Characteristics of the polymer transport in ratchet systems

Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency and non-uniform charge distributions. We also use currents in the non-equilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The dominating transport mechanisms are found via graph optimization methods. The results show that small changes in the molecule structure and the environment variables can lead to large increases of the drift. The drift and the coherence can be amplified by using deterministic flashing potentials and customized polymer charge distributions. Identifying the dominating transport mechanism by graph analysis tools is found to give insight in how the molecule is transported by the ratchet effect.Comment: 35 pages, 17 figures, to appear in Phys. Rev.

Exact de Rham Sequences of Spaces Defined on Macro-elements in Two and Three Spatial Dimensions

This paper proposes new finite element spaces that can be constructed for agglomerates of standard elements that have certain regular structure. The main requirement is that the agglomerates share faces that have closed boundaries composed of 1-d edges. The spaces resulting from the agglomerated elements are subspaces of the original de Rham sequence of H{sup 1}-conforming, H(curl) conforming, H(div) conforming and piecewise constant spaces associated with an unstructured 'fine' mesh. The procedure can be recursively applied so that a sequence of nested de Rham complexes can be constructed. As an illustration we generate coarser spaces from the sequence corresponding to the lowest order Nedelec spaces, lowest order Raviart-Thomas spaces, and for piecewise linear H{sup 1}-conforming spaces, all in three-dimensions. The resulting V-cycle multigrid methods used in preconditioned conjugate gradient iterations appear to perform similar to those of the geometrically refined case

Exact de Rham sequences of spaces defined on macro-elements in two and three spatial dimensions

Abstract. This paper proposes new finite element spaces that can be constructed for agglomerates of standard elements that have certain regular structure. The main requirement is that the agglomerates share faces that have closed boundaries composed of 1-d edges. The spaces resulting from the agglomerated elements are subspaces of the original de Rham sequence of H 1 -conforming, H(curl) conforming, H(div) conforming and piecewise constant spaces associated with an unstructured "fine" mesh. The procedure can be recursively applied so that a sequence of nested de Rham complexes can be constructed. As an illustration we generate coarser spaces from the sequence corresponding to the lowest order Nédélec spaces, lowest order Raviart-Thomas spaces, and for piecewise linear H 1 -conforming spaces, all in three-dimensions. The resulting V -cycle multigrid methods used in preconditioned conjugate gradient iterations appear to perform similar to those of the geometrically refined case

Mesh independent convergence of the modified inexact Newton method for a second order nonlinear problem

In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial nonlinear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory

H(curl) Auxiliary Mesh Preconditioning

This paper analyzes a two-level preconditioning scheme for H(curl) bilinear forms. The scheme utilizes an auxiliary problem on a related mesh that is more amenable for constructing optimal order multigrid methods. More specifically, we analyze the case when the auxiliary mesh only approximately covers the original domain. The latter assumption is important since it allows for easy construction of nested multilevel spaces on regular auxiliary meshes. Numerical experiments in both two and three space dimensions illustrate the optimal performance of the method

Single-layer metal-on-metal islands driven by strong time-dependent forces

Non-linear transport properties of single-layer metal-on-metal islands driven with strong static and time-dependent forces are studied. We apply a semi-empirical lattice model and use master equation and kinetic Monte Carlo simulation methods to compute observables such as the velocity and the diffusion coefficient. Two types of time-dependent driving are considered: a pulsed rotated field and an alternating field with a zero net force (electrophoretic ratchet). Small islands up to 12 atoms were studied in detail with the master equation method and larger ones with simulations. Results are presented mainly for a parametrization of Cu on Cu(001) surface, which has been the main system of interest in several previous studies. The main results are that the pulsed field can increase the current in both diagonal and axis direction when compared to static field, and there exists a current inversion in the electrophoretic ratchet. Both of these phenomena are a consequence of the coupling of the internal dynamics of the island with its transport. In addition to the previously discovered "magic size" effect for islands in equilibrium, a strong odd-even effect was found for islands driven far out of equilibrium. Master equation computations revealed non-monotonous behavior for the leading relaxation constant and effective Arrhenius parameters. Using cycle optimization methods, typical island transport mechanisms are identified for small islands.Comment: 39 pages, 20 figures, to appear in Phys. Rev. E [corrected typo of the x-axis label in Fig. 6

Local structure of relaxor ferroelectric SrxBa1-xNb2O6 from a pair distribution function analysis

Pair distribution function analysis of neutron-scattering data and of ab initio molecular dynamics results have been employed to study short-range structural correlations and their temperature dependence in a heavily disordered dielectric material SrxBa1-xNb2O6 (x = 0.35, 0.5, and 0.61). Intrinsic disorder caused by a partial occupation of the cationic sites by differently sized Sr and Ba atoms and their vacancies introduces important local strains to the structure and directly influences the Nb-O-6 octahedra tilting. The resulting complex system of tilts is found to be both temperature and Sr-doping sensitive with the biggest tilt magnitudes reached at low temperatures and high strontium contents, where ferroelectric relaxor behavior appears. We find evidence for two Nb-O-6 subsystems with different variations of niobium-oxygen bond lengths, distinct dynamics, and disparate levels of deviation from macroscopic polarization direction. These findings establish a detailed picture of the local structure of SrxBa1-xNb2O6 and provide a deeper insight into the origins of the materials dielectric properties.This work was supported by the Czech Science Foundation (Project No. 16-09142S). The computational part of this research was undertaken on the NCI National Facility in Canberra, Australia, which is supported by the Australian Commonwealth Government.

Vulnerable warriors: the atmospheric marketing of military and policing equipment before and after 9/11

In this article, we analyse changes in the circulation of advertisements of policing products at security expos between 1995 and 2013. While the initial aim of the research was to evidence shifts in terrorist frames in the marketing of policing equipment before and after 9/11, our findings instead suggested that what we are seeing is the rise of marketing to police as “vulnerable warriors”, law enforcement officers in need of military weapons both for their offensive capabilities and for the protection they can offer to a police force that is always under threat