The Contingency of Laws of Nature in Science and Theology

The belief that laws of nature are contingent played an important role in the emergence of the empirical method of modern physics. During the scientific revolution, this belief was based on the idea of voluntary creation. Taking up Peter Mittelstaedt’s work on laws of nature, this article explores several alternative answers which do not overtly make use of metaphysics: some laws are laws of mathematics; macroscopic laws can emerge from the interplay of numerous subsystems without any specific microscopic nomic structures (John Wheeler’s “law without law”); laws are the preconditions of scientific experience (Kant); laws are theoretical abstractions which only apply in very limited circumstances (Nancy Cartwright). Whereas Cartwright’s approach is in tension with modern scientific methodology, the first three strategies count as illuminating, though partial answers. It is important for the empirical method of modern physics that these three strategies, even when taken together, do not provide a complete explanation of the order of nature. Thus the question of why laws are valid is still relevant. In the concluding section, I argue that the traditional answer, based on voluntary creation, provides the right balance of contingency and coherence which is in harmony with modern scientific method.     

Vectorial approach of determining the wave propagation at metasurfaces

Vector approach often benefits optical engineers and physicists, and a vector formulation of the laws of reflection and refraction has been studied (Tkaczyk, 2012). However, the conventional reflection and refraction laws may be violated in the presence of a metasurface, and reflection and refraction at the metasurface obey generalized laws of reflection and refraction (Yu et al., 2011). In this letter, the vectorial laws of reflection and refraction at the metasurface were derived, and the matrix formulation of these vectorial laws are also obtained. These results enable highly efficient and unambiguous computations in ray-tracing problems that involve a metasurface.     

A general theory of conservation laws,their violation,and spontaneous phenomena

We formulate a general theory of conservation laws and other invariants for a physical system through equivalence relations. The conservation laws are classified according to the type of equivalence relation, with group equivalence, homotopical equivalence, and other types of equivalence relations giving respective kinds of conservation laws. The stability properties in the topological (and differentiable) sense are discussed using continuous deformations with respect to control parameters. The conservation laws due to the Abelian symmetries are shown to be stable through application of well-known theorems.     

渐进多焦点眼用镜片的子午线设计研究

介绍渐进多焦点眼用镜片的构造,论述镜片的设计思想,阐述渐进多焦点眼用镜片子午线设计的基本原理,构建子午线多项式,给出子午线设计需满足的准则.在子午线设计的基础上,设计渐进多焦点眼用镜片等屈光度轮廓线,确定镜片面形,并求出镜片平均球面度与像散.比较3种不同子午线设计的渐进多焦点眼用镜片,并进行实际加工与检测.研究结果表明,子午线设计是渐进多焦点眼用镜片设计的关键之一,不同的子午线屈光度分布,对应的渐进多焦点眼用镜片的球面度、像散以及畸变等差别较大.依据实际设计与检测结果,给出适用于不同个性化需求的渐进多焦点眼用镜片子午线屈光度分布的规律.     

Quantum Law of Motion: Analysis and Extension to Higher Dimensions

In this paper, we review the recently formulated quantum laws of motion and provide new observations. We also extend these laws to higher dimensions. By applying in two dimensions the obtained relations to charge submitted to an electric central potential, we decide between these laws. Furthermore, we extend the selected law to the relativistic case in higher dimensions.     

相对性原理对普遍定律和非普遍定律参考系变换性质的不同要求——关于协变性疑难的进一步讨论

提出普遍定律和非普遍定律以及“协变”与“可导出”的明确定义，证明狭义相对性原理（及其伽利略近似）要求在惯性系变换下，自然界普遍定律是协变的，非普遍定律不协变但是“可导出”的，一切定律都服从相对性原理，从而进一步解答了由爱因斯坦，朗道关于狭义相对性原理的一种错误表述所引起的“协变性疑难”，还将有关结论推广到广义相对性原理情况。     

Generalized Noether identities and application to Yang-Mills field theory

We derive generalized Noether identities for a system with noninvariant action integral under an infinite continuous group and deduce the string conservation laws of the system. We give a preliminary application to field theory and discuss the strong conservation laws for the BRS transformation and the weak conservation laws of Yang-Mills fields. The Dirac constraint of the system is examined.     

平面火花隙三电极开关研制及性能测试

研制了一种适用于平行板传输连接的平面火花隙三电极开关，开关正负电极为半圆形状，触发电极为细条状。将之替代立体式（半球形电极）火花隙三电极开关并应用于爆炸箔起爆装置中，装置回路参数将得以优化。实验测试了空气间隙为4.12， 3.14和2.2 mm的平面火花隙三电极开关的性能。结果表明，在开关间隙间距一定的情况下，随着电压的升高，开关间隙的放电时延和分散时间呈指数降低，开关电感小于15 nH；对于不同范围内的应用电压，使用不同间隙间距的开关，其分散时间不大于10 ns。该开关应用于较低充电电压（小于10 kV）的脉冲功率装置中，与立体式火花隙三电极开关相比，回路电感降低了约50 nH，放电周期缩短近1/3，峰值电流增加约1/3。     

Scaling in the ideal Bose gas

We have made a detailed study of scaling in the ideal Bose gas in order to resolve the apparent inconsistencies that occur in the scaling laws when the dimensionality of the system is greater than four. We have found that there are not one, but two critical exponents associated with the specific heat singularity that appear in the scaling laws. We have proposed a modification of the scaling laws which is correct in any dimension.     

Nonlocal conserved quantities,balance laws,and equations of motion

A formalism is developed whereby balance laws are directly obtained from nonlocal (integrodifferential) linear second-order equations of motion for systems described by several dependent variables. These laws augment the equations of motion as further useful information about the physical system and, under certain conditions, are shown to reduce to conservation laws. The formalism can be applied to physical systems whose equations of motion may be relativistic and either classical or quantum. It is shown to facilitate obtaining global conservation laws for quantities which include energy and momentum. Applications of the formalism are given for a nonlocal Schrödinger equation and for a system of local relativistic equations of motion describing particles of arbitrary integral spin.     

广义库仑定律和毕-萨定律的同时形式

把广义库仑定律和毕－萨定律表示成了同时形式，以期有助于拓展它们的应用。     

Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System

In this paper we investigate the semi-discrete Ablowitz–Kaup–Newell–Segur (sdAKNS) hierarchy, and specifically their Lax pairs and infinitely many conservation laws, as well as the corresponding continuum limits. The infinitely many conserved densities derived from the Ablowitz-Ladik spectral problem are trivial, in the sense that all of them are shown to reduce to the first conserved density of the AKNS hierarchy in the continuum limit. We derive new and nontrivial infinitely many conservation laws for the sdAKNS hierarchy, and also the explicit combinatorial relations between the known conservation laws and our new ones. By performing a uniform continuum limit, the new conservation laws of the sdAKNS system are then matched with their counterparts of the continuous AKNS system.     

Conservation laws in stochastic deposition-evaporation models in one dimension

An infinite number of conservation laws is identified for a stochastic model of deposition and evaporation of trimers on a linear chain. These laws can be encoded into a single nonlocal invariant, the irreducible string, which uniquely lables an exponentially large number of kinetically disconnected sectors of phase space. This enables the number and sizes of sectors to be determined. The effects of conservation laws on some thermodynamic properties are studied.     

Conservation laws and normal forms of evolution equations

We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Examples include Harry Dym equation, Korteweg-de Vries-type equations, and Schwarzian KdV equation. It is also shown that for linear evolution equations all their conservation laws are (modulo trivial conserved vectors) at most quadratic in the dependent variable and its derivatives.     

Generalization of the radiation laws of a Kerr nonlinear blackbody

Within the framework of nonextensive statistical mechanics (NSM), we generalize the radiation laws, which include the Planck radiation law and Stefan-Boltzmann law, of a Kerr nonlinear blackbody (KNB) in the normalized form. In order to illustrate the influence of the parameter q on the two generalized radiation laws, we make a numerical calculation of the two laws under appropriate conditions. Furthermore, we make an attempt to extend the theory of KNB to the whole Universe.     

Duality for systems of conservation laws

Letters in Mathematical Physics - For one-dimensional systems of conservation laws admitting two additional conservation laws, we assign a ruled hypersurface of codimension two in projective space....     

Potentials of divergent equations and new additional conservation laws for two-dimensional steady gas flows

An algorithm is constructed that compares a new divergent equation (the additional conservation law) to each of two divergent equations. Both the starting divergent equations themselves and their potentials participate in the additional conservation law, and both the first and second participate symmetrically. A characteristic feature of such additional conservation laws is that not only are the functions of gas-dynamic parameters and their derivatives taken along streamlines but so are the integrals, i.e., the functionals, and their derivatives participate in them. All these facts reveal the physical sense of the topical conservation laws constructed. A comparison with the asymmetric conservation laws constructed previously by the author (Doklady Physics, 2002) is performed. As an example, the relation that connects four additional laws comparable by dimensionality is constructed as an example. This is the conservation law of the momentum and its three analogs. Two laws are asymmetric (from Doklady Physics, 2002), while two others are constructed in this study.     

On symmetries,conservation laws and exact solutions of the nonlinear Schrödinger–Hirota equation

In this paper, conservation laws and exact solution are found for nonlinear Schrödinger–Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger–Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.     

Reconsidering a Scientific Revolution: The Case of Einstein <Emphasis Type="Italic">versus</Emphasis> Lorentz

The relationship between Albert Einstein's special theory of relativity and Hendrik A. Lorentz's ether theory is best understood in terms of competing interpretations of Lorentz invariance. In the 1890s, Lorentz proved and exploited the Lorentz invariance of Maxwell's equations, the laws governing electromagnetic fields in the ether, with what he called the theorem of corresponding states. To account for the negative results of attempts to detect the earth's motion through the ether, Lorentz, in effect, had to assume that the laws governing the matter interacting with the fields are Lorentz invariant as well. This additional assumption can be seen as a generalization of the well-known contraction hypothesis. In Lorentz's theory, it remained an unexplained coincidence that both the laws governing fields and the laws governing matter should be Lorentz invariant. In special relativity, by contrast, the Lorentz invariance of all physical laws directly reflects the Minkowski space-time structure posited by the theory. One can use this observation to produce a common-cause argument to show that the relativistic interpretation of Lorentz invariance is preferable to Lorentz's interpretation.