Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. ...Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. In this model, as a convolution response with non-parabolic symmetry, Δn2 （I）≈ρ（b0＋ b1f - b2 f^2 with b2/b1 〉 0 is assumed. Furthermore, instead of the wave function Ψ, the high-order nonlinear equation for the beam intensity distribution f has been derived and the bell-shaped soliton solution with the envelope form has been obtained. The results demonstrate that, since the existence of the terms of non-parabolic response, the nonlocal spatial soliton has the bistable state solution. If the frequency shift of wave number β satisfies 0 〈 4（β - ρbo/μ） 〈 3η0/8α, the bistable state soliton solution is stable against perturbation. It should be emphasized that the soliton solution arising from a parabolic-symmetry response kernel is trivial. The sufficient condition for the existence of bistable state soliton solution b2/b1〉 0 has been demonstrated.展开更多
While hysteresis in the adsorption of fluids in porous material is known since about one century, the thermodynamic treatment of this phenomenon is still not settled. We propose to accept that thermodynamics is not de...While hysteresis in the adsorption of fluids in porous material is known since about one century, the thermodynamic treatment of this phenomenon is still not settled. We propose to accept that thermodynamics is not designed to deal with confined systems and we propose to introduce a new set of rules for describing the behavior of confined systems. This proposal is based on a large number of simulation calculations. The employed method of simulation has been shown to describe static and dynamic phenomena encountered in this field. The newly formulated theory incorporates the phenomenon of hysteresis without inconsistencies. Further, it will be shown that the theory allows simulating diffusional and convectional transport （nanofluidics） by a unified approach without the need to introduce capillary forces （surface or interface tensions） by phenomenological parameters. The second part of the paper is devoted to the potential for practical use. It turns out that the new concepts open the route to employing unusual states of matter found in porous systems which may lead to improved applications. In particular we will focus on the possibility to drive a fluid in a pore into states with negative pressure under static and under dynamic conditions. It turns out that states with negative pressure can be reproducibly controlled. Negative pressure states are in principal known since the time of Torricelli and they have been discussed in the literature as experimentally accessible situations. Still, they have not been turned into practical usefulness which is likely to be caused by the notion of their metastability in macroscopic systems. Possible applications refer to controlling chemical reactions as well as new routes to efficient separation processes that are difficult to handle by conventional techniques.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10574163
文摘Based on the picture of nonJinear and non-parabolic symmetry response, i.e., Δn2 （I） ≈ ρ（ao ＋ a1x - a2 x^2）, we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. In this model, as a convolution response with non-parabolic symmetry, Δn2 （I）≈ρ（b0＋ b1f - b2 f^2 with b2/b1 〉 0 is assumed. Furthermore, instead of the wave function Ψ, the high-order nonlinear equation for the beam intensity distribution f has been derived and the bell-shaped soliton solution with the envelope form has been obtained. The results demonstrate that, since the existence of the terms of non-parabolic response, the nonlocal spatial soliton has the bistable state solution. If the frequency shift of wave number β satisfies 0 〈 4（β - ρbo/μ） 〈 3η0/8α, the bistable state soliton solution is stable against perturbation. It should be emphasized that the soliton solution arising from a parabolic-symmetry response kernel is trivial. The sufficient condition for the existence of bistable state soliton solution b2/b1〉 0 has been demonstrated.
基金The theoretical basis of this study has been developed with financial support by the German Science Foundation under grant Mo288/26 within the Priority program 1105 ＂Non equilibrium processes in Fluid/fluid systems＂. Dr. Yves-Gorat Stommel has contributed to the application part of the paper by motivating calculations on separation and by critical comments.
文摘While hysteresis in the adsorption of fluids in porous material is known since about one century, the thermodynamic treatment of this phenomenon is still not settled. We propose to accept that thermodynamics is not designed to deal with confined systems and we propose to introduce a new set of rules for describing the behavior of confined systems. This proposal is based on a large number of simulation calculations. The employed method of simulation has been shown to describe static and dynamic phenomena encountered in this field. The newly formulated theory incorporates the phenomenon of hysteresis without inconsistencies. Further, it will be shown that the theory allows simulating diffusional and convectional transport （nanofluidics） by a unified approach without the need to introduce capillary forces （surface or interface tensions） by phenomenological parameters. The second part of the paper is devoted to the potential for practical use. It turns out that the new concepts open the route to employing unusual states of matter found in porous systems which may lead to improved applications. In particular we will focus on the possibility to drive a fluid in a pore into states with negative pressure under static and under dynamic conditions. It turns out that states with negative pressure can be reproducibly controlled. Negative pressure states are in principal known since the time of Torricelli and they have been discussed in the literature as experimentally accessible situations. Still, they have not been turned into practical usefulness which is likely to be caused by the notion of their metastability in macroscopic systems. Possible applications refer to controlling chemical reactions as well as new routes to efficient separation processes that are difficult to handle by conventional techniques.
