A Matter of Size and Placement: Varying the Patch Size of Anisotropic Patchy Colloids

Non-spherical colloids provided with well-defined bonding sites—often referred to as patches—are increasingly attracting the attention of materials scientists due to their ability to spontaneously assemble into tunable surface structures. The emergence of two-dimensional patterns with well-defined architectures is often controlled by the properties of the self-assembling building blocks, which can be either colloidal particles at the nano- and micro-scale or even molecules and macromolecules. In particular, the interplay between the particle shape and the patch topology gives rise to a plethora of tilings, from close-packed to porous monolayers with pores of tunable shapes and sizes. The control over the resulting surface structures is provided by the directionality of the bonding mechanism, which mostly relies on the selective nature of the patches. In the present contribution, we investigate the effect of the patch size on the assembly of a class of anisotropic patchy colloids—namely, rhombic platelets with four identical patches placed in different arrangements along the particle edges. Larger patches are expected to enhance the bond flexibility, while simultaneously reducing the bond selectivity as the single bond per patch condition—which would guarantee a straightforward mapping between local bonding arrangements and long-range pattern formation—is not always enforced. We find that the non-trivial interplay between the patch size and the patch position can either promote a parallel particle arrangement with respect to a non-parallel bonding scenario or give rise to a variety a bonded patterns, which destroy the order of the tilings. We rationalize the occurrence of these two different regimes in terms of single versus multiple bonds between pairs of particles and/or patches.

On the upper dual Zariski topology

Let R be a ring with identity and M be a left R-module. The set of all second submodules of M is called the second spectrum of M and denoted by Specs(M). For each prime ideal p of R we define Specsp(M) := {S? Specs(M) : annR(S) = p}. A second submodule Q of M is called an upper second submodule if there exists a prime ideal p of R such that Specs p(M)? 0 and Q = ? S2Specsp(M)S. The set of all upper second submodules of M is called upper second spectrum of M and denoted by u.Specs(M). In this paper, we discuss the relationships between various algebraic properties of M and the topological conditions on u.Specs(M) with the dual Zarsiki topology. Also, we topologize u.Specs(M) with the patch topology and the finer patch topology. We show that for every left R-module M, u.Specs(M) with the finer patch topology is a Hausdorff, totally disconnected space and if M is Artinian then u.Specs(M) is a compact space with the patch and finer patch topology. Finally, by applying Hochster?s characterization of a spectral space, we show that if M is an Artinian left R-module, then u.Specs(M) with the dual Zariski topology is a spectral space.

Topologically driven coronal dynamics – a mechanism for coronal hole jets

Bald patches are magnetic topologies in which the magnetic field is concave up over part of a photospheric polarity inversion line. A bald patch topology is believed to be the essential ingredient for filament channels and is often found in extrapolations of the observed photospheric field. Using an analytic source-surface model to calculate the magnetic topology of a small bipolar region embedded in a global magnetic dipole field, we demonstrate that although common in closed-field regions close to the solar equator, bald patches are unlikely to occur in the open-field topology of a coronal hole. Our results give rise to the following question: What happens to a bald patch topology when the surrounding field lines open up? This would be the case when a bald patch moves into a coronal hole, or when a coronal hole forms in an area that encompasses a bald patch. Our magnetostatic models show that, in this case, the bald patch topology almost invariably transforms into a null point topology with a spine and a fan. We argue that the time-dependent evolution of this scenario will be very dynamic since the change from a bald patch to null point topology cannot occur via a simple ideal evolution in the corona. We discuss the implications of these findings for recent Hinode XRT observations of coronal hole jets and give an outline of planned time-dependent 3-D MHD simulations to fully assess this scenario.

Enhanced Gain Microstrip Patches Operating on Higher Order Modes

Novel topologies of rectangular microstrip patches providing broadside radiated one point fed radiators with enhanced gain are compared. The principle of the gain enhancement is based on an extension of a source area. Dominant in-phase current distribution on the patch is maintained by using higher order mode and geometrical modification of the patch topology. That is achieved by introducing suitable perturbation elements in the shape of slots and notches. Two principal patch topologies operating on TM21 and TM03 modes are described. A comparison of simulated and measured properties of realized prototypes at 10 GHz band are presented. The results show that gain 12.3 dBi of single patch can be reached.