Water-assisted mechanical testing of polymeric thin-films

Thin films with a nanometer-scale thickness are of great interest to both scientific and industrial communities due to their numerous applications and unique behaviors different from the bulk. However, the understanding of thin-film mechanics is still greatly hampered due to their intrinsic fragility and the lack of commercially available experimental instruments. In this review, we first discuss the progression of thin-film mechanical testing methods based on the supporting substrate: film-on-solid substrate method, film-on-water tensile tests, and water-assisted free-standing tensile tests. By comparing past studies on a model polymer, polystyrene, the effect of different substrates and confinement effect on the thin-film mechanics is evaluated. These techniques have generated fruitful scientific knowledge in the field of organic semiconductors for the understanding of structure–mechanical property relationships. We end this review by providing our perspective for their bright prospects in much broader applications and materials of interest.     

固体力学有限元体系的结构拓扑变化理论

本文是文[1]的继续.文[1]提出了杆件系统的结构拓扑变化理论和拓扑变化法本文将这一理论和方法推进到连续体有限元体系;且在此基础上揭示出有限元体系的一个新性质,称为基本位移之梯度的正交性定理,从而给出一套设计敏度的显式表达式,可直接用于计算.     

Carathéodory's method for a class of dynamic games

The method of equivalent variational methods, originally due to Carathéodory for free problems in the calculus of variations is extended to investigate feedback Nash equilibria for a class of n-person differential games. Both the finite-horizon and infinite-horizon cases are considered. Examples are given to illustrate the presented results.     

An optical measurement of vortex shape at a free surface

We have proposed an optical method of vortex shape measurement based on Fourier transform profilometry (FTP) and verified it by experiment. The results of our experiment proposed in this paper show that FTP can efficiently reconstruct the vortex shape at a free surface and this method is suitable for wide use in studying such problems as liquid shear flow, wake of an object, flow behind a bluff body, and wetting angle.     

Projective geometry and special relativity

Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation for light waves to a finite one entails the replacement of a hyperplane at infinity with a light cone and the replacement of an affine hyperplane – or rest space – with a proper time hyperboloid. The transition from the metric theory of electromagnetism to the pre‐metric theory is discussed in the context of complex projective geometry, and ultimately, it is proposed that the geometrical issues are more general than electromagnetism, namely, they pertain to the transition from point mechanics to wave mechanics.     

A Continuous Transition Between Quantum and Classical Mechanics. II

Examples are worked out using a new equation proposed in the previous paper to show that it has new physical predictions for mesoscopic systems.     

A computer-assisted proof of Saari's conjecture for the planar three-body problem

The five relative equilibria of the three-body problem give rise to solutions where the bodies rotate rigidly around their center of mass. For these solutions, the moment of inertia of the bodies with respect to the center of mass is clearly constant. Saari conjectured that these rigid motions are the only solutions with constant moment of inertia. This result will be proved here for the planar problem with three nonzero masses with the help of some computational algebra and geometry.

     

Ergodic properties and thermodynamic behavior of elementary reversible cellular automata. I. Basic properties

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.