New Approaches of Theoretical Astrophysics for Application to Some Astronomical Objects: I. An Application of Non-Classical Equation Mathematical Physics to the Magneto-Hydrodynamic Equilibrium (in Case of Mixed Magnetic Field) of Magnetic Stars

In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the necessary concepts about the equation of non-classical mathematical physics and the possibility of their applicability to astrophysical problems. The conditions of magneto-hydrodynamic equilibrium are determinate, and self-consistence provides the means to derive the corresponding partial differential equations describing this equilibrium in a magnetosphere magnetic star. Namely, this process is to the non-classical equations of mathematical physics in cases of types. Keldysh-Tricomi, a common case equation of non-classical type, is at first introduced by the author. Using the two main physical efficiencies of MHD. A mathematical model of a poloidal-toroidal mixed magnetic field for magnetic stars is constructed, and this model is classified with respect to degenerating case equations. According to Hopf’s theorem, Maxwell’s equation and the magnetic force balance equation constructed equilibrium conditions of the poloidal-toroidal of the magnetic field for a magnetic star. At the same time, the taken example, which is the self-consistency of this model by observation dates, is investigated. At first, in an application, the method of straight lines for recurrent formulas of calculation of magnetic flux and stream functions is used. The physical means, the corresponding singular point of the sonic line, cutoff, and resonance phenomena are considered. In this case, a general solution equation is found, which is interpreted by this phenomenon as a cutoff, resonance. Finally, this obtained solution gives the conditions of magneto-hydrodynamic equilibrium on the magnetosphere of magnetic stars. Methodology and obtained equations are new approaches that are at first considered.

Dielectric Relaxation of Adsorbed Water in Wood Cell Wall under Equilibrium and Non-Equilibrium State

This article summarized systematically the previous investigations on t he dielectric relaxation of wood, the main substances and extractives in wood at oven-dry state, and the dielectric relaxation based on the adsorbed water in w o od cell wall under equilibrium and non-equilibrium state. Moreover, some expect a tions for future research were proposed on this basis. The purpose of this artic le is to provide other researchers an overall understanding about the research i n this region, and further to promote the research onto a new and higher level.

Equilibrium Control Theory and Direct Method of Feedback Linearization for Nonlinear Time Varying Systems

Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.

Non-equilibrium Vibration and Diagnosis Analysis of A Rainstorm

The rainstorm weather from July 15,2010 to July 18,2010 is researched by diagnosis analysis method.The results suggest that in the strong and lasting period,the upward air current in the basin is prevail and is above 300 hPa.The convergence layer during strong rainstorm period is not thick.The convergence movement of air current is under 500 hPa.In this rainstorm process,the positive vortex maximum value center of the lower layer of convection layer is perfectly corresponding to rainstorm zone.The air current convergence and divergence intensity is one magnitude larger than the turning intensity.Flux plays a leading role in the system changes process;the non-equilibrium value of the low layer of convection layer during the strong rainstorm period U<0.Strong non-equilibrium is favorable for the movement of convergence.The non-equilibrium value of the high layer of convection layer U>0,and it stimulates the divergence movement of high layer.The divergence of high layer pushes the convergence of the lower layer and thus forms strong upward movement.

Functional Equilibrium Between Photosynthetic and Above-ground Nonphotosynthetic Structures of Plants: Evidence from a Pruning Experiment with Three Subtropical Tree Species

It is well known that plants have functional equilibrium between their above-ground parts (shoots) and below-ground parts (roots), but whether the above-ground parts of plants have functional equilibrium between their photosynthetic structures (leaves) and non-photosynthetic structures (branches and stem) is unknown. The purpose of this study is to test the hypotheses that: (1) the above-ground parts of plants have functional equilibriums between their photosynthetic structures and non-photosynthetic structures; (2) the maintenance of the equilibriums is guaranteed by the alteration of biomass partitioning to photosynthetic and non-photosynthetic structures. To test these hypotheses, a pruning experiment with four pruning intensities (0%, 20%, 50%, and 70%) were carried out with three subtropical Chinese tree species ( Ficus microcarpa, Ficus virens, Cinnamomum camphora). Pruning treatments were conducted in two successive years. The results were in conformity with the hypothesis, i.e. above-ground parts of trees had functional equilibriums between photosynthetic and non-photosynthetic structures. Pruning decreased instantaneously the mass ratios of photosynthetic structures to non-photosynthetic structures (P/NP) of all three tree species, the reduction in P/NP was strengthened with pruning intensity. However, one year after pruning, the P/NP of all pruned trees increased and were not smaller than those of unpruned trees. In agreement with the expectation, the biomass partitioning of pruned trees was altered, more newly produced above-ground biomass was partitioned to leaf growth and less to branch and stem growth, thus enabled the damaged trees to restore their functional equilibrium between photosynthetic and non-photosynthetic structures. It is clear that the maintenance of functional equilibrium between photosynthetic and non-photosynthetic structures guaranteed by the alteration of biomass partitioning provides plants a good strategy to resist external disturbance and damage.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM

Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.

Critical anomaly and finite size scaling of the self-diffusion coefficient for Lennard Jones fluids by non-equilibrium molecular dynamic simulation

We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ＊ = ρσ3 = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T＊ = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of a 〈 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations fronl the literature.

Discussion on the Non-Equilibrium Phase of the Gliding Arc Plasma Driven by the Transverse Magnetic Field

a gliding arc driven by the transverse magnetic field was ignited between the electrodes with a complicated shape at atmospheric pressure and a non-equilibrium plasma was gencrated. Under our experimental conditions, a phenomenon was clearly observed where the arc power decreased with the increase in arc voltage. As the arc voltage was higher than 3.375 kV, the are power acquired from the power supply decreased, and the arc plasma began to switch to a non-equilibrium phase. The existence of the non-equilibrium arc plasma was very short, about 10 ms in one gliding arc discharge cycle.

Effect of La_2O_3/γAl_2O_3 Catalyst on the Activation of CH_4 and CO_2 to C_02 Hydrocarbons under Non-equilibrium Plasma

In the reaction of methane and carbon dioxide to C2 hydrocarbons under non-equilibrium plasma, methane conversion was decreased, but selectivity of C2 hydrocarbons was increased when using La2O3/?Al2O3 as catalyst. So the yield of C2 hydrocarbons was higher than using plasma alone. The synergism of La2O3/?Al2O3 and plasma gave methane conversion of 24.9% and C2 yield of 18.1%. The distribution of C2 hydrocarbons changed when Pd- La2O3/?Al2O3 was used as catalyst, the major C2 product was ethylene.

NON-EQUILIBRIUM SOLUTE SEGREGATION TO AUSTENITIC GRAIN BOUNDARY IN FERRUM-NICKLE ALLOY

The development of non-equilibrium segregation of boron at grain boundaries in Fe-4 0%Ni alloy during continuous cooling process was experimentally observed with boron Particle Tracking Autoradiography (PTA) and Transmission Electron Microscopy (TEM,). The samples with 10ppm boron were cooled at 2℃/s to 1040, 980, 920, 860, 780 and 640℃ respectively after pre-heat treatment of 1150℃ for 15mm with a Gleeble-1500 heat simulating machine, then water quenched to room temperature. The width of segregation layer and boron depletion zone, rich factor and other parameters were measured by a special image analysis system. The experimental results of PTA show that the grain boundary segregation of boron during cooling process is a dynamic process and the development of the non-equilibrium segregation experiences three stages: first increases rapidly from 1150 to 1040℃, then gently from 1040 to 860℃, and rapidly again from 860℃ to 640℃. The width of boron depletion zone increases from about 11μm at 1040℃ to 26μm at 640℃. TEM observation shows that boron precipitates exist at grain boundaries when the samples are cooled to below 860℃. The experimental phenomena are briefly discussed.

Catalytic Effect of Activated Carbon and Activated Carbon Fiber in Non-Equilibrium Plasma-Based Water Treatment

Catalysis and regeneration efficiency of granular activated carbon （GAC） and activated carbon fiber （ACF） were investigated in a non-equilibrium plasma water treatment reactor with a combination of pulsed streamer discharge and GAC or ACF. The experimental results show that the degradation efficiency of methyl orange （MO） by the combined treatment can increase 22% （for GAC） and 24% （for ACF） respectively compared to pulsed discharge treatment alone, indicating that the combined treatment has a synergetic effect. The MO degradation efficiency by the combined treatment with pulsed discharge and saturated GAC or ACF can increase 12% and 17% respectively compared to pulsed discharge treatment alone. Both GAC and ACF show catalysis and the catalysis of ACF is prominent. Meanwhile, the regeneration of GAC and ACF are realized in this process. When H202 is introduced into the system, the utilization efficiency of ozone and ultraviolet light is improved and the regeneration efficiency of GAC and ACF is also increased.

Separation of cobalt and nickel by non-equilibrium solvent extraction

The separation of cobalt and nickel in the ammoniacal sulfate solution by non equilibrium solvent extraction with a phosphate (P303) as extractant was studied. In the experiment, the effects of equilibrium pH value in aqueous phase, contact time of the two phases, the air blowing time for feed liquor in the open beaker on percentage extraction of cobalt and nickel and percentage reextraction of nickel from the loaded organic phase with dilute H 2SO 4. etc were studied. The results showed that: Co(Ⅱ) can be oxidized to Co(Ⅲ) ammino complex by adding (NH 4) 2S 2O 8 or blowing air to the aqueous phase, and Co(Ⅲ) ammino complex is a kind of kinetically inert complex. Its extractive speed is very slow, while the nickel′s is much faster than that of cobalt. By controlling the contact time of the two phases, nickel can be separated from cobalt by non equilibrium solvent extraction. Then nickel was reextracted from the loaded organic phase with dilute H 2SO 4.

Experimental Study of a Minitype Atmospheric Non-equilibrium Plasma Source

A mini-type of plasma source was studied experimentally. The results showed that the plasma density, which was generated by an atmospheric non-equilibrium plasma source, rises with the increase in driving electric-field and the momentum of gas particles. For a driving electricfield of 56 kV/cm and a gas particles＇ momentum of 10^9 × 10^-22 g·m/s, the ion density can exceed 10^10/cm^3 while the effective volume of the plasma source is only 2.5 cm^2. This study may help develop a method to generate a minitype plasma source with low energy consumption but high ion concentration. This source can be used in chemical industry, environmental engineering and military applications.

Non-equilibrium turbulent phenomena in the ?ow over a backward-facing ramp

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid turbulence, turbulent wakes, and homogeneous isotropic turbulence(HIT). The non-equilibrium turbulence in non-canonical flows, however, has rarely been studied due to the complexity of the flows. In the present contribution, a directnumerical simulation(DNS) database of a turbulent flow is analyzed over a backwardfacing ramp, the flow near the boundary is demonstrated, and the non-equilibrium turbulent properties of the flow in the wake of the ramp are presented by using the characteristic parameters such as the dissipation coefficient C and the skewness of longitudinal velocity gradient Sk, but with opposite underlying turbulent energy transfer properties. The equation of Lagrangian velocity gradient correlation is examined, and the results show that non-equilibrium turbulence is the result of phase de-coherence phenomena, which is not taken into account in the modeling of non-equilibrium turbulence. These findings are expected to inspire deeper investigation of different non-equilibrium turbulence phenomena in different flow conditions and the improvement of turbulence modeling.

Study of impurity behaviour in non-coronal equilibrium state

A physical model of analysing the behaviour of impurities out of coronal equilibrium in tokamak plasmas has been proposed. Through solving the time-dependent rate equations including the effects of atomic processes and the particle transport losses, the ionization state distribution is obtained for a range of low Z impurities such as helium, carbon, oxygen and argon. By using the ionization state distribution of these impurities, the radiation rate coefficients and the mean charge state changing with plasma temperature are calculated. The results show that the mean charge state （Z） is sensitively dependent on the parameter neT, and this is the reason why the radiation power of impurities under non-coronal equilibrium conditions is several orders of magnitude higher than that under coronal equilibrium condition.

Non-equilibrium ignition criterion for magnetized deuterium–tritium fuel

In this paper, non-equilibrium ignition conditions for magnetized cylindrical deuterium–tritium plasma in the presence of an axial magnetic field have been investigated. It is expected that temperature imbalance between ions and electrons as well as the axial magnetic field will relax the threshold of ignition conditions.Therefore, ignition conditions for this model are derived numerically involving the energy balance equation at the stagnation point. It has been derived using parametric space including electron and ion temperature(T_e, T_i), areal density(q R), and seed magnetic field-dependent free parameters of B/q, mB, and BR. For B/ρ < 10~6 G cm^3 g^(-1),mB < 4 × 10~4 G cm g^(-1), and BR <3 × 10~5 G cm, the minimum fuel areal density exceeds between ρR >0.002 g cm^(-2), ρR> 0.25 g cm^(-2), and ρR > 0.02 g cm^(-2),respectively. The practical equilibrium conditions also addressed which is in good agreement with the corresponding one-temperature magnetized mode proposed in previous studies. Moreover, it has been shown that the typical criterion of BR ≥(6.13–4.64) × 10~5 G cm would be expectable. It is also confirmed that the minimum product of areal density times fuel temperature in equilibrium model is located in the range of T = 6–8 keV for all these free parameters, depending on the magnitude of the magnetic field. This is the entry point for the non-equilibrium model consistent with equilibrium model.

Thermodynamic and Equilibrium Composition Analysis of Using Iron Oxide as an Oxygen Carrier in Nonflame Combustion Technology

Nonflame combustion technology （NFCT） is a harmonious energy utilization technology. There are not environmental-unfriendly gases such as NOx, CO2 discharged in the whole combustion process. Combustion processes realizes zero emission through this technology. Fe2O3 is involved as oxygen carrier, is examined thermodynamically, and the thermodynamic data of the redox reactions are calculated. Using the criteria of minimizing the Gibbs free energy, the equilibrium composition was investigated. The equilibrium analysis shows that producing complete oxidized resultants must have high molar ratio of Fe2O3/CH4. If quantity of Fe2O3 is not sufficient, more partial oxidized products such as CO, H2, even C will be produced.

A Mixed-control Mechanism Model of Proeutectoid Ferrite Growth under Non-equilibrium Interface Condition in Fe-C Alloys

By combining the α/γ interface migration and the carbon diffusion at the interface in Fe-C alloys, a mathematical model is constructed to describe the mixed-control mechanism for proeutectoid ferrite formation from austenite. In this model, the α/γ interface is treated as non-equilibrium interface, i.e., the carbon concentration of austenite at γ/α interface is obtained through theoretical calculation, instead of that assumed as the local equilibrium concentration. For isothermal precipitation of ferrite in Fe-C alloys, the calculated results show that the rate of interface migration decreases monotonically during the whole process, while the rate of carbon diffusion from γ/α interface into austenite increases to a peak value and then decreases. The process of ferrite growth may be considered as composed of three stages: the period of rapid growth, slow growth and finishing stage. The results also show that the carbon concentration of austenite at γ/α interface could not reach the thermodynamic equilibrium value even at the last stage of ferrite growth.

Partial Remelting of Thixotropic Magnesium-Rare Earth Alloy from Near Non-Equilibrium-Liquidus Casting

After the investigation on partial remelting of thixotropic magnesium serial alloys （ZK60） by near non-equilibrium liquidus casting （NNLC）, the primary solid grains of ZK60-2Ca alloy spheroidized notably during partial remelting processing, however, coarsening and polygonization as occurred holding time prolonged. The refining and globularity of the thixotropic alloys are promoted after further alloyed by Y, RE, Nd and/or Ag, and the results vary with those addition. The remelting structure of ZK60-2Ca-1Y alloy is finer than its base alloy. And the effect of RE, especially Ag, on the refinement of microstrueture is notable, but Nd does nothing on it. There is little impact of remelting temperature fluctuation on partial remelted microstrueture as holding time in general. On the contrary, it is more sensitive at longer holding time. The quality thixotropic silver-contained alloy can be achieved by remelted partially at 600℃ for 10 min.