systems and an effective iterative scheme is developed for the solution of these equations. A theoretical convergence analysis is shown generally to support the results obtained from practical computation. For the test problems considered the method is found to take between 3 and 4 times the execution time for problems soluble directly by the FFT technique.
暂无评论