Ising格子的分子热力学模型

从统计力学出发，结合Ｍｏｎｔｅ Ｃａｒｌｏ分子模拟的结果，导出了Ｉｓｉｎｇ格子的混合亥氏函数模型。该模型能非常满意地预测Ｉｓｉｎｇ格子的液液共存线，其结果明显优于Ｆｌｏｒｙ－Ｈｕｇｇｉｎｓ理论，也优于Ｆｒｅｅｄ理论。     

二维Helmholtz方程的高阶紧致差分方法

基于二阶导数的四阶Padé型紧致差分逼近式,并结合原方程本身,得到了二维Helm-holtz一种四阶精度的紧致差分格式.该格式在每个空间方向上只涉及到三个点处的未知量及其二阶导数值,边界处对于二阶导数利用四阶显式偏心格式.然后,利用Richardson外推法、算子插值法及二阶导数在边界点处的六阶显式偏心格式,将本文构造的二维Helmholtz方程四阶紧致差分格式的精度提高到六阶.最后,通过数值实验验证了本文方法的精确性和可靠性.     

解一类具有周期系数的Helmholtz方程的小波谱方法

在现代光学理论及应用中,经常要讨论周期结构介质中的散射问题,其中周期结构通常被称为衍射光栅。在某些假设条件下,这些问题可用Helmholtz型的方程来描述。考虑一类具有周期系数的Helmholtz方程,它是一类衍射光栅问题的数学模型,研究这类问题的数值解法。采用的策略是小波谱方法,即在一个坐标方向使用谱方法,在另一个坐标方向采用小波Galerkin方法,得到相应的误差估计。     

任意截面波导本征值问题的边界元分析

本文讨论了任意截面波导本征值的边界元分析方法，编制了一个通用的计算机程序。对几种不同截面形状波导的本征值进行了计算，结果与已有文献一致。     

具奇性Helmholtz型问题谱逼近

考虑具奇性Ｈｅｌｍｈｏｌｔｚ型边值问题的高阶数值逼近．通过引进虚边界并确定虚边界处的边界条件，获得除奇点小领域外的区域内问题的准确表述，并进一步证明此问题的谱逼近解具有优化的误差估计     

Helmholtz's Kant revisited (Once more). The all-pervasive nature of Helmholtz's struggle with Kant's Anschauung

In this analysis, the classical problem of Hermann von Helmholtz's (1821–1894) Kantianism is explored from a particular vantage point, that to my knowledge, has not received the attention it deserves notwithstanding its possible key role in disentangling Helmholtz's relation to Kant's critical project. More particularly, we will focus on Helmholtz's critical engagement with Kant's concept of intuition [Anschauung] and (the related issue of) his dissatisfaction with Kant's doctrinal dualism. In doing so, it soon becomes clear that both (i) crucially mediated Helmholtz's idiosyncratic appropriation and criticism of (certain aspects of) Kant's critical project, and (ii) can be considered as a common denominator in a variety of issues that are usually addressed separately under the general header of (the problem of) Helmholtz's Kantianism. The perspective offered in this analysis can not only shed interesting new light on some interpretive issues that have become commonplace in discussions on Helmholtz's Kantianism, but also offers a particular way of connecting seemingly unrelated dimensions of Helmholtz's engagement with Kant's critical project (e.g. Helmholtz's views on causality and space). Furthermore, it amounts to the rather surprising conclusion that Helmholtz's most drastic revision of Kant's project pertains to his assumption of free will as a formal condition of experience and knowledge.     

Signs, toy models, and the a priori: from Helmholtz to Wittgenstein

The Marburg neo-Kantians argue that Hermann von Helmholtz’s empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz’s account raises the ‘problem of validity’ (Gültigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz’s and Ludwig Wittgenstein’s Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz’s original account.     

论自发过程

用熵增原理分析讨论了对自发过程的各种现行叙述法和定义,给出了自发过程的严格定义,分析了自由能判据和自由焓判据的实质.     

带挠性梁的充液飞行器边界控制

考虑在惯性空间中全充液挠性飞行器的控制模型,轻挠性梁一端固于刚体,另一端自由。系统动力学方程由主刚体欧拉方程、液体的平均化Ｈｅｌｍｈｏｌｔｚ方程和梁的欧拉方程耦合而成。研究表明,借用适当的作用于梁自由端的边界控制,作用于主刚体的控制力矩及作用于液体“等效刚体”的阻尼力矩,能使整个系统稳定。     

一种多绕组磁场发生器的设计

文章依据亥姆霍兹线圈原理提出了一种多绕组结构的磁场发生器设计方案,利用Maxwell软件对其进行模拟仿真分析,并制作了一套多绕组磁场发生器。通过对比实际测量数值与模拟仿真数值,证明了该设备能产生0～2T的磁场,在中心区域磁感应强度的不均匀性小于3%,得到了预期效果。