Response to the comments by J.H. Evans on ‘On the onset of void ordering in metals under neutron or heavy-ion irradiation’

Evans's comments are related only loosely to the main body of our paper, which is devoted to the onset of void ordering: his Monte Carlo simulations of this early stage of ordering are in a qualitative agreement with our results. They question, however, the basic mechanisms of damage accumulation revealed by a number of scientists using various techniques over the years. Here we argue that his views are erroneous due to overlooking some essential features of one-dimensional defect transport.     

A Germanate Compound Constructed from Dissymmetric Ge7 Chains and Metal Complexes

Abstract. A novel germanate compound, |[Ni(dien)₂]₃(H₂O)₃|[Ge₇O₁₃F₅]₂(designated JU‐85, dien = diethylenetriamine), was solvothermally synthesized. The structure of JU‐85 was determined by single‐crystal X‐ray diffraction and further characterized by powder X‐ray diffraction, inductively coupled plasma, infrared spectroscopy, elemental analysis, and thermogravimetric analysis. JU‐85 has dissymmetric chains constructed from diagonally linked Ge₇ building units and various Ni(dien)₂²⁺ complexes formed in situ during the synthesis. Compared with its structural analogue, FJ‐6, JU‐85 contains less complex cations and different host‐guest assembly. Besides the diagonal linkage in JU‐85, other dissymmetric linkages of Ge₇ building units were enumerated, which could be used as the stereogenic centers for the design of novel chiral germanate compounds.     

A least‐square weighted residual method for level set formulation

In this paper, a least‐square weighted residual method (LSWRM) for level set (LS) formulation is introduced to achieve interface capturing in two‐dimensional (2D) and three‐dimensional (3D) problems. An LSWRM was adopted for two semi‐discretized advection and reinitialization equations of the LS formulation. The present LSWRM provided good mathematical properties such as natural numerical diffusion and the symmetry of the resulting algebraic systems for the advection and reinitialization equations. The proposed method was validated by solving some 2D and 3D benchmark problems such as those involving a rotating slotted disk, the rotation of a slotted sphere, and a time‐reversed single‐vortex flow and a deformation problem of a spherical fluid. The numerical results were compared with those obtained from essentially non‐oscillatory type formulations and particle LS methods. Further, the proposed LSWRM for the LS formulation was coupled with a splitting finite element method code to solve the incompressible Navier–Stokes equations, and then, the collapse of a 3D broken dam flow was well simulated; in the simulation, the entrapping of air and the splashing of the surge front of water were reproduced. The mass conservation of the present method was found to be satisfactory during the entire simulation. Copyright © 2011 John Wiley & Sons, Ltd.     

Brownian motion on a manifold

The question of the existence and correct form of equations describing Brownian motion on a manifold cannot be answered by mathematics alone, but requires a study of the underlying physics. As in classical mechanics, manifolds enter through the transformation of variables needed to account for the presence of constraints. The constraints are either due to a physical agency that forces the motion to remain on a manifold, or they represent conserved quantities of the equation of motion themselves. Also the Brownian motion is described either by a Smoluchowski diffusion equation or by a Kramers equation. The four cases lead to the following conclusions, (i) Smoluchowski diffusion with a conserved quantity reduces to a diffusion equation on the manifold; (ii) The same is true for diffusion with a physical constraint in three dimensions, but in more dimensions it may happen thatno autonomous equation on the manifold results; (iii) A Kramers equation with a conserved quantity reduces to an equation on the manifold, but in general not of the form of a Kramers equation; (iv) The Kramers equation with a physical constraint reduces to an autonomous Kramers equation on the manifold only for a special shape of that constraint. Throughout, only a certain type of physical constraints has been envisaged, and global questions are ignored. Finally, the customary heuristic construction of a Fokker-Planck equation for a mechanical system on a manifold is demonstrated for the case of Brownian rotation of a rigid body, and its shortcomings are emphasized.