A model for prediction SST in limited region- Ⅱ . The model's physical equation

-The model's physical equation is used to parameterize some subgrid-scale processes and physical processes in the present numerical model. The transmission and attenuation of the solar energy in the ocean are considered. A simple diagnostic equation for the cloud fractions k proposed on the basis of the humidities at the surface and the mid-troposphere. The parameterized formulae of both entrainment and Ekman pumping are improved.In the numerical integration, the treatment on damping the inertial oscillations is emphasized. The initialization and the objective analysis of the data which are necessary for the operational prediction will be presented in another paper.Results of SST prediction and some numerical experiments are given here. The model is computationally stable and successful in modelling the behaviors of the drift current and the mixed layer physics, and the AMD (absolute mean deviations) ≤1. 2℃ , RC (correlation coefficients ) ≥85% for 3-day forecasting.

The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics

Using the projective Riccati equation expansion （PREE） method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.

Hidden Properties of Mathematical Physics Equations. Double Solutions. The Realization of Integrable Structures. Emergence of Physical Structures and Observable Formations

With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.

EQUATION OF MATHEMATICAL PHYSICS AND OTHER AREAS OF APPLICATION: A CLASSICAL INTEGRABLE SYSTEM AND THE INVOLUTIVE REPRESENTATION OF SOLUTIONS OF THE HIGHER ORDER KAUP-NEWELL EQUATION

Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.

Research on numerical emulator of mine methane and coal dust explosion

The mathematical physics model of mine methane and coal dust explosion propagation was established in the research,by using continuous phase,combustion,par- ticulate equations of mathematical physics.Based upon the data from mine methane drainage roadway explosion,and mine methane and coal dust explosion propagation ex- perimental studies,the numerical emulator system of mine methane and coal dust explo- sion software was developed by using prevalent flow simulation platform,which can be used to simulate the explosion accidents process effectively.In addition,the system can also be used to determine whether coal dust involved in the explosion,and to simulate accurately the transition from deflagration to detonation in methane explosion,propagation velocity of explosion shock,attenuation pattern,and affected area of explosion.

A Monte Carlo Model of Light Propagation in Nontransparent Tissue

To sharpen the imaging of structures, it is vital to develop a convenient and efficient quantitative algorithm of the optical coherence tomography (OCT) sampling. In this paper a new Monte Carlo model is set up and how light propagates in bio-tissue is analyzed in virtue of mathematics and physics equations. The relations,in which light intensity of Class 1 and Class 2 light with different wavelengths changes with their permeation depth,and in which Class 1 light intensity (signal light intensity) changes with the probing depth, and in which angularly resolved diffuse reflectance and diffuse transmittance change with the exiting angle, are studied. The results show that Monte Carlo simulation results are consistent with the theory data.

Neutron star mass-radius relation with gravitational field shielding by a scalar field

The currently well-developed models for equations of state （EoSs） have been severely impacted by recent measurements of neutron stars with a small radius and/or large mass. To explain these measurements, the theory of gravitational field shielding by a scalar field is applied. This theory was recently developed in accor- dance with the five-dimensional （5D） fully covariant Kaluza-Klein （KK） theory that has successfully unified Einstein＇s general relativity and Maxwell＇s electromagnetic theory. It is shown that a massive, compact neutron star can generate a strong scalar field, which can significantly shield or reduce its gravitational field, thus making it more massive and more compact. The mass-radius relation developed under this type of modified gravity can be consistent with these recent measurements of neutron stars. In addition, the effect of gravitational field shielding helps explain why the supernova explosions of some very massive stars （e.g.9 40 MQ as measured recently） actually formed neutron stars rather than black holes as expected. The EoS models, ruled out by measurements of small radius and/or large mass neutron stars according to the the- ory of general relativity, can still work well in terms of the 5D fully covariant KK theory with a scalar field.