The projection operator approach to the Fokker-Planck equation. II. Dichotomic and nonlinear Gaussian noise

Two models for the Freedericksz transition in a fluctuating magnetic field are considered: one is based on a dichotomic and the other on a nonlinear Gaussian noise. Both noises are characterized by a finite correlation time. It is shown that the linear response assumption leading to the best Fokker-Planck approximation in the dichotomic and nonlinear Gaussian cases can be trusted only up to the order ¹ and ⁰, respectively. The role of the corrections to the linear response approximation is discussed and it is shown how to replace the non-Fokker-Planck terms stemming from these corrections with equivalent terms of standard type. This technique is shown to produce perfect agreement with the exact analytical results (dichotomic noise) and to satisfactorily fit the results of analog simulation (nonlinear Gaussian noise).     

The projection approach to the Fokker-Planck equation. I. Colored Gaussian noise

It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation ₁ and an unperturbed part ₀. The standard Fokker-Planck structure is recovered at the second order in ₁, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in ₁ the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in ₁, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in ₁ vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in ₁ vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation.     

大鼠肾组织的超低温快速冷冻固定和冷冻置换研究

超低温快速冷冻固定以极高的冷冻速率（１００００Ｋ／ｓ）对生物组织进行物理固定，可使生物组织结构、组织内可溶性离子及游离性物质得到保存，使被固定后的生物组织保持最接近于原自然状态，这种样品制备方法大大优于化学制备法，因而在Ｘ－射线微分析及免疫细胞化学中得到广泛应用。生物样品超低温快速冷冻后，利用冷冻置换法，在低温下将生物组织内的结晶水缓慢置换出来，而后常规包埋切片，可获得理想的组织结构及组织内待分析成分。本文应用超低温快速冷冻固定技术及冷冻置换法对大鼠肾皮质部的快速冷冻固定及损伤进行探讨。     

低温陈化法制备SO_4~(2-)/WO_3-TiO_2固体超强酸及性能研究

0引言固体超强酸的研制是近20年来催化领域中的热点研究课题之一。起初,人们所研制的SO42-/MxOy型固体超强酸中,MxOy多为ZrO2。近年来,研究者们为得到高酸强度和高催化活性的固体超强酸催化剂,以ZrO2为主体,引入第二组分、第三组分组成复合型催化剂,这方面的研究者颇多[1~4],也     

双功能催化剂体系作用下乙烯二聚和共聚合的研究

用乙烯为原料在双功能催化剂体系的作用下通过二聚和共聚合反应，直接合成线性低密度聚乙烯（ＬＬＤＰＥ）．所用二聚反应催化剂为钛酸正丁酯（Ｔｉ（ＯＢｕ）_４），共聚催化剂为ＴｉＣｌ_４／ＭｇＣｌ_２（ＺＭ－１催化剂）．研究了二聚反应动力学行为及影响双功能催化剂体系动力学过程的一些因素．结果表明利用这两种催化剂组成双功能催化剂体系能够很方便地制得密度范围在０．９０－０．９３，Ｅｔ／１０００Ｃ在１０－４０的ＬＬＤＰＥ．     

K~+-FREE INDUCED EARLY AFTERDEPOL-ARIZATION IN CARDIAC VENTRICULAR FIBERS OF GUINEA PIG AFTER COLD TREATMENT

The genesis and elimination of early afterdepolarizations (EADs) have been investigated in guinea pig cardiac ventricular fibers after a short period of cooling (5h, 2—4℃). After rewarming them to 37℃, EADs could be induced by K~+-free superfusion at an appropriate driving stimulation (0.2 Hz) in all preparations. A high level plateau, which linearly increases its duration with time, appears ahead of EADs. The critical point of the plateau occurred steadily at the level of -47±4 mV. Two types of triggered activity, all of which are the rhythmic activities in low level of membrane potential (-50 to -60 mV), appear on the platcau. There is no significant change after overdriving. Agonists of the Na-K pump (K~+ and Tl~+) could stop the rhythmic activity immediately and turn the low level of membrane potential to high one. The results showed that high level plateau is the basis of genesis of EADs, and the activation of Na-K pump plays an important part in stopping triggered rhythms arising from EADs.     

单分散纳米InVO4(正交相)的低温合成

InVO₄ is a new developed visible light responding photocatalyst for water decomposition, which is obtained by a solid-state reaction at high temperature traditionally. In this paper, pure InVO₄ nano-crystalline powder has been prepared by a hydrothermal process at low temperature and was characterized by TEM, IR, and X-ray diffraction. Many factors such as pH value, reaction time and temperature have been investigated. It is found that the optimal conditions for the preparation is: n_InCl3∶n_NaVO3=1∶2; temperature : 150 ℃; Reaction time: 4～8 h; pH=7.9～8.0. And the experimental result shows that it is a convenient way to get single dispersing InVO₄ nano-crystalline powder by flux in alkyl alcohol.     

CeO2-ZrO2-Y2O3对Pt-Rh型三效催化剂性能的影响

采用共沉淀法技术制备了Ce0.35Zr0.55Y0.10固溶体,并对其进行了比表面积、储氧量的测试和XRD的表征.将其用于低贵金属Pt-Rh型三效催化剂的制备,考察了CeO2-ZrO2-Y2O3对三效催化剂性能的影响.结果表明,Ce0.35Zr0.55Y0.10具有与Ce0.50Zr0.50O2相似的立方结构和相近的储氧量,经高温(1000 ℃)后仍能保持较大的比表面积(38.66 m2·g-1).和含Ce0.50Zr0.50O2的三效催化剂相比,含CeO2-ZrO2-Y2O3的三效催化剂经高温老化后,C3H8,CO,NO仍具有较高的转化率和较低的起燃温度.     

Investigation of glow discharge plasma for surface modification of polypropylene

Material surface properties of polymers, plastics, ceramics and textiles can be modified by atmospheric or low‐pressure glow discharge plasma. The aim of the present work is to study the surface modification of biaxially oriented polypropylene (BOPP) film in order to improve its hydrophilic and wetting properties. In this article we used low‐pressure, low‐temperature oxygen plasma for the surface treatment of BOPP. Scanning electron microscopy indicates that plasma treatment causes mainly physical changes by creating microcraters and roughness on the surface and increasing surface friction. Attenuated total reflectance infrared spectra show oxygen‐containing groups such as ? OH at 3513 cm^?1 and C?O at 1695 cm^?1. Microscopic investigations of water droplets on BOPP (treated, untreated) show that the interfacial adhesion of treated surfaces is increased. Copyright © 2003 John Wiley & Sons, Ltd.     

低硫可膨胀石墨的制备

低硫可膨胀石墨的制备宋克敏，路文义，高淑英，阎秋燕（河北教育学院石家庄０５００９１）关键词低硫可膨胀石墨，制备，过氧化氢，硫酸柔性石墨具有耐高温、耐酸碱、抗拉、抗压、抗辐射、回弹性等优良性能，被广泛应用于化工、机械、肮天、原子能等领域。但其原材料可膨...