Utlizing the factorizing F operator in the quantum space,the scalar products of the Bethe states are directly calculated and the Gaudin formula is proved for the case of XXX 12 spin chain under the integrable open boundary condition.

Optimizing open boundary conditions of nonlinear tidal model using adjoint methodⅡ. Assimilation experiment for tide in the Huanghai Sea and the East China Sea

A new class of Hubbard-type models with open boundary conditions in one dimension is studied in the frame- work of coordinate Bethe ansatz method. The energy spectrum,integrable boundary conditions and the corresponding Bethe ansatz equations are derived.

Utlizing the factorizing F operator in the quantum space,the scalar products of the Bethe states are directly calculated and the Gaudin formula is proved for the case of XXX 12 spin chain under the integrable open boundary condition.

By creating a large scale computing grid (south to Kanmen, north to Lianyun Harbor, west to 125.15°E )of Changjiang estuary and Hangzhou Bay and their neighboring sea areas and using up to date data of tidal stations, 8 major tidal constituents, M2, S2, N2, K2, K1, O1, P1 and Q1, are simulated more accurately. And thus more accurate tidal level boundary condition can be given at the open boundaries of models of Changjiang estuary.

A twenty four month control run was performed using climatological monthly mean wind stresses and heat and salt fluxes as surface forcing and observational oceanic inflow at open boundaries.

Based on the physical framework of modular ocean model(MOM) and taking the physical process at open boundaries into appropriate consideration, a regional ocean numerical model is developed.

Transport across the open boundaries has significant contribution to the distribution of the stream functions , especially to the boundary current along the northern continental slope and the western shore of the SCS.

In the second problem, the function of internal anode is served by the open boundary of plasma with zero anode drop.

Using the Hartree-Fock approximation, analytic solutions of the Schr?dinger equation were obtained for a strong electromagnetic field with open boundary conditions.

The Schr?dinger equation with open boundary conditions was solved numerically; the solutions make it possible to describe the coherent oscillations in a resonance-tunnel diode in a wide range of frequencies and amplitudes of the fields.

Approximate open boundary conditions for a class of hyperbolic equations

Initial-boundary value problems formulated in spatially unbounded domains can be sometimes reduced to problems in their bounded subdomains by using the so-called open boundary conditions.

Using the Hartree-Fock approximation, analytic solutions of the Schr?dinger equation were obtained for a strong electromagnetic field with open boundary conditions.

The Schr?dinger equation with open boundary conditions was solved numerically; the solutions make it possible to describe the coherent oscillations in a resonance-tunnel diode in a wide range of frequencies and amplitudes of the fields.

Approximate open boundary conditions for a class of hyperbolic equations

Initial-boundary value problems formulated in spatially unbounded domains can be sometimes reduced to problems in their bounded subdomains by using the so-called open boundary conditions.

In the data assimilation experiments, three types of unknown parameters (water depth, bottom friction and tidal open boundary conditions in the model equations) are chosen as control variables.

The present paper shows that -norm, which has been used in the field of control theory, can reveal the traffic jam phenomenon in an optimal velocity traffic model under an open boundary condition.

We carry out Density Matrix Renormalization Group (DMRG) calculations on the interchain coupling model for the quasi-one-dimensional organic ferromagnets under open boundary condition.

The beta effect, the momentum advection and the open boundary condition have little influence on the circulation pattern.

[2-4] there is an Adaptive Open Boundary Condition (AOBC) designed for transient waves which overcomes the limitation of the existing Open Boundary Condition (OBC) and can be used for the cases of waves with arbitrary incident angles.

A significant improvement of the open boundary condition which was originally studied by Engquist and Majda is given.

The coastal circulation model is used to simulate the semi-diurnal tidal circulation and associated nonlinear dynamics with the M2 forcing specified at the model open boundaries.

The second is an accurate absorbing impedance boundary condition to represent open boundaries which is proved to be an efficient absorbing boundary.

Correlation functions in the Calogero-Sutherland model with open boundaries

In the open boundaries case for one species of particles (particles 1), a passage from first to second order transition occurs by decreasing the jumping rate.

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries.

Surface wave propagation in shallow water of varying depth is considered.The long wave model applied in this paper is of the generalized Boussinesq class.Both the nonlinear and dispersive effects are taken into account in the model.The nonlinear governing equations are solved numerically by a finite-difference method with a simple approximate open-boundary condition as an initial-boundary value problem. The development of the original solitary wave climbing up/down over a gentle slope is described by the numerical...

Surface wave propagation in shallow water of varying depth is considered.The long wave model applied in this paper is of the generalized Boussinesq class.Both the nonlinear and dispersive effects are taken into account in the model.The nonlinear governing equations are solved numerically by a finite-difference method with a simple approximate open-boundary condition as an initial-boundary value problem. The development of the original solitary wave climbing up/down over a gentle slope is described by the numerical examples.The numerical examples also demonstrate the process of wave transformation when a solitary wave is progressing over a slope onto a shelf.On the shelf the wave disintegrates into a train of solitary waves of decreasing amplitude. New results explored here include the interesting phenomenon of two solitary waves interacting over the inclined ramp and the effect of the variation in depth on this interaction, the fission of them and their phase shift.

An improved model for the prediction numerically the nonlinear water wave force exerted on offshore structure is proposed. In a previous work, the authors presented a model for the same purpose with an open boundary condition imposed, where the wave celerity has been defined constant. Generally, the value of wave celerity is time-dependent and varying with spatial location. Within the present model the wave celerity is evaluated by an upwind difference scheme, which enables the improved model could be extended...

An improved model for the prediction numerically the nonlinear water wave force exerted on offshore structure is proposed. In a previous work, the authors presented a model for the same purpose with an open boundary condition imposed, where the wave celerity has been defined constant. Generally, the value of wave celerity is time-dependent and varying with spatial location. Within the present model the wave celerity is evaluated by an upwind difference scheme, which enables the improved model could be extended to conditions with variable finite water depth, where the value of wave celerity varies with time as the wave approching to the offshore structure. The finite difference method incorporated with the time-stepping technique in time domain developed here makes the numerical evolution effective and stable. Computation of examples on interaction between surface-piercing vertical cylinder and solitary wave or cnoidal wave train demonstrates the validability as what was expected.

The model tests of cooling water engineering for Sunan Nuclear Power Plant and for Zhanjiang Thermal Power Plant have been carried out. The advantages and disadvantages of the distorted and undistorted models are discussed. The differences of circulation from the near field between the two types of models not only depend on the distortion ratio but also depend on the layout and the type of outlet and intake. Whether the temperature rise of inlet water on undistorted model could represent the total temperature...

The model tests of cooling water engineering for Sunan Nuclear Power Plant and for Zhanjiang Thermal Power Plant have been carried out. The advantages and disadvantages of the distorted and undistorted models are discussed. The differences of circulation from the near field between the two types of models not only depend on the distortion ratio but also depend on the layout and the type of outlet and intake. Whether the temperature rise of inlet water on undistorted model could represent the total temperature rise depends on the similarity of temperature at the model open boundary.